Newton-Type Algorithms For Total Variation Based Image Restoration

In the acquisition an image has been degraded by many factors, e.g., the phasedi?erence of the optical system, the atmosphere turbulence, moving, di?usion ofthe focus and the system noise, etc. The objective of image restoration is toreconstructe the original image and to preserve the key features of the image asmany as possible. Image restoration is a very important and challenging topic inimage processing, many problems associated to this topic have not been resolvedcompletely so far.This dissertation is mainly focused on Newton-type algorithms for total vari-ation based image restoration. This dissertation is divided into five chapters:Chapter 1 is devoted to giving a review of the basic concepts and historicalorigins about digital image processing, introducing the formation and the represen-tation of digital images, and giving an outline of the background and significanceof studying image restoration.In Chapter 2 some basic mathematical concepts and preliminaries are intro-duced, including bounded variation, nonsmooth convex optimization, augmentedLagrangian technique, ill-posed problem and its regularization, etc.Chapter 3 is devoted to introducing basic concepts about image restoration,generic models of image degradation, total variation-based image restoration modeland its discretization.In Chapter 4 the semismooth Newton method for image restoration is pro-posed and its convergence analysis is given. Numerical experiments show thee?ectiveness of the proposed method.In Chapter 5 the primal-dual active-set algorithm with lower computation forimage restoration is proposed. Essentially, the proposed algorithm is equivalentto a semismooth Newton method for solving a system of nonsmooth equations,so as to possess fast rate of convergence. Numerical experiments show that theproposed algorithm is indeed much fast than the method proposed in the previouschapter.Finally, we conclude and point out the subjects of future researches.