Higher order operator splitting methods for an image de-noising model

Sant P Chawla ,Noor Badshah ,Fazal Ghafar ,Amir Khan ,Abdul Salam

doi:10.28919/jmcs/3312

Abstract

This paper is concerned with fast iterative methods with development of Euler-Lagrange equation which results from the minimization of Rudin-Osher-Fatemi (ROF) model. There are many applications of image de-noising in field of medical and astronomy. We can classify the image de-noising models into additive and multiplicative noise removal models. In case of additive noise, we have an image u corrupted with additive Gaussian noise η, the main task is to recover u from the image formation model u0 = u+η. This paper mainly focus on additive noise removal. Here semi-implicit (SIM), additive operator splitting (AOS) and additive multiplicative operator splitting (AMOS) type schemes are developed. The quality in AOS is, it treats with all coordinate axes in an equal manner. We develop a new AMOS scheme for the solution of Euler-Lagrange equation arisen from minimization of image additive noise removal model. Comparison of AMOS with SIM and AOS is also presented. Experimental results shows that by using AMOS, additive noisy image can be de-noised with best results. Numerical examples are given to show gain in CPU timing and fast convergence of AMOS-based algorithm. https://doi.org/10.28919/jmcs/3312

Highlights

In the field of image processing, image de-noising is a significant and an extraordinary field for last decades
We develop a new additive multiplicative operator splitting (AMOS) scheme for the solution of Euler-Lagrange equation arisen from minimization of image additive noise removal model
Results of experiments are given to compare the performance of AMOS with additive operator splitting (AOS) and SIM

Summary

Introduction

In the field of image processing, image de-noising is a significant and an extraordinary field for last decades. Through image de-noising, image is reconstructed by removing noise from a corrupted image. The noise removal method is designed in such a way that it suppresses the noise and preserves many image structures. The actual meaning of noise is an unwanted signal. Signals are the unwanted electrical fluctuations which are received by AM radios. Noise in images is a random variation of colour or brightness, it is a cause of sensor and circuitry of a digital camera or scanner. We can not avoid the noise in images. In image de-noising our main focus is on the development of such filters which maintains the compromise between the noise and the image. We consider the following image formation model (1)

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Conclusion