The Study Of Fast Of Magnetic Resonance Imaging Based On The Data Sparsity Representation

This paper mainly studies the principle of compressed sensing (CS) theory and themethod of rapid magnetic resonance imaging (MRI). The CS techniques based on the sparserepresentation of data was studied and applied in the rapid MRI applications. Thereconstruction algorithm with different sparse representations (wavelet transform (WT), totalvariation (TV) transform, singular value decomposition (SVD), and dictionary learning (DL))were studied and performance of these sparse representation method was compared. Thesealgorithms with different sparse representations were used to fast the data acquisition ofthree-dimensional susceptibility-weighted imaging (SWI). In this paper, we mainly focusedon following work:(1) Study of the CS algorithm based on the wavelet transform and TV transforms, and itsapplication in the fast SWI.The CS algorithm and the sparse representation of MR images in transform domain werestudied. The wavelet and TV transform were combined as a sparse representation oftwo-dimensional MR images. High quality images were reconstructed with the variantundersampling ratios after minimizing the L1norms in transform domain with the constraintof data fidality. The simulation results demonstrated that this method can be used to fast thedata acquisition of three-dimensional SWI with high quality of reconstructed images.(2) Study of the CS algorithm based on the SVD transform and its application in the fastSWI.The theory of SVD was studied and combined with CS technique based on calculatingthe SVD-based sparsity basis. The feasibility of applying CS in SWI with SVD-based sparsitybasis was investigated. It was found that CS reconstruction based on SVD sparsity basis canachieve reasonably high computing speed than that of wavelet-based sparsity basis, while stillachieving accurate image reconstruction.(3) The study of the CS algorithm based on the dictionary learning and its application ofthe SWI using the CS algorithmThe adaptive sparse representation base on the dictionary learning was investigated,which includes three main steps: dictionary learning, sparse encoding and iterativereconstruction. First, the K-SVD algorithm was used to learn the dictionary based on the fixedzero-padding reconstruction. Second, once the dictionary was learnt, sparse encoding isperformed on all patches to determine the sparse coefficients. Finally, a least square problem was solved with fixed dictionary and sparse representations, and the final image was obtainedby the updated reconstructions. The simulation results of3D SWI data demonstrated that theDL method can reconstruct high quality images even with very with very high undersamplingratios, for example, lower than30%k-space coverage, which is usually unfeasible usingnon-adaptive sparse representation method.