Convexity-edge-preserving Signal Recovery with Linearly Involved Generalized Minimax Concave Penalty Function

In this paper, we propose a new linearly involved convexity-preserving model for signal recovery by extending the idea in the generalized minimax concave (GMC) penalty [Se-lesnick’ 17]. The proposed model can use nonconvex penalties but maintain the overall convexity and is applicable to much more general scenarios of signal recovery than the original GMC model. We also propose a new iterative algorithm which has theoretical guarantee of convergence to a global minimizer of the proposed model. A numerical experiment for noise suppression shows excellent edge-preserving performance of the proposed smoother in comparison with the standard convex TV smoother.