Convergence Analysis of a Finite Difference Scheme for the Gradient Flow associated with the ROF Model

TL;DR

This paper analyzes the convergence of a finite difference scheme for the gradient flow related to the ROF model, providing theoretical proof and computational validation for image denoising applications.

Contribution

It introduces a convergence analysis and iterative algorithm for the finite difference scheme solving the gradient flow of the ROF model, with demonstrated effectiveness.

Findings

Proved convergence of the iterative algorithm.

Validated the scheme through computational experiments.

Applied the method to image denoising tasks.

Abstract

We present a convergence analysis of a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fatemi model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme. An application for image denoising is given.