Zhuo-Xu Cui

Chentao Cao, Zhuo-Xu Cui, Yue Wang et al.

Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR) reconstruction. However, low-frequency regions of $k$-space data are typically fully sampled in fast MR imaging, while existing diffusion models are performed throughout the entire image or $k$-space, inevitably introducing uncertainty in the reconstruction of low-frequency regions. Additionally, existing diffusion models often demand substantial iterations to converge, resulting in time-consuming reconstructions. To address these challenges, we propose a novel SDE tailored specifically for MR reconstruction with the diffusion process in high-frequency space (referred to as HFS-SDE). This approach ensures determinism in the fully sampled low-frequency regions and accelerates the sampling procedure of reverse diffusion. Experiments conducted on the publicly available fastMRI dataset demonstrate that the proposed HFS-SDE method outperforms traditional parallel imaging methods, supervised deep learning, and existing diffusion models in terms of reconstruction accuracy and stability. The fast convergence properties are also confirmed through theoretical and experimental validation. Our code and weights are available at https://github.com/Aboriginer/HFS-SDE.

Zhuo-Xu Cui, Chentao Cao, Shaonan Liu et al.

Recently, score-based diffusion models have shown satisfactory performance in MRI reconstruction. Most of these methods require a large amount of fully sampled MRI data as a training set, which, sometimes, is difficult to acquire in practice. This paper proposes a fully-sampled-data-free score-based diffusion model for MRI reconstruction, which learns the fully sampled MR image prior in a self-supervised manner on undersampled data. Specifically, we first infer the fully sampled MR image distribution from the undersampled data by Bayesian deep learning, then perturb the data distribution and approximate their probability density gradient by training a score function. Leveraging the learned score function as a prior, we can reconstruct the MR image by performing conditioned Langevin Markov chain Monte Carlo (MCMC) sampling. Experiments on the public dataset show that the proposed method outperforms existing self-supervised MRI reconstruction methods and achieves comparable performances with the conventional (fully sampled data trained) score-based diffusion methods.

Zhuo-Xu Cui, Chentao Cao, Yue Wang et al.

Diffusion models have emerged as a leading methodology for image generation and have proven successful in the realm of magnetic resonance imaging (MRI) reconstruction. However, existing reconstruction methods based on diffusion models are primarily formulated in the image domain, making the reconstruction quality susceptible to inaccuracies in coil sensitivity maps (CSMs). k-space interpolation methods can effectively address this issue but conventional diffusion models are not readily applicable in k-space interpolation. To overcome this challenge, we introduce a novel approach called SPIRiT-Diffusion, which is a diffusion model for k-space interpolation inspired by the iterative self-consistent SPIRiT method. Specifically, we utilize the iterative solver of the self-consistent term (i.e., k-space physical prior) in SPIRiT to formulate a novel stochastic differential equation (SDE) governing the diffusion process. Subsequently, k-space data can be interpolated by executing the diffusion process. This innovative approach highlights the optimization model's role in designing the SDE in diffusion models, enabling the diffusion process to align closely with the physics inherent in the optimization model, a concept referred to as model-driven diffusion. We evaluated the proposed SPIRiT-Diffusion method using a 3D joint intracranial and carotid vessel wall imaging dataset. The results convincingly demonstrate its superiority over image-domain reconstruction methods, achieving high reconstruction quality even at a substantial acceleration rate of 10.

Wenxin Wang, Zhuo-Xu Cui, Guanxun Cheng et al.

Accurate detection and segmentation of brain tumors is critical for medical diagnosis. However, current supervised learning methods require extensively annotated images and the state-of-the-art generative models used in unsupervised methods often have limitations in covering the whole data distribution. In this paper, we propose a novel framework Two-Stage Generative Model (TSGM) that combines Cycle Generative Adversarial Network (CycleGAN) and Variance Exploding stochastic differential equation using joint probability (VE-JP) to improve brain tumor detection and segmentation. The CycleGAN is trained on unpaired data to generate abnormal images from healthy images as data prior. Then VE-JP is implemented to reconstruct healthy images using synthetic paired abnormal images as a guide, which alters only pathological regions but not regions of healthy. Notably, our method directly learned the joint probability distribution for conditional generation. The residual between input and reconstructed images suggests the abnormalities and a thresholding method is subsequently applied to obtain segmentation results. Furthermore, the multimodal results are weighted with different weights to improve the segmentation accuracy further. We validated our method on three datasets, and compared with other unsupervised methods for anomaly detection and segmentation. The DSC score of 0.8590 in BraTs2020 dataset, 0.6226 in ITCS dataset and 0.7403 in In-house dataset show that our method achieves better segmentation performance and has better generalization.

Taofeng Xie, Zhuo-Xu Cui, Chen Luo et al.

Positron Emission Tomography and Magnetic Resonance Imaging (PET-MRI) systems can obtain functional and anatomical scans. PET suffers from a low signal-to-noise ratio. Meanwhile, the k-space data acquisition process in MRI is time-consuming. The study aims to accelerate MRI and enhance PET image quality. Conventional approaches involve the separate reconstruction of each modality within PET-MRI systems. However, there exists complementary information among multi-modal images. The complementary information can contribute to image reconstruction. In this study, we propose a novel PET-MRI joint reconstruction model employing a mutual consistency-driven diffusion mode, namely MC-Diffusion. MC-Diffusion learns the joint probability distribution of PET and MRI for utilizing complementary information. We conducted a series of contrast experiments about LPLS, Joint ISAT-net and MC-Diffusion by the ADNI dataset. The results underscore the qualitative and quantitative improvements achieved by MC-Diffusion, surpassing the state-of-the-art method.

Zhuo-Xu Cui, Congcong Liu, Xiaohong Fan et al.

In the field of parallel imaging (PI), alongside image-domain regularization methods, substantial research has been dedicated to exploring $k$-space interpolation. However, the interpretability of these methods remains an unresolved issue. Furthermore, these approaches currently face acceleration limitations that are comparable to those experienced by image-domain methods. In order to enhance interpretability and overcome the acceleration limitations, this paper introduces an interpretable framework that unifies both $k$-space interpolation techniques and image-domain methods, grounded in the physical principles of heat diffusion equations. Building upon this foundational framework, a novel $k$-space interpolation method is proposed. Specifically, we model the process of high-frequency information attenuation in $k$-space as a heat diffusion equation, while the effort to reconstruct high-frequency information from low-frequency regions can be conceptualized as a reverse heat equation. However, solving the reverse heat equation poses a challenging inverse problem. To tackle this challenge, we modify the heat equation to align with the principles of magnetic resonance PI physics and employ the score-based generative method to precisely execute the modified reverse heat diffusion. Finally, experimental validation conducted on publicly available datasets demonstrates the superiority of the proposed approach over traditional $k$-space interpolation methods, deep learning-based $k$-space interpolation methods, and conventional diffusion models in terms of reconstruction accuracy, particularly in high-frequency regions.

Chentao Cao, Zhuo-Xu Cui, Jing Cheng et al.

Diffusion model is the most advanced method in image generation and has been successfully applied to MRI reconstruction. However, the existing methods do not consider the characteristics of multi-coil acquisition of MRI data. Therefore, we give a new diffusion model, called SPIRiT-Diffusion, based on the SPIRiT iterative reconstruction algorithm. Specifically, SPIRiT-Diffusion characterizes the prior distribution of coil-by-coil images by score matching and characterizes the k-space redundant prior between coils based on self-consistency. With sufficient prior constraint utilized, we achieve superior reconstruction results on the joint Intracranial and Carotid Vessel Wall imaging dataset.

Zhuo-Xu Cui, Qingyong Zhu, Jing Cheng et al.

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have better interpretability and performance. However, to our knowledge, their accuracy and stability in solving inverse problems cannot be fully guaranteed. To bridge this gap, we modified the training procedure and proved that the unfolding method is an iterative regularization method. More precisely, we jointly learn a convex penalty function adversarially by an input-convex neural network (ICNN) to characterize the distance to a real data manifold and train a DNN unfolded from the proximal gradient descent algorithm with this learned penalty. Suppose the real data manifold intersects the inverse problem solutions with only the unique real solution. We prove that the unfolded DNN will converge to it stably. Furthermore, we demonstrate with an example of MRI reconstruction that the proposed method outperforms conventional unfolding methods and traditional regularization methods in terms of reconstruction quality, stability and convergence speed.

Yuliang Zhu, Jing Cheng, Zhuo-Xu Cui et al.

Dynamic MR images possess various transformation symmetries,including the rotation symmetry of local features within the image and along the temporal dimension. Utilizing these symmetries as prior knowledge can facilitate dynamic MR imaging with high spatiotemporal resolution. Equivariant CNN is an effective tool to leverage the symmetry priors. However, current equivariant CNN methods fail to fully exploit these symmetry priors in dynamic MR imaging. In this work, we propose a novel framework of Spatiotemporal Rotation-Equivariant CNN (SRE-CNN), spanning from the underlying high-precision filter design to the construction of the temporal-equivariant convolutional module and imaging model, to fully harness the rotation symmetries inherent in dynamic MR images. The temporal-equivariant convolutional module enables exploitation the rotation symmetries in both spatial and temporal dimensions, while the high-precision convolutional filter, based on parametrization strategy, enhances the utilization of rotation symmetry of local features to improve the reconstruction of detailed anatomical structures. Experiments conducted on highly undersampled dynamic cardiac cine data (up to 20X) have demonstrated the superior performance of our proposed approach, both quantitatively and qualitatively.

Zhuo-Xu Cui, Sen Jia, Qingyong Zhu et al.

Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approach does not fully use the MR image physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier, regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k-space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k-space data), including sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k-space data accuracy. Finally, ablation experiments show that the proposed method can more accurately characterize the physical priors of MR images than existing traditional methods. Additionally, under a series of commonly used sampling trajectories, experiments also show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and even outperforms the state-of-the-art supervised-trained k-space deep learning methods in some cases.

Chen Luo, Huayu Wang, Taofeng Xie et al.

Recently, regularization model-driven deep learning (DL) has gained significant attention due to its ability to leverage the potent representational capabilities of DL while retaining the theoretical guarantees of regularization models. However, most of these methods are tailored for supervised learning scenarios that necessitate fully sampled labels, which can pose challenges in practical MRI applications. To tackle this challenge, we propose a self-supervised DL approach for accelerated MRI that is theoretically guaranteed and does not rely on fully sampled labels. Specifically, we achieve neural network structure regularization by exploiting the inherent structural low-rankness of the $k$-space data. Simultaneously, we constrain the network structure to resemble a nonexpansive mapping, ensuring the network's convergence to a fixed point. Thanks to this well-defined network structure, this fixed point can completely reconstruct the missing $k$-space data based on matrix completion theory, even in situations where full-sampled labels are unavailable. Experiments validate the effectiveness of our proposed method and demonstrate its superiority over existing self-supervised approaches and traditional regularization methods, achieving performance comparable to that of supervised learning methods in certain scenarios.

Huayu Wang, Chen Luo, Taofeng Xie et al.

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and robustness. In response, we introduce Convex Latent-Optimized Adversarial Regularizers (CLEAR), a novel and interpretable data-driven paradigm. CLEAR represents a fusion of deep learning (DL) and variational regularization. Specifically, we employ a latent optimization technique to adversarially train an input convex neural network, and its set of minima can fully represent the real data manifold. We utilize it as a convex regularizer to formulate a CLEAR-informed variational regularization model that guides the solution of the imaging inverse problem on the real data manifold. Leveraging its inherent convexity, we have established the convergence of the projected subgradient descent algorithm for the CLEAR-informed regularization model. This convergence guarantees the attainment of a unique solution to the imaging inverse problem, subject to certain assumptions. Furthermore, we have demonstrated the robustness of our CLEAR-informed model, explicitly showcasing its capacity to achieve stable reconstruction even in the presence of measurement interference. Finally, we illustrate the superiority of our approach using MRI reconstruction as an example. Our method consistently outperforms conventional data-driven techniques and traditional regularization approaches, excelling in both reconstruction quality and robustness.

Chentao Cao, Zhuo-Xu Cui, Qingyong Zhu et al.

Deep learning methods driven by the low-rank regularization have achieved attractive performance in dynamic magnetic resonance (MR) imaging. However, most of these methods represent low-rank prior by hand-crafted nuclear norm, which cannot accurately approximate the low-rank prior over the entire dataset through a fixed regularization parameter. In this paper, we propose a learned low-rank method for dynamic MR imaging. In particular, we unrolled the semi-quadratic splitting method (HQS) algorithm for the partially separable (PS) model to a network, in which the low-rank is adaptively characterized by a learnable null-space transform. Experiments on the cardiac cine dataset show that the proposed model outperforms the state-of-the-art compressed sensing (CS) methods and existing deep learning methods both quantitatively and qualitatively.

Yue Wang, Yuanbiao Yang, Zhuo-xu Cui et al.

Magnetic Resonance Imaging (MRI) is an inherently multi-contrast modality, where cross-contrast priors can be exploited to improve image reconstruction from undersampled data. Recently, diffusion models have shown remarkable performance in MRI reconstruction. However, they still struggle to effectively utilize such priors, mainly because existing methods rely on feature-level fusion in image or latent spaces, which lacks explicit structural correspondence and thus leads to suboptimal performance. To address this issue, we propose $\mathbf{I}^2$SB-Inversion, a multi-contrast guided reconstruction framework based on the Schrödinger Bridge (SB). The proposed method performs pixel-wise translation between paired contrasts, providing explicit structural constraints between the guidance and target images. Furthermore, an Inversion strategy is introduced to correct inter-modality misalignment, which often occurs in guided reconstruction, thereby mitigating artifacts and improving reconstruction accuracy. Experiments on paired T1- and T2-weighted datasets demonstrate that $\mathbf{I}^2$SB-Inversion achieves a high acceleration factor of up to 14.4 and consistently outperforms existing methods in both quantitative and qualitative evaluations.

Baoqing Li, Yuanyuan Liu, Congcong Liu et al.

Dynamic magnetic resonance imaging (dMRI) captures temporally-resolved anatomy but is often challenged by limited sampling and motion-induced artifacts. Conventional motion-compensated reconstructions typically rely on pre-estimated optical flow, which is inaccurate under undersampling and degrades reconstruction quality. In this work, we propose a novel implicit neural representation (INR) framework that jointly models both the dynamic image sequence and its underlying motion field. Specifically, one INR is employed to parameterize the spatiotemporal image content, while another INR represents the optical flow. The two are coupled via the optical flow equation, which serves as a physics-inspired regularization, in addition to a data consistency loss that enforces agreement with k-space measurements. This joint optimization enables simultaneous recovery of temporally coherent images and motion fields without requiring prior flow estimation. Experiments on dynamic cardiac MRI datasets demonstrate that the proposed method outperforms state-of-the-art motion-compensated and deep learning approaches, achieving superior reconstruction quality, accurate motion estimation, and improved temporal fidelity. These results highlight the potential of implicit joint modeling with flow-regularized constraints for advancing dMRI reconstruction.

Jingran Xu, Yuanyuan Liu, Yuanbiao Yang et al.

Magnetic resonance imaging (MRI) is a vital clinical diagnostic tool, yet its application is limited by prolonged scan times. Accelerating MRI reconstruction addresses this issue by reconstructing high-fidelity MR images from undersampled k-space measurements. In recent years, deep learning-based methods have demonstrated remarkable progress. However, most methods rely on supervised learning, which requires large amounts of fully-sampled training data that are difficult to obtain. This paper proposes a novel zero-shot self-supervised reconstruction method named UnrollINR, which enables scan-specific MRI reconstruction without external training data. UnrollINR adopts a physics-guided unrolled reconstruction architecture and introduces implicit neural representation (INR) as a regularization prior to effectively constrain the solution space. This method overcomes the local bias limitation of CNNs in traditional deep unrolled methods and avoids the instability associated with relying solely on INR's implicit regularization in highly ill-posed scenarios. Consequently, UnrollINR significantly improves MRI reconstruction performance under high acceleration rates. Experimental results show that even at a high acceleration rate of 10, UnrollINR achieves superior reconstruction performance compared to supervised and self-supervised learning methods, validating its effectiveness and superiority.

Yihong Luo, Wenwu He, Zhuo-Xu Cui et al.

This study presents DiagCoT, a multi-stage framework that applies supervised fine-tuning to general-purpose vision-language models (VLMs) to emulate radiologists' stepwise diagnostic reasoning using only free-text reports. DiagCoT combines contrastive image-report tuning for domain alignment, chain-of-thought supervision to capture inferential logic, and reinforcement tuning with clinical reward signals to enhance factual accuracy and fluency. On the MIMIC-CXR benchmark, DiagCoT improved zero-shot disease classification AUC from 0.52 to 0.76 (absolute gain of 0.24), pathology grounding mIoU from 0.08 to 0.31 (absolute gain of 0.23), and report generation BLEU from 0.11 to 0.33 (absolute gain of 0.22). It outperformed state-of-the-art models including LLaVA-Med and CXR-LLAVA on long-tailed diseases and external datasets. By converting unstructured clinical narratives into structured supervision, DiagCoT offers a scalable approach for developing interpretable and diagnostically competent AI systems for radiology.

Chen Luo, Qiyu Jin, Taofeng Xie et al.

Interpolating missing data in k-space is essential for accelerating imaging. However, existing methods, including convolutional neural network-based deep learning, primarily exploit local predictability while overlooking the inherent global dependencies in k-space. Recently, Transformers have demonstrated remarkable success in natural language processing and image analysis due to their ability to capture long-range dependencies. This inspires the use of Transformers for k-space interpolation to better exploit its global structure. However, their lack of interpretability raises concerns regarding the reliability of interpolated data. To address this limitation, we propose GPI-WT, a white-box Transformer framework based on Globally Predictable Interpolation (GPI) for k-space. Specifically, we formulate GPI from the perspective of annihilation as a novel k-space structured low-rank (SLR) model. The global annihilation filters in the SLR model are treated as learnable parameters, and the subgradients of the SLR model naturally induce a learnable attention mechanism. By unfolding the subgradient-based optimization algorithm of SLR into a cascaded network, we construct the first white-box Transformer specifically designed for accelerated MRI. Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art approaches in k-space interpolation accuracy while providing superior interpretability.

Yuliang Zhu, Jing Cheng, Qi Xie et al.

Dynamic Magnetic Resonance Imaging (MRI) exhibits transformation symmetries, including spatial rotation symmetry within individual frames and temporal symmetry along the time dimension. Explicit incorporation of these symmetry priors in the reconstruction model can significantly improve image quality, especially under aggressive undersampling scenarios. Recently, Equivariant convolutional neural network (ECNN) has shown great promise in exploiting spatial symmetry priors. However, existing ECNNs critically fail to model temporal symmetry, arguably the most universal and informative structural prior in dynamic MRI reconstruction. To tackle this issue, we propose a novel Deep Unrolling Network with Spatiotemporal Rotation Equivariance (DUN-SRE) for Dynamic MRI Reconstruction. The DUN-SRE establishes spatiotemporal equivariance through a (2+1)D equivariant convolutional architecture. In particular, it integrates both the data consistency and proximal mapping module into a unified deep unrolling framework. This architecture ensures rigorous propagation of spatiotemporal rotation symmetry constraints throughout the reconstruction process, enabling more physically accurate modeling of cardiac motion dynamics in cine MRI. In addition, a high-fidelity group filter parameterization mechanism is developed to maintain representation precision while enforcing symmetry constraints. Comprehensive experiments on Cardiac CINE MRI datasets demonstrate that DUN-SRE achieves state-of-the-art performance, particularly in preserving rotation-symmetric structures, offering strong generalization capability to a broad range of dynamic MRI reconstruction tasks.

Zhuo-Xu Cui, Congcong Liu, Chentao Cao et al.

Magnetic resonance imaging (MRI) is known to have reduced signal-to-noise ratios (SNR) at lower field strengths, leading to signal degradation when producing a low-field MRI image from a high-field one. Therefore, reconstructing a high-field-like image from a low-field MRI is a complex problem due to the ill-posed nature of the task. Additionally, obtaining paired low-field and high-field MR images is often not practical. We theoretically uncovered that the combination of these challenges renders conventional deep learning methods that directly learn the mapping from a low-field MR image to a high-field MR image unsuitable. To overcome these challenges, we introduce a novel meta-learning approach that employs a teacher-student mechanism. Firstly, an optimal-transport-driven teacher learns the degradation process from high-field to low-field MR images and generates pseudo-paired high-field and low-field MRI images. Then, a score-based student solves the inverse problem of reconstructing a high-field-like MR image from a low-field MRI within the framework of iterative regularization, by learning the joint distribution of pseudo-paired images to act as a regularizer. Experimental results on real low-field MRI data demonstrate that our proposed method outperforms state-of-the-art unpaired learning methods.

Zhuo-Xu Cui, Jing Cheng, Qingyong Zhu et al.

Recently, model-driven deep learning unrolls a certain iterative algorithm of a regularization model into a cascade network by replacing the first-order information (i.e., (sub)gradient or proximal operator) of the regularizer with a network module, which appears more explainable and predictable compared to common data-driven networks. Conversely, in theory, there is not necessarily such a functional regularizer whose first-order information matches the replaced network module, which means the network output may not be covered by the original regularization model. Moreover, up to now, there is also no theory to guarantee the global convergence and robustness (regularity) of unrolled networks under realistic assumptions. To bridge this gap, this paper propose to present a safeguarded methodology on network unrolling. Specifically, focusing on accelerated MRI, we unroll a zeroth-order algorithm, of which the network module represents the regularizer itself, so that the network output can be still covered by the regularization model. Furthermore, inspired by the ideal of deep equilibrium models, before backpropagating, we carry out the unrolled iterative network to converge to a fixed point to ensure the convergence. In case the measurement data contains noise, we prove that the proposed network is robust against noisy interference. Finally, numerical experiments show that the proposed network consistently outperforms the state-of-the-art MRI reconstruction methods including traditional regularization methods and other deep learning methods.

Wenqi Huang, Sen Jia, Ziwen Ke et al.

Improving the image resolution and acquisition speed of magnetic resonance imaging (MRI) is a challenging problem. There are mainly two strategies dealing with the speed-resolution trade-off: (1) $k$-space undersampling with high-resolution acquisition, and (2) a pipeline of lower resolution image reconstruction and image super-resolution. However, these approaches either have limited performance at certain high acceleration factor or suffer from the error accumulation of two-step structure. In this paper, we combine the idea of MR reconstruction and image super-resolution, and work on recovering HR images from low-resolution under-sampled $k$-space data directly. Particularly, the SR-involved reconstruction can be formulated as a variational problem, and a learnable network unrolled from its solution algorithm is proposed. A discriminator was introduced to enhance the detail refining performance. Experiment results using in-vivo HR multi-coil brain data indicate that the proposed SRR-Net is capable of recovering high-resolution brain images with both good visual quality and perceptual quality.

Ziwen Ke, Zhuo-Xu Cui, Wenqi Huang et al.

Purpose: To develop a deep learning method on a nonlinear manifold to explore the temporal redundancy of dynamic signals to reconstruct cardiac MRI data from highly undersampled measurements. Methods: Cardiac MR image reconstruction is modeled as general compressed sensing (CS) based optimization on a low-rank tensor manifold. The nonlinear manifold is designed to characterize the temporal correlation of dynamic signals. Iterative procedures can be obtained by solving the optimization model on the manifold, including gradient calculation, projection of the gradient to tangent space, and retraction of the tangent space to the manifold. The iterative procedures on the manifold are unrolled to a neural network, dubbed as Manifold-Net. The Manifold-Net is trained using in vivo data with a retrospective electrocardiogram (ECG)-gated segmented bSSFP sequence. Results: Experimental results at high accelerations demonstrate that the proposed method can obtain improved reconstruction compared with a compressed sensing (CS) method k-t SLR and two state-of-the-art deep learning-based methods, DC-CNN and CRNN. Conclusion: This work represents the first study unrolling the optimization on manifolds into neural networks. Specifically, the designed low-rank manifold provides a new technical route for applying low-rank priors in dynamic MR imaging.

Wenqi Huang, Ziwen Ke, Zhuo-Xu Cui et al.

In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S) decomposition, or robust principal component analysis (PCA), has achieved stunning performance. However, the selection of the parameters of L+S is empirical, and the acceleration rate is limited, which are common failings of iterative compressed sensing MR imaging (CS-MRI) reconstruction methods. Many deep learning approaches have been proposed to address these issues, but few of them use a low-rank prior. In this paper, a model-based low-rank plus sparse network, dubbed L+S-Net, is proposed for dynamic MR reconstruction. In particular, we use an alternating linearized minimization method to solve the optimization problem with low-rank and sparse regularization. Learned soft singular value thresholding is introduced to ensure the clear separation of the L component and S component. Then, the iterative steps are unrolled into a network in which the regularization parameters are learnable. We prove that the proposed L+S-Net achieves global convergence under two standard assumptions. Experiments on retrospective and prospective cardiac cine datasets show that the proposed model outperforms state-of-the-art CS and existing deep learning methods and has great potential for extremely high acceleration factors (up to 24x).