Algorithms For Image Decomposition And Restoration Models

We study two optimization models for image processing.For the first image decomposition model,the dual based inexact alternating direction method of multipliers(ADMM)is applied to this problem.In this problem,an image is divided into two meaningful components,i.e.,a cartoon part and a texture part.The optimization algorithm that we develop not only gives the cartoon part and the texture part of an image but also gives the restored image(cartoon part + texture part).For the second image restoration model with mixed or unknown noises,the dual based inexact ADMM is applied to the problem too.The optimization algorithm for this model is effective in restoring images contaminated by mixed or unknown noises.The global convergence and local linear convergence rate of the optimization algorithm for the two models are also given under some mild conditions in this paper.Numerical experiments demonstrate the efficiency and robustness of the two algorithms.Furthermore,we can obtain relatively higher peak signal-to-noise ratio(PSNR)value comparing to other algorithms in a shorter time.