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A generalized two-level Bregman method with dictionary updating for non-convex magnetic resonance imaging reconstruction

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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.

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Authors and Affiliations

  1. Department of Electronic Information Engineering, Nanchang University, Nanchang, 330031, China

    Ming-hui Zhang  (张明辉), Xiao-yang He  (何小洋), Shen-yuan Du  (杜沈园) & Qie-gen Liu  (刘且根)

Authors
  1. Ming-hui Zhang  (张明辉)
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  2. Xiao-yang He  (何小洋)
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  3. Shen-yuan Du  (杜沈园)
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  4. Qie-gen Liu  (刘且根)
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Corresponding author

Correspondence to Qie-gen Liu  (刘且根).

Additional information

Foundation item: 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), and the Jiangxi Advanced Projects for Postdoctoral Research Funds (No. 2014KY02)

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Zhang, Mh., He, Xy., Du, Sy. et al. A generalized two-level Bregman method with dictionary updating for non-convex magnetic resonance imaging reconstruction. J. Shanghai Jiaotong Univ. (Sci.) 20, 660–669 (2015). https://doi.org/10.1007/s12204-015-1674-z

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

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