Research On Highly Undersampled Magnetic Resonance Image Reconstruction Based On Multiscale Geometric Analysis And Dictionary Learning

Magnetic Resonance Imaging (MRI) is a non-invasive imaging modality with the superiority of excellent soft tissues contrast and no ionizing radiation. However, slow imaging speed, which is essential to many of the MRI applications, remains a major challenge. Imaging speed can be improved by faster collection of data. Undersampling is a commonly used method to reduce the amount of acquired data and the scan time, which may result in quality degradation of MR images and compromises its diagnostic value. In this sense, accurate reconstruction from highly undersampled κ-space data is of great necessity for both fast MR image acquisition and clinical diagnosis. Compressed sensing (CS) theory, as a newly developed methodology, has provided a new way for fast MR imaging and shown great potential in reducing data acquisition time in MRI. As a prerequisite in CS, sparsity or compressibility plays an important role to improve the image quality.Given to some deficiencies of existing predefined sparsifying transform and single-scale dictionary in image domain for CS-MRI application, this thesis discusses the two key problems, which are to seek the optimal sparse prior and to explore the effective numerical algorithm for the reconstruction optimization suitable for the corresponding sparsifying models. Based on CS theory, this thesis studies how to reconstruct MR images with clinical diagnostic quality from undersampling κ-space data to speed up imaging and proposes improved methods in order to achieve higher reconstruction quality.The main contents of this thesis are as follows:1. In order to overcome the deficiencies of the present sparse transform employed in the CS-MRI reconstruction, a novel MRI reconstruction method from highly undersampled κ-space data using Non-Subsampled Shearlet transform (NSST) sparsity prior is proposed. Considering anisotropic characteristics existing in MR images and the accuracy of reconstruction, we have implemented a flexible decomposition with an arbitrary even number of directional subbands at each level using NSST for MR images. The highly directional sensitivity of NSST and its optimal sparse approximation properties lead to better capture of inherent characteristics and improve the quality of reconstruction images. The effective iterative soft thresholding algorithm is exploited to the numerical solution of corresponding optimization problem. Experimental results over the real-value and complex-value data of the phantoms and the human brain in vivo demonstrate that the proposed method results in the high-quality reconstruction, which is highly effective at preserving the intrinsic anisotropic features of MRI meanwhile suppressing the artifacts and added noise. In addition, the reconstruction quality exploiting the proposed method outperforms significantly comparing methods with respect to objective evaluation indices and subjective vision effect. In summary, NSST is very competitive in CS-MRI applications as sparsity prior in terms of performance and computational efficiency.2. Given to lack of adaptability for predefined sparsifying transform, based on the adaptive dictionary learning CS-MRI framework, corresponding to patch-sparsity of dictionary learning, constrained split augmented Lagrangian shrinkage algorithm (C-SALSA) is extended in order to solve the reconstruction model effectively. The extended algorithm is suitable for sparsifying structure of patch-based dictionaries. Considering CS-MRI reconstruction model by dictionary learning, data fidelity in k-space and the total fitting error of all image patches with respect to the dictionary are jointly served as the goal of minimization, subject to patch sparsity constrains. The two procedures of training sparsifying dictionary and reconstruction are implemented alternately. Experimental results under the different undersampling modes and undersampling rates reveal that the patch-based image reconstruction method can capture local image features effectively and results in a much higher reconstruction quality than global sparsifying transform-based methods. In addition, the extended patch-based C-SALSA with extensive applicability is capable of preserving the image details, texture and edge information, and greatly accelerating the convergence rate.3. Considering the deficiency of the predefined sparsifying transformation and single-scale dictionary for sparse representation, the basic dictionary learning model is improved. A novel dual sparsifying model based on multi-scale dictionary in the Uniform Discrete Curvelet Transform (UDCT) domain is proposed and applied to CS-MRI reconstruction. The dual sparsifying model is constructed by training overcomplete sparsifying dictionary over the multi-scale structure of UDCT. The multi-scale dictionary, which incorporates the multi-resolution properties with the data matching adaptability of trained dictionaries, allows sparser representation and more prominent capture of hierarchical essential features for MR images. Then sparse prior information of the multi-scale dictionary is introduced to reconstruction model. Corresponding to this brand-new sparsifying model, patch-based C-SALSA is further extended to be suitable for multi-scale hierarchical structure and patch-sparsity in order to solve the constraint optimization problem of regularized image reconstruction. Experimental results demonstrate that the proposed dual sparsifying model can adaptively match various components of images from multi scales and directions using less sparse coefficients, compared to the sparse prior information simply by pre-defined sparsifying transformation or single-scale dictionary in the. image domain. It is helpful to maintain the fine characteristics of MR images with different resolution and result in fast convergence of reconstruction. The proposed method not only improves the performance of reconstruction significantly in the case of highly undersampling, in terms of maintaining intrinsic properties, effectively suppressing aliasing, reducing unexpected artifacts and removing noise, but also achieves preeminent robustness. The results reveal the advantages of the proposed dual sparsifying model as well as the effectiveness and stability of the extended numerical algorithm.