Gill R. Tsouri and Michael H. Ostertag
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1 476 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 2, MARCH 2014 Patient-Specific 12-Lead ECG Reconstruction From Sparse Electrodes Using Independent Component Analysis Gill R. Tsouri and Michael H. Ostertag Abstract We propose and evaluate a method of 12-lead electrocardiogram (ECG) reconstruction from a three-lead set. The method makes use of independent component analysis and results in adaptive patient-specific transforms. The required calibration process is short and makes use of a single beat. We apply the method to two sets of leads: leads I, II, V2 and the Frank XYZ leads. Performance is evaluated via percent correlation calculations between reconstructed and original leads from a publicly available database of 549 ECG recordings. Results depict percent correlation exceeding 96% for almost all leads. Adaptability of the method s transform is shown to compensate for changes in signal propagation conditions due to breathing, resulting in reduced variance of reconstruction accuracy across beats. This implies that the method is robust to changes that occur after the time of calibration. Accurate and adaptive reconstruction has the potential to augment the clinical significance of wireless ECG systems since the number of sensor nodes placed on the body is limited and the subject could be mobile. Index Terms Biomedical signal processing, blind source separation, body sensor networks, electrocardiography. I. INTRODUCTION THE electrocardiogram (ECG) aids cardiologists in the diagnosis of heart conditions. There are multiple setups for ECG electrodes, but the standard clinical 12-lead ECG is the setup most commonly used. Traditionally, a clinical 12-lead ECG uses electrodes accurately placed at predefined sites on the body and requires the patient to recline and be still to avoid motion artifacts. Consequently, 12-lead ECG monitoring is limited to short timespans while remote long-term ECG monitoring relies on one-lead or three-lead ECGs, which provide limited information on heart condition. Reduced-lead ECG systems are important for improving patient comfort during long-term monitoring and in cases where placing many electrodes on a patient interferes with auscultation, examination, or resuscitation. The data from a 12-lead ECG are quite redundant. Some leads can be reconstructed with a high degree of accuracy from other Manuscript received June 14, 2013; revised September 21, 2013 and November 5, 2013; accepted November 30, Date of publication December 11, 2013; date of current version March 3, G. R. Tsouri is with the Communications Research Laboratory, Department of Electrical and Microelectronic Engineering, Rochester Institute of Technology, Rochester, NY USA ( grteee@rit.edu). M. H. Ostertag is with the Department of Electrical and Microelectronic Engineering, Rochester Institute of Technology, Rochester, NY USA ( michael.h.ostertag@gmail.com). Digital Object Identifier /JBHI leads in the set. This has been the basis for reduced-lead systems developed in the past [1] [5]. The basic idea is to provide a clinical 12-lead ECG using as little as three leads. A common assumption in previous lead reconstruction work was that the signals from the heart propagate in a homogenous medium, which allows for the use of linear transformation in the form of matrices to translate reduced-lead observations to the full 12-lead ECG. The three prominent types of lead reconstruction transforms are the universal, population-specific, and patientspecific transforms. In all cases, the transforms are fixed and do not adapt to changes over time. It is widely accepted that universal transforms are not reliable due to the wide degree of variance in the transforms across time and across patients. Each patient has a different composition of chest tissues, different size, shape, or location of the heart, and different levels of aging and disease [6]. Population-specific transforms have proven to be more effective than their universal counterparts. By segmenting patients based on their age, gender, and disease classification, the transform becomes better customized and produces more accurate reconstruction. The patient-specific transforms perform best due to the anatomical and diagnostic differences across patients [7]. In [8], a comprehensive analysis was performed to assess reconstruction accuracy of transforms derived via predictive lead fitting using linear regression. Combinations of four to five leads were used to reconstruct 12-lead ECG. Patientspecific transforms were found to perform best. The transforms in [8] were trained over vast data and were not adaptive, i.e., their coefficients were fixed after calibration. In this contribution, we propose, analyze, and evaluate a patient-specific and adaptive 12-lead reconstruction method based on independent component analysis (ICA). The 12-lead ECG is reconstructed from a set of just three leads. As with other patient-specific transforms, the proposed method relies on calibration of a transform matrix to a specific patient. However, the calibration process does not require vast data. Instead, just a single beat is required which means that calibration time is approximately 1 s. In contradistinction to previous transforms, the proposed method generates adaptive transforms capable of compensating for changes in signal propagation conditions from the time of calibration, i.e., the transform s coefficients change over time. We are unaware of previous work making use of transforms that adapt over time to reconstruct a 12-lead ECG from a reduced-lead set. ICA is a technique for blind-source separation. It extracts statistically independent sources, also known as independent components (ICs), from a set of observations. Rows of sources(s) IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See standards/publications/rights/index.html for more information.
2 TSOURI AND OSTERTAG: PATIENT-SPECIFIC 12-LEAD ECG RECONSTRUCTION FROM SPARSE ELECTRODES 477 are related to rows of observations (x) by the mixing matrix (A) as follows: x = As. (1) The mixing matrix is square in many popular ICA algorithms in order to exploit the inverse to minimize the convergence time [9]. ICA is widely used in many domains such as acoustics, image analysis noise reduction, and electroencephalography signal interpretation [9], [10]. Specifically, past use of ICA for ECG was limited to reducing noise and suppressing motion artifacts [11] and separating maternal and fetal ECGs [12]. In past work [13], we reported on a preliminary attempt to apply ICA for reconstructing precordial ECG leads. The preliminary method presented in [13] allows for reconstructing leads V1, V3, V4, and V6 from leads V2 and V5. In this contribution, we expand the work in [13] to derive a new method for a complete 12-lead ECG reconstruction from just three leads. The method uses an improved calibration technique to customize the reconstruction transforms per patient and produces much better results than before. Two different reduced-lead sets are investigated in this paper: leads I, II, V2 and Frank XYZ leads. Performance of both sets is evaluated over the Physikalisch- Technische Bundesanstalt (PTB) diagnostic ECG database as made available through PhysioNet [14]. In addition, the adaptability of the method s transforms to signal propagation conditions is demonstrated over a long period of time. II. PROPOSED METHOD We treat the sensed signals from the three leads as a sparse measure of the required 12-lead set. The first stage of the proposed method consists of basic preprocessing in which the ECG waveform is filtered and the QRS complexes are identified. Next, a training sequence from a single beat creates a patient-specific transform that relates the ICs from the reduced-lead set to the 12 to-be-reconstructed leads. After the training sequence, all electrodes that are not part of the reduced-lead set may be removed. A flow diagram of the proposed method is depicted in Fig. 1 and each step is described in more detail in the following sections. A. Signal Preprocessing The first preprocessing stage includes band-pass filtering of the ECG waveforms. Two digital filters were developed using the Parks McClellan algorithm [15]. The first is a high-pass filter with the end of the stop band at a frequency of 0.5 Hz to remove any dc offset and baseline drift. The second is a lowpass filter with the start of the stop band at 150 Hz to reduce the amount of high-frequency noise in the signal. The filters were cascaded and the specific frequencies were selected to meet the American Heart Association standards [16]. The second preprocessing stage was designed to perform QRS detection. The detection algorithm is similar to the Pan Tompkins QRS detection algorithm [17]. A 100 ms moving average is taken of the square of the approximate derivative and Fig. 1. Flow diagram of proposed method. is obtained with: y[n] = x[n 10] 2x[n 5] + 2x[n + 5]+x[n +10]. (2) The resulting function (y [n]) is normalized and any peak that has a value above the threshold of and occurs at least 200 ms from the previous peak is marked as a QRS complex. The 200 ms wait was selected because the heart cannot beat faster due to physiological limitations. Once the QRS complexes are located, the beat domain is defined as spanning three-eighths the time between the current and previous peak and five-eighths the time between the current and next peak. B. Transform Training Sequence ICA is applied to a single detected beat. The ICs are extracted from the reduced three-lead set resulting in: x RLS = x X x Y = As = a X b X c X a Y b Y c Y IC 1 IC 2 (3) x Z a Z b Z c Z IC 3 where x RLS is a matrix of the observations from the reducedlead set (each row in x RLS is comprised of samples of a single lead taken during the training beat), A is the 3 3 mixing matrix, and s is the set of ICs generated from the reduced-lead set using ICA (each row in s represents a sampled IC signal during the training beat). The patient specific 12-by-3 reconstruction transform matrix (A r ) is derived using the pseudoinverse matrix: A r = x obs s T ( ss T ) 1 (4) where x obs is a matrix of the observed 12-leads during the single detected beat (each row is comprised of samples of a single lead taken during the raining beat). Note that A r does not change during the beat, i.e., a single matrix is obtained from all samples taken during the training beat. At this point, the excess electrodes may be removed from the patient since they can be reconstructed by the previously
3 478 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 2, MARCH 2014 mentioned transform and the ICs generated from a reduced-lead set. C. Reconstruction Sequence The set of three leads used for training is also used for the reconstruction of the missing leads. ICs are generated from a one-beat segment of the reduced-lead set using ICA with an initial guess of the mixing matrix that was found during the training phase. This starting point helps the ICA algorithm to converge to a more consistent ordering and orientation of ICs. A known problem with ICA is the ordering of ICs. The ICs may alternate row positions in s, which would be compensated for by corresponding changes in the matrix A. To fix the ordering problem, ICs are sorted based upon the correlation of the current set of ICs with the original set, i.e., the ordering which correlates the best with the ICs obtained upon training is chosen. To reconstruct the missing leads, the sorted ICs are left-multiplied by the reconstruction transform as follows: x I a I b I c I x x r = II. = A a r s = II b II c II IC 1... IC 2 (5) IC 3 x V 6 a V 6 b V 6 c V 6 where s now represents the ICs obtained by applying ICA to the current beat and x r holds the 12 reconstructed leads. The adaptability of the transforms stems from the fact that although the patient-specific reconstruction matrix A r does not change after training, the matrix A obtained by the ICA algorithm per detected beat does vary. The result is that changes in A across detected beats compensate for changes in the reducedlead set observations due to variability in signal propagation conditions. This will be demonstrated in a later section. III. PERFORMANCE EVALUATION Two sets of reduced leads were evaluated: leads I, II, V2 and the Frank XYZ leads. The set comprising leads I, II, V2 was chosen due to a high degree of orthogonality between the limb leads and V2, which suggests that more information can be obtained. This lead set represents a scenario in which the method could be easily integrated into current hospital setups. The Frank XYZ lead set was chosen due to the appeal of using differential measurements, which are much more convenient to acquire compared to single-ended measurements, especially when considering a wireless ECG system. The ICA algorithm used to find the ICs throughout the evaluation was the FastICA algorithm [9]. FastICA is based on an optimization iteration scheme designed to maximize non- Gaussianity to achieve statistical independence of the ICs. The two sets were evaluated using recordings from the PTB diagnostic ECG database as made available through PhysioNet [14]. The database consists of 549 ECG recordings from 290 subjects with a variety of diagnostic classes: 52 healthy controls, 148 myocardial infarctions, and the remainder with other cardiac diagnoses. For each recording, the three limbs, three augmented, six precordial, and three Frank leads were captured simultaneously at a sampling frequency of 1 khz. The figure of merit used for comparing the actual leads to reconstructed leads was percent correlation (ρ), which is similar to the metric used in [8]. It is defined as follows: N i=1 x [i] x [i] ρ = N i=1 x N 100% (6) [i]2 i=1 x [i]2 where the index value i represents the samples within a beat of length N samples, x [i] is the original ECG signal sample, and x [i] is the reconstructed ECG signal sample. A perfect match in the timing of the two signals would correspond to a ρ value of 100%. We chose this metric instead of a mean-square error estimate since it represents the matching of signal patterns. Since cardiac activity is inferred by the changes of the signal over time, time variations in the signal pattern are more important for diagnosis than the average absolute difference between the signals. Both reduced-lead sets were used for reconstruction over the entire PTB database. Percent correlation for the first beat after the training sequence (t =0s)and a beat 30 s after the training sequence (t = 30s) was derived across reconstructed leads and across patients and the mean and standard deviation were extracted per lead. IV. RESULTS AND DISCUSSION A. Reduced-Lead Set: Leads I, II, and V2 In initial tests, we observed that different sets of limb leads generated identical ICs, which was likely due to the fact that they were physically connected in the hospital setting. Because leads I, II, and III were found to be exchangeable, leads I and II were arbitrarily selected. The third lead is required to monitor their orthogonal direction. Lead V2 was selected as the third lead since it is the most orthogonal precordial lead and had been successfully used before [2]. Eventually, the reduced-lead set of leads I, II, and V2 was selected because the three leads capture data that encompasses all orientations of the heart. The reconstructed leads were compared to original leads using ρ as defined in (6). The probability density function (PDF) of ρ was evaluated using the histogram method. We found that an overwhelming majority of reconstruction instances exhibit very high ρ for all reconstructed leads. This was the case for reconstruction at both time instances, suggesting accurate reconstruction across time. Statistical averages from the PDFs are provided in Table I, where the mean μ and standard deviation σ were calculated over the entire data. Each row in the table corresponds to a certain time difference between training and reconstruction and each table entry provides the mean and standard deviation in parenthesis. The limb and augmented leads initially provided nearly perfect reconstructions with average ρ value of 99.9% 100% for leads III, AVR, AVL, and AVF and 94.9% 98.1% for V1, V3, V4, V5, and V6. After 30 s, reconstruction accuracy remained high. Due to the spatial proximity of leads V1 and V3 to a lead from the reduced set (V2), they were reconstructed more accurately than V4 V6. The lower reconstruction correlations of leads V4 V6 suggest that the limb leads cannot as accurately
4 TSOURI AND OSTERTAG: PATIENT-SPECIFIC 12-LEAD ECG RECONSTRUCTION FROM SPARSE ELECTRODES 479 Fig. 2. Typical example of reconstructing 12-lead ECG with the proposed method using reduced-lead set of I, II, and V2. The black curves are the original leads of patient S0009 and the gray curves are the reconstructed versions. The average percent correlation across all leads is 97.99%. TABLE I STATISTICS OF CORRELATIONS BETWEEN ACTUAL AND RECONSTRUCTED LEADS FOR RECONSTRUCTION USING THE REDUCED-LEAD SET: LEADS I, II, AND V2 TABLE II STATISTICS OF CORRELATIONS BETWEEN ACTUAL AND RECONSTRUCTED LEADS FOR THE REDUCED-LEAD SET:FRANK S XYZ LEADS reconstruct the precordial leads and that a reduced-lead set containing more than one precordial lead could be chosen to improve precordial lead reconstruction. Nonetheless, reconstruction accuracy is high across all leads. A typical example for 12-lead reconstruction is depicted in Fig. 2. Note that a considerable amount of discrepancy between actual and reconstructed leads can be attributed to the difference in noise superimposed over the signals. B. Reduced-Lead Set: Frank XYZ Leads The PDF of ρ was estimated as before and the corresponding statistical averages were evaluated and are provided in Table II. Overall reconstruction accuracy is high across all leads and we observe the same trends as for the I, II, and V2 leads set. Accuracy is slightly lower than for the previous set with the exception of leads V4 V6, where reconstruction is better. A typical example of reconstruction is provided in Fig. 3. Note that the variation in accuracy across the two lead sets is low and inconsistent. We conclude that both lead sets perform well. C. Comparison With Past Work We are unaware of previous work making use of transforms that adapt over time. In past methods, the transforms remain fixed after calibration, and reconstruction accuracy is averaged across time per lead. When adaptive transforms are considered it makes sense to test for reconstruction accuracy at specific times across all subjects. Furthermore, the proposed method makes use of three leads and requires a single beat for calibration whereas previous methods with best accuracy make use of four to five leads and are calibrated using all available beats. In addition, an adaptive transform is expected to provide better performance in a dynamic environment where the subject is not forced to remain still. As all available databases and past methods assumed a stationary subject (usually in a supine position), a comparison with past work is problematic. We benchmark performance of the proposed method to the best results of nonadaptive patient-specific transforms reported
5 480 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 2, MARCH 2014 Fig. 3. Typical example of reconstructing 12-lead ECG with the proposed method using reduced-lead set of X,Y, andz. The black curves are the original leads of patient S0001 and the gray curves are the reconstructed versions. The average percent correlation across all leads is 96.73%. TABLE III MEAN OFSIMILARITYCOEFFICIENTRESULTS ASTAKENFROM [8, TABLE 8] in [8], where a reduced set of four to five leads was used and calibration considered all beats. We find that reconstruction accuracy is approximately the same. More specifically, when considering [8, Table 8] we find that the proposed method has an accuracy level across the entire data that is slightly lower than the accuracy of reconstructing QRST interval in [8] and higher than the accuracy of reconstructing deviation at J point. A relevant subset of the table in [8] is provided in Table III for reference. Note that results in [8] were generated using four predictor leads, where our proposed method uses three leads. The table summarizes results from predictor lead sets where leads I, II, and V2 were included. The same leads were used to evaluate our proposed method in Table I. D. Comparison With Fixed Transforms To further evaluate the proposed method, we implemented two fixed transforms and compared their performance with that of the proposed method over the PTB diagnostic ECG database. The first transform was the Dower universal transform [4]. The second transform was a patient-specific transform we generated using linear regression. The Dower transform is a standard transform that reconstructs a 12-lead ECG from a Vector CardioGram (VCG) lead set. The linear regression patient-specific transform was generated using least-squares estimation over the same training beat as used for generating the ICA transform. All three methods were used to reconstruct a full 12-lead ECG from the reduced-lead set of Frank s XYZ leads. After the preprocessing stage, the first beat of each patient was used to train the linear regression transform and ICA transform. All three methods were then used on all subsequent beats to reconstruct the full 12-lead ECG. If the minimum of the peak cross-correlation between the current set of ICs and the original ICs used for training was less than 0.9, then the beat was not reconstructed by any of the methods. Poor correlation between ICs likely indicates a fault in the ICA method caused by a convergence to an incorrect set of ICs or an error in the sorting of the ICs. ICA convergence can be improved using a more efficient ICA convergence algorithm. Since the focus of our investigation is ECG reconstruction and not ICA, we avoided beats that failed ICA convergence. Out of the entire database 42,008 beats generated ICs with this level of correlation. These beats were used to evaluate all three transforms. The statistical mean and standard deviation over all reconstructed beats is summarized in Table IV. As expected, the universal transform provides poor results compared to the two patient specific transforms. Both patient specific transforms perform very well with percent correlation higher than 96% across almost all leads. The linear regression transform provides slightly higher average accuracy compared to the ICA transform across some of the leads. However, note that the standard deviation of the ICA transform is noticeably lower than the standard deviation of the linear regression transform (with the exception of lead V5). This indicates that that the ICA transform s average performance is more representative of its instantaneous performance. While there are beats for which the linear regression transform performs very well, there are also cases where is performs poorly.
6 TSOURI AND OSTERTAG: PATIENT-SPECIFIC 12-LEAD ECG RECONSTRUCTION FROM SPARSE ELECTRODES 481 TABLE IV STATISTICS OF CORRELATIONS BETWEEN ACTUAL AND RECONSTRUCTED LEADS ACROSS ENTIRE DATABASE USING FRANK S XYZ LEADS AND THREE RECONSTRUCTIONMATRICES:UNIVERSALTRANSFORM,PATIENT SPECIFIC LINEAR REGRESSION, AND ADAPTIVE ICA Fig. 4. Adaptability of coefficients of mixing matrix A for patient s0404lrem. This result implies that the ICA transform adapts to changes in signal propagation conditions across beats and thus could provide a more reliable reconstruction. We elaborate on more results supporting this premise next. E. Adaptability of the Transform We observed that transform A for extracting the ICs from the observations changed over time. An example is provided in Fig. 4, where the nine coefficients of A are presented over time for patient s0404lrem from the database. It is clear that coefficients change their values periodically and that the rate of change is approximately ten cycles/min. We speculated that the coefficients are changing to compensate for the periodic changes in signal propagation conditions from the heart to the electrodes caused by breathing. We evaluated the stationarity of ICs by finding the correlation between ICs from beats across the breathing cycle and found that it is close to one. This is suggestive that the ICs are rather stationary. More research is required to fully understand the adaptability of the transform. We elaborate on that in the next section. V. CHALLENGES AND FUTURE RESEARCH The proposed method relies on efficient implementation of the ICA algorithm. A known problem with ICA is that the mixing matrix, which translates the observations to the ICs, is not unique. Many matrices would result in the same set of ICs ordered differently. This is known as the ICA sorting problem. In this paper, we resolved the sorting problem by reordering the ICs based on their correlations with the ICs from the training beat. A more efficient way can be sought by utilizing constrained ICA (cica). cica takes advantage of prior information on the ICs to help the ICA convergence process. New reconstruction algorithms may be developed where the ICs from training are used as prior knowledge. Another problem with ICA is that the convergence to ICs can sometimes fail. Although ICA convergence was not a limiting problem in the analysis we performed over the database, the issue of convergence could be looked into by assessing performance of other ICA convergence algorithms. The proposed method requires online computational power for implementing ICA since the ICs need to be found for every beat. Our implementation was in MATLAB on a standard PC and we noticed that finding ICs takes less than half a second. Since future systems can implement ICA much more efficiently using C or Field programmable gate array (FPGA), we do not identify a complexity problem in implementing our proposed method. The ability to fully evaluate the adaptability of the proposed transform depends on the variability of propagation conditions and subject s posture during the ECG recordings. Available databases provide ECG data taken from stationary subjects assuming a relaxed position. It follows that recordings were performed under relatively unchanging signal propagation conditions. The only perceived change can be attributed to breathing of the subject. All past work (including the work presented in this paper) relied on such databases. Training any reconstruction transform while the subject is in a specific posture might provide a transform inadequate for reconstructing leads when the patient assumes a different posture. This is especially true for the majority of transforms which are fixed after training and therefore do not have the capability to adapt to varying propagation conditions due to posture. The problem of posture extends beyond ECG reconstruction. Direct 12-lead measurements using a full set of electrode are strongly affected by posture. In most cases, ECG is observed while the patient is in a supine position. Despite its apparent importance, we are unaware of past work looking at the effect of posture on reconstruction. This could prove to be a very interesting topic for future research on adaptive transforms. When considering the proposed method in this paper the central question is: Are ICs obtained from data gathered in different postures always the same? If so, then our proposed method has the required adaptability to compensate for posture: ICA would reach same ICs regardless of posture and the trained transform would present a
7 482 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 2, MARCH lead ECG. If not, then our proposed method might be posture specific as all past methods are. Further research is required into the effect of changing subject postures and motion on reconstruction accuracy. It would require large studies designed to obtain sufficient data. We postulate that adaptive transforms would present performance gains in such conditions and could potentially advance cardiac monitoring for mobile subjects. VI. CONCLUSION An adaptive patient-specific method of reconstructing a 12- lead ECG from reduced sets was proposed. The method was investigated using two sets of three leads: I, II, and V2 and Frank s XYZ leads. Performance was evaluated over a publicly available database of 549 ECG recordings. The proposed method was shown to generate highly similar and reproducible ICs and provided accurate reconstruction from both sets of leads. The ability to accurately reconstruct a 12-lead ECG using Frank s XYZ leads is particularly promising due to its applicability in wireless ECG systems where differential measurements must be taken without common ground. Not only does the proposed method utilize a patient-specific transform from the ICs to the conventional leads, but the transform from observation points to ICs were shown to adapt over time. This property is useful in compensating for changes caused by breathing and could potentially compensate for patient posture. It could also prove useful for extracting vital signs such as respiration rate. REFERENCES [1] G. E. Dower, H. B. Machado, and J. A. Osborne, On deriving the electrocardiogram from vectorcardiographic leads, Clin. Cardiol., vol. 3, no. 2, pp , [2] S. P. Newlan, J. A. Kors, S. H. Meij, J. H. van Bemmel, and M. L. Simoons, Reconstruction of the 12-lead electrocardiogram from reduced lead sets, J. Electrocardiol., vol. 37, no. 1, pp , [3] D. Q. Feild, C. L. Feldman, and B. M. Horáček, Improved EASI coefficients: Their derivation, values, and performance, J. Electrocardiol., vol. 35, pp , [4] D. Dawson, H. Yang, M. Malshe, S. T. Bukkapatnam, B. Benjamin, and R. Komanduri, Linear affine transforms between 3-lead (Frank XYZ leads) vectorcardiogram and 12-lead electrocardiogram signals, J. Electrocardiol., vol. 42, pp , [5] D. Q. Feild, S. H. Zhou, E. D. Helfenbein, R. E. Gregg, and J. M Lindauer, Technical challenges and future directions in lead reconstruction for reduced-lead systems, J. Electrocardiol., vol. 41, pp , [6] R. J. A. Schijvenaars. (2000, Sep. 6). Intra-Individual Variability of the Electrocardiogram: Assessment and Exploitation in Computerized ECG Analysis. Erasmus MC: Univ. Med. Center Rotterdam. Retrieved from [7] R. E. Gregg, S. H. Zhou, J. M. Lindauer, E. D. Helfenbein, and D. Q. Feild, Limitations on the re-use of patient specific coefficients for 12-lead ECG reconstruction, Comput. Cardiol., vol. 35, pp , [8] B. M. Horáček, J. W. Warren, and J. J. Wang, On designing and testing transformations for derivation of standard 12-lead/18-lead electrocardiograms and vectorcardiograms from reduced lead sets of predictor leads, J. Electrocardiol., vol. 41, pp , Jan [9] A. Hyvärinen and E. Oja, Independent component analysis: Algorithms and applications, Neural Netw., vol. 13, no. 4/5, pp , [10] C. J. James and C. W. Hesse, Independent component analysis for biomedical signals, Physiol. Meas., vol. 26, pp. R15 R39, [11] T. He, G. Clifford, and L. Tarassenko, Application of independent component analysis in removing artefacts from the electrocardiogram, Neural Comput. Appl., vol. 15, pp , [12] J. Lee, K. L. Park, and K. J. Lee, Temporally constrained ICA-based fetal ECG separation, Electron. Lett., vol. 41, no. 21, pp , Oct [13] M. H. Ostertag and G. R. Tsouri, Reconstructing ECG precordial leads from a reduced lead set using independent component analysis, in Proc. IEEE 33rd Int. Conf. Eng. Med. Biol. Soc., Aug. 30, 2011 Sep. 3, 2011, pp [14] A. L. Goldberger, L. A. N. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C. K. Peng, and H. E. Stanley, PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals, Circulation, vol. 101, no. 23, pp. e215 e220, Jun [15] T. W. Parks and J. H. McClellan, Chebyshev approximation for nonrecursive digital filters with linear phase, IEEE Trans. Circuit Theory,vol.19, no. 2, pp , Mar [16] P. Kligfield, L. S. Gettes, R. Childers, E. W. Hancock, G. V. Herpen, P. Macfarlane, O. Pahlm, and S. Galen, Recommendations for the standardization and interpretation of the electrocardiogram, Part I: The electrocardiogram and its technology, Heart Rhythm, vol.3,no.3,pp , Mar [17] J. Pan and W. J. Tompkins, A real-time QRS detection algorithm, IEEE Trans. Biomed. Eng., vol. BME-32, no. 3, pp , Mar Gill R. Tsouri received the B.Sc., M.Sc., and Ph.D. degrees in electrical and computer engineering from Ben-Gurion University, Israel, in 2000, 2004, and 2008, respectively. In 2008, he joined the Rochester Institute of Technology, New York, USA, where he established the Communications Research Laboratory. His current research interests include body area networks, biomedical signal processing, and wireless physical layer security. Michael H. Ostertag is currently working toward the M.Sc. degree in electrical engineering at the Rochester Institute of Technology, New York, USA. In 2013, he joined BlackBox Biometrics where he is now Lead Electrical Engineer. His current interests include developing new technologies for physiological monitoring.
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