Online Program

Revisiting Convexity-Preserving Signal Recovery with the Linearly Involved GMC Penalty (308521)

Keywords: Nonconvex penalty, generalized minimax concave penalty, linearly involved convex-preserving model, split feasibility problem, saddle-point problem

The generalized minimax concave (GMC) penalty is a newly proposed regularizer which can be used for signal recovery while maintaining the convexity of the model. This paper focuses on the linearly involved GMC penalty (composing a linear operator with the GMC penalty) and the corresponding linearly involved convexity-preserving model. First, we propose a new method to set the matrix parameter in the linearly involved GMC penalty. We transform this task into a split feasibility problem and present two algorithms, CQ and ADMM, to solve this problem. In contrast to previous algorithms, both CQ and ADMM can be applied to any kind of linear operators. Then, we reconsider the linear involved GMC model as a saddle-point problem and use the PDHG algorithm to get the solution. Another important work in this paper is that we provide useful guidance on the tuning parameter selection by proving some good properties of the solution path. Finally, we apply the linearly involved GMC model to 2-D image recovery. The numerical results show that the linearly involved GMC penalty can get uniformly better estimate accuracy in comparison with the standard TV regularizer.