A Unified Framework for Constructing Nonconvex Regularizations

TL;DR

This paper introduces a unified framework for creating nonconvex regularizations using probability density functions and proposes a new sparse recovery method based on the Weibull distribution.

Contribution

It provides a systematic approach to construct nonconvex regularizations and introduces a novel Weibull-based sparse recovery method.

Findings

Unified framework for nonconvex regularizations

New Weibull distribution-based sparse recovery method

Improved sparse recovery performance

Abstract

Over the past decades, many individual nonconvex methods have been proposed to achieve better sparse recovery performance in various scenarios. However, how to construct a valid nonconvex regularization function remains open in practice. In this paper, we fill in this gap by presenting a unified framework for constructing the nonconvex regularization based on the probability density function. Meanwhile, a new nonconvex sparse recovery method constructed via the Weibull distribution is studied.