Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

Authors:
Tiemin Mei;Alfred Mertins;Fuliang Yin;Jiangtao Xi;Joe F. Chicharo
Affiliations:
Institute for Signal Processing, University of Lübeck, Ratzeburger Allee 160, Lübeck 23538, Germany and School of Information Science and Engineering, Shenyang Ligong University, Shenyan ...;Institute for Signal Processing, University of Lübeck, Ratzeburger Allee 160, Lübeck 23538, Germany;School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116023, China;School of Electrical, Computer and Telecommunications Engineering, The University of Wollongong, NSW 2522, Australia;School of Electrical, Computer and Telecommunications Engineering, The University of Wollongong, NSW 2522, Australia
Venue:
Signal Processing
Year:
2008

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Abstract

This paper studies the problem of blind separation of convolutively mixed source signals on the basis of the joint diagonalization (JD) of power spectral density matrices (PSDMs) observed at the output of the separation system. Firstly, a general framework of JD-based blind source separation (BSS) is reviewed and summarized. Special emphasis is put on the separability conditions of sources and mixing system. Secondly, the JD-based BSS is generalized to the separation of convolutive mixtures. The definition of a time and frequency dependent characteristic matrix of sources allows us to state the conditions under which the separation of convolutive mixtures is possible. Lastly, a frequency-domain approach is proposed for convolutive mixture separation. The proposed approach exploits objective functions based on a set of PSDMs. These objective functions are defined in the frequency domain, but are jointly optimized with respect to the time-domain coefficients of the unmixing system. The local permutation ambiguity problems, which are inherent to most frequency-domain approaches, are effectively avoided with the proposed algorithm. Simulation results show that the proposed algorithm is valid for the separation of both simulated and real-word recorded convolutive mixtures.