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 L 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, making it a competitive dynamic reconstruction method without constraining the temporal resolution. Particularly at high acceleration factors (R ≥ 50), NIK with PISCO can avoid temporal oversmoothing of state-of-the-art methods and achieves superior spatio-temporal reconstruction quality. 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

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.

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

Magnetic resonance (MR) image reconstruction from undersampled k-space data can be formulated as a minimization problem involving data consistency and image prior. Existing deep learning (DL)-based methods for MR reconstruction employ deep networks to exploit the prior information and integrate the prior knowledge into the reconstruction under the explicit constraint of data consistency, without considering the real distribution of the noise. In this work, we propose a new DL-based approach termed Learned DC that implicitly learns the data consistency with deep networks, corresponding to the actual probability distribution of system noise. The data consistency term and the prior knowledge are both embedded in the weights of the networks, which provides an utterly implicit manner of learning reconstruction model. We evaluated the proposed approach with highly undersampled dynamic data, including the dynamic cardiac cine data with up to 24-fold acceleration and dynamic rectum data with the acceleration factor equal to the number of phases. Experimental results demonstrate the superior performance of the Learned DC both quantitatively and qualitatively than the state-of-the-art.

Deep learning methods have achieved attractive performance in dynamic MR cine imaging. However, most of these methods are driven only by the sparse prior of MR images, while the important low-rank (LR) prior of dynamic MR cine images is not explored, which may limit further improvements in dynamic MR reconstruction. In this paper, a learned singular value thresholding (Learned-SVT) operator is proposed to explore low-rank priors in dynamic MR imaging to obtain improved reconstruction results. In particular, we put forward a model-based unrolling sparse and low-rank network for dynamic MR imaging, dubbed as SLR-Net. 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 LR-based dynamic MRI model. Experimental results on a single-coil scenario show that the proposed SLR-Net can further improve the state-of-the-art compressed sensing (CS) methods and sparsity-driven deep learning-based methods with strong robustness to different undersampling patterns, both qualitatively and quantitatively. Besides, SLR-Net has been extended to a multi-coil scenario, and achieved excellent reconstruction results compared with a sparsity-driven multi-coil deep learning-based method under a high acceleration. Prospective reconstruction results on an open real-time dataset further demonstrate the capability and flexibility of the proposed method on real-time scenarios.