Unrolling Nonconvex Graph Total Variation for Image Denoising

TL;DR

This paper introduces a novel non-convex graph total variation regularization for image denoising, ensuring convexity of the overall objective and enabling efficient optimization and learning.

Contribution

We propose a non-convex graph total variation term with a new graph Huber function, ensuring convexity and enabling a lightweight, data-driven denoising method.

Findings

Outperforms unrolled GTV and other denoising schemes

Uses fewer network parameters

Achieves superior denoising quality

Abstract

Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable as a Moreau envelope. The crux is the selection of a parameter $a$ characterizing the graph Huber function that ensures overall objective convexity; we efficiently compute $a$ via an adaptation of Gershgorin Circle Theorem (GCT). To minimize the convex objective, we design a linear-time algorithm based on Alternating Direction Method of Multipliers (ADMM) and unroll it into a lightweight feed-forward network for data-driven parameter learning. Experiments show that our method outperforms unrolled GTV and other representative image denoising schemes, while employing far fewer network parameters.