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

Authors:
Hosein Mohimani;Massoud Babaie-Zadeh;Christian Jutten
Affiliations:
Electrical Engineering Department, Sharif University of Technology, Tehran, Iran;Electrical Engineering Department, Sharif University of Technology, Tehran, Iran;GIPSA-Lab, Department of Images and Signals, Institut National Polytechnique de Grenoble, Grenoble Cedex, France
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

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 under-determined 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.