J Shanghai Jiaotong Univ Sci

Journal of Shanghai Jiaotong University(Science) >

2015 , Vol. 20 >Issue 6: 660 - 669

DOI: https://doi.org/10.1007/s12204-015-1674-z

Research article

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

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  • Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China

Received date: 2013-10-24

  Online published: 2020-10-09

Supported by

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 GJJ 14196);The National Postdoctoral Research Funds (No 2014M551867);The Jiangxi Advanced Projects for Postdoctoral Research Funds (No 2014KY02)

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Abstract

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.

Key words： laterally loaded piles; $m$-method; hydraulic head; land deformation; pumping-recovery; circular excavation; back analysis; horizontal displacement; outage performance; amplify-and-forward (AF); heterogeneous circumstance; magnetic resonance imaging (MRI); sparse representation; non-convex; generalized thresholding; dictionary updating; beamforming; channel state information (CSI); power control; cognitive radio; monotone optimization; price; Stackelberg game; fairness; supply chain coordination; alternating direction method; two-level Bregman method with dictionary updating (TBMDU); admission control scheme; heterogeneity; substitution; service parts; last stock; handover service; high-speed train communication; S-clay1 model; undrained compression test; functionally graded materials; cylindrical sandwich panel; low-velocity water entry; cylinder structure; rectangular sandwich plate; simply supported; free vibration; resting-state brain function network; supercavitating; ventilated; dynamic mesh; pitching; wall effect; model network; connection distance minimization; topological property; anatomical distance; common neighbor; underwater glider; nonlinear control; adaptive backstepping; Lyapunov function; cylinder radius; initial velocity; entry angle; soft soil; strain-dependent modulus; video capsule endoscopy (VCE); frame rate; working hours; in vivo experiment

Cite this article

Ming-hui ZHANG, Xiao-yang HE, Shen-yuan DU, Qie-gen* LIU . A Generalized Two-Level Bregman Method with Dictionary Updating for Non-Convex Magnetic Resonance Imaging Reconstruction[J]. Journal of Shanghai Jiaotong University(Science), 2015 , 20(6) : 660 -669 . DOI: 10.1007/s12204-015-1674-z

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