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.

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

“…The techniques for constructing the smoothed version of the convex sparse regularizer include but are not limited to Moreau envelope [16,28], Nesterov's smoothing [29], and infimal convolution smoothing [30]. CNC sparse regularization has shown excellent performance in signal denoising [24,31], medical image reconstruction [32][33][34][35], fault diagnosis [36,37], and other fields.…”