Research On Structured Sparse Representation-based Image Restoration

With the increasing development of the information technology,digital images have had a significant impact on people's daily social life,industrial production,and scientific research.The clear and high-resolution images can not only be used as the basis for image comprehension and recognition,but also provide the basis for analysis and decision making.However,in the imaging process,a variety of intrinsic or extrinsic factors,such as thermal noise,motion blur,low resolution due to the diffraction limit of light,etc.,may result in observed images with different types and varying degrees of degradation.Thus,the design of effective image restoration(IR)methods has always been a hot research topic in the field of signal processing,and has important theoretical and practical implications.However,as part of the information is lost during the image degradation process,IR problem is inherently ill-posed.Therefore,modeling image prior information that can effectively express the underlying structures of the image and using it as a regularizer to overcome the ill-posedness of IR is of great importance to restore degraded images.In recent years,structured sparse models have attracted much attention and have been successfully applied to many image inverse problems.When obtaining the sparse representation of the signal of interest using some appropriate overcomplete dictionary,this strategy imposes constraints on the selection of the basis functions(or atoms)in the dictionary;therefore,it can produce more stable results compared to the conventional sparse representation models.In this thesis,based on the structured sparse representation of natural images,we propose five IR algorithms by utilizing three different types of strategies,and the effectiveness of the suggested methods is verified through three IR applications which are image inpainting,deblurring,and super-resolution.The main contents of this thesis are detailed as follows:(1)A novel maximum correntropy criterion(MCC)based Gaussian mixture image restoration algorithm(MCC_GMM)is proposed.Since the number of similar patches in the neighborhood of an exemplar patch decay exponentially as the complexity of the patch increases,there may exist outliers within the k-Nearest-Neighbor(kNN)patches of a detailed patch.By analyzing the conventional Gaussian mixture model(GMM)based IR methods,we conclude that their objective functions can be expressed as the minimum of mean square error(MMSE)criterion based optimization problem.As the MMSE criterion is sensitive to outliers,the reconstruction error especially for the detailed patches may occur.To solve this problem,we propose a MCC based IR methods with GMM prior for image patches by replacing the MMSE criterion with the recently developed MCC criterion.The proposed method can automatically identify outliers and assign a proper weight for each kNN patch,and thus can robustly estimate the Gaussian parameters which can result in more accurate estimation of the image patches.Although we model image prior information in spatial domain,when viewed in transform domain the proposed algorithm can still be considered as a structured sparse representation-based IR strategy as the sparse representation vector shows high structural characteristics.Finally,an effective iterative optimization algorithm is designed to solve the proposed objective function under the MCC criterion.The experimental results for image inpainting demonstrate the capabilities of our proposed method.(2)A MCC based data-adaptive sparse prior algorithm(MCC_DAP)is proposed.In this work,we integrate the sparse estimation and MCC criterion into one unified framework by utilizing the powerful data-adaptive property of MCC.In the process,an automatically computed auxiliary variable is introduced to weigh differently each representation coefficient of an image patch and can serve as a threshold to shrink the coefficients towards to zero.By taking advantage of this weighing scheme,the proposed method can make the actual prior distribution of the transform coefficients sparser than the initially assigned Laplacian distribution,and more importantly,this sparsity is obtained in a data-adaptive fashion.In contrast to use a prior distribution with a significantly heavier tails than a Laplacian as the existing methods do,which usually results in a more difficult non-convex problem,the proposed objective function can be iteratively solved by alternating between two steps,both of which are convex optimization problems and thus can be computed more efficiently.The experimental results for image inpainting verify the effectiveness of the proposed method.(3)A generalized graph-based global IR algorithm(G3)is proposed in the context of nonlocal regularization.Based on the analysis of the existing nonlocal regularization methods,we find that the weights in the definition of the nonlocal difference operator play an important role in modeling image prior information.Thus,in this work,we introduce a new parametric nonlocal difference operator,which not only adds flexibility to the prior model of the clean image,but also leads to a novel parametric data-adaptive transformation matrix.Through analysis,we find that the proposed transformation matrix has a high-pass filtering nature,and its eigenvalues and eigenvectors can be considered as the graph frequencies and basis functions of the underlying undirected weighted graph which corresponds to the image under test;therefore,this transformation matrix encodes the underlying structure of the image content.Finally,a simple but effective algorithm is designed to solve the corresponding objective function,and the experimental results in the symmetric blur can verify the effectiveness of this parametric scheme.(4)Based on the parametric data-adaptive transformation matrix introduced in G3 algorithm,we propose a novel structured sparse model for IR(called SPDT).Basically,the existing structured sparse representation based methods can be categorized into two classes: performing patch clustering on lots of external data to model image patch prior,or exploiting the nonlocal similarities in natural images to find similar grouped patches within the image under consideration.For the former case,the learned model from the external training data may not be able to adapt to the current image.And for the latter one,as the number of the similar patches for each exemplar patch within a spatially constrained window decay exponentially as the complexity of the patch increases,these methods may not produce satisfactory results for the detailed patches due to the lack of a sufficient number of similar patches.Therefore,as an alternative strategy,we directly focus on the underlying structure representation of an image patch,and model image prior information by taking advantage of the sparse nature of responses of the data-adaptive filters(i.e.,the proposed parametric data-adaptive transformation matrix).Finally,an effective optimization algorithm is designed to solve the corresponding sparse inverse problem.Extensive experimental comparisons with state-of-the-art image deblurring and super-resolution algorithms validate the effectiveness of our proposed method.(5)A local spatial adaptation image prior based structured sparse model(LSAP)for IR is proposed.The traditional sparse representation methods assume that the overlapping patches are independent from each other and thus do not take into consideration the dependency of the representation coefficients of the patches in an image.To address this issue,the existing simultaneous sparse coding based methods usually encourage the representation coefficients of the nonlocal similar patches to admit the same generalized Gaussian distribution with some hand-selected shape parameter.Since different image texture region may possess different statistical characteristics,it is inappropriate to impose a single image prior distribution everywhere in the image.Therefore,in this work,by taking advantage of the expressiveness of generalized hyperbolic(GH)distribution,we assume that the representation coefficients of nonlocal similar patches on the same dimension follow a GH distribution with the shared shape and scale parameters but varying at different image spatial location.Utilizing the proposed Bayesian variational inference algorithm,we can jointly estimate the sparse representation coefficients and the unknown parameters in the prior distribution from the limited local spatial information.Finally,an effective iterative algorithm is designed to solve the corresponding optimization problem,and the numerical results demonstrate the performance of the proposed method.