Wenqi Huang

Jiazhen Pan, Wenqi Huang, Daniel Rueckert et al.

In cardiac CINE, motion-compensated MR reconstruction (MCMR) is an effective approach to address highly undersampled acquisitions by incorporating motion information between frames. In this work, we propose a novel perspective for addressing the MCMR problem and a more integrated and efficient solution to the MCMR field. Contrary to state-of-the-art (SOTA) MCMR methods which break the original problem into two sub-optimization problems, i.e. motion estimation and reconstruction, we formulate this problem as a single entity with one single optimization. Our approach is unique in that the motion estimation is directly driven by the ultimate goal, reconstruction, but not by the canonical motion-warping loss (similarity measurement between motion-warped images and target images). We align the objectives of motion estimation and reconstruction, eliminating the drawbacks of artifacts-affected motion estimation and therefore error-propagated reconstruction. Further, we can deliver high-quality reconstruction and realistic motion without applying any regularization/smoothness loss terms, circumventing the non-trivial weighting factor tuning. We evaluate our method on two datasets: 1) an in-house acquired 2D CINE dataset for the retrospective study and 2) the public OCMR cardiac dataset for the prospective study. The conducted experiments indicate that the proposed MCMR framework can deliver artifact-free motion estimation and high-quality MR images even for imaging accelerations up to 20x, outperforming SOTA non-MCMR and MCMR methods in both qualitative and quantitative evaluation across all experiments. The code is available at https://github.com/JZPeterPan/MCMR-Recon-Driven-Motion.

Wenqi Huang, Hongwei Li, Jiazhen Pan et al.

In this work, we propose a novel image reconstruction framework that directly learns a neural implicit representation in k-space for ECG-triggered non-Cartesian Cardiac Magnetic Resonance Imaging (CMR). While existing methods bin acquired data from neighboring time points to reconstruct one phase of the cardiac motion, our framework allows for a continuous, binning-free, and subject-specific k-space representation.We assign a unique coordinate that consists of time, coil index, and frequency domain location to each sampled k-space point. We then learn the subject-specific mapping from these unique coordinates to k-space intensities using a multi-layer perceptron with frequency domain regularization. During inference, we obtain a complete k-space for Cartesian coordinates and an arbitrary temporal resolution. A simple inverse Fourier transform recovers the image, eliminating the need for density compensation and costly non-uniform Fourier transforms for non-Cartesian data. This novel imaging framework was tested on 42 radially sampled datasets from 6 subjects. The proposed method outperforms other techniques qualitatively and quantitatively using data from four and one heartbeat(s) and 30 cardiac phases. Our results for one heartbeat reconstruction of 50 cardiac phases show improved artifact removal and spatio-temporal resolution, leveraging the potential for real-time CMR.

Jiazhen Pan, Suprosanna Shit, Özgün Turgut et al.

In dynamic Magnetic Resonance Imaging (MRI), k-space is typically undersampled due to limited scan time, resulting in aliasing artifacts in the image domain. Hence, dynamic MR reconstruction requires not only modeling spatial frequency components in the x and y directions of k-space but also considering temporal redundancy. Most previous works rely on image-domain regularizers (priors) to conduct MR reconstruction. In contrast, we focus on interpolating the undersampled k-space before obtaining images with Fourier transform. In this work, we connect masked image modeling with k-space interpolation and propose a novel Transformer-based k-space Global Interpolation Network, termed k-GIN. Our k-GIN learns global dependencies among low- and high-frequency components of 2D+t k-space and uses it to interpolate unsampled data. Further, we propose a novel k-space Iterative Refinement Module (k-IRM) to enhance the high-frequency components learning. We evaluate our approach on 92 in-house 2D+t cardiac MR subjects and compare it to MR reconstruction methods with image-domain regularizers. Experiments show that our proposed k-space interpolation method quantitatively and qualitatively outperforms baseline methods. Importantly, the proposed approach achieves substantially higher robustness and generalizability in cases of highly-undersampled MR data. For video presentation, poster, GIF results and code please check our project page: https://jzpeterpan.github.io/k-gin.github.io/.

Veronika Spieker, Wenqi Huang, Hannah Eichhorn et al.

Motion-resolved reconstruction for abdominal magnetic resonance imaging (MRI) remains a challenge due to the trade-off between residual motion blurring caused by discretized motion states and undersampling artefacts. In this work, we propose to generate blurring-free motion-resolved abdominal reconstructions by learning a neural implicit representation directly in k-space (NIK). Using measured sampling points and a data-derived respiratory navigator signal, we train a network to generate continuous signal values. To aid the regularization of sparsely sampled regions, we introduce an additional informed correction layer (ICo), which leverages information from neighboring regions to correct NIK's prediction. Our proposed generative reconstruction methods, NIK and ICoNIK, outperform standard motion-resolved reconstruction techniques and provide a promising solution to address motion artefacts in abdominal MRI.

Leonhard F. Feiner, Martin J. Menten, Kerstin Hammernik et al.

Uncertainty estimation, which provides a means of building explainable neural networks for medical imaging applications, have mostly been studied for single deep learning models that focus on a specific task. In this paper, we propose a method to propagate uncertainty through cascades of deep learning models in medical imaging pipelines. This allows us to aggregate the uncertainty in later stages of the pipeline and to obtain a joint uncertainty measure for the predictions of later models. Additionally, we can separately report contributions of the aleatoric, data-based, uncertainty of every component in the pipeline. We demonstrate the utility of our method on a realistic imaging pipeline that reconstructs undersampled brain and knee magnetic resonance (MR) images and subsequently predicts quantitative information from the images, such as the brain volume, or knee side or patient's sex. We quantitatively show that the propagated uncertainty is correlated with input uncertainty and compare the proportions of contributions of pipeline stages to the joint uncertainty measure.

Veronika Spieker, Hannah Eichhorn, Wenqi Huang et al.

Neural implicit k-space representations (NIK) have shown promising results for dynamic magnetic resonance imaging (MRI) at high temporal resolutions. Yet, reducing acquisition time, and thereby available training data, results in severe performance drops due to overfitting. To address this, we introduce a novel self-supervised k-space loss function $\mathcal{L}_\mathrm{PISCO}$, applicable for regularization of NIK-based reconstructions. The proposed loss function is based on the concept of parallel imaging-inspired self-consistency (PISCO), enforcing a consistent global k-space neighborhood relationship without requiring additional data. Quantitative and qualitative evaluations on static and dynamic MR reconstructions show that integrating PISCO significantly improves NIK representations. Particularly for high acceleration factors (R$\geq$54), NIK with PISCO achieves superior spatio-temporal reconstruction quality compared to state-of-the-art methods. Furthermore, an extensive analysis of the loss assumptions and stability shows PISCO's potential as versatile self-supervised k-space loss function for further applications and architectures. Code is available at: https://github.com/compai-lab/2025-pisco-spieker

Veronika Spieker, Hannah Eichhorn, Jonathan K. Stelter et al.

Neural implicit k-space representations have shown promising results for dynamic MRI at high temporal resolutions. Yet, their exclusive training in k-space limits the application of common image regularization methods to improve the final reconstruction. In this work, we introduce the concept of parallel imaging-inspired self-consistency (PISCO), which we incorporate as novel self-supervised k-space regularization enforcing a consistent neighborhood relationship. At no additional data cost, the proposed regularization significantly improves neural implicit k-space reconstructions on simulated data. Abdominal in-vivo reconstructions using PISCO result in enhanced spatio-temporal image quality compared to state-of-the-art methods. Code is available at https://github.com/vjspi/PISCO-NIK.

Wenqi Huang, Veronika Spieker, Siying Xu et al.

Conventional cardiac cine MRI methods rely on retrospective gating, which limits temporal resolution and the ability to capture continuous cardiac dynamics, particularly in patients with arrhythmias and beat-to-beat variations. To address these challenges, we propose a reconstruction framework based on subspace implicit neural representations for real-time cardiac cine MRI of continuously sampled radial data. This approach employs two multilayer perceptrons to learn spatial and temporal subspace bases, leveraging the low-rank properties of cardiac cine MRI. Initialized with low-resolution reconstructions, the networks are fine-tuned using spoke-specific loss functions to recover spatial details and temporal fidelity. Our method directly utilizes the continuously sampled radial k-space spokes during training, thereby eliminating the need for binning and non-uniform FFT. This approach achieves superior spatial and temporal image quality compared to conventional binned methods at the acceleration rate of 10 and 20, demonstrating potential for high-resolution imaging of dynamic cardiac events and enhancing diagnostic capability.

Zichao Meng, Ye Guo, Wenjun Tang et al.

A multivariate density forecast model based on deep learning is designed in this paper to forecast the joint cumulative distribution functions (JCDFs) of multiple security margins in power systems. Differing from existing multivariate density forecast models, the proposed method requires no a priori hypotheses on the distribution of forecasting targets. In addition, based on the universal approximation capability of neural networks, the value domain of the proposed approach has been proven to include all continuous JCDFs. The forecasted JCDF is further employed to calculate the deterministic security assessment index evaluating the security level of future power system operations. Numerical tests verify the superiority of the proposed method over current multivariate density forecast models. The deterministic security assessment index is demonstrated to be more informative for operators than security margins as well.

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).

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.