Blind Source Separation of Linear Mixtures with Singular Matrices

  • Pando Georgiev
  • Fabian J. Theis
Conference paper

DOI: 10.1007/978-3-540-30110-3_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3195)
Cite this paper as:
Georgiev P., Theis F.J. (2004) Blind Source Separation of Linear Mixtures with Singular Matrices. In: Puntonet C.G., Prieto A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg

Abstract

We consider the Blind Source Separation problem of linear mixtures with singular matrices and show that it can be solved if the sources are sufficiently sparse. More generally, we consider the problem of identifying the source matrix S ∈ IRnxN if a linear mixture X = AS is known only, where A∈ IRmxn, m ≤ n and the rank of A is less than m. A sufficient condition for solving this problem is that the level of sparsity of S is bigger than mrank(A) in sense that the number of zeros in each column of S is bigger than mrank(A). We present algorithms for such identification and illustrate them by examples.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pando Georgiev
    • 1
  • Fabian J. Theis
    • 2
  1. 1.Laboratory for Advanced Brain Signal ProcessingBrain Science Institute, The Institute for Physical and Chemical Research (RIKEN)SaitamaJapan
  2. 2.Institute of BiophysicsUniversity of RegensburgRegensburgGermany

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