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An efficient wavelet-based adaptive filtering algorithm for automatic blind speech enhancement

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Abstract

In this paper, we address the problem of speech enhancement by adaptive filtering algorithms. A particular attention has been paid to the backward blind source separation (BBSS) algorithm and its use in crosstalk resistant speech enhancement applications. In this paper, we propose to implement the BBSS algorithm in the wavelet-domain. The proposed backward wavelet BBSS (WBBSS) algorithm is then used in speech enhancement application when important crosstalk interferences are presents. The new WBBSS algorithm shows better performances in terms of convergence speed and steady state in comparison with the classical BBSS one. The performances properties of the proposed algorithm are evaluated in term of segmental SNR (SegSNR), segmental mean square error (SegMSE), and cepstral distance (CD) criteria. The obtained results have confirmed the best performance of the proposed WBBSS algorithm in a lot of situations when blind noisy observations are available.

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Abbreviations

BSS:

Blind source separation

BBSS:

Backward blind source separation

DFT:

Discrete Fourier transform

DWT:

Discrete wavelet transform

WBBSS:

Wavelet transform of BBSS

ANC:

Adaptive noise cancellation

LMS:

Least mean square

NLMS:

Normalized LMS

TSNR:

Two-step noise reduction

MSE:

Mean square error

SNR:

Signal to noise ratio

SegSNR:

Segmental signal to noise ratio

MSE:

Mean square error

SegMSE:

Segmental mean square error

CD:

Cepstral distance

dB:

Decibel

VAD:

Voice activity detector

E :

Expectation operator

H:

Mixing matrix

W:

Unmixing matrix

m:

Delay index

n:

Discrete time index

J:

DWT scale index

L:

Real and adaptive impulse responses length

M:

Mean averaging value of CD, SegSNR, SegMSE

fs :

Sampling frequency

\({\text{s}}\left( {\text{n}} \right)\) :

Speech signal

\({\text{b}}\left( {\text{n}} \right)\) :

Punctual noise

\({{\text{m}}_{\text{1}}}\left( {\text{n}} \right)\) :

First noisy observation

\({{\text{m}}_{\text{2}}}\left( {\text{n}} \right)\) :

Second noisy observation

\({{\text{h}}_{{\text{11}}}}\left( {\text{n}} \right){\text{ and }}{{\text{h}}_{{\text{22}}}}\left( {\text{n}} \right)\) :

Direct impulse responses

\({{\text{h}}_{{\text{12}}}}\left( {\text{n}} \right){\text{ and }}{{\text{h}}_{{\text{21}}}}\left( {\text{n}} \right)\) :

Cross-coupling impulse responses

\(\delta \left( {\text{n}} \right)\) :

Dirac impulse

\({{\text{v}}_{\text{1}}}{\text{(n)}}\) :

Estimated speech by forward structure

\({{\text{v}}_{\text{2}}}{\text{(n)}}\) :

Estimated noise by forward structure

\({{\text{w}}_{{\text{12}}}}\left( {\text{n}} \right)\) and \({{\text{w}}_{{\text{21}}}}\left( {\text{n}} \right)\) :

Adaptive coefficients

\({{\mathbf{w}}_{12}}\left( {\text{n}} \right)\) and \({{\mathbf{w}}_{21}}\left( {\text{n}} \right)\) :

Adaptive filter vectors

\({\mathbf{P}}_{{{\text{J, K}}}}^{{\left( {\text{1}} \right)}}\left( {\text{n}} \right)\) :

Discrete wavelet transform of \({{\text{m}}_{\text{1}}}\left( {\text{n}} \right)\)

\({\mathbf{P}}_{{{\text{J, K}}}}^{{\left( {\text{2}} \right)}}\left( {\text{n}} \right)\) :

Discrete wavelet transform of \({{\text{m}}_{\text{2}}}\left( {\text{n}} \right)\)

\({r_{{{\text{v}}_{\text{1}}}{{\text{v}}_{\text{2}}}}}\left( {\text{m}} \right){\text{ }}\) :

Cross-correlation between v1(n) and v2(n)

\({r_{{{\text{v}}_{\text{2}}}{{\text{v}}_{\text{1}}}}}\left( {\text{m}} \right)\) :

Cross-correlation between v2(n) and v1(n)

\({\uptheta _1}\) and \({\uptheta _2}\) :

Fixed step-sizes of BBSS

\({\upmu _{12}}{\text{ and }}{\upmu _{21}}\) :

Fixed step-sizes of WBBSS

\({\varsigma _1}\) and \({\varsigma _2}\) :

Small positive constant

\(\upphi \left( {\text{n}} \right)\) :

Discret wavelet function

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  1. University of Blida 1, Signal Processing and Image Laboratory (LATSI), Route de Soumaa, B.P. 270, 09000, Blida, Algeria

    Mohamed Djendi

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  1. Mohamed Djendi
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Djendi, M. An efficient wavelet-based adaptive filtering algorithm for automatic blind speech enhancement. Int J Speech Technol 21, 355–367 (2018). https://doi.org/10.1007/s10772-018-9514-9

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