title: A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction.
abstract: Nonconvex optimization has shown that it needs substantially fewer measurements than l 1 minimization for exact recovery under fixed transform/overcomplete dictionary. In this work, two efficient numerical algorithms which are unified by the method named weighted two-level Bregman method with dictionary updating (WTBMDU) are proposed for solving lp optimization under the dictionary learning model and subjecting the fidelity to the partial measurements. By incorporating the iteratively reweighted norm into the two-level Bregman iteration method with dictionary updating scheme (TBMDU), the modified alternating direction method (ADM) solves the model of pursuing the approximated lp -norm penalty efficiently. Specifically, the algorithms converge after a relatively small number of iterations, under the formulation of iteratively reweighted l 1 and l 2 minimization. Experimental results on MR image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed method can efficiently reconstruct MR images from highly undersampled k-space data and presents advantages over the current state-of-the-art reconstruction approaches, in terms of higher PSNR and lower HFEN values.
authors.affiliation: Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China.
authors.forename: Qiegen
authors.identifier: 0000-0003-4717-2283
authors.initials: Q
authors.lastname: Liu
authors.affiliation: Paul C. Lauterbur Research Centre for Biomedical Imaging, Institute of Biomedical and Health Engineering, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong 518055, China ; Shenzhen Key Laboratory for MRI, Chinese Academy of Sciences, Shenzhen 518055, China.
authors.forename: Xi
authors.initials: X
authors.lastname: Peng
authors.affiliation: Paul C. Lauterbur Research Centre for Biomedical Imaging, Institute of Biomedical and Health Engineering, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong 518055, China ; Shenzhen Key Laboratory for MRI, Chinese Academy of Sciences, Shenzhen 518055, China.
authors.forename: Jianbo
authors.initials: J
authors.lastname: Liu
authors.affiliation: Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China.
authors.forename: Dingcheng
authors.initials: D
authors.lastname: Yang
authors.affiliation: Paul C. Lauterbur Research Centre for Biomedical Imaging, Institute of Biomedical and Health Engineering, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong 518055, China ; Shenzhen Key Laboratory for MRI, Chinese Academy of Sciences, Shenzhen 518055, China.
authors.forename: Dong
authors.identifier: 0000-0001-6257-0875
authors.initials: D
authors.lastname: Liang