A Class Of Image Restoration Based On TV Model With The Method Of Optimization

The aim to repair the damaged part of an image is always based on the continuitywith the surrounding. In a statement, image restoration is an artistic synonym of imageinterpolation. Interpolation plays an extremely important role in these areas, such as theapplication of partial differential equations, numerical analysis theories, signal theoriesand so on. We know，nowadays，the software such as Adobe Photoshop or GIMP needto be executed with “manual” operation as a weak point to meet the relevantrequirements in image restoration. Since first used in image restoration, it was beentoken seriously by experts all the world as the advantages of convenient，then beenaccepted by people quickly. If the interpolation is used to process images, there will beconvenient to choose the area to restore. The computer can be able to finish the rest ofthe task, thereby significantly reduce the occupied time to improve work moreeffectively.The knowledge of partial differential equations is a part of theories about thefoundation of image restoration. The bounded variation (BV) function space is alwaysconsidered as the reasonable function space in dealing with non-texture image. Thebasic theories in variational method provide a good foundation as the bottom of visualanalysis and image restoration. The model in total variation (TV) function is the classicmodel in image restoration commonly applied in the BV space，and it usually use thetechnology in the total variation minimization to optimize image restoration to improvethe visual effect on image restoration.Although the traditional method of the TV model in the processing of textureimage has its own advantages，it also can easily to create the effect of staircase in asmooth region. Dealing with these problems, the thesis uses the application of the TVmodel in image restoration as the main object of study. The main contents:1. The TV model should be analysised in-depth to derive optimization model, inorder to find out the related condition on partial differential equations which can beapplied to optimize the image restoration. 2. Prove the TV model in the theories of partial differential equations to derive thelimitation in related theories. Then take the experiment in the two-dimensionalinterpolation direction, observe whether reduce the staircase effect, and arrival at aconclusion on the actual application and operation in TV model.