Performance of Restarted Homotopy Perturbation Method for TV-Based Image Denoising Problem

Yu Du Han,Jae Heon Yun

doi:10.1155/2015/207541

Abstract

We first propose a restarted homotopy perturbation method (RHPM) for solving a nonlinear PDE problem which repeats HPM process by computing only the first few terms instead of computing infinite terms, and then we present an application of RHPM to TV- (Total Variation-) based image denoising problem. The main difficulty in applying RHPM to the nonlinear denoising problem is settled by using binomial series techniques. We also provide finite difference schemes for numerical implementation of RHPM. Lastly, numerical experiments for several test images are carried out to demonstrate the feasibility, efficiency, and reliability of RHPM by comparing the performance of RHPM with that of existing TM and recently proposed RHAM methods.

Highlights

Digital images generated by various digital devices or used in practical applications usually contain some noises, so denoising is necessary before analyzing the images [1]
We first propose a restarted homotopy perturbation method (RHPM) for solving a nonlinear PDE problem which repeats HPM process by computing only the first few terms instead of computing infinite terms, and we present an application of RHPM to TV- (Total Variation-) based image denoising problem
We proposed a restarted homotopy perturbation method (RHPM) for solving a nonlinear PDE problem, and we presented an application of RHPM to TV-based image denoising problem

Summary

Introduction

Digital images generated by various digital devices or used in practical applications usually contain some noises, so denoising is necessary before analyzing the images [1]. Rudin et al [9] used a nonlinear parabolic PDE (Partial Differential Equation) as a solution procedure for solving the Euler-Lagrange equation arising from the TV-based denoising model and proposed TM (Time Marching) method for solving the nonlinear parabolic PDE This model is found to be a successful tool for image denoising and edge enhancement. Ghanbari et al [27] proposed RHAM (restarted homotopy analysis method), based on HAM [28], for a nonlinear denoising model problem, which is a main motivation for this paper. The purpose of this paper is to propose a restarted homotopy perturbation method (RHPM), based on the HPM, for solving a nonlinear PDE problem and to apply RHPM to the TV-based image denoising problem.

Review of TM Method for TV-Based Image Denoising Problem

Application of RHPM to TV-Based Image Denoising Problem

Numerical Experiments

Findings

Conclusion