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Sparse decomposition: Introducing a New Iterative Algorithm

we introduce a new method for sparse decomposition. Sparse decomposition aims to find sufficiently sparse solutions of a linear system of equations. As an application of SCA we consider our problem in context of blind source separation. In blind source separation problem, objective is to recover  sources from their linear mixtures (observations) where mixing matrix is also unknown. Our main interest is in underdetermined case, where mere  knowledge of mixing matrix is not enough for source separation. We will define “active subspace” (linear subspace spanned by submatrix  correspondding to active source components at a given time) and develop an iterative algorithm that detects active subspace and use the solution  with minimal l2 norm in current active subspace to redefine active subspace for next iteration. Experiments show that introduced method  compromises between convergence speed and accuracy of well-known algorithms available in literature.

Armin Eftekhari -Arash Ali Amini
K.N.Toosi University -University of California Berkeley

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