| 202C2 |
|---|
| Blind Source Separation Taking into Account the Singularity of the Mixing Process |
| AUTHORS |
| Kiyotoshi Matsuoka, Satoshi Nakashima (Kyushu Institute of Technology) |
| ABSTRACT |
| In the authors¡Ç experience, although most conventional methods for blind source separation (BSS) are able to achieve separation for artificially synthesized data, they do not necessarily work well for real-world data. The results of separation are often unsatisfactory and, what is worse, they sometimes suffer from incomprehensible computational instability. Among a lot of reasons conceivable, we want to focus on one problem here, which is often neglected though it occurs almost everywhere. Namely, we consider the case that the frequency response of the mixing process becomes almost singular at some part of frequency range. The task of BSS is to find a demixing matrix, which is basically the inverse of the mixing matrix, and to apply it to the signals observed. So, if the mixing matrix is nearly singular in some frequency ranges, then the norm of the demixing matrix becomes very large and some numerical instability can occur. ¡¡¡¡The purpose of this paper is to propose an approach for overcoming the above-mentioned problem. The approach is fundamentally based on the minimal distortion principle (MDP), an idea that was proposed by the authors to normalize the demixing matrix with certain favorable properties. However, the original algorithm derived from MDP cannot cope with the case that the mixing process is (almost) singular. In this paper, so as to solve the singularity problem, we introduce a generalized form of the original MDP, which we call ¦Å-MDP. ¡¡¡¡Based on ¦Å-MDP, we derive a new BSS algorithm in which a kind of regularization term is incorporated so as to obtain a robust separator. Roughly speaking, it determines the demixing matrix such that its gain be sufficiently small at frequencies for which the mixing matrix is almost singular. In addition of the derivation of the algorithm, we show a couple of examples, demonstrating a remarkable improvement in separation accuracy and robustness. |
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Annual Conference 2002