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An improved smoothed l0-norm algorithm based on multiparameter approximation function

In this paper, by representing the sources with subspace method, it is proved that the iteration and projection process of SL0 (Smoothed L0-norm Algorithm) is equivalent to search the sparsest solution in solution space of the system equation. Then, an improvement for over-complete sparse decomposition is introduced, which replaces the Gaussian function used in SL0 algorithm with Sigmoid one to improved its noise tolerance. And, the algorithm could convergence in less iteration. It is experimentally shown that the improved algorithm is superior to the original one on the performance of noise tolerance and speed while keeping its performance related to the probability of activity of the sources.