A Residual Solver and Its Unfolding Neural Network for Total Variation Regularized Models

TL;DR

This paper introduces a novel residual solver and its unfolded neural network for efficiently solving Total Variation regularized models, demonstrating superior performance in image processing tasks.

Contribution

The paper develops a new iterative residual solver and its neural network version, providing theoretical guarantees and practical effectiveness for TV regularized models.

Findings

Achieves the same global optimal solutions as classical methods

Unsupervised neural network performs effectively on various image tasks

Generalizable approach applicable to other TV regularized models

Abstract

This paper proposes to solve the Total Variation regularized models by finding the residual between the input and the unknown optimal solution. After analyzing a previous method, we developed a new iterative algorithm, named as Residual Solver, which implicitly solves the model in gradient domain. We theoretically prove the uniqueness of the gradient field in our algorithm. We further numerically confirm that the residual solver can reach the same global optimal solutions as the classical method on 500 natural images. Moreover, we unfold our iterative algorithm into a convolution neural network (named as Residual Solver Network). This network is unsupervised and can be considered as an "enhanced version" of our iterative algorithm. Finally, both the proposed algorithm and neural network are successfully applied on several problems to demonstrate their effectiveness and efficiency, including image smoothing, denoising, and biomedical image reconstruction. The proposed network is general and can be applied to solve other total variation regularized models.