Research On Magnetic Resonance SENSE Image Reconstruction Algorithm Based On Total Variation Regularization

Magnetic resonance imaging (MRI) is an important medical diagnosis technology in modern times. However, slow imaging speed limits its clinical application in many occasions.Parallel magnetic resonance imaging (PMRI) can increase the imaging speed by acquiring data with multiple receives coil array simultaneously, obtaining undersampled K space, and shortening scan time greatly. As the sampling rate is lower than the Nyquist sampling rate, if we carried Fourier transform for data of K space directly, we would get the image with aliasing artifacts. As a kind PMRI reconstruction method which is used for unfolding mixing pixels widely, the process of sensitivity encoding (SENSE) imaging is an ill-condition inverse problem with noise amplification phenomenon. Cutterntly, image reconstruction method based on regularization model can effectively improve this problem, and has been widely researched and applicated. This thesis mainly focuses on SENSE reconstruction algorithm based on total variation (TV) regularization.Firstly,starting from linear ill-posed problem, this thesis focuses on Tikhonov regularization and TV regularization, and builds SENSE reconstruction cost function based on regularization using prior information of an image. Although the ill-conditon of SENSE reconstruction can be alleviated by utilizing TV regularization method to obtain a certain extent, higher regularization degree causes data inconsistency and results in the exacerbation of the image artifacts in the case of the accelerated factor R is higher. Aimming at resoluting this problem, an improved SENSE reconstruction algorithm based on iterative TV regularization is proposed. For the improved method, the regularization function updates adaptively based on the Bregman distance between two consecutive iterations, while the traditional regularization function is fixed. The simulation experiments for phantom, brain, and cardic MRI data show that the improved iterative TV regularization SENSE reconstruction algorithm can obtain the reconstruction result with less aliasing artifacts and higher SNR compared with the traditional TV regularization SENSE reconstruction.Because the total variation regularization theory arguments are generally based on the continuous model, the traditional numerical solution of SENSE based on TV regularization reconstruction results in slow convergence and is not well approximate to the optimal solution of the model, and causes the slow reconstruction speed and the decline of quality. This thesis introduces an efficient and fast split Bregman iterative algorithm to solve the numerical solution of the model which based on TV regularized SENSE reconstruction. The improved algorithm converts the L1 regularized problem to a series of unconstrained optimization problems and Bregman update. The improved algorithm is very efficient because the cost function is divided into L1 part and L2 part, and iterates two parts to minimum respectively. The simulation experiments show that TV regularized SENSE based on rapid split Bregman iterative reconstruction not only has less number of iterations and higher convergence speed, but also can reduce aliasing artifacts in reconstructed results. Moreover, the normalized mean square error (NMSE) value is reduced greatly.