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Fast sparse representation based on smoothed \(\ell ^{0}\) norm. (English) Zbl 1173.94376
Davies, Mike E. (ed.) et al., Independent component analysis and signal separation. 7th international conference, ICA 2007, London, UK, September 9–12, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-74493-1/pbk). Lecture Notes in Computer Science 4666, 389-396 (2007).
Summary: In this paper, a new algorithm for Sparse Component Analysis (SCA) or atomic decomposition on over-complete dictionaries is presented. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations. The solution obtained by the proposed algorithm is compared with the minimum \(\ell ^{1}\)-norm solution achieved by Linear Programming (LP). It is experimentally shown that the proposed algorithm is about two orders of magnitude faster than the state-of-the-art \(\ell ^{1}\)-magic, while providing the same (or better) accuracy.
For the entire collection see [Zbl 1129.94002].

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
65F50 Computational methods for sparse matrices
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