Map-based underdetermined blind source separation of convolutive mixtures by hierarchical clustering and l1-norm minimization

Authors:
Stefan Winter;Walter Kellermann;Hiroshi Sawada;Shoji Makino
Affiliations:
NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Soraku-Gun, Kyoto, Japan and Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, ...;Multimedia Communications and Signal Processing, University of Erlangen-Nuremberg, Erlangen, Germany;NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Soraku-Gun, Kyoto, Japan;NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Soraku-Gun, Kyoto, Japan
Venue:
EURASIP Journal on Applied Signal Processing
Year:
2007

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Abstract

We address the problem of underdetermined BSS. While most previous approaches are designed for instantaneous mixtures, we propose a time-frequency-domain algorithm for convolutive mixtures. We adopt a two-step method based on a general maximum a posteriori (MAP) approach. In the first step, we estimate the mixing matrix based on hierarchical clustering, assuming that the source signals are suciently sparse. The algorithm works directly on the complex-valued data in the time-frequency domain and shows better convergence than algorithms based on self-organizing maps. The assumption of Laplacian priors for the source signals in the second step leads to an algorithm for estimating the source signals. It involves the l1-norm minimization of complex numbers because of the use of the time-frequency-domain approach. We compare a combinatorial approach initially designed for real numbers with a second-order cone programming (SOCP) approach designed for complex numbers. We found that although the former approach is not theoretically justified for complex numbers, its results are comparable to, or even better than, the SOCP solution. The advantage is a lower computational cost for problems with low input/output dimensions.