Research On Image Recovery Technology Via Nonconvex Regularization Method

Image recovery problem has been widely found in signal processing,computer vision and biomedical science,etc.The latent high-quality images can not be obtained from the observations by simple inverse-operation because of the ill-posedness of the observation model.Accordingly,image recovery technology has been developed in this instance.As an efficient method for solving ill-posed problem,regularization method has been ubiquitous for image recovery nowadays,which can ensure the fidelity term and restrict the solution space via modeling appropriate regularizer.After deeply analyzing and summarizing current image recovery works,this dissertation mainly focuses on efficient methods for image recovery problems based on both the prior information of image and the nonconvex sparse and low-rank theory.The main contributions of this dissertation are listed below.Firstly,a novel nonconvex-regularized method via multiple-sub-dictionaries based sparse transform(MST)is proposed for image compressive sensing reconstruction.Most of conventional orthogonal dictionary based approaches can not exploit sparse prior of image sufficiently,since atoms in this transform system must be orthogonal each other and lack diversity.To address this problem,multiple orthogonal sub-dictionaries are constructed to provide more atoms for better sparse transform,and the nonconvex-norm is utilized to address the bias problem caused by₁-norm.The adaptive scheme of regularization parameter is proposed to choose the best sparsifying transform sub-dictionary and exploit the difference of sparsity as prior knowledge for optimization.More importantly,two effective and efficient algorithms are proposed for minimizing MST-based on generalized iterative shrinkage algorithm(GISA)and iteratively reweighted₁-norm(IRL1)minimization.Secondly,a nonconvex_1?2 regularized method via tight framework based sparse transform(TST)is proposed for CS-MRI problem.Most of conventional CS-MRI reconstruction approaches usually suffer from higher dimension transform coefficients and the invertibility caused by redundant-dictionary.It is intractable for CS-MRI to design efficient reconstruction model and fast imaging algorithm.For these reasons,this thesis employs a more efficient tight framework for sparse transform,which can exploit sparse prior knowledge of MR image better.Meanwhile,the proposed method utilizes the nonconvex_1?2-norm to promote the sparsity that is able to achieve more superior performance and produce the closed-form solution efficiently.Benefiting from the pseudo-inverse matrix of tight framework,an effective and fast projected-iterative half thresholding(Fast-PIHT)algorithm is proposed for nonconvex analysis sparse recovery problem.Thirdly,a novel plug-and-play method is proposed based on group-matrix sparse coding(GSC)for generalized image compressive reconstruction problem.Most of conventional reconstruction approaches for noise-corrupted compressive measurements usually suffer from two shortcomings.First,the sparsity model destroys the important structural information and often can not exploit prior knowledge sufficiently.Second,most current group-matrix based reconstruction models fail to consider the corruption of impulsive noise.To rectify these problems,a novel plug-and-play reconstruction framework is built to split the original reconstruction problem into“reconstruction operator”and“denoising operator”by variable splitting technology.For“reconstruction operator”,the popular₂-norm and Welsch-M estimator are employed for data fitting model,respectively.For“denoising operator”,the methodology of GSC will be utilized to exploit local sparsity and nonlocal self-similarity simultaneously.Both a family of nonconvex rank relaxations and the iteratively weighting strategy are employed for nearly unbiased approximation.Furthermore,an iteratively reweighted nuclear norm(IRNN)minimization method is developed for efficient approximation of group matrix.Fourthly,a nonconvex low-rank regularization method is proposed for image restoration problem based on group-matrix denoising model.Traditional low-rank minimization approaches only exploit the NSS properties but neglect the sparsity of group-matrix,and therefore the sparse coding of group-matrix and low-rank minimization can not be unified into current image restoration framework efficiently.For these reasons,a low-rank minimization based denoising(LRGD)model is proposed to build the theory connection between the sparse coding and the low-rank approximation for group-matrix using an adaptive group-matrix dictionary.Furthermore,a weighted nonconvex rank relaxation is employed for more accurate solution of LRGD.Then this novel denoising model is integrated into image restoration problem via alternating direction method of multipliers(ADMM),in which the sparse coding and low-rank minimization of group-matrix can be unified into image restoration.