Fast Multiclass Dictionaries Learning with Geometrical Directions in MRI Reconstruction (中文，English)
Zhifang Zhan1, Jian-Feng Cai2, Di Guo3, Yunsong Liu1, Zhong Chen1, Xiaobo Qu1,*
1 Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University, Xiamen, China
2 Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China
3 School of Computer and Information Engineering, Xiamen University of Technology, Xiamen, China
* Email: quxiaobo <at> xmu.edu.cn or quxiaobo2009 <at> gmail.com.
We introduce a fast orthogonal dictionary learning method into magnetic resonance image reconstruction. To enhance the sparsity, image is divided into classified patches according to the same geometrical direction and orthogonal dictionary is trained within each class. We set up a sparse reconstruction model with the multi-class dictionaries and solve the problem with a fast alternating direction method of multipliers. We refer to this Fast Dictionary Learning method on Classified Patches as FDLCP. Experiments on real magnetic resonance imaging data demonstrate that the proposed approach achieves the lowest reconstruction error compared with several state-of-the-art methods and the computation is much faster than previous dictionary learning methods.
The proposed method loses dictionary overcompleteness but regains it implicitly by using multiple dictionaries. It shows that the sparsest representation is obtained using the proposed FDLCP (Fig. 1).
Fig. 1. Comparison on the sparsity using 2D Haar wavelets, 2D DCT, adaptive fast dictionary learning (FDL) and adaptive fast dictionary learning on classified patches (FDLCP). (a) a phantom image, (b) a zoomed-in region; (c) a class of patches with diagonal geometric direction; (d) non-adaptive 3 level 2D Haar wavelets; (e) atoms of dictionary learning without patch classification; (f) atoms of dictionary learning on patches with diagonal geometric directions in (c), (g) the sparse approximation errors by preserving the largest coefficients. Red lines in (a) and (b) indicate geometric directions of patches. Patches are in size 8× 8.
The complete procedure of the proposed method is shown in Fig. 2.
Fig. 2. The block diagram of the proposed method
1. Reconstruction with phantom
Fig. 3. Reconstructed phantom images and errors using Cartesian sampling pattern when 33% data are sampled. (a) A full sampled phantom image; (b-e) Reconstructed images based on WaTMRI, DLMRI, PBDW and the proposed FDLCP, respectively; (f) Cartesian undersampling pattern; (g-j) the reconstruction error magnitudes corresponding to the above reconstructions.
2. Reconstruction with brain data
Fig. 4. Reconstructed brain images and errors using Cartesian sampling pattern when 32% data are sampled. (a) A full sampled brain image; (b-e) Reconstructed images using WaTMRI, DLMRI, PBDW and the proposed FDLCP, respectively; (f) Cartesian undersampling pattern; (g-j) the reconstruction error magnitudes corresponding to the above reconstructions.
Fig. 5. Computation times of reconstructing brain image using the proposed FDLCP.
Note: The simulation runs on a 64-bit Window 7 operating system with an Intel Core i5 CPU at 3.30GHz and 12GB RAM.
The complete FDLCP code written in MATLAB can be downloaded at the following link: Demo_FDLCP_L1_L0.zip
Please cite this paper when using the FDLCP code or any software derived from it:
Zhifang Zhan, Jian-Feng Cai, Di Guo, Yunsong Liu, Zhong Chen, Xiaobo Qu*. Fast multiclass dictionaries learning with geometrical directions in MRI reconstruction,IEEE Transactions on Biomedical Engineering, 63(9):1850-1861, 2016. 
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We would like thank Bingwen Zheng, Feng Huang, and Xi Peng for providing data used in this paper. We would also like to thank the following scholars for sharing codes for comparisons: Yue Huang and Xinghao Ding for BPFA, Yasir Q. Mohsin and Mathews Jacob for NLS, Junzhou Huang for WaTMRI, Saiprasad Ravishankar and Yoram Bresler for DLMRI. This work was supported by the NNSF of China under Grants 61571380, 61201045, 61302174, and 11375147, Natural Science Foundation of Fujian Province of China under Gant 2015J01346, Fundamental Research Funds for the Central Universities (20720150109, 2013SH002), Important Joint Research Project on Major Diseases of Xiamen City (3502Z20149032), and NSF DMS-1418737.
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