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
Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-f...Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-forms,which leverage sparse coding(SC),have gained significant attention in the geosciences due to their ability to achieve high TF resolution.However,the iterative approaches typically employed in sparse TF transforms are computationally intensive,making them impractical for real seismic data analysis.To address this issue,we propose an interpretable convolutional sparse coding(CSC)network to achieve high TF resolution.The proposed model is generated based on the traditional short-time Fourier transform(STFT)transform and a modified UNet,named ULISTANet.In this design,we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm(LISTA)blocks,a specialized form of CSC.The LISTA block,which evolves from the traditional iterative shrinkage thresholding algorithm(ISTA),is optimized for extracting sparse features more effectively.Furthermore,we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet.Finally,the proposed method’s performance is subsequently validated using both synthetic and field data,demonstrating its potential for enhanced seismic data analysis.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.
基金supported by the National Natural Science Foundation of China under Grant 42474139the Key Research and Development Program of Shaanxi under Grant 2024GX-YBXM-067.
文摘Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-forms,which leverage sparse coding(SC),have gained significant attention in the geosciences due to their ability to achieve high TF resolution.However,the iterative approaches typically employed in sparse TF transforms are computationally intensive,making them impractical for real seismic data analysis.To address this issue,we propose an interpretable convolutional sparse coding(CSC)network to achieve high TF resolution.The proposed model is generated based on the traditional short-time Fourier transform(STFT)transform and a modified UNet,named ULISTANet.In this design,we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm(LISTA)blocks,a specialized form of CSC.The LISTA block,which evolves from the traditional iterative shrinkage thresholding algorithm(ISTA),is optimized for extracting sparse features more effectively.Furthermore,we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet.Finally,the proposed method’s performance is subsequently validated using both synthetic and field data,demonstrating its potential for enhanced seismic data analysis.
