Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
This work addresses signal denoising for applications like speech enhancement, offering an incremental improvement over existing convex and non-convex methods by combining their strengths.
The paper tackles the problem of denoising group-sparse signals, such as in speech enhancement, by proposing a method that uses non-convex regularization to promote sparsity more strongly than convex approaches while maintaining convex optimization benefits, resulting in improved SNR and perceptual quality.
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.