Yanjie Zhu

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.

Ling Lin, Yihang Zhou, Zhanqi Hu et al.

Tuberous sclerosis complex (TSC) manifests as a multisystem disorder with significant neurological implications. This study addresses the critical need for robust classification models tailored to TSC in pediatric patients, introducing QResNet,a novel deep learning model seamlessly integrating conventional convolutional neural networks with quantum neural networks. The model incorporates a two-layer quantum layer (QL), comprising ZZFeatureMap and Ansatz layers, strategically designed for processing classical data within a quantum framework. A comprehensive evaluation, demonstrates the superior performance of QResNet in TSC MRI image classification compared to conventional 3D-ResNet models. These compelling findings underscore the potential of quantum computing to revolutionize medical imaging and diagnostics.Remarkably, this method surpasses conventional CNNs in accuracy and Area Under the Curve (AUC) metrics with the current dataset. Future research endeavors may focus on exploring the scalability and practical implementation of quantum algorithms in real-world medical imaging scenarios.

Fanshi Li, Zhihui Wang, Yifan Guo et al.

In this paper, a dynamic dual-graph fusion convolutional network is proposed to improve Alzheimer's disease (AD) diagnosis performance. The following are the paper's main contributions: (a) propose a novel dynamic GCN architecture, which is an end-to-end pipeline for diagnosis of the AD task; (b) the proposed architecture can dynamically adjust the graph structure for GCN to produce better diagnosis outcomes by learning the optimal underlying latent graph; (c) incorporate feature graph learning and dynamic graph learning, giving those useful features of subjects more weight while decreasing the weights of other noise features. Experiments indicate that our model provides flexibility and stability while achieving excellent classification results in AD diagnosis.

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.

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.

Yanjie Zhu, Zhen Zhang, Yunli Wang et al.

Cascade ranking is a widely adopted paradigm in large-scale information retrieval systems for Top-K item selection. However, the Top-K operator is non-differentiable, hindering end-to-end training. Existing methods include Learning-to-Rank approaches (e.g., LambdaLoss), which optimize ranking metrics like NDCG and suffer from objective misalignment, and differentiable sorting-based methods (e.g., ARF, LCRON), which relax permutation matrices for direct Top-K optimization but introduce gradient conflicts through matrix aggregation. A promising alternative is to directly construct a differentiable approximation of the Top-K selection operator, bypassing the use of soft permutation matrices. However, even state-of-the-art differentiable Top-K operator (e.g., LapSum) require $O(n \log n)$ complexity due to their dependence on sorting for solving the threshold. Thus, we propose DFTopK, a novel differentiable Top-K operator achieving optimal $O(n)$ time complexity. By relaxing normalization constraints, DFTopK admits a closed-form solution and avoids sorting. DFTopK also avoids the gradient conflicts inherent in differentiable sorting-based methods. We evaluate DFTopK on both the public benchmark RecFLow and an industrial system. Experimental results show that DFTopK significantly improves training efficiency while achieving superior performance, which enables us to scale up training samples more efficiently. In the online A/B test, DFTopK yielded a +1.77% revenue lift with the same computational budget compared to the baseline. To the best of our knowledge, this work is the first to introduce differentiable Top-K operators into recommendation systems and the first to achieve theoretically optimal linear-time complexity for Top-K selection. We have open-sourced our implementation to facilitate future research in both academia and industry.

Yunli Wang, Zhen Zhang, Zixuan Yang et al.

The scaling law is a notable property of neural network models and has significantly propelled the development of large language models. Scaling laws hold great promise in guiding model design and resource allocation. Recent research increasingly shows that scaling laws are not limited to NLP tasks or Transformer architectures; they also apply to domains such as recommendation. However, there is still a lack of literature on scaling law research in online advertisement retrieval systems. This may be because 1) identifying the scaling law for resource cost and online revenue is often expensive in both time and training resources for industrial applications, and 2) varying settings for different systems prevent the scaling law from being applied across various scenarios. To address these issues, we propose a lightweight paradigm to identify online scaling laws of retrieval models, incorporating a novel offline metric and an offline simulation algorithm. We prove that under mild assumptions, the correlation between the novel metric and online revenue asymptotically approaches 1 and empirically validates its effectiveness. The simulation algorithm can estimate the machine cost offline. Based on the lightweight paradigm, we can identify online scaling laws for retrieval models almost exclusively through offline experiments, and quickly estimate machine costs and revenues for given model configurations. We further validate the existence of scaling laws across mainstream model architectures (e.g., Transformer, MLP, and DSSM) in our real-world advertising system. With the identified scaling laws, we demonstrate practical applications for ROI-constrained model designing and multi-scenario resource allocation in the online advertising system. To the best of our knowledge, this is the first work to study identification and application of online scaling laws for online advertisement retrieval.

Chiyi Huang, Longwei Sun, Dong Liang et al.

Cardiac T1 mapping can evaluate various clinical symptoms of myocardial tissue. However, there is currently a lack of effective, robust, and efficient methods for motion correction in cardiac T1 mapping. In this paper, we propose a deep learning-based and topology-preserving image registration framework for motion correction in cardiac T1 mapping. Notably, our proposed implicit consistency constraint dubbed BLOC, to some extent preserves the image topology in registration by bidirectional consistency constraint and local anti-folding constraint. To address the contrast variation issue, we introduce a weighted image similarity metric for multimodal registration of cardiac T1-weighted images. Besides, a semi-supervised myocardium segmentation network and a dual-domain attention module are integrated into the framework to further improve the performance of the registration. Numerous comparative experiments, as well as ablation studies, demonstrated the effectiveness and high robustness of our method. The results also indicate that the proposed weighted image similarity metric, specifically crafted for our network, contributes a lot to the enhancement of the motion correction efficacy, while the bidirectional consistency constraint combined with the local anti-folding constraint ensures a more desirable topology-preserving registration mapping.

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.

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.

Taofeng Xie, Chentao Cao, Zhuoxu Cui et al.

MRI and PET are crucial diagnostic tools for brain diseases, as they provide complementary information on brain structure and function. However, PET scanning is costly and involves radioactive exposure, resulting in a lack of PET. Moreover, simultaneous PET and MRI at ultra-high-field are currently hardly infeasible. Ultra-high-field imaging has unquestionably proven valuable in both clinical and academic settings, especially in the field of cognitive neuroimaging. These motivate us to propose a method for synthetic PET from high-filed MRI and ultra-high-field MRI. From a statistical perspective, the joint probability distribution (JPD) is the most direct and fundamental means of portraying the correlation between PET and MRI. This paper proposes a novel joint diffusion attention model which has the joint probability distribution and attention strategy, named JDAM. JDAM has a diffusion process and a sampling process. The diffusion process involves the gradual diffusion of PET to Gaussian noise by adding Gaussian noise, while MRI remains fixed. JPD of MRI and noise-added PET was learned in the diffusion process. The sampling process is a predictor-corrector. PET images were generated from MRI by JPD of MRI and noise-added PET. The predictor is a reverse diffusion process and the corrector is Langevin dynamics. Experimental results on the public Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that the proposed method outperforms state-of-the-art CycleGAN for high-field MRI (3T MRI). Finally, synthetic PET images from the ultra-high-field (5T MRI and 7T MRI) be attempted, providing a possibility for ultra-high-field PET-MRI imaging.

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.

Yanjie Zhu, Haoxiang Li, Yuanyuan Liu et al.

Purpose: To propose a novel deep learning-based method called RG-Net (reconstruction and generation network) for highly accelerated MR parametric mapping by undersampling k-space and reducing the acquired contrast number simultaneously. Methods: The proposed framework consists of a reconstruction module and a generative module. The reconstruction module reconstructs MR images from the acquired few undersampled k-space data with the help of a data prior. The generative module then synthesizes the remaining multi-contrast images from the reconstructed images, where the exponential model is implicitly incorporated into the image generation through the supervision of fully sampled labels. The RG-Net was evaluated on the T1\r{ho} mapping data of knee and brain at different acceleration rates. Regional T1\r{ho} analysis for cartilage and the brain was performed to access the performance of RG-Net. Results: RG-Net yields a high-quality T1\r{ho} map at a high acceleration rate of 17. Compared with the competing methods that only undersample k-space, our framework achieves better performance in T1\r{ho} value analysis. Our method also improves quality of T1\r{ho} maps on patient with glioma. Conclusion: The proposed RG-Net that adopted a new strategy by undersampling k-space and reducing the contrast number simultaneously for fast MR parametric mapping, can achieve a high acceleration rate while maintaining good reconstruction quality. The generative module of our framework can also be used as an insert module in other fast MR parametric mapping methods. Keywords: Deep learning, convolutional neural network, fast MR parametric mapping

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).

Wei Wang, Yanjie Zhu, Zhuoxu Cui et al.

Convolutional neural network (CNN) models have achieved great success in many fields. With the advent of ResNet, networks used in practice are getting deeper and wider. However, is each layer non-trivial in networks? To answer this question, we trained a network on the training set, then we replace the network convolution kernels with zeros and test the result models on the test set. We compared experimental results with baseline and showed that we can reach similar or even the same performances. Although convolution kernels are the cores of networks, we demonstrate that some of them are trivial and regular in ResNet.

Wei Wang, Lin Cheng, Yanjie Zhu et al.

In recent times, using small data to train networks has become a hot topic in the field of deep learning. Reusing pre-trained parameters is one of the most important strategies to address the issue of semi-supervised and transfer learning. However, the fundamental reason for the success of these methods is still unclear. In this paper, we propose a solution that can not only judge whether a given network is reusable or not based on the performance of reusing convolution kernels but also judge which layers' parameters of the given network can be reused, based on the performance of reusing corresponding parameters and, ultimately, judge whether those parameters are reusable or not in a target task based on the root mean square error (RMSE) of the corresponding convolution kernels. Specifically, we define that the success of a CNN's parameter reuse depends upon two conditions: first, the network is a reusable network; and second, the RMSE between the convolution kernels from the source domain and target domain is small enough. The experimental results demonstrate that the performance of reused parameters applied to target tasks, when these conditions are met, is significantly improved.

Ziwen Ke, Wenqi Huang, Jing Cheng et al.

The deep learning methods have achieved attractive performance in dynamic MR cine imaging. However, all of these methods are only driven by the sparse prior of MR images, while the important low-rank (LR) prior of dynamic MR cine images is not explored, which limits the further improvements on dynamic MR reconstruction. In this paper, a learned singular value thresholding (Learned-SVT) operation is proposed to explore deep low-rank prior in dynamic MR imaging for obtaining improved reconstruction results. In particular, we come up with two novel and distinct schemes to introduce the learnable low-rank prior into deep network architectures in an unrolling manner and a plug-and-play manner respectively. In the unrolling manner, we put forward a model-based unrolling sparse and low-rank network for dynamic MR imaging, dubbed SLR-Net. The SLR-Net is defined over a deep network flow graph, which is unrolled from the iterative procedures in the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a sparse and low-rank based dynamic MRI model. In the plug-and-play manner, we present a plug-and-play LR network module that can be easily embedded into any other dynamic MR neural networks without changing the network paradigm. Experimental results show that both schemes can further improve the state-of-the-art CS methods, such as k-t SLR, and sparsity-driven deep learning-based methods, such as DC-CNN and CRNN, both qualitatively and quantitatively.

Ziwen Ke, Jing Cheng, Leslie Ying et al.

Deep learning has achieved good success in cardiac magnetic resonance imaging (MRI) reconstruction, in which convolutional neural networks (CNNs) learn a mapping from the undersampled k-space to the fully sampled images. Although these deep learning methods can improve the reconstruction quality compared with iterative methods without requiring complex parameter selection or lengthy reconstruction time, the following issues still need to be addressed: 1) all these methods are based on big data and require a large amount of fully sampled MRI data, which is always difficult to obtain for cardiac MRI; 2) the effect of coil correlation on reconstruction in deep learning methods for dynamic MR imaging has never been studied. In this paper, we propose an unsupervised deep learning method for multi-coil cine MRI via a time-interleaved sampling strategy. Specifically, a time-interleaved acquisition scheme is utilized to build a set of fully encoded reference data by directly merging the k-space data of adjacent time frames. Then these fully encoded data can be used to train a parallel network for reconstructing images of each coil separately. Finally, the images from each coil are combined via a CNN to implicitly explore the correlations between coils. The comparisons with classic k-t FOCUSS, k-t SLR, L+S and KLR methods on in vivo datasets show that our method can achieve improved reconstruction results in an extremely short amount of time.

Jing Cheng, Haifeng Wang, Yanjie Zhu et al.

Medical imaging is playing a more and more important role in clinics. However, there are several issues in different imaging modalities such as slow imaging speed in MRI, radiation injury in CT and PET. Therefore, accelerating MRI, reducing radiation dose in CT and PET have been ongoing research topics since their invention. Usually, acquiring less data is a direct but important strategy to address these issues. However, less acquisition usually results in aliasing artifacts in reconstructions. Recently, deep learning (DL) has been introduced in medical image reconstruction and shown potential on significantly speeding up MR reconstruction and reducing radiation dose. In this paper, we propose a general framework on combining the reconstruction model with deep learning to maximize the potential of deep learning and model-based reconstruction, and give the examples to demonstrate the performance and requirements of unrolling different algorithms using deep learning.