Diffusion optical tomography reconstruction based on convex–nonconvex graph total variation regularization

Abstract

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.