A Research On The Regularization For Image Restoration

This thesis,which does a study on the construction of regularizations for image restoration by analyzing and modeling the image prior,mainly covers two parts.In the first part,this thesis introduces that many analysis-based regularizations proposed so far employ a common prior information,i.e.,edges in an image are sparse.However,in edge regions and texture regions,this prior does not hold.As a result,the performance of regularizations based on the edge sparsity will be unsatisfactory in such regions for imagerelated inverse problems.These regularizations tend to smooth out edges while eliminating the noise.In other words,these regularizations' abilities of preserving edges are limited.In this thesis,a new prior that corner points in a natural image are sparse is proposed to construct regularizations.Intuitively,even in edge regions and texture regions,the sparsity of corner points still exists,and hence,the regularizations based on it can achieve better performance than those based on the edge sparsity.As an example,by utilizing the corner point sparsity,this thesis proposes a new regularization based on the Noble's corner measure function.The experiments demonstrate the excellent performance of the proposed regularization for both image denoising and deblurring problems,especially in edge regions and texture regions.In the second part,this thesis introduces that the Gaussian mixture model(GMM)based regularization can be regarded as a sparse representation based regularization that incorporates the strategy of classification.However,sparse representation based regularizations can only capture local features of the image patch.The recent progress in the field of image process has shown that group sparsity based regularizations,which utilizes the nonlocal similarity of natural images,can always achieve better image restoration results than sparse representation based regularizations.Inspired by this,this thesis proposes a new model,called the group sparsity mixture model,that can capture both image patches' local features and the relation among different patches,and designs a parameter estimation algorithm based on EM algorithm for this new model.Based on the group sparsity mixture model,this thesis proposes a group sparsity based regularization incorporating the strategy of classification.As the experiments show,utilizing both the classification strategy and the nonlocal similarity enables this new regularization achieve state-of-the-art performance on the image denoising task.