Abstract
Recently, dictionary learning (DL) based methods have been introduced to compressed sensing magnetic resonance imaging (CS-MRI), which outperforms pre-defined analytic sparse priors. However, single-scale trained dictionary directly from image patches is incapable of representing image features from multi-scale, multi-directional perspective, which influences the reconstruction performance. In this paper, incorporating the superior multi-scale properties of uniform discrete curvelet transform (UDCT) with the data matching adaptability of trained dictionaries, we propose a flexible sparsity framework to allow sparser representation and prominent hierarchical essential features capture for magnetic resonance (MR) images. Multi-scale decomposition is implemented by using UDCT due to its prominent properties of lower redundancy ratio, hierarchical data structure, and ease of implementation. Each sub-dictionary of different sub-bands is trained independently to form the multi-scale dictionaries. Corresponding to this brand-new sparsity model, we modify the constraint splitting augmented Lagrangian shrinkage algorithm (C-SALSA) as patch-based C-SALSA (PB C-SALSA) to solve the constraint optimization problem of regularized image reconstruction. Experimental results demonstrate that the trained sub-dictionaries at different scales, enforcing sparsity at multiple scales, can then be efficiently used for MRI reconstruction to obtain satisfactory results with further reduced undersampling rate. Multi-scale UDCT dictionaries potentially outperform both single-scale trained dictionaries and multi-scale analytic transforms. Our proposed sparsity model achieves sparser representation for reconstructed data, which results in fast convergence of reconstruction exploiting PB C-SALSA. Simulation results demonstrate that the proposed method outperforms conventional CS-MRI methods in maintaining intrinsic properties, eliminating aliasing, reducing unexpected artifacts, and removing noise. It can achieve comparable performance of reconstruction with the state-of-the-art methods even under substantially high undersampling factors.
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Project supported by the National Natural Science Foundation of China (Nos. 61175012 and 61201422), the Natural Science Foundation of Gansu Province of China (No. 1208RJ-ZA265), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 2011021111-0026), and the Fundamental Research Funds for the Central Universities of China (Nos. lzujbky-2015-108 and lzujbky-2015-197)
ORCID: Min YUAN, http://orcid.org/0000-0001-7855-8678
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Yuan, M., Yang, Bx., Ma, Yd. et al. Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm. Frontiers Inf Technol Electronic Eng 16, 1069–1087 (2015). https://doi.org/10.1631/FITEE.1400423
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DOI: https://doi.org/10.1631/FITEE.1400423
Keywords
- Compressed sensing (CS)
- Magnetic resonance imaging (MRI)
- Uniform discrete curvelet transform (UDCT)
- Multi-scale dictionary learning (MSDL)
- Patch-based constraint splitting augmented Lagrangian shrinkage algorithm (PB C-SALSA)