Variational Iteration Method for Image Restoration

TL;DR

This paper introduces the Variational Iteration Method (VIM) as a novel numerical approach to solve the Perona-Malik equation for image restoration, providing new approximations with error analysis.

Contribution

The paper is the first to apply VIM to the Perona-Malik equation, offering an alternative numerical solution with error assessment.

Findings

Effective approximate solutions obtained

Error analysis confirms method's reliability

Comparable results to existing methods

Abstract

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Through implementation of our algorithm we will access some effective results which are deserved to be considered as worthy as the other solutions issued by the other methods.