On The Nonmonotone Gradient Projection Algorithm For LLT Image Restoration

Image processing technique based on partial differential equation due tothe nation of PDEs and its superiority has been widely used in imagerestoration. Its study has very important theoreticalvalue and practicalsignificance. ROF model proposed by Rudin、Osher and Fatemi is regarded asa classic model in the filde of image denoising, which can be utilized to obtainthe denoised image with removing noise while preserving the edge of an image,but this model would bring the“staircase”effect in flat areas on non-piecewiseconstant intensities areas and.(the “false edges”that doesn’t exist actually). Inorder to overcome the above disadvantage, Lysaker、 Lundervold and Taipresented the four-order LLT model, which can not only preserve edges wellbut also weaken the staircasing effects.Non-monotone gradient projection algorithm has been extensivelyresearched in recent years, because of its quick convergence and higheffectiveness in the restoration of some large images, many scholars use thismethod to the more complex problems and its effectiveness is not lost. Non-monotone gradient projection algorithm uses the well-known Barzilai-Borwein stepsize instead of the fixed stepsize in the classical Chambollemethod, at the same time the adaptive non-monotone linear search is adopted toguarantee the global convergence of this method. In this thesis we will studythe nonmonotone gradient projection algorithm for the high order isotropy LLTmodel with the structure as follows:In the first chapter, we mainly introduce the development history of imageprocessing, as well as the research background、the progress and applicationadvantages on PDEs-based image restoration technology, especially thedevelopment status of image denoising. And the main work and thearrangement of chapters of this thesis are briefly presented.The second chapter is devoted to reviewing some basic mathematicalpreminary knowledge, including the bounded variation function space closelyrelated to the total variational model and the BB stepsize which has directrelationship with nonmonotone algorithms. At the same time, the evaluation criteria for the quality of image restoration are given.In the third chapter, we introduce the ROF and LLT image denoisingmodels, on the analysis of the advantages and disadvantages of these twomodels while reviewing the general algorithm of solving them.In Chapter4, the Chambolle’s dual algorithm based on LLT model isintroduced. the nonmonotone gradient projection algorithm for solving LLTmodel is proposed and the convergence of the algorithm is given.In the last chapter, the numerical experiments with algorithms mentionedin the thesis are implemented and the analyses of the experimental results arepresented. Finally, we conclude the whole thesis, analyze the feasibility andefficiency of the algorithm proposed in this thesis and point out the subjects offurther researches.