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

In recent years,with the rapid changes in the field of information exchange,the image has become an indispensable form of information dissemination.However,in the processes of collection,transmission and so on,the image can be easily interfered by a variety of factors,which may result in the reduction of image quality.In order to solve this problem,image restoration has become a new kind of technology which can restore the low quality image to the high quality image,and it has been widely applied in various disciplinary fields.Among all of the techniques of image restoration,due to the application of mature mathematical theory,the partial differential equations method has become an important method to restore the image and has been widely accepted by the researchers.Therefore,this thesis aims to study the two important branches of image inpainting and denoising based on the partial differential equations theory,and applies the denoising image quality assessment to the optimal selection of denoising algorithm.The main contents of the study include:Based on the analysis of the existing classical inpainting model,due to the characteristics of its iterative convergence is slow resulting in a long time to inpainting,since the block energy operator can be simply acchieved and can accurately reflect the image feature,which can distinguish the image flat and texture area well,thus,the block energy operator is applied to the adaptive diffusion coefficient design of the inpainting model,and a total variational image inpainting model based on the local block energy operator is established.The result of the experiments show that the model has the advantage of faster iterative convergence than the existing classical inpainting model.Based on the analysis of harmonic model and local differential curvature denoising model,aiming at the deficiency of the local differential curvature model in distinguishing the image corner and flat area,a hybrid denoising model will be studied based on the idea of local difference curvature model to distinguish between image corner and flat area,introducing weight function and mixed model.The model can better distribute the diffusion coefficient of the image flat,the edge and the corner region,and makes a balance between the removal of the image noise and the maintenance of the detail information.Experiments show that compared with the existing classical image denoising model,the model has significant denoising effect on subjective and objective evaluation,especially when the noise intensity is moderate or strong.The noise type and intensity of the images collected in real life are generally unknown,and there isn't any original image can be used as a reference.Inspired by the image denoising algorithm,the existing denoising algorithms are mostly specific,which have good effect for one or several kinds of noise,but can not be applied to all kinds of noise or all kinds of noise with different intensity.Because the local structure tensor has the characteristic of reflecting the geometrical structure of the image,the relationship among the tensor eigenvalues is used to measure the image noise intensity.A no-reference denoising image quality assessment algorithm based on the local structure tensor is studied and applied in the method optimal selection of denoising algorithm.Experiments show that the method can effectively evaluate the performance of the denoising algorithm and obtain a better denoising image,which is of great practical value.