A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction
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 diction...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Biomedical Imaging |
| Online Access: | http://dx.doi.org/10.1155/2014/128596 |
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| _version_ | 1849399100513976320 |
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| author | Qiegen Liu Xi Peng Jianbo Liu Dingcheng Yang Dong Liang |
| author_facet | Qiegen Liu Xi Peng Jianbo Liu Dingcheng Yang Dong Liang |
| author_sort | Qiegen Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a3bf22d96a2d4782ac00d25f4ef39c01 |
| institution | Kabale University |
| issn | 1687-4188 1687-4196 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Biomedical Imaging |
| spelling | doaj-art-a3bf22d96a2d4782ac00d25f4ef39c012025-08-20T03:38:25ZengWileyInternational Journal of Biomedical Imaging1687-41881687-41962014-01-01201410.1155/2014/128596128596A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image ReconstructionQiegen Liu0Xi Peng1Jianbo Liu2Dingcheng Yang3Dong Liang4Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, ChinaPaul 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, ChinaPaul 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, ChinaDepartment of Electronic Information Engineering, Nanchang University, Nanchang 330031, ChinaPaul 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, ChinaNonconvex 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.http://dx.doi.org/10.1155/2014/128596 |
| spellingShingle | Qiegen Liu Xi Peng Jianbo Liu Dingcheng Yang Dong Liang A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction International Journal of Biomedical Imaging |
| title | A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction |
| title_full | A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction |
| title_fullStr | A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction |
| title_full_unstemmed | A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction |
| title_short | A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction |
| title_sort | weighted two level bregman method with dictionary updating for nonconvex mr image reconstruction |
| url | http://dx.doi.org/10.1155/2014/128596 |
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