SPEECH ENHANCEMENT BASED ON A HYBRID A PRIORI SIGNAL-TO-NOISE RATIO (SNR) ESTIMATOR AND A SELF-ADAPTIVE LAGRANGE MULTIPLIER

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1 16t European Signal Processing Conference (EUSIPCO 8), Lausanne, Switzerlan, August -9, 8, copyrigt by EURASIP SPEECH ENHANCEMENT BASED ON A HYBRID A PRIORI SIGNAL-TO-NOISE RATIO () ESTIMATOR AND A SELF-ADAPTIVE LAGRANGE MULTIPLIER M. Jaangir Alam 1, Si-Ame Selouani an Douglas O Saugnessy 3 1,3 INRS-Energie-Matériau-Télécommunications, Université u Québec, Montréal QC HA 1K6, Canaa Université e Moncton, Campus e Sippagan NB E8S 1P6, Canaa Pone : , Fa : , 1 alam@emt.inrs.ca, 3 ougo@emt.inrs.ca, selouani@umcs.ca Web: ABSTRACT Speec enancement tecniques, using spectral subtraction, ave te rawbac of generating an annoying resiual noise wit musical caracter. An accurate estimate of te a priori is critical for eliminating musical noise. In tis paper, for an accurate estimate of te a priori we ave propose a ybri a priori estimator an a self-aaptive Lagrange multiplier wit Wiener enoising tecnique. Objective evaluations sowe tat te propose meto performe better tan te Decision-Directe () approac. Keywor: a priori, ybri, ecision irecte, Wiener filter, speec enancement 1. INTRODUCTION Most voice communication systems are esigne for processing noise-free speec. Speec signals use as an input to tese systems are often egrae by aitive noise. Speec enancement as terefore attracte a great eal of researc interest to reuce te noise level in noisy speec. Altoug most speec enancement tecniques improve speec quality, tey often suffer from an annoying artifact calle musical noise, cause by ranomly space spectral peas tat come an go in eac frame, an at ranom frequencies. Te ranomly space peas are ue to inaccurate an large variance estimates of te spectra of te noise an noisy signals [3]. Many approaces on noisy speec enancement ave been investigate in te last few ecaes. Among tem, te minimum mean square error (MMSE) estimation approac is one of te most popular speec enancement tecniques, as it can reuce te musical noise tat is a common feature eisting in oter approaces [1]. Te ominant point bein te reuction of musical noise by te MMSE approac is te approac for te a priori estimation, but te a priori follows te a posteriori wit a frame elay []. Since te spectral gain function epens on te estimate a priori, spectral gain compute at te current frame matces te previous frame an terefore te performance of te speec enancement tecnique is egrae. We ave propose a new meto calle a ybri a priori estimation approac, wic solves tis problem wile maintaining te avantages of te approac. Te propose meto sows improve performance over te meto wen applie wit or witout a self-aaptive Lagrange multiplier. Te organization of tis paper is as follows: Section of tis paper presents a escription of te well nown Wiener enoising meto. A escription of te propose ybri a priori estimation approac is mae in section 3. Section 4 provies a escription of te self-aaptive Lagrange multiplier. Performance evaluations an te conclusion of tis paper are mae in section an section 6, respectively.. WIENER DENOISING METHOD Let te istorte signal be epresse as y( n) ( n) + ( n), (1) were ( n) is te clean signal an ( n) is te aitive ranom noise signal, uncorrelate wit te original signal. If at te mt frame an t frequency bin Y, X an D represent te spectral components of y( n ), ( n ) an ( n ), respectively, ten te istorte signal in te transforme omain is Y X + D. () An estimate X of X is given by X H Y, (3) were H is te noise suppression gain (enoising filter), wic is a function of a priori an a posteriori, given by ξ β H, (4) + ξ were is a constant, β is te orer of te filter an ξ is te a priori. If 1 an β 1/ ten (4) correspons to power spectrum filtering. For a generalize Wiener Filter β 1. Te first parameter of te noise suppression rule is te a posteriori given by Y γ, ()

2 16t European Signal Processing Conference (EUSIPCO 8), Lausanne, Switzerlan, August -9, 8, copyrigt by EURASIP m, E{ D } is te noise power spectrum estimate uring speec pauses using te classical recursive relation: were λ ( m 1, D + (1 λ ) Y D ( m,, (6) were λ D 1 is te smooting factor. In tis paper we ave cosen λ D.9 for all cases. E{}. is te epectation operator. Te a priori, wic is te secon parameter of te noise suppression rule, is epresse as ξ, (7) m, were E{ X }. Te instantaneous [6] can be efine as Y ϑ 1. (8) Te temporal-omain enoise speec is obtaine wit te following relation jarg( Y ) ( n) IFFT ( X. e ). (9) 3. ESTIMATION OF A PRIORI An important parameter of numerous speec enancement tecniques is te a priori. Altoug most speec enancement tecniques improve speec quality, tey suffer from an annoying artifact calle musical noise cause by ranomly space spectral peas tat come an go in eac frame, an at ranom frequencies. Te ranomly space peas are ue to te inaccurate estimate of te a priori [3]. An accurate estimate of te a priori is critical for eliminating musical noise. 3.1 DECISION-DIRECTED APPROACH A wiely use meto to etermine te a priori from istorte speec is te ecision-irecte () approac. In [] te approac was efine as a linear combination of (7) an (8). Wit a weigting parameter α tat is constraine to be < α < 1, te linear combination results in ξ X E{ α + (1 α ) ϑ }. (1) However, as tis epression is ar to implement in practice, approimations were mae. Tis le to te following epression: H( m 1, ) Y( m 1, ) ξ α + (1 α) P [ ϑ ], (11) m, were P [ ] if an P [ ] oterwise. In tis paper we ave cosen α.98 by te simulations an informal listening tests. Te multiplicative gain function for tis approac is H. (1) + Ten te enance speec spectrum is obtaine using (3). is escribe in section 4. An important caracteristic of te approac is te epenency on previously enance frames, wic results in biase estimates of te a priori uring speec transitions. Tis meto results in a significant elimination of musical noise. 3. PROPOSED HYBRID A PRIORI ESTIMATOR In te conventional approac te weigting factor α is of constant value (close to unity), te speec spectrum estimate in te previous frame is use to estimate te current a priori an te a priori follows te a posteriori wit a elay of one frame wen te a posteriori eibits an abrupt increase []. Tis frame elay prouces unesire gain istortion an tus generates auible istortion uring abrupt transient perios. Te musical noise is significantly reuce uring noise frames wen te weigting factor α increases but uring te speec onset perios te speec signal coul be istorte. To suppress te problem of te ecision-irecte approac wile maintaining its benefits, we propose a ybri a priori estimation meto, wic can provie fast response to an abrupt increase in te speec signal witout introucing musical noise. We ave use te approac wen te cange in a posteriori between te current frame an te previous frame is greater tan a certain tresol; oterwise te moifie approac is applie so tat te estimate a priori can appropriately follow te sape of te original speec uring transient perios. Te algoritm is iscusse below: If γ( ) > Trl α α, H( m 1, ) Y( m 1, ) ξ α + (1 α) P [ ϑ ], ) else α αm, H ( m 1, ) Y( m 1, ) ξ αm + (1 αm) P [ ϑ ], m, were < α ( m m, < 1, is te moifie weigting factor, base on te previous a posteriori an is given by te following relation: α ( m, 1 m, (13) γ ( ) 1+ ma( γ, γ ( m 1, )) + 1 w e r e γ ( ) γ γ ( m 1, ), t e t r e s o l i s { γ } Trl E, 1,,3,.., K is te spectral bin ine an m 1,,3,.., M is te frame ine, K is te frame lengt an M is te number of frames. Te estimate of te a priori in te propose approac is given by: H ( m 1, ) Y( m 1, ) ξ( m, ) α ( m, ) + (1 α ( m, )) P [ ϑ( m, )], (14) m,

3 16t European Signal Processing Conference (EUSIPCO 8), Lausanne, Switzerlan, August -9, 8, copyrigt by EURASIP were H is te spectral gain for te propose approac an is given by H. (1) + Figure 1 epicts te bloc iagram of te propose ybri a priori estimator for te mt frame wit frame lengt K. Figure represents te variation of te average weigting factor (per frame) of bot approaces. Figure 3 represents te variation of te a priori of te propose approac an tat of te approac wit te a posteriori. Te propose ybri approac efficiently avois te elay generate by te approac an te estimate a priori resembles te a posteriori uring speec onset perios. γ T rl γ ( γ ( m 1, ) Yes α γ ( ) > Trl α m No tose frames an woul lie to reuce resiual noise in noise-ominate frames. Figure 3 Variations of te a priori of te approac an tat of te propose approac wit te a posteriori. Noise, B. ξ ( m 1, ) Moifie ξ ( m 1, ) approac approac ϑ ϑ ξ ( m, Combine Figure 1 Bloc iagram of te propose ybri a priori estimation approac for te mt frame wit frame lengt K. Figure Average (frequency-average) value of te weigting factor (α an α ( m, ) of te bot approaces. Noise, 1 B. 4. SELF-ADAPTIVE LAGRANGE MULTIPLIER Te role of te Lagrange multiplier [3] is te same as tat of te over-subtraction factor in [4]. Te Lagrange multiplier ( 1) in (4), (1) an (16) controls te trae off between speec istortion an resiual noise. A large woul prouce more speec istortion wit less resiual noise. Conversely a small woul prouce a smaller amount of speec istortion wit more resiual noise. Since te speec signal will mas te noise in te speec-ominate frames, we woul lie to reuce te speec istortion in Figure 4 Variation of wit te a priori (B) at ifferent values of. We ave mae te value of epenent on te estimate a priori, ξ ( m, an it is epresse by te following relation B e ξ +, (16) were ξ (, ) 1log B m 1( ξ (, ) m, an is a constant cosen eperimentally. We ave use 9 on te basis of simulations. Figure 4 sows te variation of te self-aaptive Lagrange multiplier, wit te a priori (B) at ifferent values of.. PERFORMANCE EVALUATION AND DISCUSSION A. OBJECTIVE QUALITY MEASURES To measure te quality of te enance signal we ave use te Log Lielioo Ratio (LLR), te Log Spectral Distance (LSD), an te Segmental [7]. All tree measures sow ig correlation wit informal listening tests. Te most popular class of te time omain measures is te segmental. It is well nown tat segmental is more accurate in inicating te speec istortion tan te overall. Te frame base segmental is forme by averaging frame level estimates an is efine by

4 16t European Signal Processing Conference (EUSIPCO 8), Lausanne, Switzerlan, August -9, 8, copyrigt by EURASIP M 1 i mk + K 1 1 ( i) Seg log1, (17) M m i mk ( ( i) ˆ ( i)) were ( i ) is te original speec, ˆ( i) is te processe speec reprouce by a speec processing system, K is te lengt of te segment an M is te number of segments in te speec signal. Te iger value of te segmental inicates te weaer speec istortions. Te LLR is referre to as te Itaura istance measure. It is efine as were T ar ˆa LLR log T, (18) a ˆRˆ a ˆ a is te LPC coefficient vector { 1, a (1), a (),..., a ( p) } for te original speec signal ( n ), a is te LPC coefficient vector 1, a (1), a (),..., a ( p) for te processe { } ˆ ˆ ˆ speec ˆ( n ), p is te orer of LPC coefficient, an R ˆ is te autocorrelation matri for te processe speec. Te lower te LLR measure for an enance speec, te better is its perceive quality. Te Log Spectral Distance is efine as M 1 mk + K 1 1 ˆ 1 M m mk LSD log X ( ) X ( ), (19) were X ( is te power spectra of te original speec, X ˆ ( ) is te power spectra of te processe speec reprouce by a speec processing system, K is te lengt of te segment an M is te number of segments in te speec signal. Te iger LSD reflects te stronger speec istortions. B. EXPERIMENTAL RESULTS In tis section, te performance of te propose approac is teste for speec enancement an compare to tat of te approac wit an witout te propose self-aaptive Lagrange multiplier. In orer to evaluate te performance of te propose ybri a priori estimation approac escribe in section 3., we conucte etensive objective quality tests uner various noisy environments. Te frame sizes were cosen to be 6 samples (3 msec) long wit 4% overlap; a sampling frequency of 8 Hz an a amming winow were applie. To evaluate an compare te performance of te a priori estimators, we carrie out simulations wit te TEST A an te TEST B atabases of Aurora [8]. Speec signals were egrae wit five types of noise at global levels of B, B, 1 B, 1 B an B. Te noises were N1 ( noise), N ( Noise) from te TEST A atabase, N1 ( Noise), N ( Noise), an N3 ( Noise) from te TEST B atabase. Table 1, Table, an Table 3 represent te Average segmental, te LSD, an te LLR, respectively, of te enance signals at ifferent input levels. Eperimental results sow tat te propose ybri a priori estimator (wit an witout )-base meto performe better tan te conventional approac-base meto. Figure represents te spectrograms of te clean signal an enance signals obtaine wit te approac an te propose ybri approac. Te speec spectrograms provie more accurate information about te resiual noise an speec istortion tan te corresponing time omain waveforms. We compare te spectrograms for eac of te metos an confirme a reuction of te resiual noise an speec istortion. Speec spectrograms presente in te figure use a amming winow of lengt 6 samples wit % overlap an te noisy signals inclue noise wit B. Eperimental results, plotte spectrograms, an informal listening tests sow tat te propose tecnique performs better in all teste objective quality measures; it oes not introuce aitional speec istortion, an results in significant reuction of te musical noise penomenon. (a) (b) (c) () (e) (f) Figure Speec Spectrograms, Noise, B:(a) clean signal, (b) noisy signal, an enance signals obtaine using (c) te approac, () te approac wit, (e) te ybri approac, an (f) te ybri approac wit.

5 16t European Signal Processing Conference (EUSIPCO 8), Lausanne, Switzerlan, August -9, 8, copyrigt by EURASIP Table 1 Average segmental Noise Type (B) wit Table Log Spectral Distance (LSD) Noise Type (B) wit Table 3 Log Lielioo Ratio (LLR) Noise Type (B) 1 1 wit Hybri wit Hybri wit Hybri wit Hybri Hybri Hybri CONCLUSION In tis paper we ave propose a ybri a priori estimator wic avois te elay problem of te approac wile eeping its avantages an a self-aaptive Lagrange multiplier for te wiener enoising tecnique. Performance evaluations of te propose approac are carrie out using tree objective quality measures [7]. Simulation results sow tat te propose algoritm possesses better performance for speec enancement in various noisy environments tan tat of te conventional approac. REFERENCES [1] J. S. Lim an A. V. Oppeneim, Enancement an banwit compression of noisy speec, Proc. IEEE, vol. 67, pp , [] Y. Epraim an D. Mala, Speec enancement using a minimum mean-square error sort-time spectral amplitue estimator, IEEE Trans. on Acoustics, Speec an Signal Processing, vol. 3, pp , [3] Yi Hu, Pillips C. Loizu, Speec Enancement base on wavelet tresoling te Multitaper Spectrum, IEEE Trans. on Speec an Auio Processing, vol. 1, no. 1,pp. 9-67, January 4. [4] M. Berouti, R. Scwartz, an J. Maoul, Enancement of speec corrupte by acoustic noise, in Proc. IEEE Int. Conf. Acoust., Speec, Signal Processing, 1979, pp [] O. Cappe, Elimination of te musical noise penomenon wit te Epraim an Mala noise suppressor, IEEE Trans. Speec an Auio Processing, vol., no. 1, pp , April [6] Cyril Plapous, Claue Marro, Laurent Mauuary an Pascal Scalart, A Two Step Noise Reuction Tecnique, IEEE Trans. Acoustic, Speec an Signal Processing, vol. 1, pp. 89 9, 4. [7] S. R. Quacenbus, T. P. Barnwell an M. A. Clements, Objective measures of speec quality. Prentice-Hall, Englewoo Cliffs, New Jersey, [8] H. Hirsc an D. Pearce, Te Aurora eperimental framewor for te performance evaluation of speec recognition systems uner noisy environments, ISCA ITRW ASR, September.