A fast approach for overcomplete sparse decomposition based on smoothed ` 0 norm

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 £eld codes. Contrary to previous methods, which usually solve this problem by minimizing the ` norm using Linear Programming (LP) techniques, our algorithm tries to directly minimize the ` 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.