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Front. Inform. Technol. Electron. Eng.  2015, Vol. 16 Issue (12): 1069-1087    DOI: 10.1631/FITEE.1400423
    
Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm
Min Yuan, Bing-xin Yang, Yi-de Ma, Jiu-wen Zhang, Fu-xiang Lu, Tong-feng Zhang
School of Information Science & Engineering, Lanzhou University, Lanzhou 730000, China
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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.

Key words： 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)     
Received: 08 December 2014      Published: 07 December 2015
CLC:  TN911  
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Min Yuan
Bing-xin Yang
Yi-de Ma
Jiu-wen Zhang
Fu-xiang Lu
Tong-feng Zhang
Cite this article:

Min Yuan, Bing-xin Yang, Yi-de Ma, Jiu-wen Zhang, Fu-xiang Lu, Tong-feng Zhang. Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm. Front. Inform. Technol. Electron. Eng., 2015, 16(12): 1069-1087.

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http://www.zjujournals.com/xueshu/fitee/10.1631/FITEE.1400423     OR     http://www.zjujournals.com/xueshu/fitee/Y2015/V16/I12/1069


基于多尺度UDCT域字典学习及分块约束型分裂增广拉格朗日收缩算法的高度欠采样磁共振图像重构

目的：针对现有预定义分析型变换和图像域单尺度字典在稀疏表示中存在的不足，从寻求最优的稀疏先验信息和探索重构最优化问题的有效数值求解算法以适用于相应稀疏化结构两个方面，基于CS理论开展通过欠采样k空间数据重构高质量MR图像的研究，提出改进方法，从而达到改善重构图像质量的目的。
创新点：改进了基本的字典学习模型，提出了一种基于均匀离散Curvelet变换(Uniform Discrete Curvelet Transform, UDCT)域多尺度字典学习的稀疏化模型，并应用于CS-MRI重构。为适应多尺度分层和分块稀疏化结构，进一步扩展约束型分裂增广拉格朗日收缩方法，并用于模型的数值求解。
方法：文中图2为提出的UDCT域多尺度字典学习的CS-MRI重构方法的流程框图。如算法2中描述，整个UDPC方法包含两个阶段：多尺度字典学习阶段和PBC-SALSA重构阶段。在UDCT域多尺度字典学习阶段，提出的模型通过在UDCT的多尺度结构上训练过完备字典来构建。构造的UDCT域多尺度字典融合了多分辨率特性与字典学习的自适应数据匹配能力。在重构问题的求解过程中，将训练字典的稀疏先验信息引入到重构模型中，对分块约束型分裂增广拉格朗日算法进一步扩展以适应于多尺度字典结构。该算法能够稳定快速地收敛，从而重构出高质量的MR图像。
结论：相比于仅使用预定义的分析型变换和图像域单尺度字典稀疏先验，该稀疏化模型能够用更少的稀疏系数自适应地匹配图像在多尺度多方向的各种结构成分，有利于保留MR图像不同分辨率的精细特征和重构的快速收敛。提出的方法显著改善了高度欠采样情况下重构图像的质量，充分体现了UDCT域多尺度字典学习稀疏化模型的优势以及扩展的数值求解算法的有效性和稳定性。

关键词： 压缩感知,  磁共振成像,  均匀离散curvelet变换,  多尺度字典学习,  分块约束型分裂增广拉格朗日收缩算法 
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