A robust and precise method for solving the permutation problem of frequency-domain blind source separation

Blind source separation (BSS) for convolutive mixtures can be solved efficiently in the frequency domain, where independent component analysis (ICA) is performed separately in each frequency bin. However, frequency-domain BSS involves a permutation problem: the permutation ambiguity of ICA in each frequency bin should be aligned so that a separated signal in the time-domain contains frequency components of the same source signal. This paper presents a robust and precise method for solving the permutation problem. It is based on two approaches: direction of arrival (DOA) estimation for sources and the interfrequency correlation of signal envelopes. We discuss the advantages and disadvantages of the two approaches, and integrate them to exploit their respective advantages. Furthermore, by utilizing the harmonics of signals, we make the new method robust even for low frequencies where DOA estimation is inaccurate. We also present a new closed-form formula for estimating DOAs from a separation matrix obtained by ICA. Experimental results show that our method provided an almost perfect solution to the permutation problem for a case where two sources were mixed in a room whose reverberation time was 300 ms.

[1]  S.C. Douglas,et al.  Multichannel blind deconvolution and equalization using the natural gradient , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

[2]  Daniel W. E. Schobben,et al.  A frequency domain blind signal separation method based on decorrelation , 2002, IEEE Trans. Signal Process..

[3]  Philip Schniter,et al.  FREQUENCY DOMAIN REALIZATION OF A MULTICHANNEL BLIND DECONVOLUTION ALGORITHM BASED ON THE NATURAL GRADIENT , 2003 .

[4]  Kiyotoshi Matsuoka,et al.  A neural net for blind separation of nonstationary signals , 1995, Neural Networks.

[5]  Hiroshi Sawada,et al.  A robust approach to the permutation problem of frequency-domain blind source separation , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[6]  B. Kollmeier,et al.  Convolutive blind source separation of speech signals based on amplitude modulation decorrelation , 2000 .

[7]  Walter Kellermann,et al.  A GENERALIZATION OF A CLASS OF BLIND SOURCE SEPARATION ALGORITHMS FOR CONVOLUTIVE MIXTURES , 2003 .

[8]  Andreas Ziehe,et al.  An approach to blind source separation based on temporal structure of speech signals , 2001, Neurocomputing.

[9]  Scott C. Douglas,et al.  Convolutive blind separation of speech mixtures using the natural gradient , 2003, Speech Commun..

[10]  Reinhold Orglmeister,et al.  Blind source separation of real world signals , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[11]  Russell H. Lambert,et al.  Blind separation of multiple speakers in a multipath environment , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[13]  Kazuya Takeda,et al.  Evaluation of blind signal separation method using directivity pattern under reverberant conditions , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[14]  Noboru Ohnishi,et al.  A method of blind separation for convolved non-stationary signals , 1998, Neurocomputing.

[15]  Hiroshi Sawada,et al.  Convolutive blind source separation for more than two sources in the frequency domain , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[16]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[17]  B.D. Van Veen,et al.  Beamforming: a versatile approach to spatial filtering , 1988, IEEE ASSP Magazine.

[18]  Dennis R. Morgan,et al.  A beamforming approach to permutation alignment for multichannel frequency-domain blind speech separation , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[20]  Hiroshi Sawada,et al.  Geometrical understanding of the PCA subspace method for overdetermined blind source separation , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[21]  Shoko Araki,et al.  Equivalence between Frequency-Domain Blind Source Separation and Frequency-Domain Adaptive Beamforming for Convolutive Mixtures , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[22]  Hiroshi Sawada,et al.  Polar coordinate based nonlinear function for frequency-domain blind source separation , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[23]  Te-Won Lee,et al.  Independent Component Analysis , 1998, Springer US.

[24]  Nobuhiko Kitawaki,et al.  Combined approach of array processing and independent component analysis for blind separation of acoustic signals , 2003, IEEE Trans. Speech Audio Process..

[25]  Arthur H. M. van Roermund,et al.  Unsupervised adaptive filtering, volume I: blind source separation [Book Review] , 2002, IEEE Circuits and Devices Magazine.

[26]  Birger Kollmeier,et al.  Amplitude Modulation Decorrelation For Convolutive Blind Source Separation , 2000 .

[27]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[28]  Paris Smaragdis,et al.  Blind separation of convolved mixtures in the frequency domain , 1998, Neurocomputing.

[29]  Ah Chung Tsoi,et al.  Blind deconvolution of signals using a complex recurrent network , 1994, Proceedings of IEEE Workshop on Neural Networks for Signal Processing.

[30]  Lucas C. Parra,et al.  Convolutive blind separation of non-stationary sources , 2000, IEEE Trans. Speech Audio Process..

[31]  K. Matsuoka,et al.  Minimal distortion principle for blind source separation , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[32]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[33]  Shoko Araki,et al.  ARRAY GEOMETRY ARRANGEMENT FOR FREQUENCY DOMAIN BLIND SOURCE SEPARATION , 2003 .