Fast MRI Image Reconstruction Based On Compressed Sensing

Magnetic resonance imaging(MRI)is an important method for medical imaging that can make detailed diagnostic images of living organs and tissues.Its advantages are no harm to the human body and no radiation.However,the lack of MRI imaging speed is slow.There are two ways to solve this problem.One is to improve the hardware,such as the use of multi-coil imaging,the design of fast step matrix sequence,etc;the other is by reducing the K space data and then reconstructed by reconstruction algorithm.This method is also called K-space reconstruction.Some of the K-space reconstructions do not need to improve the hardware,and only need to improve the K-space reconstruction algorithm can achieve the purpose of improving the imaging speed.Since the development of sparse representation and pressure perception theory provides a powerful theoretical basis for reconstructing MRI images effectively by K-space data,reconstruction of MRI images from partial K-space data is essentially a solution to inverse problems;whereas effective prior information is the key to solve the inverse problem.In this dissertation,we mainly study a priori information in image,then reconstruct it with fast reconstruction algorithm,and design an effective loop measurement matrix.The main contents are as follows:(1)The design of the compression-sensing magnetic resonance imaging measurement matrix needs to satisfy the non-coherence of the sparse transformation matrix,while ensuring that it can be applied to the hardware.In this dissertation,the loop measurement matrix is optimized and constructed from the phase and amplitude of the elements generated by the cyclic measurement matrix.The amplitude of the generated elements is proposed and the optimization of the cyclic measurement matrix is realized by combining chaotic random phase.Compared with the existing cyclic matrices,the equivalence dictionary vectors of the corresponding cyclic measurement matrices constructed in this dissertationhave lower mutual coherence,and the quality of reconstructed images is better under the same measurement data.(2)Curvelet wave analysis is a directional multi-scale analysis method,which is based on the development of wavelet analysis and ridge wave analysis.The constructed curvelet transform can strengthen the edge of image and solve the problem of singularity of image jump.Alternating Direction Method of Multipliers(For short ADMM)can effectively solve the separable convex programming problem by iteration of the1 l norm parts of objective function,thus reducing the computational complexity of the algorithm and speeding up the convergence time of the algorithm.Based on ADMM,the compressed perceptual MRI images are reconstructed using the curvelet transform and the total variation as regular terms in this dissertation.This method can fully exploit the sparsity of different features of MRI images in different transform domain.On the basis of the same measurement matrix,the reconstruction quality is improved.