Research On Image Restoration Model Based On Fractal-dictionary Coding And Weighted Nuclear Norm

With the development of science and technology and the popularization of the Internet,society has gradually entered the digital age.Image,as the most direct way for people to perceive the world,also plays an important role in the digital age.But when digitalizing,images are often degraded due to the process of production,transmission and reception,which makes people unable to obtain the real information in images,and different factors result in different types of noise.Therefore,more and more people are studying image restoration,especially image denoising.The most common noise in natural images is additive white Gaussian noise.The common noise in Magnetic Resonance Imaging(MRI)is Rician noise,due to its imaging principle.In this paper,the two kinds of noise are briefly introduced,and the corresponding denoising models are proposed,which are as follows:(1)For the additive white Gaussian noise in natural image,A Dictionary Learning Approach for Fractal Image Coding is proposed.This model introduces sparse representation with dictionary on the classical fractal coding,which makes the model not only have the compressibility of fractal coding,but also have the effectiveness of sparse dictionary representation to remove noise.The model consists of three parts: fidelity term,fractal coding term and sparse representation with dictionary term.For this model,we also propose a three-step algorithm to solve the model.Experiments show that the model can not only effectively remove the noise in the image,but also compress the image.(2)With the wide application of MRI,more and more people are studying Rician noise removal in MRI.In view of Rician noise,this paper proposes Rician Noise Removal via the Weighted Nuclear Norm Penalization for MRI noise removal.This model is improved on the MAP model,and uses the weighted nuclear norm term as a regular term instead of TV regular term in the original model.In order to solve the new model conveniently,we introduce the Clarke subdifferential and apply the first IRSVM algorithm to solve the model.Experiments are carried out on natural and medical images respectively.The experimental results show that the proposed model can remove noise more effectively than the current efficient model.