Delay-&-Predict Equalization For Blind Speech Dereverberation

Transkript

1 Delay-&-Predict Equalization For Blind Speech Dereverberation Mahdi Triki and Dirk T.M. Slock CNRS - Eurecom Institute, Sophia Antipolis {triki, slock}@eurecom.fr 1

2 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 2

3 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 3

4 Blind dereverberation for a single source The quality of speech captured in real-word environment is degraded by acoustic interference : Additive interference noise reduction Convolutive interference signal dereverberation 4

5 Blind dereverberation for a single source (2) Blind speech dereverberation is a challenging problem: Both source signal statistics and the channel impulse responses (CIRs) are time-varying We need extra information to make the problem identifiable Source signal correlations lead to poor channel equalization performance 5

6 Blind dereverberation for a single source (3) Three key ingredients to solve the problem : Spatial diversity: multi-channel aspect Temporal diversity: CIRs are slowly varying with time whereas speech signal statistics vary quickly Spectral diversity: in the cepstral domain, the channel and the speech signal can be separated 6

7 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 7

8 Multichannel spatial diversity A rectangular room: Dimensions : 8 x 10 x 4 m Wall reflection coefs : ρ x =ρ y =0.5, ρ z = 0.2 A speech signal: Duration : 8.8 s Sampling freq : 8 khz The reverberant signal is observed on 8 distinct microphones 8

9 Multichannel spatial diversity (2) 4 m 10 m 8 m 9

10 Multichannel spatial diversity (3) Multi-channel transfer function magnitudes and their sum 10

11 Multichannel spatial diversity (4) Averaged periodogram of the original clean signal and the reconstructed one M welch k = 1 Py k y k ( f ) P welch ( f ss ) 11

12 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 12

13 Speech dereverberation procedure Motivated by the previous observation, we propose a three stages scheme Source whitening stage: removes correlations due to the speech signal Multichannel prediction stage: computes a blind multichannel predictor (using the whitened obs. signal) Dereverberation stage: equalizes the CIR (using a ZF equalizer based on the predictor computed in 13

14 Speech dereverberation procedure Source whitening Multichannel prediction Source dereverberation 14

15 The source whitening stage Due to the multichannel spatial diversity, the superposition of the spectra of the received signal can estimate the source spectrum (up to a multiplicative factor). Remove correlations due to the speech signal by compensating the common part on the multi-channel impulse response 15

16 16 The source whitening stage (2) As the common part is due to the anechoic speech signal, it can be modeled as an AR process The common AR coefs can be estimated as those tha minimize Normal equations = l l l l l r r r a a a r r r r r r r r r M M L M O M L ) ( ) ( ) ( = = = = = = = M k n l j k j k M k n k j n y a n y n e e

17 The source whitening stage (3) Source periodogram, spectrum of AR process estimated using the clean an the reverberant signal (l=20,m=8) 17

18 The source whitening stage (4) A periodic signal (perfectly predictable) may lead to identifiability problem for SIMO channel: the predictor will have tendency to kill the signal rather to whiten it Considering the totality of the speech signal in order to calculate the AR coefs (which estimates the averaged speech spectrum) Exploit the speech non-stationarity (temporal diversity) to avoid singularities due to voiced frames. 18

19 Speech dereverberation procedure Source whitening Multichannel prediction Source dereverberation 19

20 20 The multichannel prediction stage The source-whitened reverberant signal: where is the whitened speech input We consider now the problem of predicting x(k) form the L latest observation ) ) ~ ( ( ) ( ) ( ) ( q s q H q y q a k x = = [ ] ) ( ) ~ ( 1, 1, k X A x x A A I k x L L L k k L L L m + = = M M L ) ( ~ k s

21 The multichannel prediction stage (2) Minimizing the energy of the prediction error leads (for large enough L) to: where + H S~ x~ x ( z) = AL ( z) Sxx( z) AL = h0 S~~ s s ( z) h0 - A(z)= A L,i z -i denotes the MIMO prediction error filter computed by solving the normal equations - h 0 =H(+ ) represents the first vector coefficient of the SIMO channel filter 21

22 Speech dereverberation procedure Source whitening Multichannel prediction Source dereverberation 22

23 The dereverberation stage Based on the multichannel LP, the SpatioTemporal zero-forcing equalizer is given by H F q) h A ( q) D( q) D & P ( = 0 where D(q) is a diagonal matrix of delays, aligning the M reverb signals Thus, the dereverberated speech signal can be produced as: L sˆ ( k) = FD & P( q) y( k) = h0 H A L ( q) D( q) y( k) 23

24 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 24

25 Time delay estimation A relevant issue is the alignment (same delay) of the received signals: leads to an increase in performance allows the use of a shorter predictor Several approach have been proposed and studied to solve the problem (CC, GCC ) Still insufficient to solve the bias introduced by multi-path propagation 25

26 Time delay estimation (2) We propose an iterative scheme to align the received signals Perform Multichannel LP (for a time-lag λ=1) Computes h 0, which can be estimated as the eigenvector corresponding to the maximum eigenvalue of the multichannel LP residual correlation matrix Detect the position of non-zero coefficient in h 0, and delay the corresponding received signals by 1 Repeat, until all received signal are aligned This procedure can be followed by a CC based refinement step 26

27 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 27

28 Experimental Results Room L x =8m L y =10m L z =4m ρ x = ρ y = ρ z =0.9 Input duration = 8.8 s f s = 8 khz. 28

29 Experimental Results (2)

30 Experimental Results (3) early reflections late reflections T 60 The direct to reverberant energy ratio: DRR = 10 log ~ h τ 1 2 n = 0 n 10 L 1 ~ 2 h n = τ n ( n ) ( n ) db 30

31 Experimental results (4) Equalized CIR and spectrum, and the whitened source spectrum. (a) l =20, (b) l =100 31

32 Experimental results (5) D&P DDR (in db) M = 2 M = 4 M = whitening order (in db) Direct-to-Reverb energy Ratio (DRR) v.s. whitening order for 2, 4, and 8 microphones 32

33 Experimental results (6) Mean DDR D-&-S DRR D-&-P DRR 8 DDR (in db) N microphones D&P equalizer v.s D&S beamformer (l =100) for 2, 4, and 8 microphones 33

34 Outline Blind dereverberation for a single source Multichannel spatial diversity Speech dereverberation procedure Time delay estimation Experimental results Multi-frame Delay-&-Predict Equalization 34

35 Multi-frames D&P Equalization The residual error can be broadly classified into two distinct categories Estimation error: due to the use of the sampling covariance matrices. Modeling error: due to the assumptions on the channel and the input signal structures. 35

36 Multi-frames D&P Equalization (2) The more data we have, the lower the estimation error will be. However, it has a very little influence on the modeling error. The temporal diversity of the input signal is used just to avoid singularities due to the prediction of the voiced frames. A frame-by-frame based approach 36

37 Multi-frames D&P Equalization (3) 37

38 Multi-frames D&P Equalization (4) M=2 M=4 M=8 D&S classic D&P multi-frames D&P The multi-frame approach does not always improve the equalization DDR!!!! 38

39 Windowed D&P equalization Due to the segmentation process, the received signal can be written as: x i ( n) = s ( n) h( n) + v ( n) u ( n) i where v i (n) is the "extra" echo from the previous segment; and u i (n) is the "missing" tail of echo of the current segment. i i As f D&P is a zero-forcing equalizer, it may amplify the additive noise e i =v i -u i Use smoother windows 39

40 Windowed D&P equalization (2) M=2 M=4 M=8 Rectangular window Hamming window Exponential window

41 Iterated D&P equalization Initialization Error cancellation D-&-P P Equalization Convergence 41

42 Iterated D&P equalization (2) M=2 M=4 M=8 Rectangular window Hamming window Exponential window Iterated D-&-P

43 Experimental Results M=2 clean D&S classic D&P windowed D&P iterated D&P M=4 M=8 43

44 Conclusions A LP based dereverberation technique was proposed Spatial, temporal, and spectral diversities are exploited to whiten speech signal The Delay-&Predict equalizer is then computed based on multichannel LP technique Simulations show that the D&P equalizer performs much better than D&S beamformer. 44