Research On Image Restoration Technology Based On The Theory Of Partial Differential Equations

In Modern society, the development of the information industry and technologyis rapid. Image is an important medium for human to obtain the information. However,the image is destroyed inevitably during imaging, copying, transmission and so on.Such as image information is polluted by noise. The high-quality images arenecessary in many areas. So the image restoration is a very important task.The focus of this paper is mainly around the technology of digital imagerestoration. The method used is the theory of partial differential equations. Partialdifferential equation is an important mathematical tool and has well anisotropicdiffusion properties for image processing. The so-called image restoration is to repairthe defect or remove the noise by the known information of the image, which belongsto the Bayesian prior probability and contains image inpainting and denoising.Because the information contained in image is very complex and includes both thetexture and structure. One restoration method could not solve multifarious imageproblems. Based on the types of the known information, this paper is divided intolocal and global image restoration. The main work in this paper is summarized asfollows:1. From the mathematical perspective, the inpainting model based on totalvariation is analyzed in the local coordinate system. An adaptive model is proposed todiffuse information flexibly according to the image properties, meanwhile it avoidsthe staircase effect. An image inpainting based on the Poisson equation is proposedfor repairing the gradient field of the image. This algorithm first repairs the gradientfield, then solves Poisson equation to recover the complete image.2. The parameters in regularization term and fidelity term of the classicaldenoising model is analyzed. And the ability of the denoising model is improved bymodifying the parameters. Based on the property of the regularization term, somepreviously well-known models are analyzed. A unified framework is proposed forimage denoising. A coupled model is proposed by introducing a new couplingoperator and the scale factor, which has edge preservation and fast convergence.3. An exemplar based image inpainting method is proposed for repairing largeregion of complicated image. This model improves image sampling and matchingtechnology. Based on the non-local operators, a global TV model is proposed forinpainting texture image. This paper compares the texture extraction of the two models which have two different fidelity terms, and a more suitable model for textureimage is proposed.The first and second items are image inpainting and denoising based on localinformation respectively. Some appropriate solutions are put forward to repair smallstructural defects and remove noise. The third item is image restoration based onglobal information. It does well in texture image restoration.