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

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