Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization

TL;DR

This paper introduces a non-convex regularization approach that enhances group-sparse signal denoising by maintaining convexity of the overall cost function, leading to improved speech enhancement results.

Contribution

It proposes a novel non-convex regularization method that preserves convexity of the total cost function, improving group-sparse signal denoising without losing convex optimization benefits.

Findings

Improved SNR in speech enhancement

Enhanced perceptual quality of denoised signals

Maintained convexity for robust optimization

Abstract

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed 'overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.