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1 This rticle ppered in journl published by Elsevier. The ttched copy is furnished to the uthor for internl non-commercil reserch nd eduction use, including for instruction t the uthors institution nd shring with collegues. Other uses, including reproduction nd distribution, or selling or licensing copies, or posting to personl, institutionl or third prty websites re prohibited. In most cses uthors re permitted to post their version of the rticle (e.g. in Word or Tex form) to their personl website or institutionl repository. Authors requiring further informtion regrding Elsevier s rchiving nd mnuscript policies re encourged to visit:

2 Author's personl copy Avilble online t ScienceDirect Speech Communiction 57 (14) Speech enhncement using Byesin estimtors of the perceptully-motivted short-time spectrl mplitude (STSA) with Chi speech priors Mrek B. Trwicki, Michel T. Johnson Mrquette University, Deprtment of Electricl nd Computer Engineering, Speech nd Signl Processing Lbortory, P.O. Box 1881, Milwukee, WI 53181, United Sttes Received 3 My 13; received in revised form 3 August 13; ccepted 18 September 13 Avilble online 5 October 13 Abstrct In this pper, the uthors propose new perceptully-motivted Weighted Eucliden (WE) nd Weighted Cosh (WCOSH) estimtors tht utilize more pproprite Chi sttisticl models for the speech prior with Gussin sttisticl models for the noise likelihood. Wheres the perceptully-motivted WE nd WCOSH cost functions emphsized spectrl vlleys rther thn spectrl peks (formnts) nd indirectly ccounted for uditory msking effects, the incorportion of the Chi distribution sttisticl models demonstrted distinct improvement over the Ryleigh sttisticl models for the speech prior. The estimtors incorporte both weighting lw nd shpe prmeters on the cost functions nd distributions. Performnce is evluted in terms of the Segmentl Signl-to-Noise Rtio (SSNR), Perceptul Evlution of Speech Qulity (PESQ), nd Signl-to-Noise Rtio (SNR) Loss objective qulity mesures to determine the mount of noise reduction long with overll speech qulity nd speech intelligibility improvement. Bsed on experimentl results cross three different input SNRs nd eight unique noises long with vrious weighting lw nd shpe prmeters, the two generl, less-complicted, closedform derived solution estimtors of WE nd WCOSH with Chi speech priors provide significnt gins in noise reduction nd noticeble gins in overll speech qulity nd speech intelligibility improvements over the bseline WE nd WCOSH with the stndrd Ryleigh speech priors. Overll, the gol of the work is to cpitlize on the mutul benefits of the WE nd WCOSH cost functions nd Chi distributions for the speech prior to improvement enhncement. Ó 13 Elsevier B.V. All rights reserved. Keywords: Speech enhncement; Probbility; Amplitude estimtion; Phse estimtion; Prmeter estimtion 1. Introduction Speech enhncement systems concern themselves with reducing the corrupting bckground noise in the noisy signl (Loizou, 7). The most common pproch is to perform sttisticl estimtion: minimize the Byes Risk of the squred-error of the spectrl mplitude cost function, which leds to the subsequent nd trditionl Ephrim nd Mlh Minimum Men-Squre Error (MMSE) short-time spectrl mplitude (STSA) estimtor Ephrim nd Mlh, Corresponding uthor. Tel.: E-mil ddresses: mrek.trwicki@mrquette.edu (M.B. Trwicki), mike.johnson@mrquette.edu (M.T. Johnson). Bsed on the effectiveness of tht STSA estimtor, reserchers begn to modify the squred-error of the spectrl mplitude cost function to utilize more subjectively meningful cost functions. Ephrim nd Mlh (Ephrim nd Mlh, 1985) lso developed nd implemented the MMSE log-spectrl mplitude (LSA) estimtor tht minimizes the squrederror of the log-spectrl mplitude, which is more subjectively meningful cost function tht correltes well with humn perception. From the STSA nd LSA cost functions, Loizou (5) constructed severl perceptully-motivted spectrl mplitude cost functions tht emphsized spectrl vlleys rther thn spectrl peks (formnts) nd indirectly ccounted for uditory msking effects. Specificlly, the /$ - see front mtter Ó 13 Elsevier B.V. All rights reserved.

3 Author's personl copy 1 M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) Weighted Eucliden (WE) nd Weighted Cosh (WCOSH) Byesin estimtors, which pplied weighting lw prmeter to the STSA cost function, hd the best performnces for reducing residul noise nd producing better speech qulity. In ech of those corresponding spectrl mplitude, log-spectrl mplitude, nd perceptully-motivted spectrl mplitude estimtors, the cost functions employed Ryleigh distributions for the sttisticl models of the speech priors nd noise likelihoods. Eventully, reserchers begn to exploit lterntive nd more ccurte sttisticl modeling ssumptions to the Ryleigh distribution for both the speech prior nd noise likelihood using the STSA cost function. Andrinkis nd White (9) continued with the MMSE spectrl mplitude estimtors using the Gmm distribution but introduced the Chi distribution for modeling the speech priors. The Chi speech prior contins shping prmeter tht ws vried to determine its effect on the qulity of enhnced speech. From the results, the performnce of the estimtors ws dependent on the shping prmeter, which controlled the trde-off between the level of residul noise nd musicl tones. As generliztion to the Ephrim nd Mlh s MMSE STSA nd LSA estimtors long with Andrinkis nd White s Chi distribution speech priors, Breithupt et l. (8) developed MMSE STSA estimtor tht uses both vrible compression function in the error criterion nd the Chi distribution s prior model. The resulting two prmeters provide for the reduction of musicl noise, speech distortion, nd noise distortion. Through the incorportion of Chi distribution sttisticl models for the speech prior, the squred-error cost functions demonstrted distinct improvement over the Ryleigh sttisticl models. Despite the success of the spectrl mplitude, log-spectrl mplitude, nd perceptully-motivted cost functions with Ryleigh sttisticl models nd spectrl mplitude cost functions with Chi distributions for the speech priors, there hs not been ny work to cpitlize on their mutul benefits for speech enhncement. Specificlly, the improved sttisticl models for the speech prior hve only been incorported with the originl MMSE STSA estimtor, not with the spectrl mplitude perceptully-motivted spectrl mplitude (WE nd WCOSH) cost functions. The fundmentl purpose is to determine the effectiveness tht more ccurte speech priors would hve on improved cost functions for noise reduction. Insted of utilizing the Ryleigh distributions for the speech prior, the Chi distribution is employed in this work since it leds to more generl, less complicted, nd more closed-form estimtor solutions. For specific vlues of the shping prmeter, Chi distribution is equivlent to the hlf-gussin nd Ryleigh distribution s specil cses. Therefore, the focus of this work is to use the MMSE WE nd WCOSH estimtors with the Chi spectrl speech prior distribution (Johnson et l., 1994) for reducing the bckground noise long with improving overll speech qulity nd speech intelligibility. The reminder of this pper is orgnized into the following sections: system nd sttisticl models (Section ), perceptully-motivted cost functions with Chi speech priors (Section 3), experiments nd results (Section 4), nd conclusion (Section 5).. System nd sttisticl models In the time domin, the single chnnel dditive noise model is given s yðtþ ¼sðtÞþdðtÞ ð1þ where s(t), d(t), nd y(t) represent the clen, noise, nd noisy signls. By tking the short-time Fourier Trnsform, (1) cn be written in the frequency domin s Y ðl; kþ ¼Sðl; kþþdðl; kþ Rðl; kþe j#ðl;kþ ¼ X ðl; kþe jðl;kþ þ Nðl; kþe jhðl;kþ where l nd k re the prticulr frme nd frequency bin index with noisy, clen, nd noise clen spectrl mplitudes R, X, nd N nd noisy, clen, nd noise spectrl phses #,, nd h. As opposed to using the trditionl Ryleigh sttisticl models for both the speech prior nd noise likelihood, the trditionl Ryleigh speech prior given s pðx ; Þ ¼ X pr X exp X r X is modified through the use of Chi speech priors (Johnson et l., 1994), where r X is the speech spectrl vrince. Specificlly, the Chi speech prior is given s pðx ; Þ ¼ h CðÞ X 1 exp X ; ð4þ h where r X ¼ h with shpe prmeter nd scling prmeter h nd C() is the gmm function. With =.5 nd = 1,(4) is equivlent to the Hlf-Gussin nd Ryleigh distributions. The noise likelihood is still modeled s Gussin distribution given s! pðyjx; Þ¼ 1 exp jy Xej j ; ð5þ pr N r N where r N is the noise spectrl vrince. In order to simplify the nottion, k ¼ r, k X ¼ r X, nd k N ¼ r N is utilized s the spectrl vrinces in the derivtion of the WE with Chi speech prior estimtor nd WCOSH with Chi speech prior estimtor. 3. Perceptully-motivted cost functions with Chi speech priors 3.1. Weighted Eucliden (WE) From the work in Loizou (5), the Weighted Eucliden (WE) cost function is given s X p d WE ðx ; ^X Þ¼ X ^X ð6þ with estimtor eqution ðþ ð3þ

4 Author's personl copy M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) bx WE ¼ R 1 R p R 1 X pþ1 pðyjx; ÞpðX ; ÞddX R p X p pðyjx; ÞpðX ; ÞddX ; ð7þ where p is the weighting lw prmeter. For p =, (7) is equivlent to the MMSE STSA estimtor in Ephrim nd Mlh (1984), Loizou (5), Gry et l. (198). Through the substitution of the sttisticl models in (4) nd (5) nd using nd in Grdshteyn nd Ryzhik (7), the spectrl phse is integrted from the two integrls s Z 1 Z p / nd Z 1 / Z 1 Z p Z 1 X pþ1 pðyjx; ÞpðX ; ÞddX X pþ exp X k J X p pðyjx; ÞpðX ; ÞddX X pþ 1 exp X where k is defined s 1 k ¼ 1 þ 1 k X k N k rffiffiffi v ix dx k J rffiffi v ix dx ; k ð8þ ð9þ ð1þ in (A.3) of Ephrim nd Mlh (1984), J () is the th-order Bessel function of the first-kind, nd 1 ¼ þ 1 ð11þ k k X k N which is equivlent to 1=k in (1) for = 1. By utilizing nd in Grdshteyn nd Ryzhik (7), (8) nd (9) re given s Z 1 Z p / C pþþ1 nd Z 1 Z p / C pþ X pþ1 pðyjx; ÞpðX ; ÞddX 1 p 1F 1 ; 1; v=k 1=k k 1 ðpþþ1þ X p pðyjx; ÞpðX ; ÞddX p 1F 1 ; 1; v=k 1=k k 1 ðpþþ ð1þ ð13þ where 1 F 1 ð; ; Þ is the confluent hypergeometric function. With the combintion of simplifiction of the integrls in (1) nd (13), the finl form of the new WE estimtor with Chi speech prior in (4) is given s ^X WE;CHI ¼ G WE;CHI R ¼ C pþþ1 pffiffiffiffi 1 p v 1F 1 ; 1; vf R; ð14þ C pþ p c 1F 1 ; 1; vf where v ¼ nd n þ n c f ¼ 1 þ n þ n ð15þ ð16þ for p + > with gin function G WE,CHI nd priori n ¼ r X =r N nd posteriori c ¼ R =r N SNRs. For =1 nd p =,(14) is exctly equivlent to the STSA estimtor with Ryleigh speech prior (Ephrim nd Mlh, 1984). 3.. Weighted Cosh (WCOSH) In Loizou, 5, the Weighted Cosh (WCOSH) cost function is given s ^X d WCOSH ðx ; ^X Þ¼ þ X^X X 1 X p ð17þ with estimtor eqution " R 1 R p X ^X pþ1 #1 pðyjx; ÞpðX ; ÞddX WCOSH ¼ R 1 R p ; ð18þ X p 1 pðyjx; ÞpðX ; ÞddX where p is the weighting lw prmeter. For p =,(18) is equivlent to the Cosh cost function given in Loizou (5) nd Gry et l. (198). In order to determine the finl estimtor eqution for the WCOSH with Chi speech prior, the integrls re derived in sme pproch s with the WE with Chi speech prior estimtor in (14). By the substitution of the sttisticl models in (4) nd (5) nd using nd in Grdshteyn nd Ryzhik (7), the spectrl phse is integrted from the two integrls s Z 1 Z p / nd Z 1 / Z 1 Z p Z 1 X pþ1 pðyjx; ÞpðX ; ÞddX X pþ exp X k J X p 1 pðyjx; ÞpðX ; ÞddX X pþ exp X k rffiffi v ix dx k J rffiffi v ix dx ; k ð19þ ðþ where 1=k is defined in (11). Through nd in Grdshteyn nd Ryzhik (7), (19) nd () re given s Z 1 Z p X pþ1 pðyjx; ÞpðX ; ÞddX / C pþþ1 nd 1 p 1F 1 ; 1; v=k 1=k k 1 ðpþþ1þ ð1þ

5 Author's personl copy 14 M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) Z 1 Z p / C pþ 1 X p 1 pðyjx; ÞpðX ; ÞddX 3 p 1F 1 k 1 ðpþ 1Þ ; 1; v=k 1=k : ðþ With the combintion of simplifiction of the integrls in (1) nd () nd using v nd B in (15) nd eqution, the finl form of the new WCOSH estimtor with Chi speech prior in (4) is given s ^X WCOSH;CHI ¼ G WCOSH;CHI R " ¼ C pþþ1 #1 C pþ 1 pffiffiffiffi " #1 1 p v 1F 1 ; 1; vf R ð3þ 3 p c 1F 1 ; 1; vf for p + > 1 with gin function G WCOSH,CHI. For =1 nd p =, (3) is similr to the LSA estimtor with Ryleigh speech prior (Ephrim nd Mlh, 1985). By compring the WE nd WCOSH estimtors given in (18) (3), the only differences consist of the integrl in the denomintor nd squre root. Figs. 1 3(WE with Chi speech prior estimtor) nd Figs. 4 6 (WCOSH with Chi speech prior estimtor) present the gin functions G WE,CHI nd G WCOSH,CHI for the WE nd WCOSH with Chi speech prior estimtors given in (14) nd (3) using representtive weighting lw prmeters of p WE ={ 1.,.5,.5} nd p WCOSH = {.75,.5,.5} s function of instntneous SNR c k 1 for three fixed priori SNR n k vlues of, 5, nd 1 db nd vlid shping prmeter vlues. From the gin curves, there re severl interesting observtions to note from both the WE nd WCOSH with Chi nd Ryleigh speech prior estimtors. Bsed on both sets of estimtors cross the different priori SNR n k, the gins were smller in vlue (more ttenution) s the shping prmeter pproched its limiting vlue with decrese in the instntneous posteriori SNR c k 1. As the shping prmeter! 1, which is the Ryleigh speech prior, the gins hd fltter shpe nd lrger vlue (less ttenution). Regrdless of the priori SNR n k nd shping prmeter, the gins ll eventully converged to pproximtely 6 db t round n posteriori SNR of 8 1 db with n increse of the instntneous posteriori SNR c k 1, which ws essentilly independent of the weighting lw prmeter p. With the WE with Chi speech prior estimtor, the increse in the weighting lw prmeter p, which in turn cuses n increse in the rnge of vlid shping prmeters, generted gins with more ttenution t lower instntneous posteriori SNR c k 1 (nd less ttenution t higher instntneous posteriori SNR c k 1) using the limiting vlue of the shping prmeter. The gins with n increse of weighting lw prmeter p nd shping prmeter! 1 (Ryleigh speech prior) hd less ttenution t lower instntneous posteriori SNR c k 1 nd no substntil chnge in ttenution t higher instntneous posteriori SNR c k 1. For the WCOSH with Chi speech prior estimtor, the gins were much more dependent on the priori SNR n k thn the WE with Chi speech prior estimtor. For prticulr weighting lw prmeter p cross ll shping prmeter, the gins hd less ttenution with n increse in the priori SNR n k. By compring the sme weighting lw prmeter p =.5 (Figs. nd 5) ndp =.5 (Figs. 3 nd 6) cross the WE nd WCOSH with Chi speech prior estimtors, the gins ssocited with the WE with Chi speech prior estimtor hd significntly more ttenution log 1 (GAIN) [db] =.6 =.7 =.8 =.9 = 1(Ryleigh) = db = 5 db - -1 = 1 db γ k -1 [db] Fig. 1. Gin curves for WE (p = 1.) estimtor with Chi prior.

6 Author's personl copy M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) log 1 (GAIN) [db] =.3 =.5 =.7 =.9 = 1(Ryleigh) = db = 5 db - -1 = 1 db γ k -1 [db] Fig.. Gin curves for WE (p =.5) estimtor with Chi prior. log 1 (GAIN) [db] =.15 =.4 =.65 =.9 = 1(Ryleigh) = db = 5 db - -1 = 1 db γ k -1 [db] Fig. 3. Gin curves for WE (p =.5) estimtor with Chi prior. t lower instntneous posteriori SNR c k 1 (nd similr ttenution t higher lower instntneous posteriori SNR c k 1) thn the gins ssocited with the WCOSH with Chi speech prior estimtor. 4. Experiments nd results The proposed WE nd WCOSH with Chi speech prior optiml estimtors given in (14) nd (3) were evluted using the objective mesures of Segmentl Signl-to-Noise Rtio (SSNR) Ppmichlis, 1987, Perceptul Evlution of Speech Qulity (PESQ) ITU, 3; Hu nd Loizou, 7, 8; Rix et l., 1, nd Signl-to-Noise Rtio (SNR) Loss M nd Loizou, 11 to ccess noise reduction, overll speech qulity, nd speech intelligibility, where PESQ nd SNR Loss hve rnge of (higher scores indicte better performnce) nd.. (lower scores indicte better performnce). In prticulr, the performnce is given vi SSNR, PESQ, nd SNR Loss improvements, where the improvements re clculted s SSNR/PESQ/SNR Loss output (enhnced signl) minus SSNR/PESQ/SNR Loss input (noisy signl). Clen nd noisy speech were tken from the noisy speech corpus (NOIZEUS) Hu nd Loizou, 7, which contins 3

7 Author's personl copy 16 M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) log 1 (GAIN) [db] =.8 =.85 =.9 =.98 = 1(Ryleigh) = db = 5 db - -1 = 1 db γ k -1 [db] Fig. 4. Gin curves for WCOSH (p =.75) estimtor with Chi prior. log 1 (GAIN) [db] =.88 =.9 =.94 =.96 = 1(Ryleigh) = db = 5 db - -1 = 1 db γ k -1 [db] Fig. 5. Gin curves for WCOSH (p =.5) estimtor with Chi prior. IEEE sentences (Subcommittee, 1969) (produced by three mle nd three femle spekers) corrupted by eight different rel-world noises t different SNRs rnging from to 15 db t increments of 5 db, where the noises were tken from the AURORA dtbse (Perce nd Hirsch, ), which includes irport, bbble, cr, exhibition, resturnt, sttion, street, nd trin noises. The nlysis conditions consisted of frmes of 56 smples (5.6 ms) with 5% overlp using Hnning windows. Noise estimtion ws performed on n initil silence of 5 frmes. The decision-directed (DD) Ephrim nd Mlh, 1984 smoothing pproch ws utilized to estimte n with SNR =.98 using thresholds of n min =1 5/1 nd c min = 4. In order to evlute the performnce, the enhnced signls were reconstructed using the overlp-dd technique. The shpe prmeter in the Chi speech prior ws vried for specific weighting lw prmeters p to determine its effect on enhncement, qulity, nd intelligibility with results verged over 3 utternces cross the 8 different noises t input SNRs of, 5, nd 1 db. As recommended by Loizou (5),

8 Author's personl copy M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) log 1 (GAIN) [db] =.65 =.75 =.85 =.95 = 1(Ryleigh) = db = 5 db - -1 = 1 db γ k -1 [db] Fig. 6. Gin curves for WCOSH (p =.5) estimtor with Chi prior. SSNR Improvement SSNR Improvement SNR = db SNR = 5 db SNR = 1 db Ryleigh 14 irport bbble cr exhibition resturnt sttion street trin Fig. 7. SSNR improvements for MMSE WE estimtor with Chi prior (p = 1). p WE = 1 nd p WCOSH =.5 were selected s the weighting lw prmeter p to chieve the best overll speech qulity in the enhncement process. Figs. 7 nd 8 illustrte the SSNR improvements for the WE nd WCOSH with Chi speech prior estimtors t vrious input SNRs, noises, nd shping prmeter with prticulr weighting lw prmeter p. The WE nd WCOSH with Chi speech prior estimtors consistently produced 3 db ( db input SNR), 1 db (5 db input SNR), nd db (1 db input SNR) over the bseline WE nd WCOSH with Ryleigh speech prior estimtors, which typiclly occurred t the limiting vlue of the shping prmeter for the corresponding weighting lw prmeter p of!.5 (p WE = 1.) nd!.75 (p WCOSH =.5). At the limiting shping prmeter, the WE nd WCOSH with Chi speech prior estimtors chieved mximum SSNR improvements of 9 13 db ( db input SNR), 6 9 db (5 db input SNR), nd 4 5 db (1 db input SNR) cross the cr, trin, sttion, exhibition, street, bbble, nd irport noises. In compring the WE nd WCOSH with Chi speech prior estimtors, the WE with Chi speech prior estimtor hd slightly better SSNR improvement performnce over the WCOSH with Chi speech prior estimtor for noise reduction. Figs. 9 nd 1 present the PESQ improvements for the WE nd WCOSH with Chi speech prior estimtors t

9 Author's personl copy 18 M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) SSNR Improvement SSNR Improvement SNR = db SNR = 5 db SNR = 1 db Ryleigh 14 irport bbble cr exhibition resturnt sttion street trin Fig. 8. SSNR improvements for MMSE WCOSH estimtor with Chi prior (p =.5). PESQ Improvement PESQ Improvement SNR = db SNR = 5 db SNR = 1 db Ryleigh irport bbble cr exhibition resturnt sttion street trin Fig. 9. PESQ improvements for MMSE WE estimtor with Chi prior (p = 1). vrious input SNRs, noises, nd shping prmeter with prticulr weighting lw prmeter p. In similr fshion to the SSNR improvements, the WE nd WCOSH with Chi speech prior estimtors generted..3 nd..1 gins over the bseline WE nd WCOSH estimtors with Ryleigh speech prior with the most pronounced improvements occurring t input SNRs of 5 nd 1 db. In contrst to the SSNR improvements tht were lmost exclusively dependent on the limiting shping prmeter, the PESQ improvements diminished t =.7.8 (WE with Chi speech prior estimtor) nd =.85.9 (WCOSH with Chi speech prior estimtor). For both the WE nd WCOSH with Chi prior estimtors, the mximum PESQ improvements rnged from..55 (5 db input SNR),..5 (1 db input SNR), nd ( db input SNR) cross the resturnt, irport, bbble, street, exhibition, sttion, trin, nd cr noises. After exmintion of the WE nd WCOSH with Chi speech prior estimtors, the WE with Chi speech prior estimtor hd slightly better PESQ improvement performnce over the WCOSH with Chi speech prior estimtor for speech qulity. Figs. 11 nd 1 demonstrte the SNR Loss improvements for the WE nd WCOSH with Chi speech prior estimtors t vrious input SNRs, noises, nd shping

10 Author's personl copy M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) PESQ Improvement PESQ Improvement SNR = db SNR = 5 db SNR = 1 db Ryleigh irport bbble cr.6 exhibition resturnt sttion street trin Fig. 1. PESQ improvements for MMSE WCOSH estimtor with Chi prior (p =.5). SNR Loss Improvement SNR Loss Improvement SNR = db SNR = 5 db SNR = 1 db Ryleigh -.6 irport bbble cr exhibition resturnt sttion street trin Fig. 11. SNR Loss improvements for MMSE WE estimtor with Chi prior (p = 1). prmeter with prticulr weighting lw prmeter p. The WE nd WCOSH with Chi speech prior estimtors typiclly yielded.1 ( db input SNR),.5 (5 db input SNR), nd.5 (1 db input SNR) over the corresponding bseline WE nd WCOSH with Ryleigh speech prior estimtors, which occurred t wide rnge of shping prmeters. In contrst to the SSNR nd PESQ improvements, the SNR Loss improvements were most noticeble t input SNRs of 5,, nd 1 db nd cr, sttion, bbble, irport, exhibition, resturnt, trin, nd street noises. In more specific terms, the WE nd WCOSH with Chi speech prior estimtors relized mximum SNR Loss improvements of ( db input SNR),.1.95 (5 db input SNR), nd From the WE nd WCOSH with Chi speech prior estimtors, the WE with Chi speech prior estimtor often hd lrger decreses in SNR Loss over the bseline Ryleigh speech prior estimtors thn the WCOSH with Chi speech prior estimtor. Tbles 1 6 show the SSNR improvement, PESQ improvement, nd SNR Loss improvement for the WE nd WCOSH with Chi speech prior estimtors for two dditionl nd representtive weighting lw prmeters p. Wheres the WE with Chi speech prior estimtor ws

11 Author's personl copy 11 M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) SNR Loss Improvement SNR Loss Improvement SNR = db SNR = 5 db SNR = 1 db Ryleigh irport bbble cr exhibition resturnt sttion street trin Fig. 1. SNR Loss improvements for MMSE WCOSH estimtor with Chi prior (p =.5). Tble 1 SSNR improvements for MMSE WE estimtor with Chi prior (p =.5 nd p =.5). SNR [db] Bbble Cr Trin p =.5 p =.5 p =.5 p =.5 p =.5 p = AVG Tble SSNR improvements for MMSE WCOSH estimtor with Chi prior (p =.75 nd p =.5). SNR [db] Bbble Cr Trin p =.75 p =.5 p =.75 p =.5 p =.75 p = AVG exmined with the weighting lw prmeters p =.5 ( >.5) nd p =.5 ( >.15), the WCOSH with Chi speech prior estimtor ws exmined with the weighting lw prmeters p =.75 ( >.875) nd p =.5 ( >.65) ccording to the reltionships p + > nd p + > 1. For ech weighting lw prmeter p of the WCOSH nd WE with Chi speech prior estimtors t the prticulr noise nd input SNR, the SSNR improvement, PESQ improvement, nd SNR Loss improvement results re provided longside their corresponding shping prmeter, where the shping prmeter! 1 represents the bseline WE nd WCOSH with Ryleigh speech prior estimtors. In terms of SSNR improvements, the WE nd WCOSH with Chi speech prior estimtors generlly produced.5.5 db gins over the bseline WE nd WCOSH with Ryleigh speech prior estimtors. As the weighting lw prmeter p ws decresed in vlue, the SSNR improvement incresed in vlue, where the mximum SSNR improvement rnged from 6 to 9 db cross the cr, trin, nd bbble noises. The WCOSH with Chi speech

12 Author's personl copy M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) Tble 3 PESQ improvements for MMSE WE estimtor with Chi prior (p =.5 nd p =.5). SNR [db] Bbble Cr Trin p =.5 p =.5 p =.5 p =.5 p =.5 p = AVG Tble 4 PESQ improvements for MMSE WCOSH estimtor with Chi prior (p =.75 nd p =.5). SNR [db] Bbble Cr Trin p =.75 p =.5 p =.75 p =.5 p =.75 p = AVG Tble 5 SNR Loss improvements for MMSE WE estimtor with Chi prior (p =.5 nd p =.5). SNR [db] Bbble Cr Trin p =.5 p =.5 p =.5 p =.5 p =.5 p = AVG Tble 6 SNR Loss improvements for MMSE WCOSH estimtor with Chi prior (p =.75 nd p =.5). SNR [db] Bbble Cr Trin p =.75 p =.5 p =.75 p =.5 p =.75 p = AVG prior typiclly hd less performnce gins over the bseline WCOSH with Ryleigh speech prior becuse of the higher bseline SSNR improvements. For ech the WE nd WCOSH with Chi speech prior estimtors, the limiting fctor in SSNR improvement ws the lower bound of the shping prmeters. For the PESQ improvements, the WE nd WCOSH with Chi speech prior estimtors generted upwrds of.14 gins over the bseline WE nd

13 Author's personl copy 11 M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) WCOSH with Ryleigh speech prior estimtors. In similr wy to the SSNR improvements, the increse in the weighting lw prmeter p cused decrese in PESQ improvement. The mximum PESQ improvement rnged from.4 to.56 cross the cr, trin, nd bbble noises, where the shping prmeter reched the mximum t =.5.7 (WE with Chi speech prior estimtor) nd =.9.99 (WCOSH with Chi speech prior estimtor). In generl, the WCOSH with Chi speech prior estimtor did not lwys follow the sme reltionship between the weighting lw prmeter p nd PESQ improvement s the WE with Chi speech prior estimtor. With the SNR Loss improvements, the WE nd WCOSH with Chi speech prior estimtors supplied nerly.19 gins over the bseline WE nd WCOSH with Ryleigh speech prior estimtors. As with SSNR improvement nd PESQ improvement, the SNR Loss improvement decresed in vlue with n increse in the weighting lw prmeter p vlue. The cr, bbble, nd trin noises chieved mximum SNR Loss improvements of.88.11, which occurred in the rnge of =.5.45 (WE with Chi speech prior estimtor) nd /1. (WCOSH with Chi speech prior estimtor). In most cses, the WCOSH with Chi speech prior estimtor did not produce nerly s pronounced SNR Loss improvement gins compred to the WE with Chi speech prior estimtor over the bseline nd WE nd WCOSH with Ryleigh speech prior estimtors. 5. Conclusion In this pper, the uthors derived novel perceptullymotivted WE nd WCOSH estimtors using more pproprite Chi speech prior s substitute for the trditionl Ryleigh speech prior to model the speech spectrl mplitude. Fundmentlly, the gol of the work is to cpitlize on the mutul benefits of the WE nd WCOSH cost functions nd Chi distributions for the speech prior to provide gins in ll phses of enhncement. The WE nd WCOSH with Chi speech prior estimtors incorported weighting lw nd shpe prmeters on the cost functions nd distributions. Insted of mesuring the performnce simply with the SSNR objective qulity metric to determine the mount of noise reduction, the estimtors were evluted using the PESQ nd SNR Loss objective qulity metrics to scertin the level of overll speech qulity nd speech intelligibility compred to the originl noisy signls corrupted by input SNRs of, 5, nd 1 db cross irport, bbble, cr, exhibition, resturnt, sttion, street, nd trin noises. With the WE nd WCOSH with stndrd Ryleigh speech prior estimtors serving s the bseline results, the experimentl results indicted tht the new WE nd WCOSH with Chi speech prior estimtors provided significnt gins in noise reduction nd noticeble gins in overll speech qulity nd speech intelligibility improvements. Generlly, the best results for the vrious objective qulity metrics occurred for prticulr weighting lw prmeter t the limiting vlue of the shping prmeter t lower input SNRs (SSNR improvement) nd vrious vlues of the shping prmeter t higher input SNRs (PESQ improvement nd SNR Loss improvement). In more specific terms, the WE nd WCOSH with Chi speech prior estimtors consistently produced upwrds of pproximtely 3 db (SSNR improvement),.3 (PESQ improvement), nd.5 (SNR Loss improvement) over the bseline WE nd WCOSH with Ryleigh speech prior estimtors. In compring the WE with Chi speech prior nd WCOSH with Chi speech prior estimtors, the WE with Chi speech prior estimtor often times hd slightly better overll performnce cross the SSNR, PESQ, nd SNR Loss objective qulity metrics thn the WCOSH with Chi speech prior estimtor nd would be the recommended estimtor for filtering noisy signls with more negtive vlues of the weighting lw prmeter. For future work, the WE nd WCOSH estimtors would involve further modifictions to integrte even more generlized speech prior sttisticl estimtors, nmely the generlized Gmm speech prior, to obtin more gins in SSNR, PESQ, nd SNR Loss improvements over the trditionl Ryleigh speech prior. References Loizou, P.C., 7. Speech Enhncement Theory nd Prctice. CRC Press. Ephrim, Y., Mlh, D., Speech enhncement using minimum men-squre error short-time spectrl mplitude estimtor. IEEE Trnsctions on Acoustics, Speech nd Signl Processing ASSP-3, Ephrim, Y., Mlh, D., Speech enhncement using minimum men-squre error log-spectrl mplitude estimtor. IEEE Trnsctions on Acoustics, Speech nd Signl Processing 33, Loizou, P.C., 5. Speech enhncement bsed on perceptully motivted Byesin estimtors of the mgnitude spectrum. IEEE Trnsctions on Acoustics, Speech nd Signl Processing 13, Andrinkis, I., White, P.R., 9. Speech spectrl mplitude estimtors using optimlly-shped gmm nd chi priors. Speech Communiction 51, Breithupt, C., Krwczyk, M., Mrtin, R., 8. Prmeterized MMSE spectrl mgnitude estimtion for the enhncement of noisy speech. In: Presented t Interntionl Conference on Acoustics, Speech, nd, Signl Processing. Johnson, N., Kotz, S., Blkrishnn, N., Continuous Univrite Distributions, nd ed. John Wiley nd Sons, New York, vol. 1. Gry, R.M., Buzo, A., Gry, J.A.H., Mtsuym, Y., 198. Distortion mesures for speech processing. IEEE Trnsctions on Acoustics, Speech nd Signl Processing ASSP-8, Grdshteyn, I.S., Ryzhik, I.M., 7. Tbles of Integrls, Series, nd Products. Acdemic Press. Ppmichlis, P.E., Prcticl Approches to Speech Coding. Prentice-Hll, New York, NY. ITU, Subjective test methodology for evluting speech communiction systems tht include noise suppression lgorithm, ITU-T Recommendtion, 3. Hu, Y., Loizou, P.C., 7. Subjective comprison nd evlution of speech enhncement lgorithms. Speech Communiction 49, Hu, Y., Loizou, P., 8. Evlution of objective qulity mesures for speech enhncement. IEEE Trnsctions on Audio, Speech, nd Lnguge Processing 16, 9 38.

14 Author's personl copy M.B. Trwicki, M.T. Johnson / Speech Communiction 57 (14) Rix, A., Beerends, J., Hollier, M., Hekstr, A., 1. Perceptul evlution of speech qulity (PESQ)-A new method for speech qulity ssessment of telephone networks nd codecs. In: Presented t IEEE Interntionl Conference of Acoustics, Speech, nd, Signl Processing. M, J., Loizou, P.C., 11. SNR loss: new objective mesure for predicting the intelligibility of noise-suppressed speech. Speech Communiction 53, Subcommittee, I., IEEE recommended prctice for speech qulity mesurements. IEEE Trnsctions on Audio nd Electrocoustics AU-17, Perce, D., Hirsch, H.-G.,. Performnce evlution of speech recognition systems under noisy conditions. In: Presented t 6th Interntionl Conference on Spoken Lnguge Processing (ICSLP), Beijing, Chin.