A Unified Framework for Constructing Nonconvex Regularizations
This addresses a practical gap in sparse recovery for researchers and practitioners, though it appears incremental as it builds on existing nonconvex methods.
The paper tackles the problem of constructing valid nonconvex regularization functions for sparse recovery, presenting a unified framework based on probability density functions and introducing a new method using the Weibull distribution.
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.