Revisiting convexity-preserving signal recovery with the linearly involved GMC penalty

The generalized minimax concave (GMC) penalty is a newly proposed regularizer that can maintain the convexity of the objective function. This paper deals with signal recovery with the linearly involved GMC penalty. First, we propose a new method to set the matrix parameter in the penalty via solving a fea-sibility problem. The new method possesses appealing advantages over the existing method. Second, we recast the linearly involved GMC model as a saddle-point problem and use the primal-dual hybrid gradi-ent (PDHG) algorithm to compute the solution. Another important work in this paper is that we provide guidance on the tuning parameter selection by proving desirable properties of the solution path. Finally, we apply the linearly involved GMC penalty to 1-D signal recovery and matrix regression. Numerical re-sults show that the linearly involved GMC penalty can obtain better recovery performance and preserve the signal structure more successfully in comparison with the total variation (TV) regularizer. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The paper introduces a newly proposed regularizer called the generalized minimax concave (GMC) penalty, which maintains the convexity of the objective function. The paper focuses on signal recovery with the linearly involved GMC penalty and presents a new method for setting the matrix parameter and solving the penalty. The paper also analyzes the desirable properties of the solution path and applies the linearly involved GMC penalty to 1-D signal recovery and matrix regression, demonstrating its superior performance compared to the total variation (TV) regularizer.