Linear-Model-inspired Neural Network for Electromagnetic Inverse Scattering

Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the issue, this letter exploits a linear model-based network (LMN) learning strategy, which benefits from both model complexity and data learning. By introducing a linear model for ISPs, a new model with network-driven regular-izer is proposed. For attaining efficient end-to-end learning, the network architecture and hyper-parameter estimation are presented. Experimental results validate its superiority to some state-of-the-arts.Comment: 5 pages, 6 figures 3 table

Stage-by-stage Wavelet Optimization Refinement Diffusion Model for Sparse-View CT Reconstruction

Diffusion models have emerged as potential tools to tackle the challenge of sparse-view CT reconstruction, displaying superior performance compared to conventional methods. Nevertheless, these prevailing diffusion models predominantly focus on the sinogram or image domains, which can lead to instability during model training, potentially culminating in convergence towards local minimal solutions. The wavelet trans-form serves to disentangle image contents and features into distinct frequency-component bands at varying scales, adeptly capturing diverse directional structures. Employing the Wavelet transform as a guiding sparsity prior significantly enhances the robustness of diffusion models. In this study, we present an innovative approach named the Stage-by-stage Wavelet Optimization Refinement Diffusion (SWORD) model for sparse-view CT reconstruction. Specifically, we establish a unified mathematical model integrating low-frequency and high-frequency generative models, achieving the solution with optimization procedure. Furthermore, we perform the low-frequency and high-frequency generative models on wavelet's decomposed components rather than sinogram or image domains, ensuring the stability of model training. Our method rooted in established optimization theory, comprising three distinct stages, including low-frequency generation, high-frequency refinement and domain transform. Our experimental results demonstrate that the proposed method outperforms existing state-of-the-art methods both quantitatively and qualitatively

Generative Modeling in Structural-Hankel Domain for Color Image Inpainting

In recent years, some researchers focused on using a single image to obtain a large number of samples through multi-scale features. This study intends to a brand-new idea that requires only ten or even fewer samples to construct the low-rank structural-Hankel matrices-assisted score-based generative model (SHGM) for color image inpainting task. During the prior learning process, a certain amount of internal-middle patches are firstly extracted from several images and then the structural-Hankel matrices are constructed from these patches. To better apply the score-based generative model to learn the internal statistical distribution within patches, the large-scale Hankel matrices are finally folded into the higher dimensional tensors for prior learning. During the iterative inpainting process, SHGM views the inpainting problem as a conditional generation procedure in low-rank environment. As a result, the intermediate restored image is acquired by alternatively performing the stochastic differential equation solver, alternating direction method of multipliers, and data consistency steps. Experimental results demonstrated the remarkable performance and diversity of SHGM.Comment: 11 pages, 10 figure

Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction

Although recent deep learning methods, especially generative models, have shown good performance in fast magnetic resonance imaging, there is still much room for improvement in high-dimensional generation. Considering that internal dimensions in score-based generative models have a critical impact on estimating the gradient of the data distribution, we present a new idea, low-rank tensor assisted k-space generative model (LR-KGM), for parallel imaging reconstruction. This means that we transform original prior information into high-dimensional prior information for learning. More specifically, the multi-channel data is constructed into a large Hankel matrix and the matrix is subsequently folded into tensor for prior learning. In the testing phase, the low-rank rotation strategy is utilized to impose low-rank constraints on tensor output of the generative network. Furthermore, we alternately use traditional generative iterations and low-rank high-dimensional tensor iterations for reconstruction. Experimental comparisons with the state-of-the-arts demonstrated that the proposed LR-KGM method achieved better performance

Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction

Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for diagnosis. In this study, leveraging a combination of the properties of k-space data and the diffusion process, our novel scheme focuses on mining the multi-frequency prior with different strategies to pre-serve fine texture details in the reconstructed image. In addition, a diffusion process can converge more quickly if its target distribution closely resembles the noise distri-bution in the process. This can be accomplished through various high-frequency prior extractors. The finding further solidifies the effectiveness of the score-based gen-erative model. On top of all the advantages, our method improves the accuracy of MRI reconstruction and accel-erates sampling process. Experimental results verify that the proposed method successfully obtains more accurate reconstruction and outperforms state-of-the-art methods