Algorithmic Versatility of SPF-regularization Methods

TL;DR

This paper explores the use of nonconvex sparsity promoting functions in optimization models, developing algorithms that leverage their structure, and demonstrates their effectiveness in image denoising tasks.

Contribution

It introduces nonconvex SPF-based models and algorithms, moving beyond traditional convex approaches for improved sparsity promotion.

Findings

Nonconvex SPFs can outperform convex SPFs in denoising tasks.

Algorithms exploiting nonconvex SPF structures are effective.

Simulations show enhanced image denoising performance.

Abstract

Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are assumed or desired to be sparse in some basis. For example, the l1-regularized variation model and the Rudin-Osher-Fatemi total variation (ROF-TV) model are some of the most well-known variational models for signal and image denoising, respectively. However, recent work demonstrates that convexity is not always desirable in sparsity promoting functions. In this paper, we replace convex SPFs with their induced nonconvex SPFs and develop algorithms for the resulting model by exploring the intrinsic structures of the nonconvex SPFs. We also present simulations illustrating the performance of the SPF and the developed algorithms in image denoising.