Underdetermined blind source separation based on sparse representation

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)423-437
Journal / PublicationIEEE Transactions on Signal Processing
Volume54
Issue number2
Publication statusPublished - Feb 2006

Abstract

This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in [7], a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented. © 2006 IEEE.

Research Area(s)

  • Blind source separation (BSS), l1-norm, Probability, Recoverability, Sparse representation, wavelet packets

Citation Format(s)

Underdetermined blind source separation based on sparse representation. / Li, Yuanqing; Amari, Shun-Ichi; Cichocki, Andrzej et al.
In: IEEE Transactions on Signal Processing, Vol. 54, No. 2, 02.2006, p. 423-437.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review