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
This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is m...This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT;similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.展开更多
It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality.Recently,we have proposed a unified algorithmic framework which can guide ...It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality.Recently,we have proposed a unified algorithmic framework which can guide us to construct the solution methods for solving these monotone variational inequalities.In this work,we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago.In particular,exploiting this framework,we are able to give a very clear and elementary proof of the convergence of these solution methods.展开更多
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.
文摘This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT;similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.
基金The author was supported by the NSFC Grant No.11871029.
文摘It is well recognized the convenience of converting the linearly constrained convex optimization problems to a monotone variational inequality.Recently,we have proposed a unified algorithmic framework which can guide us to construct the solution methods for solving these monotone variational inequalities.In this work,we revisit two full Jacobian decomposition of the augmented Lagrangian methods for separable convex programming which we have studied a few years ago.In particular,exploiting this framework,we are able to give a very clear and elementary proof of the convergence of these solution methods.
