TEL AVIV UNIVERSITY The Iby and Aladar Fleischman Faculty of Engineering The Zandman-Slaner School of Graduate Studies

Transcription

1 TEL AVIV UNIVERSITY The Iby and Aladar Fleischman Faculty of Engineering The Zandman-Slaner School of Graduate Studies Heart Sound Background Noise Removal A thesis submitted toward the degree of Master of Science in Engineering Sciences By Haim Appleboim March

2 Abstract Continuous noninvasive monitoring of cardiac functionality is highly desirable. Heart sounds may be a practical addition to EKG in such monitoring, to help in earlier detection of malfunctions in the mechanical activity of the heart, e.g., congestive heart failure and ischemia. However, non-invasive monitoring requires mounting sensors on the surface of the chest, making them vulnerable to external noise. Furthermore, the sensors are most vulnerable to sounds created by the monitored person as there is a significant overlap in frequency range between heart sounds and speech. To achieve heart sound continuous monitoring, with high sensitivity and low number of false alarms, background noises must be eliminated. Unfortunately, due to the large frequency overlap, regular filters are ineffective in removing the noise. Even adaptive filters such as the Wiener Filter are not good enough as they do not find such a difference in the statistics of the heart sound and that of speech. We provide here a method for background sound removal based on a statistical method which tries to separate independent sources by maximizing the non-gaussianity of the reconstructed distribution of each source. Three sensors are placed on the chest. Two sensors are put at the Pulmonary and the Aortic area for best identification of the first S1, and second S2 heart sounds. The third sensor is put on the chest at a location where little or no heart sound is heard. A computationally efficient version of Independent Components Analysis (ICA), the so called FastICA is used. For best performance, the FastICA method is applied to the spectral representation of the signal and with the Gauss Non-linearity. The sensors closer to the heart receive stronger heart signal whereas the sensor that is far from the heart receives weaker and slightly different heart signal, thus, relatively stronger background sound energy. This difference is sufficient for the Spectral ICA algorithm, to produce from the three sensor inputs, three outputs. One or Two of them contain heart sounds with reduced background noise which becomes more emphasized in the third output. We demonstrate that the proposed heart sound noise removal method outperforms conventional methods for noise removal

3 Contents Abstract... 2 Acknowledgements... 9 Chapter Introduction General background of the problem Specific problem to be addressed Past addressing of similar problems and deficiencies in past solutions Thesis Overview Chapter Overview of Heart Physiology and Heart Sounds Physiological Background Heart activity Heart sounds Auscultation sites Heart diseases Noise and Noise types Noise Possible Noise Types and properties Recording of Heart Sounds Sensor Information Data Collection System Chapter Current State of the Art in Noise Removal Methods Filters in general Digital Filters FIR Filter IIR Filter Chebyshev filter The Wiener Filter Spectral Subtraction Chapter Overview of Independent Components Analysis ICA - Independent Components Analysis ICA Definition ICA Assumptions Independent Components Computation Ambiguities of ICA ICA Estimation Principles of ICA estimation Measures of non-gaussianity FastICA Algorithm Spectral ICA The Cosine Transform Why Using Spectral ICA?

4 4.5 PCA Principal Components Analysis ICA compared to PCA Chapter Noise Removal Using Spectral ICA Main algorithm ICA How doe s ICA reduce noise Band Pass Filtering MATLAB program Algorithm Flow Overview Filter Reorganize Data Set ICA Parameters Run Algorithmic Analysis Making sure that the right signal gets its noise removed Algorithm quality Assessment Human eye assessment Algorithmic assessment Chapter Results Results Overview Setup description and types of noise used Setup description Types of noise used Noises out of the scope of the current research Graphs demonstrating the noise removal Assessment of the noise addition on the ICA algorithm output Noise removal with ICA vs. Wiener Quality evaluation results Noise removal from a heart sound in a noisy environment Graphs demonstrating the HS enhancement Noise removal with different ICA parameters Spectral vs. Time domain ICA Results Chapter Conclusion Appendix A Some Statistics Appendix B Why Gaussian variables are forbidden in ICA References

5 Table of Figures Figure The anatomy of the human heart Figure Phases of the cardiac cycle Figure Heart Important Auscultation Sites Figure Schematic drawing and a simplified model of a relative displacement sensor Figure Experimental setup diagram Figure Band-pass filter example Figure FIR Filter block diagram Figure Gain and group delay of a fifth order type I Chebyshev Low-Pass filter with ε= Figure Spectral Subtraction noise removal Figure Time and Spectral (DCT) domain representation of delayed sine waves Figure Main Noise Removal Research GUI Figure General_Options_GUI Figure General Algorithmic Flow Schematic view Figure Filter_Reorhenize_GUI window Figure ICA_Parameters_Select_GUI window Figure Signal Spectrum Plot Example for 3 channel Spectral ICA Analysis Figure Signal Spectrum Plot Example Wiener Filter Analysis Figure Spectrogram Plot Example for 3 channel Spectral ICA Analysis Figure Example of the heart sound quite period marking and noise peaks Figure Noise and heart sound spectral overlap example Figure Noise and heart sound spectral overlap example Figure Unsuccessful noise removal attempt for a heart sound with a peak noise caused by microphone movement Figure Noise Removal from a HS Time Series representation (0-30.4Sec) Figure Noise Removal from a HS Time Series representation (21-23Sec) Figure Noise Removal from a HS, 3 channels spectral representation (0-400Hz) Figure Noise Removal (in and out of band noise) from a HS, one channels spectral representation (0-150Hz) Figure Spectrogram presentations of ch2 (2 nd ICS LSB) heart sounds in Figure Figure Comparison of the ICA output (Time domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time Figure Comparison of the ICA output (Spectral domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time Figure Comparison of the Wiener Filter output (Time domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time Figure Comparison of the Wiener Filter output (Spectral domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time Figure Comparison of the ICA output (Time domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre Figure Comparison of the ICA output (Spectral domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre Figure Comparison of the Wiener filter output (Time domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre Figure Comparison of the Wiener filter output (Spectral domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre

6 Figure Microphone placement for Wiener Filter based noise removal Figure Wiener Filter vs. ICA noise removal time domain plots (15-21Sec) HS=YS_TubeMedium, Noise=snor_with_pre Figure Wiener Filter vs. ICA noise removal time domain plots (16-17Sec) HS=YS_TubeMedium, Noise=snor_with_pre Figure Wiener Filter vs. ICA noise removal spectrogram plots (15-21Sec) - HS=YS_TubeMedium, Noise=snor_with_pre Figure Wiener Filter vs. ICA noise removal spectral domain plots (0-400Hz) HS=YS_TubeMedium, Noise=snor_with_pre Figure Spectral Domain plots of Noise Removal with Wiener Filter vs. ICA with a zoom on the noise area ( Hz) HS=YS_TubeMedium, Noise=snor_with_pre Figure Wiener Filter vs. ICA noise removal time domain plots (2-4Sec) HS=GA_Normal_1, Noise=count_time Figure Wiener Filter vs. ICA noise removal spectrogram plots (15-21Sec) - HS=GA_Normal_1, Noise=count_time Figure Wiener Filter vs. ICA noise removal spectral domain plots (0-400Hz) HS=GA_Normal_1, Noise=count_time Figure Spectral Domain plots of Noise Removal with Wiener Filter vs. ICA with a zoom on the noise area (75-200Hz) HS=GA_Normal_1, Noise=count_time Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 3D plots HS=GA_Halt_1, Noise=snor_with_pre Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 2D plots HS=GA_Halt_1, Noise=snor_with_pre Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 3D plots HS=GA_Normal_1, Noise=count_time Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 2D plots HS=GA_Normal_1, Noise=count_time Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 3D plots HS=GA_Halt_1, Noise=television Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 2D plots HS=GA_Halt_1, Noise=television Figure Microphone places for ICA based noise removal in a noisy environment Figure Noise Removal from a HS (in a real noisy environment) Time Series representation HS=HAIM_COUNT_ Figure Noise Removal from a HS (in a real noisy environment) spectrogram representation HS=HAIM_COUNT_ Figure Noise Removal (in a real noisy environment) from a HS spectral representation (0-200Hz) HS=HAIM_COUNT_ Figure Noise Removal from a HS (in a real noisy environment) Time Series representation HS=HAIM_COUNT_ Figure Noise Removal from a HS (in a real noisy environment) spectrogram representation HS=HAIM_COUNT_ Figure Noise Removal (in a real noisy environment) from a HS spectral representation (0-200Hz) HS=HAIM_COUNT_ Figure S2 heart sound enhancement time domain example Figure Spectral heart sounds enhancement example three HS channels presented Figure Spectral heart sounds enhancement example one HS channel (ch2) presented Figure Comparison between results with different ICA nonlinearity parameters Figure Comparison between results with Time and Spectral ICA methods HS=GA_Normal_1, Noise=count_time

7 Figure Quality Assessment Results of Spectral ICA compared to Time ICA Figure Comparison between results with Time and Spectral ICA methods (16-20Sec) HS=Halt_Supine_1, Noise=count_time Figure Comparison between results with Time and Spectral ICA methods (19-20Sec) HS=Halt_Supine_1, Noise=count_time

8 Table of Tables Table Noise types, their typical amplitudes and spectrum Table ICA vs. PCA Table File names and their corresponding setup descriptions Table Noise names and description

9 Acknowledgements I would like to thank NATAN INTRATOR for the huge support and guidance provided during the last two years, for the understanding, flexibility and the willingness to meet at none regular hours and places. Also I would like to thank GUY AMIT for his help with gathering the required measurements, supplying the basic SW platform and help with other thesis related issues. Finally I would like to thank my wife for the great understanding, support and love during all that time and my children SHIR and SHAHAR for just being who they are. Haim Appleboim March

10 Chapter 1 Introduction 1.1 General background of the problem Heart diseases are the major killer of our times. This work relies on the hypothesis that heart sounds can be used for continues heart monitoring. We can use heart sounds for non-invasive continues monitoring of the cardiovascular mechanical functionality and identify early symptoms of heart diseases such as heart failure and other possible heart diseases (coronary artery disease, Cardiomyopathy, Valve defects and others). Heart sounds are the acoustic vibrations generated by the beating heart and the resultant flow of blood through it. Heart sounds are usually divided into the normal heart sounds and the pathological sounds which indicate disease. The first heart tone, or S1, is caused by the closure of the atrioventricular valves at the beginning of systole. The second heart tone, or S2, is caused by the closure of the aortic and pulmonic valves at the end of ventricular systole. Asside from S1 and S2 there are more heart sounds which have lower intensities and different spectral parameters. Heart sounds are generated from a combination of few sources within the heart (closing and opening of valves) and its surrounding environment (lungs, blood flow through the arteries). 1.2 Specific problem to be addressed Continuous monitoring have to be performed at a non-clinical setup where background sounds occurs often. Thus, to practically achieve a reliable continuous monitoring, the background noise should be removed to a level which enables extraction of cardiac features from the heart sound. Heart sounds have very low intensity. Therefore the measurement may suffer from noise generated from internal or external sources. Noise sources usually have higher intensities than the heart sounds and spectral boundaries which coincide to the heart sounds. In the domestic environment, external noise sources such as dog bark, speech and others or internally generated sounds such as snoring, coughing and others may corrupt the heart sound signal. The background acoustic environment as well as internal organ sounds degrade the ability of continues monitoring of heart sounds

11 1.3 Past addressing of similar problems and deficiencies in past solutions Several methods have been used for noise removal from Heart Sounds. The methods found are based on single-sensor noise removal approaches. Among the single-sensor methods used we can mention wavelet denoising [6] and Time- Varying Wiener filtering of the First and Second Heart Sounds [7]. The noise we must deal with is In-Band noise which we have no prior information related to it (except for its possible frequency range). Each of the methods mentioned above uses only one heart sound Channel as their input. The problem associated with this fact is that no matter how good and dynamic will the filtering algorithm be there is no reference signal for making sure the algorithm really removes only the additive noise and not some parts of the original heart sound signal. No multi-sensor method for noise removal (at the same spectral bands) has been discussed in the literature, although, there was a related work of separating between heart sounds and breathing sounds [9]. This work used independent components analysis, although, in that case, the spectral energy of the two signals is different, thus making the separation problem much simpler. Existing methods for general noise removal such as Spectral Subtraction (SS) may be considered as well. Spectral Subtraction is implemented by estimating the noise spectrum from regions that are estimated as noise-only and subtracting it from the rest of the noisy speech signal. Two channel Spectral Subtraction assumptions: - Primary microphone signal consists of two additive components: Speech (desired) + Noise (undesired) - Use secondary microphone to capture and subtract noise (noise reference) With Spectral Subtraction it is assumed that the noise remains relatively constant prior to, and during speech activity. Spectral Subtraction method will probably produce insufficient results in cases of human internal noises (since in these cases there are no regions which only receive the noise). 1.4 Thesis Overview The thesis is split into seven main parts: 1. Chapter 1 (Introduction) Presents the problem discussed and past addressing of the problem. 2. Chapter 2 (Overview of Heart Physiology and Heart Sounds) Presents an overview of the heart physiology, heart diseases, heart sounds, noises and noise types, sensor information and data collection system description. 3. Chapter 3 (Current State of the Art in Noise Removal Methods) Presents the current conventional noise removal methods such as digital FIR, IIR filters, adaptive filters such as wiener filter and Spectral Subtraction. 4. Chapter 4 (Overview of Independent Components Analysis) Explains the ICA theory, FastICA, Spectral ICA algorithms and PCA. 5. Chapter 5 (Noise Removal Using Spectral ICA) Methodology chapter which presents the MATLAB program, the main algorithms and GUI s used for the research. This

12 chapter also describes the Algorithmic analysis used to determine the algorithm quality in noise removal from heart sounds. 6. Chapter 6 (Results) Presents the results achieved during the research. Includes plots of the received results and estimations of the quality of noise removal with different scenarios. 7. Chapter 7 (Conclusion) Summarizes the conclusion from the work

13 Chapter 2 Overview of Heart Physiology and Heart Sounds 2.1 Physiological Background Heart activity Figure The anatomy of the human heart The heart is a four chambered (The left atrium and left ventricle and the right atrium and right ventricle) pump which pumps oxygen-poor blood into the pulmonary circulation (to the lungs) and oxygen-rich blood into the systemic circulation (to the rest of the body). The two atria receive blood from the main veins of the body (pulmonary veins and the inferior and superior vena cava) and also act as a reservoir of blood between the contractions of the heart. The ventricles are responsible for pumping the blood into the arteries of the body (pulmonary arterial trunk and the aorta). The generation of an action potential within the SA node initiates the cardiac cycle which is roughly composed of two basic phases: Systole Contraction phase during which blood is ejected from the heart. Diastole Relaxation phase during which blood fills the heart chambers

14 After the generation of the action potential the pulse spreads through the atrial muscle and leads to atrial contraction. During the atria contraction the AV valves remain open (The aortic and pulmonary semilunar valves remain closed) and blood enters into the ventricles from the veins (A large amount of blood has already entered to the ventricles prior to atrial contraction). After the ventricles have filled and the atria have contracted, the AV valves close as the ventricles begin their contraction. Ventricular contraction forces blood into the aorta and pulmonary trunk. Next, as the ventricles begin to relax, the aortic and pulmonary semilunar valves close, the AV valves open, and blood flows into the ventricles to begin another cycle. While the atria are in systole, the ventricles are relaxed (in diastole). The atria relax during ventricular systole and remain in this phase even during a portion of ventricular diastole. When a heart chamber fills with blood its inner pressure increases. During that period the one-way valves keep the blood from leaving the chamber. As the ventricles contract, the blood is forced back against the AV valves, which causes them to bulge inward slightly toward the atria and which also elevates atrial pressure. In doing so, the AV valves are effectively closed and blood is prevented from regurgitating back into the atria. Near the end of ventricular systole the AV valves are still closed and since the atria are in the process of filling, this too contributes to a rise in intra-atrial pressure. Even before the atria enter systole, the ventricles are filled with blood to approximately 70% of their capacity. When the atria finally contract, additional blood enters the ventricles and elevates the intraventricular pressure. As the ventricles contract, blood is forced backward, closing the AV valves and a sharp rise in ventricular pressure occurs. The pressure within the ventricles during systole exceeds that in the aorta and pulmonary trunk very fast. At this stage the aortic and pulmonary semilunar valve are forced open under pressure and blood rushes out of the ventricles and is driven into these large vessels. Accompanying the opening of the semilunar valves is a rapid decline in intraventricular pressure that continues until the pressure within the ventricles becomes less than that of the atria. When this pressure differential is reached, blood within the atria pushes the AV valves open and begins to fill the ventricles once again

15 2.1.2 Heart sounds Heart sounds are the acoustic vibrations generated by a combination of the beating heart (contraction and relaxation of the heart, valve movement), blood flow in the heart and its surrounding environment (atria and ventricles). In addition to the sounds generated by the heart and its close surrounding environment the sounds measured includes also the birthing sounds and are strongly influenced by the anatomical structure of each person. Figure Phases of the cardiac cycle The aortic pressure, left ventricular pressure, left atrial pressure, aortic flow, ECG, and heart sounds There is a very close relationship between the cardiac cycles and the evolving heart sounds. The main heart sounds which also have the largest amplitudes are S1 and S2. The first heart sound S1 starts at the beginning of ventricular systole and indicates the beginning of the ventricular systole. The second heart sound S2 occurs at the end of ventricular systole (the beginning of ventricular relaxation). The third heart sound S3 may be generated during the ventricular filling in early diastole. It can be normally found in young children with thin chest walls or in patients with left ventricular failure. The fourth heart sound S4 may be generated due to blood circulation and cardiac chambers created by atrial contraction

16 Valvular Theory S1 consists of two main high frequency components M1 and T1 which are a result of the mitral and tricuspid valves stopping their movement. The second heart sound S2 consists of two high frequency components A2 and P2 which are a result of the aortic and pulmonary valves stopping their movement. S3 and S4 are caused by the halting of the mitral valve leaflets at the end of opening [1] Cardiohemic Theory The cardiohemic theory takes into account the entire complex of the heart and blood accelerations and decelerations as the generator of heart sounds. According to this theory S1 consists of four main components. First component of S1 has low freq and is synchronous to the first myocardial contraction after the ventricular pressure starts to rise. Second component of S1 has a higher frequency and is caused by the contraction of the myocardium and deceleration of blood. Third component of S1 is caused by the sudden acceleration of blood into the aorta. Fourth component of S1 is caused by the blood turbulence in the aorta. S2 is produced by the deceleration of blood flow into the aorta and the blood flow into the pulmonary artery. S3 and S4 are caused by the blood deceleration into the ventricles during the early and late diastolic filling phases of the ventricles [1] Auscultation sites Figure Heart Important Auscultation Sites

17 Aortic 2 nd ICS (Intercostal spaces) RSB (Right Sternal Border) Pulmonic 2 nd ICS LSB (Left Sternal Border) Tricuspid 4 th ICS LSB Apex 5th ICS MSL (mid-clavicular line) Heart diseases Heart failure (HF) Heart failure is defined as the inability of the heart either to pump a sufficient amount of blood to the metabolizing tissues or to do so without an increased filling pressure. Clinically, heart failure is generally described as left ventricular failure, right ventricular failure, and biventricular failure [3]. Coronary artery disease (CAD) CAD is when the coronary arteries that supply blood to the heart muscle become hardened and stiff due to buildup of a material called plaque on their inner walls. The process of arteries hardening and becoming stiffer takes years and is influenced from genetics and leaving habits. As the plaque increases in size, the insides of the coronary arteries get narrower and less blood can flow through them. Eventually, blood flow to the heart muscle is reduced and the heart muscle is not able to receive the amount of oxygen it needs. Cardiomyopathy A primary disorder of the heart muscle that causes abnormal myocardial performance. HF, CAD, Cardiomyopathy, Valvular heart diseases and Congenital Heart Defects are only part of the heart diseases which attach us. Some of these diseases can be detected with continues heart sound monitoring and thus prevent death or damage that can be caused due to late detection

18 2.2 Noise and Noise types Noise In general noise is an interference which is added to the required signal. Specifically in our case, noise is an external or internal sound interference (unwanted sound) which is added to the Heart Sound measured with the microphones. Noise is divided into several categories and types which differ one from each other by their source and features. For example white noise has a flat power spectral density; human speech noise has different spectral features than a hum noise, etc. Since the heart sound is not a regular periodic signal and the influence of the change caused to the heart sound due to additive noise is not easily measured, it is important to set some parameters to the quality of the signal after noise removal (some SNR equivalent criterion). The criterions for the noise removal quality of the algorithms used are discussed in section Possible Noise Types and properties Noises generated in or by the human body. Possible Human Internal Noise can be speech, coughing, snoring, heavy breathing, etc. Noises generated outside of the human body. Possible Externally generated noises can be human speech, music, television, radio, dog bark etc Internal/External Noise type Noise typical spectrum Noise typical amplitude Internal/External Speech Full Varying Bandwidth Internal snoring <500Hz High music Full Varying External Bandwidth Television Full Varying Bandwidth Table Noise types, their typical amplitudes and spectrum Full Bandwidth means that the spectrum of the specific signal is beyond the sampling rate/2 frequency

19 2.3 Recording of Heart Sounds Sensor Information The sensor used for heart sound recordings is a type of microphone also called piezoelectric displacement transducer. In a piezoelectric microphone, sound waves bend the piezoelectric material (by causing presure), creating a changing voltage. Figure Schematic drawing and a simplified model of a relative displacement sensor The active part of the transducer consists of a flexible metallic membrane coupled to a piezoelectric element. When a force (F) is applied to the surface (A) of the membrane, it is deformed relative to the heavier housing. The deformation (x) of the membrane relative to the housing generates an electric output from the piezoelectric element [8]. The sensor is attached directly to the chest or other parts close to the chest and is sensitive to mechanical motion rates starting from less than 1Hz. When connected to an amplifier with 1MΩ input impedance, its output voltage range is mV

20 2.4 Data Collection System The algorithms studied in this research is intended for continues heart sound monitoring. Nevertheless, this study has been performed on a data which has been measured, stored and only than transferred and analyzed off-line. For continues heart sound monitoring some minor adjustments must be performed. Data Measurement and Storage Transducers analog sigl Signal Conditioning amplified sig A/D digital sig Data Storage Noise Removal Algorithm Off Line Analysis Algorithm Communication Path Figure Experimental setup diagram The data measurement and storage system includes the following parts: Transducers Piezoelectric devices which transform the mechanical vibration of the chest to voltage. Signal conditioning Amplifies the transducer output voltage and performs impedance matching between the transducers and A/D Converters. A/D Converters Converts the Analog signal to a Digital stream which can be read by a computer. Data storage Stores the sampled data in a predetermined format

21 Chapter 3 Current State of the Art in Noise Removal Methods 3.1 Filters in general Real-world signals contain both wanted and unwanted information. Therefore, some kind of signal filtering technique must separate the two before processing and analysis can begin. A filter eliminates unwanted frequencies from a signal. There are several kinds of electronic filters: A low-pass filter passes low frequencies A high-pass filter passes high frequencies A band-pass filter passes a limited range of frequencies A band-stop filter passes all frequencies except a limited range A notch filter is a type of band-stop filter that acts on a particularly narrow range of frequencies The illustration bellow is amplitude vs. frequency graph, also called a spectral plot, of the characteristic curve of a band pass filter. The cutoff frequencies, f 1 and f 2, are the frequencies at which the output signal power falls to half of its level at f 0, the center frequency of the filter. The value f 2 - f 1, expressed is the filter bandwidth. The range of frequencies between f 1 and f 2 is called the filter pass band. Figure Band-pass filter example

22 3.2 Digital Filters A digital filter is an electronic filter (usually linear), in discrete time, that is implemented through digital electronic computation of digital signals FIR Filter A finite impulse response (FIR) filter is a type of a digital filter, which is normally implemented through digital electronic computation. The Z-transform of an FIR filter has only zeros and no poles. The number of coefficients in an FIR filter is its order. Figure FIR Filter block diagram IIR Filter An infinite impulse response (IIR) filter has an impulse response which lasts forever. An IIR has infinite duration because feedback of the outputs is used to calculate other output values. Unlike the finite impulse response (FIR) filter, the IIR filter must have an initial condition for each feedback value

23 3.2.3 Chebyshev filter Chebyshev Type I filters are equiripple in the passband and monotonic in the stopband. Type I filters roll off faster than type II filters, but at the expense of greater deviation from unity in the passband. Chebyshev filters have the property that they minimize the error between the ideal filter characteristic and the actual over the range of the filter, but with ripples in the passband. Figure Gain and group delay of a fifth order type I Chebyshev Low-Pass filter with ε=0.5. The gain response as a function of angular frequency ω of the n th order low pass filter is: G n ( ) T n 0 where ε is the ripple factor, ω0 is the cutoff frequency and T n is a Chebyshev polynomial of the nth order. The passband exhibits equiripple behavior, with the ripple determined by the ripple factor ε. In the passband, the Chebyshev polynomial alternates between 0 and 1 so the filter gain will alternate between maxima at G=1 and minima at G At the cutoff frequency ω0 the gain again has the value but continues to drop into the stop band as the frequency increases

24 3.3 The Wiener Filter The Wiener filter is a filter proposed by Norbert Wiener during the 1940s. Unlike the typical filtering theory of designing a filter for a desired frequency response the Wiener filter approaches filtering from a different angle. By creating a filter that filters only on the frequency domain it is possible for the filter to pass noise. Wiener's solution was to require additional information regarding the spectral content of the original signal and the noise. Wiener filters are characterized by the following: 1. Assumption: signal and (additive) noise are stochastic processes with known spectral characteristics or known autocorrelation and cross-correlation 2. Performance criteria: minimum mean-square error 3. An optimal filter can be found from a solution based on scalar methods The goal of the Wiener filter is to filter out noise that has corrupted a signal by statistical means. The input to the Wiener filter is assumed to be additive noise meaning x( t) s( t) n( t) Where s(t) is the original signal n(t) is the noise x(t) is the corrupted signal The output, x(t), is calculated by means of a wiener filter, g(τ), using the following convolution: x(t) = g(τ) * (s(t) + n(t)) The error is e( t) s( t d) x( t) and the squared error is e ( t) s ( t d) 2s( t d) x( t) x ( t) where s(t + d) is the desired output of the filter e(t) is the error Depending on the value of d the problem name can be changed: If d > 0 then the problem is that of prediction If d = 0 then the problem is that of filtering If d < 0 then the problem is that of smoothing Writing x(t) as a convolution integral: x ( t) g( ) s( t ) n( t ) d Taking the expectation of the squared error results in: E( e 2 ) R s (0) 2 g( ) Rxs ( d ) d g( ) g( ) Rx ( ) Rs is the autocorrelation function of s(t) Rx is the autocorrelation function of x(t) Rxs is the cross-correlation function of x(t) and s(t) If the signal s(t) and the noise n(t) are uncorrelated (i.e., the cross-correlation is zero) then: Rxs = Rs dd

25 Rx = Rs + Rn The goal is to then minimize E ( e 2 ) by finding the optimal wiener filter g(t). 3.4 Spectral Subtraction Spectral subtraction method performs noise spectrum subtraction from a noisy signal. Estimated clean speech x n Inverse DFT P x Subtraction Noise Spectrum P n P y DFT Noisy Signal y n Figure Spectral Subtraction noise removal The power spectrum of noise is estimated during signal inactive periods and subtracted from the power spectrum of the current frame resulting in the power spectrum of the original signal. Generally Spectral subtraction is suitable for stationary or very slow varying noises (so that the statistics of noise could be updated during signal inactive periods)

26 Chapter 4 Overview of Independent Components Analysis The sensors used for continues heart sound monitoring are most vulnerable to sounds created by the monitored person as there is a significant overlap in frequency range between heart sounds, speech, internal human noises and other background noises. To achieve heart sound continuous monitoring, with high sensitivity and low number of false alarms, background noises must be eliminated. Unfortunately, due to the large frequency overlap, regular filters and even adaptive filter are ineffective and insufficient in removing the noise. Although the heart sound and noise frequencies overlap, they have independent sources (and different statistical properties), therefore ICA (Independent Component Analysis) which can separate independent sources is most suitable for such an application. Moreover Spectral ICA as is even more efficient is such noise removals since it performs the source separation on the spectral domain which is less sensitive to delays and nonlinearities between the signals. 4.1 ICA - Independent Components Analysis ICA Definition There are two possible definitions to ICA: 1. Statistical and computational technique for revealing hidden factors that underlie sets of random variables, measurements, or signals. 2. ICA of a random vector X consists of estimating the following generative model for the data: x A s n i1 a i s i a. The independent components are latent variables they cannot be directly observed. b. The mixing matrix is assumed to be unknown. c. All we observe is the general vector x and we must estimate both A and s using it. d. x and s are random vectors ICA Assumptions Some starting point assumptions for ICA are: - s i is a random variable and not a time signal - The vectors s i in the vector S are assumed to be Statistically Independent [ Appendix A] - The independent components have a non-gaussian distributions [ Appendix B]

27 4.1.3 Independent Components Computation After estimating the matrix A we can compute it s inverse matrix: Then we obtain the independent components simply by: W 1 A s W x Ambiguities of ICA Two main ambiguities can be found in the ICA model: 1. The variance (energies) of the Independent Components can not be determined. Both A and s are unknown, therefore any scalar multiplier in one of the sources s i can always be canceled by dividing the corresponding column a i of A by the same scalar. For example: a11 a12 x1 a11 s1 a12 s2 A a21 a 22 x2 a21 s1 a22 s2 If we multiply s 1 by z then x will not change if we divide both a 11 and a 21 by z a11 s1 z a12 s2 z a11 s1 a12 s2 X a21 a21 s1 a22 s2 s1 z z22 s2 z 2. The sign of he Independent Components can not be determined. 3. The order of the Independent Components can not be determined. Since both A and s are unknown we can change the order of the terms in x As n i1 a i s i by using a permutation matrix R and its inverse which will give us the equation: 1 x As AP Ps 1 Where A P becomes the new unknown mixing matrix and P s become the new independent variables in a new order. 4.2 ICA Estimation Principles of ICA estimation The fundamental restriction in ICA is that the fundamental components must be non- Gaussian for ICA to be possible [ Appendix B]. To estimate one of the Independent components s i we will first write: y w W is one of the rows of A -1 and should be estimated. We will define z A T w. T x wi x i i

28 T T T Than we will receive y w x w A s z s. y is thus a linear combination of s i According to the central limit theorem, a linear combination of independent variables is more Gaussian than each of the variables therefore z T s is more Gaussian than each of the s i variables and the minimal Gaussianity is achieved when it equals to one of the s i (In this case only one of the elements z i of z is non zero). Therefore we can say the w is a vector which maximizes the non-gaussianity of w T x (which is one of the Independent Components). To maximize the non-gaussianity we must have a quantitative measure of non-gaussianity of a random variable. There are several possible methods for measuring non-gaussianity of a random variable such as Kurtosis, skewness and negentropy Measures of non-gaussianity Kurtosis The kurtosis of y is defined as: kurt( y) Ey 4 3( E y ) Since we assume that y has a unit variance: E y 1 kurt ( y) Ey 3 2 For a Gaussian y the fourth moment is 3 Ey 2 kurt 0 y gaussian Typically non-gaussianity is measured by the absolute value of kurtosis. Kurtosis can be positive or negative. Random variables which have negative kurtosis are called sub Gaussian while those with positive kurtosis are called super Gaussian Negentropy The entropy of a random variable is the degree of information that an observation of the variable gives. Entropy is related to the coding length of the random variable. The more random the variable, the larger is its entropy. For a discrete random variable entropy is defined as: H Y PY a log PY a For continues random variable differential entropy is defined as: H y f y log f ydy A fundamental result of information theory is that a Gaussian variable has the largest entropy among all random variables of equal variance therefore entropy can be used as a measure of non-gaussianity. Negentropy (modified version of differential entropy) is defined as: J y H y gauss H y i According to the above definition Negentropy is always non-negative and is zero if and only if y has Gaussian distribution. i i

29 In practice estimating negentropy using its definition is rather difficult, therefore we can use some simpler methods for estimating the negentropy. The classical approximation for estimating negentropy is using higher order momentums such as: J y Ey kurty Another approximation based on the maximum entropy principle is: k i ν y Gi positive constant Gaussian variable of zero mean and unit variance Variable of zero mean and unit variance. Non quadratic functions p i1 G y EG J ( y) k E By choosing the functions G wisely (G which doe s not grow to fast), we can obtain good and robust approximations of negentropy. Classical widely used functions include: 1 - G1 ( u) log cosh( a1 u), g1( u) G 1( u) tanh( a1 u) a 1 (tanh) u u - G2 ( u) exp( a2 ), g 2 ( u) G 2 ( u) u exp( a2 ) a (gauss) G3 ( u) u, g3 ( u) G3( u) u 4 (pow3) When selecting G 3 function the algorithm performs kurtosis minimization. When the independent components are highly super-gaussian, or when robustness is very important, G2 is recommended for use. i i i

30 4.3 FastICA Algorithm The convergence in ICA algorithms is usually slow, and depends on the choice of the learning rate sequence. A remedy for this problem is computational effective algorithms based on fixed point iteration. The FastICA algorithm is a computational effective algorithm which is suitable for maximizing the contrast function. FastICA for one unit Let us assume w is a weight vector of a neuron, which is updated by a learning rule. The FastICA learning rule finds a direction, a unit vector w such that the projection w T x maximizes Gaussianity. We will measure non-gaussianity by an approximation of the negentropy of w T x meaning J(w T x) and find its maximum. The FastICA for one unit consists of the following steps: 1. Choose an initial weight vector w T T 2. w Ex gw x Eg w x w w 3. w w 4. If w did not converge go back to 2 The function g is the derivative of the function G used in the contrast function. FastICA for several units The FastICA for one unit algorithm estimates just one of the independent components. To estimate several independent components the one unit algorithm must run using several units with weight vectors w 1,,w n. To prevent different vectors converging to the same maxima, T T after each iteration the outputs w1 x,......, w x must be decorrelated. The FastICA algorithm is neural in the fact that it is parallel and distributed, but it is not adaptive. The convergence speed of the fixed point algorithms and FastICA among them is times faster than the more neural algorithms [11]. n

31 4.4 Spectral ICA Spectral ICA is performing the FastICA on a signal represented in the spectral domain instead of a signal represented in time domain. Since the spectral and time representations have exactly the same information on the signal, the representation in the spectral domain is legal. There are several ways to perform the transform from time to spectral domain (and vice versa). The most common is the FFT (Fast Fourier Transform). Since the FFT representation of a time series signal in the frequency domain contains complex values it is hard to perform the Basic FastICA algorithm on the FFT transform. Therefore a more suitable method is the COSINE TRANSFORM which represents the time domain signal as real values in the spectral domain. After performing the FastICA algorithm on the spectral signal the signal must be converted back to the time domain with an INVERSE COSINE TRANSFORM The Cosine Transform DCT (discrete cosine transform) is a Fourier-related transform similar to the DFT, but using only real numbers. DCTs have twich the length of a DFTs. DCT expresses a signal in terms of a finite sum of cosines with different frequencies and amplitudes. The DCT equation: where y( k) ( k) ( k) 1, N 2, N N n1 K 1 x( n) cos 2K N 2n 1k 1 2N, k 1,..., N The Inverse DCT equation: N (2n 1)( k 1) x( n) ( k) y( k)cos, k 1 2N where 1, K 1 N ( k) 2, 2K N N n 1,..., N

32 4.4.2 Why Using Spectral ICA? The ICA algorithm in the time domain doe s not deal well with real heart signals and the speech noises that are present during continues heart sound monitoring. The main reason for the deficiency in time domain ICA is that in the real world the heart signals measured in the different microphones are slightly delayed from each other (have different phases). Also the additive noise signal has a different phase in each of the measured channels (according to its relative place to the noise source). Since the ICA algorithm finds the matrix A according to all the input channels, a delay between the channels may cause false or unwanted results in calculating A. When transferring the signals to the spectral domain, small time delays between the measured heart signals and time delays between the noises added to these heart signals are not noticeable (although they are represented in the spectral signal), therefore the ICA algorithm deals better with the spectral domain than with the time domain for the type signals we deal with. Figure Time and Spectral (DCT) domain representation of delayed sine waves The plots above represent sine waves of the same frequency but with different delays between each other. In the time domain, the delay is quite noticeable whereas in the spectral domain the differences between the signals are quite small. For larger delays between the signals we will see more significant differences in the spectral domain but still the differences in the spectral domain will be smaller than the ones in the time domain representation

33 4.5 PCA Principal Components Analysis PCA is a linear transformation that chooses a new coordinate system for the data set such that the greatest variance by any projection of the data set comes to lie on PC 1 (First Principle Component), the second greatest variance on PC 2 and so on. PCA can be used for reducing dimensionality in a dataset while retaining those characteristics of the dataset that contribute most to its variance by eliminating the later principal components. ADD Additional PCA formulas 4.6 ICA compared to PCA Both ICA and PCA are linear transformations. ICA Non-orthogonal transform High order statistics Minimizes the statistical dependence between the input vectors Assumes non-gaussian distributions Better in classification tasks More biological meaningful analysis PCA Orthogonal Transform Second order statistics Maximizes the variance between the input vectors Assumes Gaussian distributions Optimal coding and calculation time Table ICA vs. PCA

34 Chapter 5 Noise Removal Using Spectral ICA The main purpose of the research was achieving good noise removal from a noisy heart sound. The goal was to find the best algorithm, domain (time or spectral), and required number of microphones and algorithm parameters which will best remove the noise added to the heart sounds. Three sensors are placed on the chest. Two sensors are put at the Pulmonary and the Aortic area for best identification of the first S1, and second S2 heart sounds. The third sensor is put on the chest at a location where little or no heart sound is heard, thus, receives a relatively stronger background sound energy. It is expected that One or Two of the ICA algorithm outputs will contain heart sounds with reduced background noise which should become more emphasized in the third output. 5.1 Main algorithm ICA The basic algorithm used in the current research is the FastICA algorithm. The FastICA package used in this research is version 2.5 and it was developed in Helsinki University of Technology by Hugo Gävert, Jarmo Hurri, Jaakko Särelä, and Aapo Hyvärinen. The FastICA algorithm can be found under the following web address: The algorithm used receives as an input the measured heart signals after initial filtering (Band Pass Chebyshev Filter). In the current study three to five heart sound channels may be entered as an input to the algorithm. Each channel may have different filtering (band pass filtering). After running different scenarios it has been observed that the best noise removal is accomplished by performing the ICA algorithm on three heart sound channels (each of the channels is band pass filtered according to the same filter parameters). 5.2 How doe s ICA reduce noise The ICA algorithm performs Independent Component separation. Since the heart sound and noise (which is usually speech) have different statistical characteristics the ICA algorithm is capable of separating the heart sound and noise components into different output channels. Therefore, the output of the ICA algorithm will be at list one noise free heart sound output channel and at list one noise only output channel

35 5.3 Band Pass Filtering The sampling frequency of the Heart Signal is 4000Hz, therefore according to Nyquist theory the maximum Heart Signal frequency which can be sampled is 2000Hz. For Heart Signal continues monitoring and for the purpose of this research the frequencies studies are in the ranges of 20Hz up to a maximum of 400Hz. Therefore, band pass filtering has to be implemented. In this research Chebyshev Type I filter has been selected for band pass filtering of the heart sound. 5.4 MATLAB program The analysis has been done with different data types to check the robustness of the algorithm, meaning: Data from different patients (Healthy, Sick) Patient positions (Sitting, lying on the back, lying on the left side). Patient s normal birthing, birthing trough a tube, halt birthing. Different microphone positions. The Noise Removal Algorithm was written in Matlab 6.5 (The Mathworks Inc.) running on a mobile computer and includes all the research related programming. It includes several important functions and GUI used for the convenience of the research. Figure shows the Main GUI used. The main and most important parts of the program are explained in some of the following sections

36 Figure Main Noise Removal Research GUI. The snap shot of the Main Noise Removal GUI above presents 4 subplots. The topmost subplot is the patients EKG measurement which is used as a visual reference for the heart sounds and doe s not participate in the noise removal algorithm. The three plots (maybe two or four, depending on the number of channels selected for the ICA) bellow the EKG are the heart sound plots (before and after the algorithmic analysis). As can be noted, each plot contains both red and blue graphs. The blue graphs are the heart sounds before algorithmic analysis (including noise) and the red graphs are the heart sounds after algorithmic analysis. This way one can distinguish between the heart sounds before and after ICA. Explanation on the MAIN GUI different options and activation: Filter & Reorganize pushbutton Opens the Filter_Reorganize_GUI where the number of channels, their order, the filtering for each of the channels and noise edition is defined Start Time (Sec) textbox Sets the start time (Sec) from which the plots will appear End Time (Sec) textbox Sets the end time (Sec) until which the plots will appear Mix Data pushbutton Used for performing a mix of the input channels to see if the Mixed and Unmixed ICA outputs are the same Perform Algorithm on EKG checkbox If the check box is unselected (default state) the ICA Algorithm is not performed on ch1 (which

37 First ICA Options pushbutton Original Data or Mixed Data label ICA parameters label DO First ICA pushbutton F (Fourier) radiobutton T (Time) radiobutton Original Data - ICA Data checkbox DO_Wiener_Filter pushbutton Zoom In pushbutton Zoom Out pushbutton General Options pushbutton is usually set as the EKG channel), otherwise the ICA is performed on all channels Opens the ICA_Parameters_Select_GUI where the ICA parameters such as Non Linearity are selected Represents the color (BLUE) of the original data or data after filtering and noise addition (before algorithmic analysis) in the plots. This label and color always appear. Represents the color (RED) and parameters of the data after ICA. This label appears only after running the ICA algorithm Runs the Spectral ICA or Time ICA algorithm, depending on the state of the F and T radiobuttons When set the DO First ICA runs the Spectral ICA algorithm When set the DO First ICA runs the Time ICA algorithm For each of the channels, performs subtraction of the Original Data (or data after Filter and Reorganize) from the data after ICA and plots the subtraction results Runs the Wiener Filter algorithm Performs an amplitude zoom in on each of the channels (the Start and End times are not changed) Performs an amplitude zoom out on each of the channels (the Start and End times are not changed) Opens the General_Options_GUI Figure General_Options_GUI Noise File Name textbox Externally recorder additive noise file name Signal Spectrum pushbutton Performs Spectral Analysis on the signals Spectrogram pushbutton Performs Spectrogram Analysis on the signals Analyze R2_R1 Quite Periods pushbutton Finds and marks the Diastole Periods according to the EKG

38 Create_QP_Base pushbutton Plot_QP_Graph pushbutton Sample_Rate label Creates a data base of the Diastole Analysis Plots 3D and 2D Diastole Analysis results according to the data base created by the Create_QP_Base function Displays the sample rate as data acquisition system sample rate

39 5.5 Algorithm Flow Overview To perform the noise removal and assessment of the noise removal quality some major steps must be followed. These steps can be seen in Figure Recorded Noise Measured HS Filter Reorgenize Data Set ICA Parameters Run Algorithmic Analysis Noise Free HS Algorithm Quality Algorithm Quality Assesment Figure General Algorithmic Flow Schematic view

40 5.5.1 Filter Reorganize Data Before performing an Algorithmic Analysis on the heart sounds, the signal must first go through some manipulations such as Sorting, Filtering, and Noise addition (Only when the heart sound is noise free and an external noise should be added). This is performed with the Filter_Reorgenize_GUI which can be seen in Figure If the Measured heart sound is noise free, external noise can be added by setting the appropriate Noise Mul values. On the other hand, if the heart sound is measured in a noisy environment Noise Mul values should be set to 0. Figure Filter_Reorhenize_GUI window Filter_Reorhenize_GUI window is used to select the number of channels, appropriate band pass filters and the Noise Multipliers for the heart sound channels Set ICA Parameters For ICA Algorithmic Analysis, before running the algorithmic analysis, the ICA Parameters must be set. This is performed with the ICA_Parameters_Select_GUI which can be seen in Figure

41 Figure ICA_Parameters_Select_GUI window For Wiener Filter Algorithmic Analysis, there is no need to set the ICA parameters and the wiener filter algorithm can run directly after Filter Reorganize Data Run Algorithmic Analysis Running the main algorithm The first step performing the algorithmic analysis is running the Spectral ICA algorithm with the required parameters. This step is divided into three sub steps: a. Transforming the input data to the spectral domain with the DCT function. b. Running the ICA algorithm with the required parameters on the spectral domain data. c. Transforming the data after ICA back to the time domain with the IDCT function Association of the original signal with the new ICA transformed signals As already mentioned, we can not determine the order of the independent components at the output of the ICA algorithm. Therefore to make sure each signal at the output of the algorithm is associated with its originating signal, a cross correlation test is performed between each input channel to each of the output channels. The result is a matrix which includes all possible correlations between the input and output channels. According to the cross correlation matrix a Max_Possition vector which contains the ICA output channel number for each data input channel is created

42 5.6 Making sure that the right signal gets its noise removed With the ICA algorithm, the signal from which the noise will be removed can not be determined in advance. To make sure the noise is removed from a specific required heart sound channel the noise amplitude in one of the channels at which we don t want to remove the noise from must be larger than the heart sound amplitude. This is done by placing the two microphones where both heart sounds and noise have significant amplitudes and placing the third microphone where heart sound amplitude is relatively low as explained in section Algorithm quality Assessment One of the most important parts of the research is the ability to determine whether the algorithm works according to the expectations or not. This is called the algorithm quality assessment. The algorithm quality assessment is roughly constructed of two parts: 1. Human eye assessment 2. Algorithmic assessment Human eye assessment This part is in my opinion the most important part since currently I see no algorithm which can compete or be general enough to measure all assessment related issues. This doe s not mean that the human eye can make all possible assessments but we can see just by glance how good or bad is the noise removal, a parameter which can not be simply measured. In general, I can say that whenever it is seen that the noise removal is good or poor, the algorithmic assessment only approves what is already known and seen Algorithmic assessment After running several Data files with different noise data and different ICA parameters, and seeing that the noise is removed very well it was the time for additional algorithmic assessment for the measurement of noise removal quality. The algorithmic assessment includes several parts which are: 1. Signal spectrum plots 2. Spectrogram (Time-dependent frequency analysis) plots 3. Diastole analysis

43 Signal Spectrum Plots This part of the assessment includes spectral plots of the Analyzed signal (After ICA algorithm or after wiener filtering), the Filtered Reorganized Data (the Original signal after filtering) and the Noise Data. This method of assessment supplies us with general view of the noise removal quality but still doe s not include numeric answers to the quality issue. Also, since the Signal spectrum plots are FFT (Fast Fourier Transform) of the signals, if we have a singular event in which the frequency changes, although it may have physiological significance, it won t necessarily be noted (or just slightly noted) with the FFT. Even if the event will be noted with the FFT, we won t have any information on the time at which this specific frequency component occurred. To overcome these possible problems we can use time dependent FFT (spectrogram) which will show us time dependent changes in the spectrum. Figure Signal Spectrum Plot Example for 3 channel Spectral ICA Analysis

44 Figure Signal Spectrum Plot Example Wiener Filter Analysis The pictures above are examples of the spectral plots generated for Noise Removal Quality analysis with multi-channel ICA algorithm and with a one channel Wiener Filter algorithm. The spectral plots include 3 rows and 1 to 3 columns (depending on the number of channels used as an input for the algorithm). Each row represents a different data type: 1. The first row represents the data after the algorithmic analysis ( ICA Data or Wiener Filter Data ). 2. The second row represents the Filtered Reorganized Data (Data after initial filtering and reorganization). 3. The third row represents the Noise Data meaning the noise added to each channel (in case there is more than one input channel). The columns (if we have more than one column) represent the different channels. In case of the Spectral ICA analysis we use 3 input channels for the Spectral ICA, therefore the Signal Spectrum plot will show 9 different plots organized as 3x3 graphs as in Figure

45 Spectrogram Plots Spectrogram is a MATLAB function that returns the time-dependent Fourier transform. The time-dependent Fourier transform (Also known as the Short-Time Fourier transform STFT) is the discrete-time Fourier transform for a sequence computed using a sliding window. In STFT a moving window is applied to the signal and the Fourier transform is applied to the signal within the window as the window is moved. This part of the assessment includes time domain signal plots of the signal before and after analysis and spectrogram plots of the Filtered Reorganized Data (the Original signal after filtering), the Noise Data and the Analyzed signal (After ICA algorithm or after wiener filtering). The spectrum axis of the spectrogram shown in the plots depends on the filtering used for the signals meaning if we used a band pass filter from 20Hz to 400Hz before performing the ICA, the spectrogram will show the spectrum from 0Hz to 400Hz. The time axis of the spectrogram shown in the plots is set according to the Start Time and Stop Time in the main page meaning in the spectrogram plot the time shown will be between Start Time to Stop Time. Figure Spectrogram Plot Example for 3 channel Spectral ICA Analysis

46 Diastole (Quite period) analysis The diastole period is the quite period between S2 and the corresponding S1. Quite period s analysis is a method which analyses the highest peaks in the heart sound quite periods before and after performing algorithmic analysis ( ICA Data or Wiener Filter Data ). The reason for using the quite period s analysis method and not measurement of the energetic periods in the heart sound is that the quite periods do not contain significant energy in them and if there is some noise added to the quite period the program can easily estimate how well is it removed. Heart sound quite period is the period between the end of S2 and the start of S1 coming right after the specific S2. For the calculation of the quite period highest peaks three steps must be performed: 1. Finding the center (S2_S1_Centers) of the quite period for each heart sound cycle (this step must be performed for each measured cycles). 2. Defining the quite period limits (same limits for all cycles) which is S2_S1_Centers -100mSec S2_S1_Centers 100mSec 3. Calculating the highest peaks average (1000 peaks) for all cycles. For finding the S2_S1_Centers the program uses the function segment_ekg_sa which returns the EKG R and T wave locations time stamps. The center of the quite period is calculated according to the following equation: R i 1 T i S2_S1_Centers T i 2 Diastole period Noisy HS Diastole Peak ICA HS Diastole Peak Figure Example of the heart sound quite period marking and noise peaks

47 After calculating the quite period highest peaks average of the noise free heart sound, the Noisy heart sound and the signal after the algorithmic analysis ( ICA Data or Wiener Filter Data ), the program calculates: Noisy _ HS Diastole Peaks Average Noise AdditionBefore _ ICA db 20 log10 Noisefree _ HS Diastole Peaks Average And ICA _ HS Diastole Peaks Average Noise Addition After _ ICA db 20 log10 Noisefree _ HS Diastole Peaks Average The Diastole Analysis Value (noise removal quality) is simply: Diastole Analysis Value db Noise Addition After _ ICA Noise AdditionBefore _ ICA These ratios give a good indication on how well was the noise removed from the signal after the algorithmic analysis

48 Chapter 6 Results 6.1 Results Overview The goal of this research is to suggest a method for removing in and out of band noise from a noisy heart signal and demonstrate that the noise can be removed effectively better than filtering methods. The following sections present noise removal results from different heart signals and different noise types. The setup used includes three microphones, two of which are closer to the heart and one is far from the heart. The microphones close to the heart receive better heart signal whereas the microphone far from the heart receives relatively more noise energy. We expect that when the three sensored signals will produce three independent components following and ICA algorithm, the noise will be concentrated only in one of the signals and will be removed from the others. Each heart signal cycle has a quite period (diastole). The research utilizes the fact that there are times of quite periods to demonstrate that the noise signal energy is dramatically reduced in those regions. The following sections include demonstrations of the noise removal in the time domains, spectral domains and spectrogram representations. In addition to noise removal, the ICA algorithm also performs heart sound enhancement of the required channel (the same channel from which the noise is removed) as demonstrated in this chapter

49 6.2 Setup description and types of noise used Several different setups and noise types have been used as the input for the algorithm to ensure the algorithm used is robust enough and can deal with different heart sounds and noise types: 1. Heart sounds measurement in a noise free environment and addition of a separately measured noise. 2. Heart sounds measurement in a noisy environment. Using two types of environments had two purposes: 1. Heart sounds measurement in a noise free environment and addition of a separately measured noise used to evaluate how well the noise is removed as the non-noisy target was unknown. 2. Heart sounds measurement in a noisy environment was essential since it is important to know how well the algorithm performs in a real noisy environment and with a real noise distribution between the different heart sound channels. It is important to emphasis that the noise spectrum overlaps with the spectrum of the heart sound, otherwise, one could use simple filter to remove the noise. The heart sound and noise spectral overlap can be seen in the following few examples: Figure Noise and heart sound spectral overlap example 1 The figures depict an overlap between the heart sound and the noise spectrum. It can be clearly seen that although there is an overlap between the heart sound and the noise, the ICA algorithm output removes the noise. The noise data is presented in the lower two plots, the noise free heart sound is presented in the middle two plots and the data after the ICA algorithm is presented in the upper two plots. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The spectral domain presentations are from 0-100Hz. Heart sounds file name used in this example is GA_Normal_1, ICA nonlinearity is Gauss, Noise Levels are: ch2 (2 nd ICS LSB) noise level = 0.6, ch3 (2 nd ICS RSB) noise level = 0.65, ch4 (Left carotid) noise level = 0.7. Noise file name used is in the left plots is television and in the right plots count_time

50 Figure Noise and heart sound spectral overlap example 2 The figures depict an overlap between the heart sound and the noise spectrum. It can be clearly seen that although there is an overlap between the heart sound and the noise, the ICA algorithm output removes the noise. The noise data is presented in the lower two plots, the noise free heart sound is presented in the middle two plots and the data after the ICA algorithm is presented in the upper two plots. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The spectral domain presentations are from 0-100Hz. Heart sounds file name used in this example is GA_Halt_1, ICA nonlinearity is Gauss, Noise Levels are: ch2 (2 nd ICS LSB) Noise Level = 0.8, ch3 (2 nd ICS RSB) Noise Level = 0.5, ch4 (Left carotid) Noise Level = 0.8. Noise file name used is in the left plots is count_time and in the right plots snor_with_pre

51 6.2.1 Setup description Several setups have been used for the heart sounds measurements. The setups differed in microphone locations, patient positions (sitting, lying on left side or lying on right side) and breathing routine (normal birthing, birthing trough a tube, halt birthing). For the heart sound measurements three sensored inputs have been used. Therefore, even if the number of sensors used for the data collection was more than three, only three sensors were selected as an input to the algorithm. The sensor locations usually selected have been: 1. LSB (2 nd ICS LSB or 4 th ICS LSB) 2. RSB (2 nd ICS RSB) 3. Carotid (Right Carotid or Left Carotid) or APEX A description of each file name and its corresponding setup can be found in Table bellow. File Subject Positio Microphones Breathing Environment n GA_Halt_1 Healthy Sitting 2 nd ICS LSB No Quiet office 2 nd ICS RSB Left carotid GA_Normal_1 Healthy Sitting 2 nd ICS LSB Yes Quiet office 2 nd ICS RSB Left carotid GA_TubeMedium_1 Healthy Sitting 2 nd ICS LSB 2 nd ICS RSB Left carotid Yes, through a tube Quiet office YS_TubeMedium_1 Healthy Sitting 2 nd ICS LSB 2 nd ICS RSB Left carotid Halt_supine_1 Healthy Lying on left side GA_ACG_supine_1 Healthy Lying on left side Apex 4 th ICS LSB 2 nd ICS RSB Right carotid Apex 2 nd ICS RSB Right carotid HAIM_COUNTING_1 Healthy Sitting 2 nd ICS LSB 2 nd ICS RSB Apex HAIM_COUNTING_2 Healthy Sitting 2 nd ICS LSB 2 nd ICS RSB Apex Table File names and their corresponding setup descriptions Yes, through a tube No No Yes Yes Quiet office Quiet office Quiet office Noisy office Noisy office

52 6.2.2 Types of noise used Knowing the exact noise is essential for estimating how well it can be removed. Therefore, most of the analysis has been performed with noises which have been recorded separately from the heart sounds recordings and added manually to the heart sounds. Some of the heart sounds recordings have been performed in a noisy environment, to make sure the proposed algorithm works well with real noisy environments. With these kinds of recordings only Human eye assessment method can be used for algorithm quality assessment. The noises were measured separately and were added to the heart sounds so the new signal was a summation of the heart sound and the noise signal: Signal Measured _ HS Const Noise _ Signal 0 Const 2 Four different noises have been used. The noises and their description can be found in Table below. Noise File Name Noise source Noise description Count_time Human Voice Recording from a human counting from 1 to 30. Recording Duration 66 Seconds Snor Snor_with_pre Television Human snore, cough and count Human snore and cough Television Speakers. Recording from a human snoring, coughing and counting. Recording Duration 33 Seconds Recording from a human snoring and coughing. The recording start with a snore (the snore begin before the recording and continued after the recording has started) Recording Duration 33 Seconds Recording from a television speaker. The recording includes both television sounds and speech sounds emerging from the environment. Recording Duration 60 Seconds Table Noise names and description Each of the four noises mentioned has been added to each of the heart sound signals mentioned in Table to create a matrix of different combinations

53 6.2.3 Noises out of the scope of the current research The current research deals with noises which are generated inside or outside the measured person and appear in all channels. Since the research is based on the ICA algorithm, noises which appear only in one or two of the three input channels are not removed. Therefore the algorithm doe s not deal with cases where a peak noise is added to one of the channels or in cases where only one or two of the channels pick the noise and the third channels is noise free. Figure Unsuccessful noise removal attempt for a heart sound with a peak noise caused by microphone movement The figures present an example of a peak noise removal attempt in one of the channels. As can be seen, the peak noise in HS-R is not removed at all with the ICA algorithm. The three plots bellow the EKG are the heart sound plots (before and after the ICA). The blue graphs are the heart sounds before ICA and the red graphs are the heart sounds after ICA. The data was filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 15-55Sec. Heart sounds file name used in this example is hs t145356, ICA nonlinearity is Gauss

54 6.3 Graphs demonstrating the noise removal To have some visual understanding of how well does the ICA algorithm removes the noise from a heart sound one could just look at the time domain, spectral domain and spectrogram figures bellow. Figure Noise Removal from a HS Time Series representation (0-30.4Sec) The figures present an example of a noise removal in a time scale representation. It can be clearly seen how well the noise removed from the HS. The topmost subplot is the patients EKG measurement which is used as a visual reference for the HS and doe s not participate in the noise removal algorithm. The three plots bellow the EKG are the HS plots (before and after ICA). The blue graphs are the HS before ICA (including noise) and the red graphs are the HS after ICA. The data and noise were filtered with a 20Hz- 400Hz band pass filter before running the algorithm. The time domain presentations are from Sec. Heart sounds file name used in this example is GA_Halt_1, ICA nonlinearity is Gauss, Noise file is television, Noise Levels are: ch2 (2 nd ICS LSB) Noise Level = 0.7, ch3 (2 nd ICS RSB) Noise Level = 1, ch4 (Left carotid) Noise Level =

55 Figure Noise Removal from a HS Time Series representation (21-23Sec) This figure is a view from 21Sec to 23Sec of Figure

56 Figure Noise Removal from a HS, 3 channels spectral representation (0-400Hz) The spectral presentation above is a transformation of the time presentation in Figure The Noise data is presented in the lower three plots, the noise free HS is presented in the middle three plots and the data after the ICA algorithm is presented in the upper two plots. Figure Noise Removal (in and out of band noise) from a HS, one channels spectral representation (0-150Hz) The spectral presentation above is a presentation of the ch2 HS (2 nd ICS LSB) plots in Figure at a frequency range of 0-150Hz. The Noise data is presented in the bottom plot, the noise free HS is presented in the middle plot and the data after the ICA algorithm is presented in the upper plot

57 Figure Spectrogram presentations of ch2 (2 nd ICS LSB) heart sounds in Figure The figures above depict noise removal in a spectrogram representation of ch2 (2 nd ICS LSB) heart sound in Figure The topmost subplot is the time domain presentation of the noisy heart sound (Blue) and the heart sound after ICA (Red). Bellow the time domain presentation are the spectrogram noise free heart sound, noisy heart sound and heart sound after ICA plots. It can be clearly seen that heart sound reconstructed from the noisy heart sound is very similar to the noise free heart sound. Although the noisy signal spectrum overlaps the noise free signal, the ICA successfully removes the noise

58 6.3.1 Assessment of the noise addition on the ICA algorithm output The figures bellow show the output of the ICA and Wiener filter algorithms before and after the noise addition. In time domain presentations it can be clearly seen that the output of the ICA algorithm before and after the noise addition looks the same regardless of the added noise. In the wiener filter case it can be seen that the noise added to the signal also appears in the Wiener filter output meaning the noise is not removed well. In spectral domain presentations it is harder to determine how similar the original heart sound is to the signal after algorithmic analysis (both ICA and Wiener) but it can be seen that some additive noise is not removed well with Wiener filtering. Figure Comparison of the ICA output (Time domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time ICA output time scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be clearly seen that although there is a large amount of additive noise, in time domain the ICA output is quite similar to the signal without the noise. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from Sec. Heart sounds file name used in this example is GA_Halt_1, ICA nonlinearity is Gauss, Noise file is count_time, Noise Levels for the HS without noise addition (left plot) are all zeros and for the HS with noise addition (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.6, ch3 (2 nd ICS RSB) Noise Level = 0.65, ch4 (Left carotid) Noise Level =

59 Figure Comparison of the ICA output (Spectral domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time ICA output spectral scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be clearly seen that although there is a large amount of additive noise, in spectral domain the ICA output is quite similar to the signal without the noise. The data and noise were filtered with a 20Hz- 400Hz band pass filter before running the algorithm. The spectral domain presentations are from 0-400Hz. Heart sounds file name used in this example is GA_Halt_1, ICA nonlinearity is Gauss, Noise file is count_time, Noise Levels for the HS without noise addition (left plot) are all zeros and for the HS with noise addition (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.6, ch3 (2 nd ICS RSB) Noise Level = 0.65, ch4 (Left carotid) Noise Level =

60 Figure Comparison of the Wiener Filter output (Time domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time Wiener Filter output time scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be seen that in time domain the Wiener Filter output is quite similar to the signal with the noise addition, meaning the noise is not removed well. The data and noise were filtered with a 20Hz- 400Hz band pass filter before running the algorithm. The time domain presentations are from Sec. Heart sounds file name used in this example is GA_Halt_1, Noise file is count_time, Noise Level for the HS without noise addition (left plot) is 0 and for the HS with noise addition (right plot) is: ch2 (2 nd ICS LSB) Noise Level = 0.6. Figure Comparison of the Wiener Filter output (Spectral domain) for a HS with and without noise addition HS=GA_Halt_1, Noise=count_time Wiener Filter output spectral scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be seen that in spectral domain the Wiener Filter output is quite similar to the original signal but is has lower spectral intensity. In addition, some noise in the Hz is not removed and appears at the output. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The spectral domain presentations are from 0-400Hz. Heart sounds file name used in this example is GA_Halt_1, Noise file is count_time, Noise Level for the HS without noise addition (left plot) is 0 and for the HS with noise addition (right plot) is: ch2 (2 nd ICS LSB) Noise Level =

61 Figure Comparison of the ICA output (Time domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre ICA output time scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be easily seen that although there is a large amount of additive noise, in time domain the ICA output is quite similar to the signal without the noise and it can also be seen the S2 signal enhancement appears. The data and noise were filtered with a 20Hz-200Hz band pass filter before running the algorithm. The time domain presentations are from 16-18Sec. Heart sounds file name used in this example is GA_Normal_1, ICA nonlinearity is Gauss, Noise file is snor_with_pre, Noise Levels for the HS without noise addition (left plot) are all zeros and for the HS with noise addition (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.7, ch3 (2 nd ICS RSB) Noise Level = 0.65, ch4 (Left carotid) Noise Level = 0.6. Figure Comparison of the ICA output (Spectral domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre ICA output spectral scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. The spectral domain plots show that signal encounters a significant signal enhancement and a good noise removal. The data and noise were filtered with a 20Hz-200Hz band pass filter before running the algorithm. The spectral domain presentations are from 0-200Hz. Heart sounds file name used in this example is GA_Normal_1, ICA nonlinearity is Gauss, Noise file is snor_with_pre, Noise Levels for the HS without noise addition (left plot) are all zeros and for the HS with noise addition (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.7, ch3 (2 nd ICS RSB) Noise Level = 0.65, ch4 (Left carotid) Noise Level =

62 Figure Comparison of the Wiener filter output (Time domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre Wiener Filter output time scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be seen that in time domain the Wiener Filter output is quite similar to the signal with the noise addition, meaning the noise is not removed well. The data and noise were filtered with a 20Hz- 200Hz band pass filter before running the algorithm. The time domain presentations are from 16-18Sec. Heart sounds file name used in this example is GA_Normal_1, Noise file is snor_with_pre, Noise Level for the HS without noise addition (left plot) is 0 and for the HS with noise addition (right plot) is: ch2 (2 nd ICS LSB) Noise Level = 0.7. Figure Comparison of the Wiener filter output (Spectral domain) for a HS with and without noise addition HS=GA_Normal_1, Noise=snor_with_pre Wiener Filter output spectral scale comparison of a HS with (Right Plot) and without (Left Plot) noise addition. It can be seen that in spectral domain the Wiener Filter output is quite similar to the original signal. The data and noise were filtered with a 20Hz-200Hz band pass filter before running the algorithm. The spectral domain presentations are from 0-200Hz. Heart sounds file name used in this example is GA_Normal_1, Noise file is snor_with_pre, Noise Level for the HS without noise addition (left plot) is 0 and for the HS with noise addition (right plot) is: ch2 (2 nd ICS LSB) Noise Level =

63 6.3.2 Noise removal with ICA vs. Wiener The figures bellow show comparisons between noise removals with ICA vs. Wiener filtering. Since the wiener filter used (WienerScalart96) requires a period of 0.25mSec of adaptation to the signal, I recorded a special noise file named snor_with_pre which starts with the snoring signal and enables the Wiener filter to adapt to it. In the setup used for the wiener filter the sensored input receives both the heart signal and noise sound. Pulmonic - 2nd ICS LSB Figure Microphone placement for Wiener Filter based noise removal In the time domain plots, it can be clearly seen that ICA removes the noise (although also slightly changes the heart sound) whereas the Wiener filter has almost no impact on the noise or the signal. On the other hand, in the spectral domain plots it can be also seen that the noise is better removed but the original signal also changes much more. Since the ICA algorithm used receives three heart sound channels located in different locations it also has much more impact on the signal in the measured channel. This is heart sound enhancement meaning the ICA uses all three channels to output one channel which combines the properties of all other channels. The signal enhancement received at the output must be further analyzed and it must be decided whether this signal enhancement enhances the original heart sound or corrupts it

64 Figure Wiener Filter vs. ICA noise removal time domain plots (15-21Sec) HS=YS_TubeMedium, Noise=snor_with_pre Wiener Filter (Left Plot) vs. ICA (Right Plot) noise removal time scale comparison. It can be clearly seen that the additive noise is removed much better with the ICA algorithm compared to the noise removal with the wiener filter. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 15-21Sec. Heart sounds file name used in this example is YS_TubeMedium_1, ICA nonlinearity is Gauss, Noise file is snor_with_pre, Noise Level for the HS before wiener filter (left plot) is ch2 (2 nd ICS LSB) Noise Level = 0.6 and for the HS before ICA (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.6, ch3 (2 nd ICS RSB) Noise Level = 0.65, ch4 (Left carotid) Noise Level = 0.7. Figure Wiener Filter vs. ICA noise removal time domain plots (16-17Sec) HS=YS_TubeMedium, Noise=snor_with_pre The plots above are a time scale zoom in (16-17Sec) of the plots in Figure

65 Figure Wiener Filter vs. ICA noise removal spectrogram plots (15-21Sec) - HS=YS_TubeMedium, Noise=snor_with_pre Wiener Filter (Left Plot) vs. ICA (Right Plot) noise removal spectrogram comparison. It can be clearly seen that the additive noise is removed much better with the ICA algorithm compared to the noise removal with the wiener filter. The noise appears in the noisy heart sound both in the quite periods and during S1 and S2. Although the noisy heart sound is very corrupted relatively to the noise free heart sound, the heart sound after ICA (right plot) looks similar to the original noise free heart sound. Figure Wiener Filter vs. ICA noise removal spectral domain plots (0-400Hz) HS=YS_TubeMedium, Noise=snor_with_pre Wiener Filter (Left Plot) vs. ICA (Right Plot) noise removal spectral scale comparison. From this figure no significant difference can be noticed between the original signal and the signal after wiener filtering. On the other hand significant signal enhancement can be noticed in the HS after the ICA algorithm. The signal, filtering and noise parameters are as in Figure

66 The plots bellow show how well the additive noise is removed from the HS with ICA vs. Wiener filtering. It can be clearly seen the ICA algorithm removes the noise much better than the Wiener filter. Figure Spectral Domain plots of Noise Removal with Wiener Filter vs. ICA with a zoom on the noise area ( Hz) HS=YS_TubeMedium, Noise=snor_with_pre Figure is a spectral presentation of the Noise, Filtered HS, Wiener Filtered HS and HS after ICA in the Hz spectrum. It can be noticed that for the same HS and Noise in the specific frequency range the ICA algorithm removes the noise much better than the wiener filter. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. Heart sounds file name used in this example is YS_TubeMedium_1, ICA nonlinearity is Gauss, Noise file is snor_with_pre, Noise Level for the HS before wiener filter (left plot) is ch2 (2 nd ICS LSB) Noise Level = 0.6 and for the HS before ICA (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.6, ch3 (2 nd ICS RSB) Noise Level = 0.65, ch4 (Left carotid) Noise Level =

67 Figure Wiener Filter vs. ICA noise removal time domain plots (2-4Sec) HS=GA_Normal_1, Noise=count_time Wiener Filter (Left Plot) vs. ICA (Right Plot) noise removal time scale comparison. It can be clearly seen that the additive noise is removed much better with the ICA algorithm compared to the noise removal with the wiener filter. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 2-4Sec. Heart sounds file name used in this example is GA_Normal_1, ICA nonlinearity is Gauss, Noise file is count_time, Noise Level for the HS before wiener filter (left plot) is ch2 (2 nd ICS LSB) Noise Level = 0.6 and for the HS before ICA (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.6, ch3 (2 nd ICS RSB) Noise Level = 0.5, ch4 (Left carotid) Noise Level = 0.7. Figure Wiener Filter vs. ICA noise removal spectrogram plots (15-21Sec) - HS=GA_Normal_1, Noise=count_time Wiener Filter (Left Plot) vs. ICA (Right Plot) noise removal spectrogram comparison. It can be clearly seen that the additive noise is removed much better with the ICA algorithm compared to the noise removal with the wiener filter. The noise appears in the noisy heart sound both in the quite periods and during S1 and S2.Although the noisy heart sound is corrupted relatively to the noise free heart sound, the heart sound after ICA (right plot) looks similar to the original noise free heart sound

68 Figure Wiener Filter vs. ICA noise removal spectral domain plots (0-400Hz) HS=GA_Normal_1, Noise=count_time Wiener Filter (Left Plot) vs. ICA (Right Plot) noise removal spectral scale comparison. From this figure it can be seen that the wiener filter output lowers the spectral power of the HS and the ICA output spectral power of the HS is higher regardless of the noise meaning some signal enhancement occurs. Also it can be seen that some of the noise spectrum also appears in the wiener filter output whereas the ICA output does not include there noise spectral components. The signal, filtering and noise parameters are as in Figure

69 Figure Spectral Domain plots of Noise Removal with Wiener Filter vs. ICA with a zoom on the noise area (75-200Hz) HS=GA_Normal_1, Noise=count_time Figure is a spectral presentation of the Noise, Filtered HS, Wiener Filtered HS and HS after ICA in the Hz spectrum. It can be noticed that for the same HS and Noise in the specific frequency range the ICA algorithm removes the noise much better than the wiener filter. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. Heart sounds file name used in this example is GA_Normal_1, ICA nonlinearity is Gauss, Noise file is count_time, Noise Level for the HS before wiener filter (left plot) is ch2 (2 nd ICS LSB) Noise Level = 0.6 and for the HS before ICA (right plot) are: ch2 (2 nd ICS LSB) Noise Level = 0.6, ch3 (2 nd ICS RSB) Noise Level = 0.5, ch4 (Left carotid) Noise Level =

70 6.4 Quality evaluation results To estimate how well the noise is removed with the diastole analysis (see section ) several heart sound files and noises with different energies have been used. As already mentioned in section the diastole analysis calculates two different ratios: Noisy _ HS Diastole Peaks Average Noise AdditionBefore _ ICA db 20 log10 And Noisefree _ HS Diastole Peaks Average ICA _ HS Diastole Peaks Average Noise Addition After _ ICA db 20 log10 Noisefree _ HS Diastole Peaks Average The noise removal quality (Diastole Analysis Value) is simply: Diastole Analysis Value db Noise Addition After _ ICA Noise AdditionBefore _ ICA The Noise Addition After_ICA ratio measures how close the signal is after the algorithmic analysis ( ICA Data or Wiener Filter Data ) to the noise free heart sound. The smaller this value is the better (this means the algorithmic analysis did not change the signal too much). The Noise Addition Before_ICA ratio measures the level of noise that is added to the noise free Heart Sound (in the quite periods only). If Noise Addition Before_ICA gets large and Noise Addition After_ICA remains low or grows in a ratio which is much smaller than the ratio at which Noise Addition Before_ICA grows, this means that the noise is removed well from the heart sound

71 Wiener Filter ICA Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 3D plots HS=GA_Halt_1, Noise=snor_with_pre The 3D plots depict the noise removal quality of the ICA and Wiener Filter Algorithms with different Noise Levels for ch2 (2 nd ICS LSB), ch3 (2 nd ICS RSB) and ch4 (Left carotid) Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Halt_1, Noise file name used is snor_with_pre and ICA nonlinearity (for the ICA 3D plot) is Gauss. In each of the plots, the wiener filter results are the flat area above zero meaning the Diastole Analysis Value is low; therefore the noise removal quality is low. It can be clearly seen that the ICA Diastole Analysis Value is high which means that the noise removal quality is very good. It can also be seen that the noise removal quality is better for higher Ch4 Noise Levels (and also Ch2, Ch3 Noise Levels) which means the ICA algorithm removes well high noise levels

72 ICA ICA Wiener Filter Wiener Filter Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 2D plots HS=GA_Halt_1, Noise=snor_with_pre The 2D plots depict the noise removal quality of the ICA and Wiener Filter Algorithms with different Noise Levels for ch2 (2 nd ICS LSB), ch3 (2 nd ICS RSB) and ch4 (Left carotid) Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Halt_1, Noise file name used is snor_with_pre and ICA nonlinearity (for the ICA 2D plot) is Gauss. The left plot is the Diastole Analysis Value vs. Noise Levels where Ch2, Ch3 and Ch4 Noise Levels are equal. The right plot is the Diastole Analysis Value vs. Noise Levels where Ch2 Noise Level = 1 and Ch3 Noise Level = Ch4 Noise Level. The plots above clearly show that for higher noises, the noise removal quality (Diastole Analysis Value) is better

73 Wiener Filter ICA Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 3D plots HS=GA_Normal_1, Noise=count_time The 3D plots depict the noise removal quality of the ICA and Wiener Filter Algorithms with different Noise Levels for ch2 (2 nd ICS LSB), ch3 (2 nd ICS RSB) and ch4 (Left carotid) Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Normal_1, Noise file name used is count_time and ICA nonlinearity (for the ICA 3D plot) is Gauss. In each of the plots, the wiener filter results are the flat area above zero meaning the Diastole Analysis Value is low; therefore the noise removal quality is low. For high Noise Levels the ICA Diastole Analysis Value is high which means that the noise removal quality is very good. Low Ch4 Noise Levels lead to low Noise removal quality

74 ICA ICA Wiener Filter Wiener Filter Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 2D plots HS=GA_Normal_1, Noise=count_time The 2D plots depict the noise removal quality of the ICA and Wiener Filter Algorithms with different Noise Levels for ch2 (2 nd ICS LSB), ch3 (2 nd ICS RSB) and ch4 (Left carotid) Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Normal_1, Noise file name used is count_time and ICA nonlinearity (for the ICA 2D plot) is Gauss. The left plot is the Diastole Analysis Value vs. Noise Levels where Ch2, Ch3 and Ch4 Noise Levels are equal. The right plot is the Diastole Analysis Value vs. Noise Levels where Ch2 Noise Level = 1 and Ch3 Level = Ch4 Noise Level. The plots above clearly show that for higher noises, the noise removal quality (Diastole Analysis Value) is better. Also the plots show that high Ch2 (the ICA output) noise levels and low Ch3 and Ch4 noise levels lead to bad noise removal quality (Low Diastole Analysis Value) which means the ICA did not remove the noises in these cases

75 Wiener Filter ICA Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 3D plots HS=GA_Halt_1, Noise=television The 3D plots depict the noise removal quality of the ICA and Wiener Filter Algorithms with different Noise Levels for ch2 (2 nd ICS LSB), ch3 (2 nd ICS RSB) and ch4 (Left carotid) Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Halt_1, Noise file name used is television and ICA nonlinearity (for the ICA 3D plot) is Gauss. In each of the plots, the wiener filter results are the flat area above zero meaning the Diastole Analysis Value is low; therefore the noise removal quality is low. It can be clearly seen that the ICA Diastole Analysis Value is high which means that the noise removal quality is very good. It can also be seen that the noise removal quality is better for higher Ch4 Noise Levels (and also Ch2, Ch3 Noise Levels)

76 ICA ICA Wiener Filter Wiener Filter Figure Noise removal Quality (ICA and Wiener) vs. ch2, ch3, ch4 Noise Levels 2D plots HS=GA_Halt_1, Noise=television The 2D plots depict the noise removal quality of the ICA and Wiener Filter Algorithms with different Noise Levels for ch2 (2 nd ICS LSB), ch3 (2 nd ICS RSB) and ch4 (Left carotid) Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Halt_1, Noise file name used is television and ICA nonlinearity (for the ICA 2D plot) is Gauss. The left plot is the Diastole Analysis Value vs. Noise Levels where Ch2, Ch3 and Ch4 Noise Levels are equal. The right plot is the Diastole Analysis Value vs. Noise Levels where Ch2 Noise Level = 1 and Ch3 Noise Level = Ch4 Noise Level. The plots above clearly show that for higher noises, the noise removal quality (Diastole Analysis Value) is better. In the right plot it can be seen that for Ch2 Noise Level=1 and Ch3 Noise Level = Ch4 Noise Level = 0.2 the Diastole Analysis Value is very low. This singular event indicates that the noise was not removed from Ch2 (The ICA output) but rather Ch2 was mistakenly chosen by the ICA algorithm as the noise output channel

77 6.5 Noise removal from a heart sound in a noisy environment Heart sounds measurement in noisy environment presents quite significant challenges to the proposed algorithm for heart sound noise removal. This research presents several examples of noise removal in a noisy environment. It should be further investigated and defined what setup and algorithm parameters best suit for the purpose of noise removal from a heart sound in a real noisy environment. The microphones used in this research isolate the external noises quite well. External noises added are quite low and are hardly noticed. Therefore only heart sounds measurements with internal human voices have been performed. The internal human voices used in the following examples are speech. In this setup 3 microphones have been attached to the body (as presented in Figure 6.5-1), therefore, all 3 microphones receive both the heart signal and noise sounds. Each of the three microphones receives a different amplitude, phase and shape of the heart sound and noise. Microphones 1 (2 nd ICS RSB) and 2 (2 nd ICS LSB) receive high intensity of the internal speech noise relative to Microphone 3 (5 th ICS MSL) since they are closer to the vocal chords. Microphones 2 (2 nd ICS LSB) and 3 (5 th ICS MSL) receive high intensity of the heart sound relative to Microphone 1 (2 nd ICS RSB) since they are on the left side in which the heart sounds intensity is higher. Aortic - 2nd ICS RSB 1 2 Pulmonic - 2nd ICS LSB 3 Apex - 5th ICS MSL Figure Microphone places for ICA based noise removal in a noisy environment

78 Figure Noise Removal from a HS (in a real noisy environment) Time Series representation HS=HAIM_COUNT_1 The figures present an example of a noise removal in a time scale representation. The noise in this example is the speech (counting from 1 to 30) of the measured subject. It can be clearly seen how well the noise is removed from the HS. The topmost subplot is the patients EKG measurement which is used as a visual reference for the HS and doe s not participate in the noise removal algorithm. The three plots bellow the EKG are the HS plots (before and after the ICA). The blue graphs are the HS before ICA (including noise) and the red graphs are the HS after ICA. The data was filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 11-22Sec (upper left plot), Sec (upper right plot) and Sec (lower left plot). Heart sounds file name used in this example is HAIM_COUNT_1 ; ICA nonlinearity is Gauss

79 Figure Noise Removal from a HS (in a real noisy environment) spectrogram representation HS=HAIM_COUNT_1 The noise appears during the S1 and S2 heart sounds. The noise is partially removed from the heart sound but there is some small noise still left after ICA. Figure Noise Removal (in a real noisy environment) from a HS spectral representation (0-200Hz) HS=HAIM_COUNT_1 The spectral presentation above is a presentation of the ch2 HS (2 nd ICS LSB) plots in Figure at a frequency range of 0-200Hz. The heart sound + noise are presented in the bottom plot and the data after the ICA algorithm is presented in the upper plot

80 Figure Noise Removal from a HS (in a real noisy environment) Time Series representation HS=HAIM_COUNT_2 The data was filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 20-30Sec (left plot) and Sec (right plot). Heart sounds file name used in this example is HAIM_COUNT_2 ; ICA nonlinearity is Gauss. Figure Noise Removal from a HS (in a real noisy environment) spectrogram representation HS=HAIM_COUNT_2 The noise appears both during the quite periods and during the S1 and S2 heart sounds. The noise is partially removed from the heart sound but there is some small noise still left after ICA

81 Figure Noise Removal (in a real noisy environment) from a HS spectral representation (0-200Hz) HS=HAIM_COUNT_2 The spectral presentation above is a presentation of the ch2 HS (2 nd ICS LSB) plots in Figure at a frequency range of 0-200Hz. The heart sound + noise are presented in the bottom plot and the data after the ICA algorithm is presented in the upper plot

82 6.6 Graphs demonstrating the HS enhancement In addition to the heart sound noise removal, the ICA also performs heart sound enhancement meaning the algorithm gives more weight to some heart sound parameters in different channels and this way strengths these parameters in its output. For example if we have three input channels (ch2, ch3 and ch4) to the ICA algorithm, the S1 or S2 in the algorithm output (ch2) sometimes look different and with stronger amplitudes than the original heart sound in ch2. The amplitude enhancement in the algorithm output (ch2) comes from the heart sounds in ch3 and ch4. Heart sound enhancement, as can been seen from the spectral (Figure and Figure 6.6-3) and time domain (Figure 6.6-1) plots moves some of the heart sounds in different channels to the output channel. This can be accomplished since the ICA output is a linear multiplication of the HS with a matrix A. HS enhancement example S2 at the output of the ICA algorithm (ch2) is taken from the HS in ch4. Figure S2 heart sound enhancement time domain example S2 heart sound enhancement snapshot before and after Spectral ICA The topmost subplot is the patients EKG measurement which is used as a visual reference for the HS and doe s not participate in the noise removal algorithm. The three plots bellow the EKG are the heart sound plots (before and after ICA). The blue graphs are the heart sounds before ICA (including noise) and the red graphs are the heart sounds after ICA. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentation is from 2Sec to 3Sec. Heart sounds file name used in this example is GA_Normal_1, Noise file name used is count_time and ICA nonlinearity is Gauss

83 The spectrum of ch2 is a combination of the ch2, ch3 and ch4 spectrums (unlike the time domain, this is not a linear combination) Figure Spectral heart sounds enhancement example three HS channels presented The columns in the plot represent the different heart sound channels (ch2, ch3 and ch4). The channel of our interest is ch2. The first row graphs represent the data after the ICA algorithm. The second row graphs represent the data before ICA. The third row graphs represent the noise data for each channel. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The spectral domain presentation is from 0Hz to 150Hz. Heart sounds file name used in this example is GA_Normal_1, Noise file name used is count_time. ICA nonlinearity is Gauss. Figure Spectral heart sounds enhancement example one HS channel (ch2) presented This plot is a zoom in on ch2 plot in Figure

84 6.7 Noise removal with different ICA parameters As mentioned in section there are different ICA parameters which can be used when running the ICA algorithm. During the analysis of the different heart sounds and different noises, all four ICA nonlinearity parameters have been used. After running the heart sounds and noises with all ICA parameters numerously I have come to the conclusion that running the ICA algorithm with Gauss nonlinearity parameter provides the optimal noise removal results. In most cases the tanh nonlinearity also provides similar results. With each of the other two nonlinearities (pow3 and skew) the results received were not consistent although they were sometimes good, depending on the noise and heart signal used. ICA nonlinearity = pow3 ICA nonlinearity =tanh ICA nonlinearity =Gauss ICA nonlinearity =skew Figure Comparison between results with different ICA nonlinearity parameters Each of the four plots above represents the ICA algorithm output with a different ICA nonlinearity parameter. In the examples above, the Gauss and tanh nonlinearities best remove the noise from the heart sound. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 2-6.5Sec. Heart sounds file name used in this example is GA_Normal_1, Noise file is count_time, Noise Levels are: ch2 (2 nd ICS LSB) Noise Level = 0.7, ch3 (2 nd ICS RSB) Noise Level = 0.5, ch4 (Left carotid) Noise Level =

85 6.8 Spectral vs. Time domain ICA Results At the beginning of the research, time domain ICA method has been used, trying to remove the noises added to the heart sounds. Since the results using time domain ICA were not sufficient, I have started looking for other methods which could improve the noise removal from the measured signal. The Spectral ICA method has been tried and found to be much better in terms of noise removal. Both methods remove the noise but as can be seen in the plots bellow, the Spectral ICA method is better and removes the noises more efficiently. Spectral ICA Time ICA Figure Comparison between results with Time and Spectral ICA methods HS=GA_Normal_1, Noise=count_time In the above example the noise removal with the Spectral ICA is better than with the Time ICA. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 16-22Sec. Heart sounds file name used in this example is GA_Normal_1, Noise file is count_time, ICA nonlinearity is Gauss, Noise Levels are: ch2 (2 nd ICS LSB) Noise Level = 0.7, ch3 (2 nd ICS RSB) Noise Level = 0.5, ch4 (Left carotid) Noise Level =

86 Spectral ICA Time ICA Figure Quality Assessment Results of Spectral ICA compared to Time ICA The 2D plots depict the noise removal quality of the Spectral ICA and the Time ICA with different Noise Levels for ch2, ch3 and ch4 Heart Signals. The data and noise were filtered with a 20Hz-400Hz band pass filter. Heart sounds file name used in this example is GA_Halt_1, Noise file name used is snor_with_pre and ICA nonlinearity (for the ICA 2D plot) is Gauss. The two left plots represent the Diastole Analysis Value vs. Noise Levels where Ch2, Ch3 and Ch4 Noise Levels are equal. The two right plots represent the Diastole Analysis Value vs. Noise Levels where Ch2 Noise Level = 1 and Ch3 Noise Level = Ch4 Noise Level. Zooming in the plots above shows that the Spectral ICA Quality Assessment results are about 2db better than the Time ICA Quality Assessment results

87 Spectral ICA Time ICA Figure Comparison between results with Time and Spectral ICA methods (16-20Sec) HS=Halt_Supine_1, Noise=count_time In the above example the noise removal with the Spectral ICA is better than with the Time ICA. The data and noise were filtered with a 20Hz-400Hz band pass filter before running the algorithm. The time domain presentations are from 16-20Sec. Heart sounds file name used in this example is Halt_Supine_1, Noise file is count_time, ICA nonlinearity is Gauss, Noise Levels are: ch2 (2 nd ICS RSB) Noise Level = 0.6, ch3 (4 th ICS LSB) Noise Level = 0.7, ch4 (Apex) Noise Level = 0.9. Spectral ICA Time ICA Figure Comparison between results with Time and Spectral ICA methods (19-20Sec) HS=Halt_Supine_1, Noise=count_time The plots in Figure above are a time scale zoom in (19-20Sec) of the plots in Figure