Sparse component analysis and blind source separation of underdetermined mixtures

By Pando G. Georgiev, Fabian J Theis, Andrzej S. Cichocki. IEEE Transactions on Neural Networks, 2005

357 citations recorded by the source corpus.

In this letter, we solve the problem of identifying matrices S /spl isin/ /spl Ropf//sup n/spl times/N/ and A /spl isin/ /spl Ropf//sup m/spl times/n/ knowing only their multiplication X = AS, under some conditions, expressed either in terms of A and sparsity of S (identifiability conditions), or in terms of X (sparse component analysis (SCA) conditions). We present algorithms for such identification and illustrate them by examples.

Subfields: Analytical Chemistry, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/84ae614ef9007262e509101b16e41bf6f0a7086a

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In Analytical Chemistry

In Computational Mechanics

In Signal Processing

Citations in the corpus

Fourth-Order Cumulant-Based Blind Identification of Underdetermined Mixtures (2007, background): “A large class of algorithms for underdetermined ICA starts from the assumption that the sources are (quite) sparse [5], [26], [ 29 ], [33], [39].”
On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD (2013, background): “On the other hand there is only a handful of dictionary learning schemes, for which theoretical results are available, [2], [15], [17], [14], [18].”