Cardiovascular health is vital to human well-being, and cardiac magnetic resonance (CMR) imaging is considered the clinical reference standard for diagnosing cardiovascular disease. However, its adoption is hindered by long scan times, complex contrasts, and inconsistent quality. While deep learning methods perform well on specific CMR imaging sequences, they often fail to generalize across modalities and sampling schemes. The lack of benchmarks for high-quality, fast CMR image reconstruction further limits technology comparison and adoption. The CMRxRecon2024 challenge, attracting over 200 teams from 18 countries, addressed these issues with two tasks: generalization to unseen modalities and robustness to diverse undersampling patterns. We introduced the largest public multi-modality CMR raw dataset, an open benchmarking platform, and shared code. Analysis of the best-performing solutions revealed that prompt-based adaptation and enhanced physics-driven consistency enabled strong cross-scenario performance. These findings establish principles for generalizable reconstruction models and advance clinically translatable AI in cardiovascular imaging.

Soft-thresholding (ST) has been widely used in deep neural networks. Its fundamental network structure is a deep soft-thresholding fully connected network (ST-FCN). However, training deep ST-FCN to achieve convergence remains time-consuming or even encounters gradient explosion, in part because the convergence behavior is not fully understood. To address this issue, this article proves the relationship between the convergence of deep ST-FCN and the values of network weights and biases. Theoretical analysis shows that, as the number of network layers approaches infinity, deep ST-FCN converges when the network weights tend to an identity matrix, while the biases tend to zero. Following this guidance, we initialize the network weights as the identity matrix, compare it with other representative initialization methods (Gaussian, He, LeCun, Xavier, and Uniform), and quantify their effects on network convergence. Extensive results on a synthetic spectrum dataset and real-world datasets (MNIST and CIFAR-10) demonstrate that initializing the weights to the identity matrix and the bias to zero leads to fast and stable convergence. These conclusions are further supported by additional experiments and statistical analysis on deeper ST networks (with more than ten layers) and other representative architectures (DenseNet-161, ResNet-152, and VGG-19), and more challenging benchmarks (CIFAR-100, STL-10, and Tiny ImageNet). This work provides a theoretical foundation for understanding the convergence of ST neural networks. Furthermore, convergence theory analysis for deep recurrent neural networks (RNNs) with ST is deduced.

Implicit regularization induced by gradient optimization is an important way to understand generalization in neural networks. Recent theory explains implicit regularization over the deep matrix factorization (DMF) model and analyzes the trajectory of discrete gradient dynamics in the optimization process. These discrete gradient dynamics can mathematically characterize the practical learning rate of adaptive gradient (AdaGrad) optimization, such as root-mean-square propagation (RMSProp). Discrete gradient dynamics analysis has been successfully applied to shallow networks but encounters difficulty in complex computation for deep networks. In this work, we introduce another discrete gradient dynamics, landscape analysis, to theoretically and experimentally explain the implicit regularization of RMSProp-based deep networks. It mainly focuses on gradient regions like saddle points and local minima. We investigate the benefits of increasing learning rates in saddle point escaping (SPE) stages. We prove that, for a rank-R matrix reconstruction, DMF will converge to a second-order critical point after R stages of SPE. Besides, we analyze the time it takes to escape from the plateau of the SPE stage. These conclusions are further experimentally verified on low-rank matrix, image reconstruction, and Hankel matrix reconstruction problems. Our proof is also applicable to gradient descent (GD) and adaptive moment estimation (Adam) but cannot apply to AdaGrad, further showing experimentally that the implicit regularization capability of RMSProp is stronger than GD and AdaGrad and weaker than Adam.

Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinear and nonconvex, the training process heavily depends on an appropriate initialization of network parameters, resulting in the difficulty of obtaining a globally optimal solution. To address this issue, a convex dual network is designed here. We theoretically analyze the network convexity and prove that the strong duality holds. Extensive results on both simulation and real-world datasets show that strong duality holds, the dual network does not depend on initialization and optimizer, and enables faster convergence than the state-of-the-art two-layer network. This work provides a new way to convexify soft-thresholding neural networks. Furthermore, the convex dual network model of a deep soft-thresholding network with a parallel structure is deduced.

Magnetic resonance imaging (MRI) plays a pivotal role in modern medical diagnosis yet is often hindered by the long imaging time. MRI imaging can be accelerated through undersampling, but the introduced aliasing artifacts should be removed during image reconstruction. While deep learning reconstruction methods excel at image de-aliasing, they may yield suboptimal results when training sampling settings differ from those at the time of reconstruction. To decouple from specific sampling settings, we propose using synthetic data to generate a substantial training dataset and pre-train a 1D deep denoiser. We then integrate the trained deep denoiser into the iterative reconstruction process as a replacement for the approximation operator within the deep plug-and-play framework. In vivo results indicate that the proposed method exhibits robust and visually appealing image reconstruction when there is a mismatch between the training and reconstruction undersampling settings, such as different undersampling patterns and sampling rates.

Efficient collaboration between engineers and radiologists is important for image reconstruction algorithm development and image quality evaluation in magnetic resonance imaging (MRI). Here, we develop CloudBrain-ReconAI, an online cloud computing platform, for algorithm deployment, fast and blind reader study. This platform supports online image reconstruction using state-of-the-art artificial intelligence and compressed sensing algorithms with applications for fast imaging (Cartesian and non-Cartesian sampling) and high-resolution diffusion imaging. Through visiting the website, radiologists can easily score and mark images. Then, automatic statistical analysis will be provided.

Magnetic resonance imaging (MRI) is an essential diagnostic tool that suffers from prolonged scan time. To alleviate this limitation, advanced fast MRI technology attracts extensive research interests. Recent deep learning has shown its great potential in improving image quality and reconstruction speed. Faithful coil sensitivity estimation is vital for MRI reconstruction. However, most deep learning methods still rely on pre-estimated sensitivity maps and ignore their inaccuracy, resulting in the significant quality degradation of reconstructed images. In this work, we propose a Joint Deep Sensitivity estimation and Image reconstruction network, called JDSI. During the image artifacts removal, it gradually provides more faithful sensitivity maps with high-frequency information, leading to improved image reconstructions. To understand the behavior of the network, the mutual promotion of sensitivity estimation and image reconstruction is revealed through the visualization of network intermediate results. Results on in vivo datasets and radiologist reader study demonstrate that, for both calibration-based and calibrationless reconstruction, the proposed JDSI achieves the state-of-the-art performance visually and quantitatively, especially when the acceleration factor is high. Additionally, JDSI owns nice robustness to patients and autocalibration signals.

Deep learning has shown astonishing performance in accelerated magnetic resonance imaging (MRI). Most state-of-the-art deep learning reconstructions adopt the powerful convolutional neural network and perform 2D convolution since many magnetic resonance images or their corresponding k-space are in 2D. In this work, we present a new approach that explores the 1D convolution, making the deep network much easier to be trained and generalized. We further integrate the 1D convolution into the proposed deep network, named as One-dimensional Deep Low-rank and Sparse network (ODLS), which unrolls the iteration procedure of a low-rank and sparse reconstruction model. Extensive results on in vivo knee and brain datasets demonstrate that, the proposed ODLS is very suitable for the case of limited training subjects and provides improved reconstruction performance than state-of-the-art methods both visually and quantitatively. Additionally, ODLS also shows nice robustness to different undersampling scenarios and some mismatches between the training and test data. In summary, our work demonstrates that the 1D deep learning scheme is memory-efficient and robust in fast MRI.

Exponential function is a basic form of temporal signals, and how to fast acquire this signal is one of the fundamental problems and frontiers in signal processing. To achieve this goal, partial data may be acquired but result in severe artifacts in its spectrum, which is the Fourier transform of exponentials. Thus, reliable spectrum reconstruction is highly expected in the fast data acquisition in many applications, such as chemistry, biology, and medical imaging. In this work, we propose a deep learning method whose neural network structure is designed by imitating the iterative process in the model-based state-of-the-art exponentials' reconstruction method with the low-rank Hankel matrix factorization. With the experiments on synthetic data and realistic biological magnetic resonance signals, we demonstrate that the new method yields much lower reconstruction errors and preserves the low-intensity signals much better than compared methods.

The nonuniform sampling (NUS) is a powerful approach to enable fast acquisition but requires sophisticated reconstruction algorithms. Faithful reconstruction from partially sampled exponentials is highly expected in general signal processing and many applications. Deep learning (DL) has shown astonishing potential in this field, but many existing problems, such as lack of robustness and explainability, greatly limit its applications. In this work, by combining the merits of the sparse model-based optimization method and data-driven DL, we propose a DL architecture for spectra reconstruction from undersampled data, called MoDern. It follows the iterative reconstruction in solving a sparse model to build the neural network, and we elaborately design a learnable soft-thresholding to adaptively eliminate the spectrum artifacts introduced by undersampling. Extensive results on both synthetic and biological data show that MoDern enables more robust, high-fidelity, and ultrafast reconstruction than the state-of-the-art methods. Remarkably, MoDern has a small number of network parameters and is trained on solely synthetic data while generalizing well to biological data in various scenarios. Furthermore, we extend it to an open-access and easy-to-use cloud computing platform (XCloud-MoDern), contributing a promising strategy for further development of biological applications.

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

Abstract Nuclear magnetic resonance with diffusion‐ordered spectroscopy (DOSY) serves as an important analytical tool to non‐destructively separate a molecule from a compound in medicine and chemistry. However, the data acquisition time increases rapidly for multidimensional DOSY. To enable fast DOSY, partial data are acquired with non‐uniform sampling, and the spectrum can be reconstructed with a proper constraint, such as sparsity in the state‐of‐the‐art method. However, the reconstructed spectrum is observed to have isolated artefacts, which can be easily recognised as fake peaks and affect the estimated diffusion coefficients severely. The authors introduce the low‐rank constraint as an effective remedy to remove these artefacts and derive a fast algorithm to solve the reconstruction problem. Results on both synthetic and realistic DOSY spectra show that a better spectrum and more accurate diffusion coefficients can be achieved.

Abstract The nuclear magnetic resonance (NMR) spectroscopy has fruitful applications in chemistry, biology and life sciences, but suffers from long acquisition time. Non‐uniform sampling is a typical fast NMR method by undersampling the time‐domain data of the spectrum but need to restore the fully sampled data with proper constraints. The state‐of‐the‐art method is to model the time‐domain data as the sum of exponential functions and reconstruct these data by enforcing the low rankness of Hankel matrix. However, this method is solved by minimizing the sum of singular values of the Hankel matrix, which leads to the distortion of low‐intensity spectral peaks. Here, a low rank Hankel matrix reconstruction approach with a partial sum of singular values is proposed to protect small singular values, which can faithfully reconstruct all peaks. Results on both synthetic and realistic NMR spectroscopy show that the proposed method can reconstruct a more consistent spectrum to the fully sampled one than other state‐of‐the‐art methods and have particular advantages on preserving low‐intensity peaks .

Conventional sparse coding based super-resolution (SR) methods obtained promising performance by learning overcomplete dictionaries for low-resolution (LR) and high-resolution (HR) feature spaces, and assuming that the sparse representation of a HR feature vector was identical or linear to the sparse representation of the corresponding LR one. However, in fact, the relationship between LR and HR sparse domains is nonlinear due to the complicated degradation of the observed image. To learn the relation more precisely, an assumption called “the same-support constraint” is adopted in our proposed method, which forces LR/HR image patches to activate the atoms lying in the same locations of the LR/HR dictionaries. Under the same-support constraint, our approach first learns LR dictionary, and then obtains HR dictionary and a nonlinear mapping between LR/HR sparse domains by training them iteratively. LR/HR dictionaries learned individually can explore structural characteristics of their corresponding feature spaces well, while the mapping learned iteratively can reveals accurately the intrinsic non-linear relationship between LR and HR sparse domains. Experimental results show that the proposed method outperforms the compared sparse learning based single image super-resolution methods.

Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). Recently, a spread spectrum compressed sensing MRI method modulates an image with a quadratic phase. It performs better than the conventional compressed sensing MRI with variable density sampling, since the coherence between the sensing and sparsity bases are reduced. However, spread spectrum in that method is implemented via a shim coil which limits its modulation intensity and is not convenient to operate. In this letter, we propose to apply chirp (linear frequency-swept) radio frequency pulses to easily control the spread spectrum. To accelerate the image reconstruction, an alternating direction method of multipliers (ADMM) algorithm is modified by exploiting the complex orthogonality of the quadratic phase encoding. Reconstruction on the acquired data demonstrates that more image features are preserved using the proposed approach than those of conventional compressed sensing MRI.

Compressed sensing (CS) has exhibited great potential for accelerating magnetic resonance imaging (MRI). In CS-MRI, we want to reconstruct a high-quality image from very few samples in a short time. In this paper, we propose a fast algorithm, called projected iterative soft-thresholding algorithm (pISTA), and its acceleration pFISTA for CS-MRI image reconstruction. The proposed algorithms exploit sparsity of the magnetic resonance (MR) images under the redundant representation of tight frames. We prove that pISTA and pFISTA converge to a minimizer of a convex function with a balanced tight frame sparsity formulation. The pFISTA introduces only one adjustable parameter, the step size, and we provide an explicit rule to set this parameter. Numerical experiment results demonstrate that pFISTA leads to faster convergence speeds than the state-of-art counterpart does, while achieving comparable reconstruction errors. Moreover, reconstruction errors incurred by pFISTA appear insensitive to the step size.

In sensor networks, due to power outage at a sensor node, hardware dysfunction, or bad environmental conditions, not all sensor samples can be successfully gathered at the sink. Additionally, in the data stream scenario, some nodes may continually miss samples for a period of time. In this paper, a sparsity-based online data recovery approach is proposed. We construct an over complete dictionary composed of past data frames and traditional fixed transform bases. Assuming the current frame can be sparsely represented using only a few elements of the dictionary, missing samples in each frame can be estimated by Basis Pursuit. Our method was tested on data from a real sensor network application: monitoring the temperatures of the disk drive racks at a data center. Simulations show that in terms of estimation accuracy and stability, the proposed approach outperforms existing average-based interpolation methods, and is more robust to burst missing along the time dimension.

Undersampling the k-space is an efficient way to speed up the magnetic resonance imaging (MRI). Recently emerged compressed sensing MRI shows promising results. However, most of them only enforce the sparsity of images in single transform, e.g. total variation, wavelet, etc. In this paper, based on the principle of basis pursuit, we propose a new framework to combine sparsifying transforms in compressed sensing MRI. Each transform can efficiently represent specific feature that the other can not. This framework is implemented via the state-of-art smoothed l0norm in overcomplete sparse decomposition. Simulation results demonstrate that the proposed method can improve image quality when comparing to single sparsifying transform.