Approximate Sparse Decomposition Based on Smoothed L0-Norm

TL;DR

This paper introduces SL0DN, an enhanced sparse source estimation method that relaxes constraints and improves accuracy in noisy environments by combining smoothed L0-norm minimization with denoising techniques.

Contribution

It extends the SL0 method by removing the exact constraint and incorporating denoising, leading to better performance in noisy source estimation scenarios.

Findings

Significant improvement in noisy source estimation accuracy.

Effective relaxation of the equality constraint in sparse decomposition.

Enhanced robustness of the method in noisy conditions.

Abstract

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 L0-norm instead of L1-norm, while being very fast. SL0 is based on minimization of the smoothed L0-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 L0-norm Denoising or SL0DN). The final result can then be obtained by minimization of a proper linear combination of the smoothed L0-norm and a cost function for the approximation. Experimental results emphasize on the significant enhancement of the modified method in noisy cases.