Traditional 1 -regularized compressed sensing magnetic resonance imaging (CS-MRI) model tends to underestimate the fine textures and edges of the MR image, which play important roles in clinical diagnosis. In contrast, the convex nonconvex (CNC) strategy allows the use of nonconvex regularization while maintaining the convexity of the total objective function. Plug-and-play (PnP) algorithm is a powerful framework for sparse regularization problems, which plug any advanced denoiser into traditional proximal algorithms. In this paper, we propose a PnP-ADMM algorithm for CS-MRI reconstruction with CNC sparse regularization. We first obtain the proximal operator for CNC sparse regularization. Then we present PnP-ADMM algorithm by replacing the proximal operator of ADMM with properly pretrained denoisers. Furthermore, we conduct comparison experiments using various denoisers under different sampling templates for different images. The experimental results verify the effectiveness of the proposed algorithm with both numerical criteria and visual effects.

Graph total variation (GTV) is a powerful regularization tool for diffuse optical tomography (DOT) reconstruction since it combines the powerful representation ability of graph and the edge-preserving ability of total variation (TV) regularization. However, as everyone knows, the classical TV regularization trend underestimates the large edge values. In this paper, we propose a convex-nonconvex graph total variation (CNC-GTV) regularization for DOT reconstruction. In particular, we construct a nonconvex regularization by subtracting the generalized Huber function from the GTV regularization. We show that the global convexity of the objective function can be guaranteed by adjusting the nonconvex control parameters. Moreover, we present an alternating direction multiplier method (ADMM) to solve the proposed DOT reconstruction model. Numerical experiments show that the proposed model outperforms existing models in visual and numerical results.