Approximate Sparse Decomposition Based on Smoothed L0-Norm

In this paper, we propose a method to address the problem of source estimation for Sparse Component Analysis (SCA) in the presence of additive noise. Our method is a generalization of a recently proposed method (SL0), which has the advantage of directly minimizing the ℓ 0-norm instead of ℓ 1-norm, while being very fast. SL0 is based on minimization of the smoothed ℓ 0-norm subject to As = x. In order to better estimate the source vector for noisy mixtures, we suggest then to remove the constraint As = x, by relaxing exact equality to an approximation (we call our method Smoothed ℓ 0-norm Denois-ing or SL0DN). The final result can then be obtained by minimization of a proper linear combination of the smoothed ℓ 0-norm and a cost function for the approximation. Experimental results emphasize on the significant enhancement of the modified method in noisy cases.