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A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction
Journal article   Open access   Peer reviewed

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

Qiegen Liu, Xi Peng, Jianbo Liu, Dingcheng Yang and Dong Liang
International journal of biomedical imaging, Vol.2014(2014), pp.128596-23
01/01/2014
DOI: 10.1155/2014/128596
PMCID: PMC4241317
PMID: 25431583
url
https://doi.org/10.1155/2014/128596View
Published (Version of record) Open Access

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.

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