Table of Contents Author Guidelines Submit a Manuscript
International Journal of Biomedical Imaging
Volume 2014, Article ID 128596, 23 pages
http://dx.doi.org/10.1155/2014/128596
Research Article

A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction

1Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China
2Paul 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
3Shenzhen Key Laboratory for MRI, Chinese Academy of Sciences, Shenzhen 518055, China

Received 6 July 2014; Revised 10 September 2014; Accepted 10 September 2014; Published 30 September 2014

Academic Editor: Jun Zhao

Copyright © 2014 Qiegen Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Nonconvex optimization has shown that it needs substantially fewer measurements than l1 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 l1 and l2 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.