Fast Algorithm For Parallel Magnetic Resonance Image Reconstruction Based On Total Variations Model

In recent years,parallel magnetic resonance imaging technology has developed rapidly.Parallel magnetic resonance imaging is a technique that uses multiple receiver coils to acquire signals simultaneously,thereby reducing signal acquisition time and accelerating imaging speed.Image reconstruction based on the full variational model is now The focus of the study is that the full variational model can better preserve the edge information of the image.In order to apply to largescale parallel magnetic resonance imaging applications,the research goal of this paper is a fast image reconstruction algorithm based on the full variational model.In this paper,we mainly focus on the fast reconstructing algorithm of the full variational model for the large and ill-conditioned measurement matrix in parallel magnetic resonance imaging.The main content of this article is as follows:(1)Because the measurement matrix matrix dimension of the full variational model is very large and ill-conditioned,the original complex image reconstruction problem is decomposed into two simple sub-problems by using the alternating direction method of variable splitting,and then the subproblems are solved separately.The experimental results show that the proposed method based on alternating splitting of variables can obtain better image reconstruction effect and fast convergence speed.(2)For the problem of the slow speed of solving the problem of the fixed step size in the alternating direction method,the solution of the full variational model can be obtained simply by using the linearized approximate function.In the subproblem,using Barzilai-Borwein(BB)step rule,a fast variable step size algorithm is established.Numerical experiments show that the algorithm is effective.(3)Combine the alternating direction method with the approximate Newton method and take predetermined steps along the approximate Newton direction during each iteration.Compared with the image reconstruction algorithm of BOS and BOSVS parallel magnetic resonance,the proposed method is more stable and simpler,and almost monotonically convergent.