Research On Magnetic Resonance Image Reconstruction Based On Sparse Representation And Nonlocal Similarity

As a noninvasive imaging technique,magnetic resonance imaging（MRI）can provide high resolution anatomical structures with no ionizing radiation.However,a long scanning period is usually required to obtain fully sampled k-space data,which seriously limits the application and development of MRI.Compressed sensing theory makes it possible to exactly recover a sparse signal from far fewer measurements than those required by Nyquist sampling theorem.Applying compressed sensing theory to MRI can greatly reduce the scanning time of imaging process through highly undersampling k-space data,but it renders the image reconstruction from undersampled k-space data an ill-posed inverse problem.Since the signal with high sparsity can achieve less error in compressed sensing reconstruction,a proper sparse representation of MR image is vital to high-quality reconstruction.Conventional MR image reconstruction methods use fixed transforms to sparsely represent images,but lead to insufficient sparsity of image coefficients as well as limited reconstruction performance.For the sake of sparser representations of realistic images with various structural features,patch-level sparse representation model can learn dictionaries or transforms from abundant patches extracted by the reconstructed image itself,thereby realizing adaptive sparse representations of images along with better reconstruction results.In addition,as a common prior existing in images,the nonlocal similarity can be exploited to construct the associated regularization constraints,which are integrated into the sparse representation of images to further achieve significant improvement in the quality of reconstructed images.The problem of compressed sensing reconstruction of undersampled MR image is studied in this dissertation.Specifically,the adaptive sparse representation and nonlocal similarity are explored to build image reconstruction models.Furthermore,efficient numerical optimization algorithms are designed to stably obtain high-quality reconstructed images.The main research contents of this dissertation are shown as follows:（1）A MR image reconstruction method based on sparse representation of classified patches is proposed.Regarding the insufficient sparsity of image coefficients under fixed transforms,the proposed reconstruction model divides the patches of the image to be reconstructed into multiple classes according to local features,and then learns an orthogonal dictionary from the patches in each class for adaptive sparse representations of them.On the other hand,since the common sparsity based regular functions are difficult to meet the feasibility of accurate optimization and the strong sparsity constraint on image coefficients at the same time,a nonconvex regular function that approximates l₀ norm is used to fully constrain the sparsity of image coefficients.Besides,in the case that the parameter of nonconvex regular function takes special value,a fast shrinkage operator is derived to speed up the solution of sparse coding in the reconstruction algorithm.Experimental results show that the proposed method achieves better reconstruction performance than the existing reconstruction methods based on patch-level sparse representation under learned dictionaries.（2）A MR image reconstruction method based on orthogonal dictionary and group sparsity is proposed.Adaptive patch-level sparse representation models usually lead to independent sparse coding of each patch,but fails to utilize the nonlocal similarity in images.In order to exploit both sparsity and nonlocal similarity in images,the proposed reconstruction model uses the same orthogonal dictionary to sparsely represent the similar patches of the image to be reconstructed,further enforces their coefficients to be sparse and share the same sparse profile through a nonconvex mixed norm.Furthermore,it is proposed to learn one orthogonal dictionary from each set of similar patches to improve the reconstruction model.Meanwhile,the proposed sparse representation model for similar patches under the optimal learned orthogonal dictionary is proved to be equivalent to the low rank model for the matrix formed by similar patches.Experimental results show that the proposed method yields better reconstructed image quality than the main reconstruction methods.（3）A MR image reconstruction method based on analysis dictionary and manifold structure constraint is proposed.In conventional synthesis sparse representation,dictionary learning involves an optimization problem with high complexity.In order to efficiently learn dictionary,the proposed reconstruction model adopts the analysis sparse representation model to learn one overcomplete analysis dictionary from patches,and imposes a certain constraint on it to prevent scaling ambiguity and limit correlations among internal bases.On the other hand,the common regular functions are difficult to maintain different degrees of similarity among similar patches in different regions of realistic images.Therefore,a weighted graph is used to characterize the different correlations among similar patches,by which the corresponding manifold structure constraint is constructed and integrated into the reconstruction model to precisely preserve the correlations among similar patches.Experimental results show that the proposed method obtains higher quality of reconstructed images than the existing reconstruction methods based on dictionary learning and nonlocal similarity.