Research On Reconstruction Algorithm Of Compressed Sensing Magnetic Resonance Imaging

With safety and high imaging quality properties,magnetic resonance imaging(MRI)has become one of the important means in the clinical examinationis.As a non-invasive imaging method,it can provides abundant information for clinical diagnosis.However,long scanning time is the main disadvantage of MRI,which results in long scanning time and affects its further popularization and application.Due to the limitation of Nyquist sampling frequency,the traditional accelerated method of MRI is hard to improve the scanning speed of MRI greatly.Compressed sensing(CS)which introduced by Donoho and Candès breaks through this limitation,and the sampling frequency can be much lower than the Nyquist sampling frequency.This provides a new direction for accelerating MRI.In recent years,the use of CS theory to improve the imaging speed is becoming more and more in-depth in the field of MRI.Image sparse representation and reconstruction algorithm are two main research problems.There are some algorithms to improve the imaging quality and reduce the imaging time.Some algorithms have emerged to improve the quality of imaging and reduce the time of imaging.However,the existing algorithms need to be further explored because they are not perfect and have some problems,such as high complexity,slow convergence speed,and so on.In order to solve these problems,several compressed sensing MRI(CS-MRI)algorithms are studied.The experimental results show that these proposed algorithms can improve the image quality of the MRI reconstruction,shorten the running time of the algorithm and speed up the MRI process.The main research contents of this dissertation include four parts.Firstly,in order to further improve the convergence speed of the conjugate gradient(CG)method and reduce the execution time of the algorithm,prediction line search(PLS)and bi-prediction line search(BPLS)are proposed,which reduce the time of obtaining reasonable step size and improve the execution speed of the algorithm.Based on the fact that the step size is decreasing in iterations,the PLS uses the step size in the current iteration to predict the initial value of line search in next iteration.Simulation experiments show that the start point gained by this method is more reasonable,which significantly reduces the number of cycles in line search and gets shorter running time than traditional backtracking line search algorithm.The BPLS dynamically adjusts the initial value using the number of line search in iterations,which further improves the efficiency of line search and enhances the adaptability of the algorithm.Secondly,based on the classic conjugate gradient method and its improved method,a novel hybrid conjugate gradient method(H-CG)is proposed in this paper,in which a new update parameter is proposed.With detailed mathematical proofs,the proposed method has be proved to have sufficient descent and global convergence properties under strong Wolfe conditions.The experimental results show that H-CG achieves better image quality and requires less running time than other two widely uesed CG methods in MRI reconstruction.Thirdly,to solve the complex sparse models that is difficult to be solved directly,the proximal algorithm is studied.By the derivation of proximal operators under the Dykstra-like proximal algorithm(DPA)frame,the complex joint sparse optimization problem is converted into two simple optimization problems,and the description of the algorithm is followed.The experimental tests shows that the algorithm can effectively solve the problem of reconstruction of CS-MRI.In order to further improve the convergence speed of the previous algorithm,a fast Dykstra-like proximal algorithm(FDPA)is proposed using the accelerating idea of the fast iterative shrinkage/thresholding algorithm(FISTA).The experimental results show that the MRI speed is improved while the quality of the reconstruction is also guaranteed by the proposed algorithm.Finally,the problem of using alternating direction method of multipliers(ADMM)to solve the joint sparse model of MRI is studied.The ADMM algorithm combines the characteristics of the augmented Lagrange method of multipliers,the variable splitting method and the alternating minimization method,so it has convergence and decomposability.In order to solve different optimization problems,there are many decomposition methods in the ADMM.In this paper,an approximate solution method is used to derive the ADMM iterative expressions for solving the joint sparse model of CS-MRI,then the according algorithm is listed.Finally,it is proved that the algorithm can effectively solve the minimizing optimal problem of the reconstruction of non-uniform sampled MRI.