Decomposing a signal based upon redundan dictionaries is a new method for data representation on sig- nal processing. It approximates a signal with an overcom- plete system instead of an orthonormal basis to provide a...Decomposing a signal based upon redundan dictionaries is a new method for data representation on sig- nal processing. It approximates a signal with an overcom- plete system instead of an orthonormal basis to provide a sufficient choice for adaptive sparse decompositions. Re- placing the original data with a sparse approximation can result in not only a higher compression ratio, but also greater flexibility in capturing the inherent structure of the natura signals with the redundancy of dictionaries. This paper gives an overview of a series of recent results in this field, and deals with the relationship between sparsity of signal de- composition and incoherence of dictionaries with BP and MP algorithms. The current and future challenges of the dic- tionary construction are discussed.展开更多
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 dictio...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.展开更多
在多孔隙含水层中地面磁共振(surface nuclear magnetic resonance,SNMR)信号呈现多弛豫衰减特性,常规盲源分离方法和单指数拟合方法引起信号严重失真和信息缺失等问题.本文提出了基于稀疏表示的随机噪声背景下多弛豫SNMR信号的提取方法...在多孔隙含水层中地面磁共振(surface nuclear magnetic resonance,SNMR)信号呈现多弛豫衰减特性,常规盲源分离方法和单指数拟合方法引起信号严重失真和信息缺失等问题.本文提出了基于稀疏表示的随机噪声背景下多弛豫SNMR信号的提取方法.根据SNMR信号的衰减特征,设计了精确刻画SNMR信号且与随机噪声不相关的离散衰减余弦冗余字典.其次,针对多弛豫SNMR信号稀疏度未知的问题,通过设置合理的残差比阈值控制迭代次数,改进了广义正交匹配追踪(generalized orthogonal matching pursuit,gOMP)算法,使得该方法应用于SNMR信号的提取时,具有更好的自适应性和普适性.再次,鉴于SNMR测量数据为多次独立重复采集的结果,提出了基于数据流的SNMR信号提取策略,在提高算法鲁棒性的同时,保证了信号提取结果的唯一性.最后,通过仿真和实测数据证明了基于gOMP算法的稀疏表示方法可以显著地提升多弛豫SNMR信号的提取质量,降低随机噪声对含水层反演结果的影响,提高SNMR探测能力.展开更多
基金This work was supported in part by the National Committee for Nationalities,China Scholarship Council and Education Department of China.
文摘Decomposing a signal based upon redundan dictionaries is a new method for data representation on sig- nal processing. It approximates a signal with an overcom- plete system instead of an orthonormal basis to provide a sufficient choice for adaptive sparse decompositions. Re- placing the original data with a sparse approximation can result in not only a higher compression ratio, but also greater flexibility in capturing the inherent structure of the natura signals with the redundancy of dictionaries. This paper gives an overview of a series of recent results in this field, and deals with the relationship between sparsity of signal de- composition and incoherence of dictionaries with BP and MP algorithms. The current and future challenges of the dic- tionary construction are discussed.
基金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)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.2011021111-0026)the Fundamental Research Funds for the Central Universities of China(Nos.lzujbky-2015-108 and lzujbky-2015-197)
文摘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.
