The use of discrete gradient methods for total variation type regularization problems in image processing
For researchers in image processing, this work introduces a numerical integration approach that ensures dissipation preservation, though it is an incremental application of existing methods to known problems.
The paper applies discrete gradient methods from geometric numerical integration to nonlinear total variation regularization for image deblurring, denoising, and inpainting, demonstrating that these methods preserve dissipation and yield stable solutions.
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.