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- W2105454037 abstract "In this letter, we analyze a two-stage cluster-then-l 1 -optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l 1 norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l 1 —norm solution and the l 0 —norm solution is also analyzed according to a probabilistic framework. If the obtained l 1 —norm solution is sufficiently sparse, then it is equal to the l 0 —norm solution with a high probability. Furthermore, the l 1 —norm solution is robust to noise, but the l0—norm solution is not, showing that the l 1 —norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed" @default.
- W2105454037 created "2016-06-24" @default.
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- W2105454037 date "2004-06-01" @default.
- W2105454037 modified "2023-10-04" @default.
- W2105454037 title "Analysis of Sparse Representation and Blind Source Separation" @default.
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- W2105454037 doi "https://doi.org/10.1162/089976604773717586" @default.
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