Autoformalizing the calculation of $\pi_3(S^2)$
We report our findings and the results of our experiment of autoformalizing the homotopy type theoretic computation of $\pi_3(S^2)$ in agda-unimath using Codex.
math.AT↗
arXiv subjects
Chunyi Liu
Publications and source records attributed to Chunyi Liu.
Two-stage Respiratory Motion-resolved Radial MR Image Reconstruction Using an Interpretable Deep Unrolled Network
Due to the prolonged MRI encoding process, respiratory motion can cause undesired artifacts and image blurring, degrading image quality and limiting clinical applications in abdominal and pulmonary imaging. In this work, we develop a two-stage respiratory motion-resolved radial MR image reconstruction pipeline using an interpretable deep unrolled network (MoraNet), enabling high-quality imaging under free-breathing conditions. Firstly, low-resolution images are reconstructed from the central region of successive golden-angle radial k-space to extract respiratory motion signals. The binned k-space data based on the respiratory signal are then used to reconstruct the motion-resolved high-resolution image for each motion state. The MoraNet applies nonuniform fast Fourier transform (NUFFT) to operate radial encoding and convolutional neural network (CNN) modules to conduct image regularizations. The MoraNet was trained on retrospectively acquired lung MRI images for both fully sampled and undersampled acquisitions. The performance of the proposed method was evaluated on digital CT/MRI breathing XCAT (CoMBAT) phantom data, QUASAR motion phantom data acquired from a 1.0T MRI scanner and volunteer chest data acquired from a 1.5T MRI scanner. The MoraNet pipeline was compared with motion-averaged reconstruction and a conventional compressed sensing (CS)-based method in terms of SSIM, RMSE and computation time. Simulation and experimental results demonstrated that the proposed network could provide accurate respiratory signal estimation and enable effective motion correction. Compared with the CS method, the MoraNet preserved better structural details with lower RMSE and higher SSIM values at acceleration factor of 4, and meanwhile took ten-fold faster inference time.
physics.med-ph↗
Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models
Incoherent k-space undersampling and deep learning-based reconstruction methods have shown great success in accelerating MRI. However, the performance of most previous methods will degrade dramatically under high acceleration factors, e.g., 8$\times$ or higher. Recently, denoising diffusion models (DM) have demonstrated promising results in solving this issue; however, one major drawback of the DM methods is the long inference time due to a dramatic number of iterative reverse posterior sampling steps. In this work, a Single Step Diffusion Model-based reconstruction framework, namely SSDM-MRI, is proposed for restoring MRI images from highly undersampled k-space. The proposed method achieves one-step reconstruction by first training a conditional DM and then iteratively distilling this model four times using an iterative selective distillation algorithm, which works synergistically with a shortcut reverse sampling strategy for model inference. Comprehensive experiments were carried out on both publicly available fastMRI brain and knee images, as well as an in-house multi-echo GRE (QSM) subject. Overall, the results showed that SSDM-MRI outperformed other methods in terms of numerical metrics (e.g., PSNR and SSIM), error maps, image fine details, and latent susceptibility information hidden in MRI phase images. In addition, the reconstruction time for a 320$\times$320 brain slice of SSDM-MRI is only 0.45 second, which is only comparable to that of a simple U-net, making it a highly effective solution for MRI reconstruction tasks.
eess.IV↗
Image Reconstruction with B0 Inhomogeneity using an Interpretable Deep Unrolled Network on an Open-bore MRI-Linac
MRI-Linac systems require fast image reconstruction with high geometric fidelity to localize and track tumours for radiotherapy treatments. However, B0 field inhomogeneity distortions and slow MR acquisition potentially limit the quality of the image guidance and tumour treatments. In this study, we develop an interpretable unrolled network, referred to as RebinNet, to reconstruct distortion-free images from B0 inhomogeneity-corrupted k-space for fast MRI-guided radiotherapy applications. RebinNet includes convolutional neural network (CNN) blocks to perform image regularizations and nonuniform fast Fourier Transform (NUFFT) modules to incorporate B0 inhomogeneity information. The RebinNet was trained on a publicly available MR dataset from eleven healthy volunteers for both fully sampled and subsampled acquisitions. Grid phantom and human brain images acquired from an open-bore 1T MRI-Linac scanner were used to evaluate the performance of the proposed network. The RebinNet was compared with the conventional regularization algorithm and our recently developed UnUNet method in terms of root mean squared error (RMSE), structural similarity (SSIM), residual distortions, and computation time. Imaging results demonstrated that the RebinNet reconstructed images with lowest RMSE (<0.05) and highest SSIM (>0.92) at four-time acceleration for simulated brain images. The RebinNet could better preserve structural details and substantially improve the computational efficiency (ten-fold faster) compared to the conventional regularization methods, and had better generalization ability than the UnUNet method. The proposed RebinNet can achieve rapid image reconstruction and overcome the B0 inhomogeneity distortions simultaneously, which would facilitate accurate and fast image guidance in radiotherapy treatments.
physics.med-ph↗
AutoBCS: Block-based Image Compressive Sensing with Data-driven Acquisition and Non-iterative Reconstruction
Block compressive sensing is a well-known signal acquisition and reconstruction paradigm with widespread application prospects in science, engineering and cybernetic systems. However, state-of-the-art block-based image compressive sensing (BCS) methods generally suffer from two issues. The sparsifying domain and the sensing matrices widely used for image acquisition are not data-driven, and thus both the features of the image and the relationships among subblock images are ignored. Moreover, doing so requires addressing high-dimensional optimization problems with extensive computational complexity for image reconstruction. In this paper, we provide a deep learning strategy for BCS, called AutoBCS, which takes the prior knowledge of images into account in the acquisition step and establishes a subsequent reconstruction model for performing fast image reconstruction with a low computational cost. More precisely, we present a learning-based sensing matrix (LSM) derived from training data to accomplish image acquisition, thereby capturing and preserving more image characteristics than those captured by existing methods. In particular, the generated LSM is proven to satisfy the theoretical requirements of compressive sensing, such as the so-called restricted isometry property. Additionally, we build a noniterative reconstruction network, which provides an end-to-end BCS reconstruction framework to eliminate blocking artifacts and maximize image reconstruction accuracy, in our AutoBCS architecture. Furthermore, we investigate comprehensive comparison studies with both traditional BCS approaches and newly developed deep learning methods. Compared with these approaches, our AutoBCS framework can not only provide superior performance in terms of image quality metrics (SSIM and PSNR) and visual perception, but also automatically benefit reconstruction speed.
eess.SP↗