Research On Highly Undersampled Rapid Magnetic Resonance Imaging Based On Uniform Discrete Curvelet Transform

Magnetic resonance imaging(MRI) is regarded as an essential medical diagnostic tool. However, MRI can merely acquire data at a limited speed, which restricts its wide application severely. Considering this problem, new methods have been developed to reduce the number of sampled data dramatically while preserve MRI quality based on compressed sensing(CS) in this thesis. The main innovations includes: 1) Based on the prominent structural sparse performance of uniform discrete curvelet transform(UDCT), excellent edge details preservation of total variation(TV) and accurate reconstruction of constrained split augmented Lagrangian shrinkage algorithm(C-SALSA), one CS MRI method is proposed, which consists of pixel domain image TV regularization and UDCT coefficients 1? norm sparse regularization. Based on the fast convergence and accuracy of C-SALSA, an improved algorithm of C-SALSA is presented to solve the forming imaging model numerically. 2) Based on the various structural features of UDCT coefficient sub-bands and the adaptivity of dictionary learning(DL), one local sparsity enhanced CS MRI method is proposed.Based on the thought of double sparsity DL in wavelet domain, an efficient composite sparse structure is presented, which learns adaptive dictionary from low-pass UDCT coefficients of image to choose the most important information of images twice while reserves the high-pass sub-bands coefficients with edges and phase information. Then a new imaging model including pixel domain image, low-pass sub-band coefficients TV and transform sub-bands coefficients 1? norm sparse regularization is provided. The representation coefficients of low-pass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements are restored by the improved algorithm of C-SALSA.Simulated experiments on phantom and data in vivo exhibit that the proposed methods outperform the state-of-the-arts in maintaining edges and restraining noise and artifacts. On condition of plentiful noise in k-space, the second method of this thesis outperforms the first one. These results indicate that UDCT can provide more efficient sparse priors compared with traditional wavelets, and the proposed composite sparse structure could suppress noise furthest. Besides, the new imaging method provides solutions fully matching the imaging model with fast convergence speed.