The use of discrete gradient methods for total variation type regularization problems in image processing

TL;DR

This paper explores the application of discrete gradient methods, known for preserving system dissipation, to enhance total variation regularization techniques in image processing tasks like deblurring, denoising, and inpainting.

Contribution

It introduces the use of discrete gradient methods for TV regularization in image processing, demonstrating their effectiveness through experimental results.

Findings

Discrete gradient methods effectively preserve dissipation in TV regularization.

Improved image quality in deblurring, denoising, and inpainting tasks.

Potential for better numerical stability and accuracy.

Abstract

Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing tasks. We promote the use of discrete gradient methods in image processing by exhibiting experiments with nonlinear total variation (TV) deblurring, denoising, and inpainting.