Approximate Sparse Decomposition Based on Smoothed L0-Norm

摘要

In this paper, we propose a method to address the problem of sourceestimation for Sparse Component Analysis (SCA) in the presence of additivenoise. Our method is a generalization of a recently proposed method (SL0),which has the advantage of directly minimizing the L0-norm instead of L1-norm,while being very fast. SL0 is based on minimization of the smoothed L0-normsubject to As=x. In order to better estimate the source vector for noisymixtures, we suggest then to remove the constraint As=x, by relaxing exactequality to an approximation (we call our method Smoothed L0-norm Denoising orSL0DN). The final result can then be obtained by minimization of a properlinear combination of the smoothed L0-norm and a cost function for theapproximation. Experimental results emphasize on the significant enhancement ofthe modified method in noisy cases.