PISCO: Self-Supervised k-Space Regularization for Improved Neural Implicit k-Space Representations of Dynamic MRI

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

From Model Based to Learned Regularization in Medical Image Registration: A Comprehensive Review

Image registration is fundamental in medical imaging applications, such as disease progression analysis or radiation therapy planning. The primary objective of image registration is to precisely capture the deformation between two or more images, typically achieved by minimizing an optimization problem. Due to its inherent ill-posedness, regularization is a key component in driving the solution toward anatomically meaningful deformations. A wide range of regularization methods has been proposed for both conventional and deep learning-based registration. However, the appropriate application of regularization techniques often depends on the specific registration problem, and no one-fits-all method exists. Despite its importance, regularization is often overlooked or addressed with default approaches, assuming existing methods are sufficient. A comprehensive and structured review remains missing. This review addresses this gap by introducing a novel taxonomy that systematically categorizes the diverse range of proposed regularization methods. It highlights the emerging field of learned regularization, which leverages data-driven techniques to automatically derive deformation properties from the data. Moreover, this review examines the transfer of regularization methods from conventional to learning-based registration, identifies open challenges, and outlines future research directions. By emphasizing the critical role of regularization in image registration, we hope to inspire the research community to reconsider regularization strategies in modern registration algorithms and to explore this rapidly evolving field further.

Subspace Implicit Neural Representations for Real-Time Cardiac Cine MR Imaging

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.

Self-Supervised k-Space Regularization for Motion-Resolved Abdominal MRI Using Neural Implicit k-Space Representation

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.

Physics-Informed Deep Learning for Motion-Corrected Reconstruction of Quantitative Brain MRI

We propose PHIMO, a physics-informed learning-based motion correction method tailored to quantitative MRI. PHIMO leverages information from the signal evolution to exclude motion-corrupted k-space lines from a data-consistent reconstruction. We demonstrate the potential of PHIMO for the application of T2* quantification from gradient echo MRI, which is particularly sensitive to motion due to its sensitivity to magnetic field inhomogeneities. A state-of-the-art technique for motion correction requires redundant acquisition of the k-space center, prolonging the acquisition. We show that PHIMO can detect and exclude intra-scan motion events and, thus, correct for severe motion artifacts. PHIMO approaches the performance of the state-of-the-art motion correction method, while substantially reducing the acquisition time by over 40%, facilitating clinical applicability. Our code is available at https://github.com/HannahEichhorn/PHIMO.

ICoNIK: Generating Respiratory-Resolved Abdominal MR Reconstructions Using Neural Implicit Representations in k-Space

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.

Deep Learning for Retrospective Motion Correction in MRI: A Comprehensive Review

Motion represents one of the major challenges in magnetic resonance imaging (MRI). Since the MR signal is acquired in frequency space, any motion of the imaged object leads to complex artefacts in the reconstructed image in addition to other MR imaging artefacts. Deep learning has been frequently proposed for motion correction at several stages of the reconstruction process. The wide range of MR acquisition sequences, anatomies and pathologies of interest, and motion patterns (rigid vs. deformable and random vs. regular) makes a comprehensive solution unlikely. To facilitate the transfer of ideas between different applications, this review provides a detailed overview of proposed methods for learning-based motion correction in MRI together with their common challenges and potentials. This review identifies differences and synergies in underlying data usage, architectures and evaluation strategies. We critically discuss general trends and outline future directions, with the aim to enhance interaction between different application areas and research fields.

Deep Learning-Based Detection of Motion-Affected k-Space Lines for T2*-Weighted MRI

T2*-weighted gradient echo MR imaging is strongly impacted by subject head motion due to motion-related changes in B0 inhomogeneities. Within the oxygenation-sensitive mqBOLD protocol, even mild motion during the acquisition of the T2*-weighted data propagates into errors in derived quantitative parameter maps. In order to correct these images without the need of repeated measurements, we propose to learn a classification of motion-affected k-space lines. To test this, we perform realistic motion simulations including motion-induced field inhomogeneity changes for supervised training. To detect the presence of motion in each phase encoding line, we train a convolutional neural network, leveraging the multi-echo information of the T2*-weighted images. The proposed network accurately detects motion-affected k-space lines for simulated displacements of $\geq$ 0.5mm (accuracy on test set: 92.5%). Finally, we show example reconstructions where we include these classification labels as weights in the data consistency term of an iterative reconstruction procedure, opening up exciting opportunities of k-space line detection in combination with more powerful reconstruction methods.