Study On Image Restoration Algorithm And Partial Differential Equations Based On Texture Synthesis

The image restoration, which is the foundation of image processing problem, including image denoising and image inpainting, is one of the most basic research contents in image processing. It means a lot in the domain of theory and practice. Since1990s, image restoration algorithm based on partial differential equations which has been developed. Compared with the traditional algorithms, it has a better theoretical basis and stable performance.We introduce the background, significance, researching status at home and abroad and basic theories of image restoration in the first part. We present some classic models of image restoration. And we present two kinds of algorithms which based on partial differential equations in the domain of image denoising of image restoration in this dissertation. First, we analyse the characteristic of the ROF model and harmonical model and calculcate the form of the numerical discretization. Second, by exploiting the local features of the image, the ability of the ROF model in denoising completely, protecting image edges and producing "ladder effect" for processing image smoothing areas, the ability of the harmonical model in denoising incompletely, blurring image edges and overcoming the "ladder effect" for processing image smoothing areas, and the advantages of the Laplacian operator in enhancing edges, the first image denoising model, RHL was proposed. And we designed and implemented the RHL algorithm. Addition, syncretizing the characteristics of the image inpainting model which can remove salt and pepper noise, we proposed the second model RHI on the basis of the proposed RHL model. And we designed and implemented the RHI algorithm. Through a large number of experimental simulation, the results show that the proposed two algorithms, RHL and RHI, have better performance in terms of visually and quantitatively than other algorithms, which combine the advantages of the ROF model and harmonical model in image denoising effectively. Compared with other PDE based algorithms, our proposed two algorithms can better remove noise, protect smooth regions and edge information much better.In this dissertation, we propose two kinds of algorithms, which based on partial differential equations and texture synthesis in the region of image inpainting of image restoration. The traditional image inpainting algorithms based on partial differential equations applies to repair the image with cracks and stains. Compared with the algorithms based on texture synthesis, they have not a satisfactory result for the area of big-scale defect, defect area width is greater than repaired area width and containing rich texture information. To solve these problems, image inpainting algorithms based on texture synthesis is better able to repair these areas. Therefore, in this paper, we present an improved adaptive image inpainting algorithm based on texture synthesis. This algorithm performs a task through the best-first inpainting strategy based on priority defined to each boundary pixels. The priority computation is biased toward these areas which contain a wealth of know information and structure information. So that these areas with texture and structure information is repaired firstly. Meanwhile, this algorithm overcome the difficult problems of the inpainting algorithm based on texture synthesis searching the optimal matching block globally easily causes some matching errors. In addition, to further improve the effect of image inpainting, this algorithm assigns the size of repaired pixel block based on the local characteristics of image. Taking into account the image includes various types of repaired areas and single-layer inpainting algorithms can not be satisfied with the effect of inpainting, this paper presents a new image multi-level-inpainting algorithm based on partial differential equation and texture synthesis. This algorithm repairs image by using the inpainting algorithms based on partial differential equations in the first place and then deals with unsatisfied areas by using the inpainting algorithms based on texture synthesis. The experimental results show that the two kinds of algorithms in this paper improve the quality of image inpainting.