The Research And Solving Of The ILL-posed Inverse Problem In Image Restoration

Due to various inevitable factors in the course of the imaging, copying,transmission, storage, etc of the image, it will produce the occurrence of thephenomenon of degradation of the digital image. The degraded image will lost parts ofthe important information, so the obtained image and the real image differ from greatly.In real life, we need the clear image. Therefore, image restoration has importantsignificance.Image restoration problems include many aspects, such as the image restoration,the super-resolution of the image, the deblurring of the image and the denoising of theimage. The research of this thesis is about the deblurring and denoising of the image.First of all, we introduce the degradation of image restoration model, and describe thestructure of the point spread function and the special structure of the blurring matrix ofthe image restoration、the boundary conditions of the image, and common noise model.Secondly, we introduce the large ill-posed inverse problem, then do the research ofregularization method for solving the large ill-posed inverse problem. We use thecommon regularization methods such as CGLS, MINRES, Hybrid method in theprocess of recovering image. At last, we compare the advantages and disadvantages ofthe different methods.In the end of the thesis, a new image restoration solution model is used to handlethe impulse noise in the image. The method is decomposing the image into a cartoonportion and a texture portion, using different regularization methods to solve differentparts of the model. We use the ADMM to solve the new obtained model. Numericalexperiments show that the results of the new obtained model is better than the old modelin both recovery results and computation time.