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  1. A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm

A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 norm

Mohimani, H ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1109/TSP.2008.2007606
  3. Publisher: 2009
  4. Abstract:
  5. In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined sparse component analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Contrary to previous methods, which usually solve this problem by minimizing the ℓ1 norm using linear programming (LP) techniques, our algorithm tries to directly minimize the ℓ0 norm. It is experimentally shown that the proposed algorithm is about two to three orders of magnitude faster than the state-of-the-art interior-point LP solvers, while providing the same (or better) accuracy. © 2008 IEEE
  6. Keywords:
  7. Atomic decomposition ; Overcomplete signal representation ; Sparse decomposition ; Sparse source separation ; Algorithms ; Apartment houses ; Atomic physics ; Atoms ; Decoding ; Independent component analysis ; Linearization ; Object recognition ; Separation ; Signal analysis ; Signal reconstruction ; Speech analysis ; Atomic decomposition ; Blind source separation (BSS) ; Compressed sensing ; Sparse component analysis (SCA)
  8. Source: IEEE Transactions on Signal Processing ; Volume 57, Issue 1 , 2009 , Pages 289-301 ; 1053587X (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/4663911