title: Highly undersampled magnetic resonance image reconstruction using two-level Bregman method with dictionary updating.
abstract: In recent years Bregman iterative method (or related augmented Lagrangian method) has shown to be an efficient optimization technique for various inverse problems. In this paper, we propose a two-level Bregman Method with dictionary updating for highly undersampled magnetic resonance (MR) image reconstruction. The outer-level Bregman iterative procedure enforces the sampled k-space data constraints, while the inner-level Bregman method devotes to updating dictionary and sparse representation of small overlapping image patches, emphasizing local structure adaptively. Modified sparse coding stage and simple dictionary updating stage applied in the inner minimization make the whole algorithm converge in a relatively small number of iterations, and enable accurate MR image reconstruction from highly undersampled k-space data. Experimental results on both simulated MR images and real MR data consistently demonstrate that the proposed algorithm can efficiently reconstruct MR images and present advantages over the current state-of-the-art reconstruction approach.
authors.affiliation: Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China. liuqiegen@ncu.edu.cn
authors.forename: Qiegen
authors.initials: Q
authors.lastname: Liu
authors.forename: Shanshan
authors.initials: S
authors.lastname: Wang
authors.forename: Kun
authors.initials: K
authors.lastname: Yang
authors.forename: Jianhua
authors.initials: J
authors.lastname: Luo
authors.forename: Yuemin
authors.initials: Y
authors.lastname: Zhu
authors.forename: Dong
authors.initials: D
authors.lastname: Liang
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology; D002941:Circle of Willis / Q000033:anatomy & histology; D003198:Computer Simulation; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D008159:Lumbar Vertebrae / Q000033:anatomy & histology; D008279:Magnetic Resonance Imaging / Q000379:methods*; D019047:Phantoms, Imaging