A Generalized Two-Level Bregman Method with Dictionary Updating for Non-Convex Magnetic Resonance Imaging Reconstruction  

作　　者：张明辉 何小洋 杜沈园 刘且根 

机构地区：[1]Department of Electronic Information Engineering Nanchang University

出　　处：《Journal of Shanghai Jiaotong university(Science)》2015年第6期660-669,共10页上海交通大学学报（英文版）

基　　金：the National Natural Science Foundation of China(Nos.61362001;61365013 and 51165033);the Natural Science Foundation of Jiangxi Province(Nos.20132BAB211030 and 20122BAB211015);the Technology Foundation of Department of Education in Jiangxi Province(Nos.GJJ 13061 and GJJ14196);the National Postdoctoral Research Funds(No.2014M551867);the Jiangxi Advanced Projects for Postdoctoral Research Funds(No.2014KY02)

摘　　要：In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p 〈 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating（TBMDU）, we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU（GTBMDU） algorithm.The experimental results on magnetic resonance（MR） image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.

关 键 词：magnetic resonance imaging(MRI) sparse representation non-convex generalized thresholding dictionary updating alternating direction method two-level Bregman method with dictionary updating(TBMDU) 

分 类 号：TN911.73[电子电信—通信与信息系统]