Independent Component Analysis and Blind Signal Separation

Volume 3195 of the series Lecture Notes in Computer Science pp 121-128

Blind Source Separation of Linear Mixtures with Singular Matrices

  • Pando GeorgievAffiliated withLaboratory for Advanced Brain Signal Processing, Brain Science Institute, The Institute for Physical and Chemical Research (RIKEN)
  • , Fabian J. TheisAffiliated withInstitute of Biophysics, University of Regensburg

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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 ∈ IR nxN if a linear mixture X = AS is known only, where A∈ IR mxn , 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.