Magnetic Resonance Image Reconstruction Based On Compressed Sensing

Magnetic resonance imaging (MRI) is currently one of the most advanced techniquesin medical imaging field, which has been widely used in clinical medicine diagnostics.However, the relatively slow imaging speed has been always a major factor affecting MRIclinical throughput and imaging quality. This thesis aims to speed up the imaging process.Based on compressed sensing (CS), several novel effective MR image reconstructionmethods have been proposed by studying and exploiting prior information of MR images.The main content of this thesis can be summarized as follows:1. Considering the fact that the sparsity constraint by l1norm will require moremeasurements than l0norm, this thesis proposes a hybrid weighted l1-TV minimizationmethod for CS-MRI. The method assigns different weights to the elements of the imageand its gradients to approximate l0norm constraint. The robust selection rules for theweights and an adaptively reweighting iterative algorithm are presented. Byreconstructing images and updating the weights alternately, good reconstructions can beobtained. The experiments on practical MR images demonstrate that the proposed methodcan preserve image details and edges effectively. It produces more accurate reconstructioncompared with conventional CS-MRI and other weighted methods with the sameundersampled measurements.2. By utilizing the structural information besides sparsity of the MR image, a novelCS-MRI method based on union of subspaces is proposed. The method models the MRimage within union of subspaces framework and projects the MR image to aK-dimensional union of subspaces. An algorithm named as Subspace Update Algorithm(SUA) is proposed to locate the subspace where the image resides. Finally, the value ofthe K coefficients is obtained via minimizing the objective function which involves a TVregularization term. Experimental results on sparse Shepp-logan phantom and practicalMR images demonstrate that estimating the largest K coefficients can obtain moreaccurate reconstruction than estimating all the coefficients.3. By utilizing the similarity between the high resolution reference image and thetarget image, a novel CS-MRI method based on nonlocal total variation (NLTV) andpartially known support is proposed. In this method, the known support of the targetimage is extracted from the reference image, and regarded as the structural prior information for reconstruction. Furthermore, it uses NLTV regularization, whichovercomes the blocky effects and the losing of edges and details. Experimental resultsdemonstrate that the proposed method can effectively overcome blocky effects. It canfurther reduce the sampling ratio and increase imaging speed without degrading the imagequality.4. The reference-driven MR image reconstruction problem is investigated, and anovel CS-MRI method based on the non-uniform free form deformation (FFD)motion-compensated reference is proposed. The method formulates the target image asthe sum of the combined motion-compensated reference image and a difference image, sothe reconstruction of the target image becomes a joint estimation to motion parametersand the difference image. To enhance the sparsity of the difference image, multi-levelFFDs with non-uniform control points at each level are introduced to describe thenonrigid deformation, which highly decrease the computational complexity withoutlosing any registration accuracy. An alternating minimization algorithm is used to solvethe joint estimation problem, in which motion estimation and the difference imagereconstruction are performed alternately. Experimental results demonstrate that theproposed method can not only compensate the motion successfully, but also achieveaccurate reconstruction at a low sampling ratio.5. Based on the further research on the reference-driven CS-MRI methods, a newreconstruction scheme is proposed which exploits wavelet sparsity of the differenceimage and total generalized variation (TGV) regularization. The target image is modeledas a sum of the compensated reference image and a difference image. Then the sparsity ofthe difference image in the wavelet transform and discrete gradient domains is exploitedfor reconstruction. The notable superiority of the proposed method lies in it does notrequire to model and estimate the contrast changes, and needs only once compensation,which avoids the huge computational burden resulting from iterative estimation of themotion effects. In addition, second order TGV is introduced to eliminate the staircasingartifacts and preserve details. Experimental results demonstrate that the proposed methodcan improve imaging quality and effectively eliminate the staircasing artifacts at the samesampling ratio.6. Medical image registration technique is investigated, and a new similarity measureis proposed, which combines the sum of squared differences (SSD) and the differencesparsity (SSD-Sparsity). By minimizing the intensity differences and the amount of pixels with different intensity values simultaneously, SSD-Sparsity strengthens the spatialcoherence of the registration. Experimental results demonstrate that the proposedSSD-Sparsity can obtain more accurate registration than classic SSD.