Research Of The Image Restoration Problems Based On Total Variation Type Functional

Digital image processing is a treatment or technology that uses the computer tech-nique to process the image information in order to meet visual psychology and the appli-cation demand of people. Digital image processing mainly includes the related felds, suchas image enhancement, image segmentation, image restoration and image compression,etc. Image restoration is based on the degraded image and some prior knowledge, anddesigns a mathematical model, then fts degraded image to reverse the information oforiginal image as much as possible. Image inpainting is an important subject in the studyof image restoration and mainly used to reconstruct the damaged image or remove theredundant objects in the image. In this thesis, based on total variation type functional,we research on the image restoration and inpainting problems.In chapter1, we introduce the research background and present situation of thedigital image processing, image restoration and image inpainting.In chapter2, we briefy review some preliminaries, which consist of the models, theconjugate gradient method, the Chambolle projection algorithm and symbolic notation.In chapter3, we mainly discuss the image restoration method by the half-quadratictechnique to solve the bilateral constraint problems. The image pixel values usuallyrepresent physical energy of the image and are required to be non-negative in theory,we introduce the bilateral constrained TV-1model to limit the dynamic range of thepixel values. In order to make the images restored appear to be less blocky, the model issolved by the half-quadratic regularization approach and we analyze the convergence ofthe algorithm. The numerical experiments show that the algorithm is fast and efcientin restoring blurred images that are corrupted by impulse noise.In chapter4, we study the fast image inpainting algorithm based on the high-ordermodel. In allusion to the staircase efect in the fat regions of total variational modelin restoring images, in the meantime, in order to make full use of the advantages of thehigh-order model which requires much stronger smoothness and damps the oscillationsmuch faster, we frst introduce the high-order partial diferential equation into the imageinpainting, and propose the high-order image inpainting model, then use the penaltymethod and the alternating minimization algorithm to solve it. Finally, the simulation experiments and the result analysis show the superiority of our proposed model andalgorithm.