MoSAIK: Motion Search with Artificial Intelligence in K-space

Oscar Dabrowski; Abijith Jagannath; Frédéric Grouiller; Sébastien Courvoisier

cs.AIOct 19, 2026

MoSAIK: Motion Search with Artificial Intelligence in K-space

Authors: Oscar Dabrowski, Abijith Jagannath, Frédéric Grouiller, Sébastien Courvoisier

Organizations: CIBM Center for Biomedical Imaging, Geneva, Switzerland · Department of Radiology and Medical Informatics, Faculty of Medicine, University of Geneva, Geneva, Switzerland · Biomedical Imaging Group, École polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland · Signal Processing EPFL, CIBM Center for Biomedical Imaging, Lausanne, Switzerland

Abstract

Object: Motion artefacts remain a major limitation of routine two-dimensional T2-weighted turbo spin-echo (TSE) brain MRI, reducing diagnostic confidence and often necessitating repeated acquisitions. MoSAIK (Motion Search with AI in K-space) retrospectively estimates in-plane rigid-body motion directly from standard multi-coil TSE k-space. Without a motion-free reference, external navigators, or additional acquisitions, MoSAIK infers motion from k-space self-consistency violations and incorporates predicted parameters into model-based, motion-aware reconstruction rather than synthesizing corrected images. Materials and Methods: Selected complex coil data were represented as log-magnitude and phase channels. A decoupled convolutional embedding and Transformer encoder estimated phase-encoding-line-indexed rotation and two-dimensional translations. Training used motion-free clinical acquisitions with simulated motion; four held-out subjects were evaluated. Component-wise errors assessed estimation; SSIM and PSNR in silico and entropy focus criterion (EFC) in vivo assessed reconstruction. Results: Motion estimation errors were low for both rotation (MSE $<$ 0.2 deg $^2$ ) and translation (MSE $<$ 0.2 pixels $^2$ ), with Pearson correlations of approximately 0.96 and 0.94, respectively. In every in-vivo acquisition, more than 75% of slices showed information gain relative to uncorrected reconstructions. MoSAIK reduced visible artefacts while preserving anatomical detail. Discussion: Transformer-based k-space motion-trajectory estimation enables fast retrospective correction of standard clinical TSE brain MRI.

Figures & tables

Figure 1: Overview of the MoSAIK pipeline. Raw scanner measurements ( $\bm{X}$ ) are analysed by our deep neural network to estimate patient’s head motion trajectory. A separate non-deep learning algorithm reconstructs the clean image. The two-step approach avoids deep hallucinations by design. ( $\mathcal{F}^{-1}$ is the inverse Fourier transform).

Figure 2: Conceptual description of the TSE pulse sequence we are targeting. During each TR, an ETL is acquired for each slice. The acquired phase encoding lines in each ETL follow a comb-like pattern that covers a wide range of spatial frequencies. Depending the subject’s motion trajectory during the scan, slices may not all suffer from the same motion artefacts. A typical ETL ranges from 14 to 18 with $N\approx 33$ slices.

Figure 3: (Top) Simulated motion trajectory over the full TSE acquisition, in temporal order. (Bottom) One-slice trajectory ordered by acquired PE line, i.e. in k-space order. The oscillation effect is due to the TSE sampling pattern.

Figure 4: MoSAIK deep learning model. Input is split in $2\times 4$ channels grouped by representation (real and imaginary or magnitude and phase) and processed in a decoupled manner in parallel. Following this convolutional embedding subnetwork, the extracted representation is fed to a Transformer encoder network, operating in dimension $d$ , and finally to a linear regression head which predicts 3 motion parameters per PE line.

Figure 5: Aggregate motion estimation on simulated motion-corrupted brain MRI from subjects unseen during training. Estimated motion is plotted against ground truth for in-plane rotations $\theta$ , and translations $T_{x}$ and $T_{y}$ . Curves show the average predicted motion for each Ground truth motion range, gray shading shows $\pm$ one standard deviation, and histograms show the simulation parameter distributions.

Panel of Figure 6 — Figure 6: Subject-wise metric gains on a dataset of simulated motion from three subjects unseen during training. Motion was corrected using MoSAIK-estimated trajectories followed by CG-SENSE reconstruction. EFC: Entropy focus criterion. (PSNR is reported for reference only, as it is a poor proxy of perceptual image quality.)

Panel of Figure 7 — Figure 7: EFC gain for four subjects acquired with the in-vivo ChoCo protocol, with six prescribed motion types. Motion correction was performed with motion-aware CG-SENSE reconstruction using MoSAIK-estimated trajectories. EFC gains are summarized by subject (a) and by motion type (b).

Panel of Figure 8 — Figure 8: Representative in vivo ChoCo acquisition in which the volunteer was asked to perform three motion events. The top panel compares the corrupted inverse-Fourier image with motion-aware CG-SENSE reconstructions using MoSAIK-estimated trajectories and either Tikhonov or TV regularization. The lower panels show the raw and post-processed estimated motion trajectories.

Panel of Figure 9 — Figure 9: Idealized ChoCo trajectory simulation. A three-event motion trajectory, matching the motion pattern requested during the in-vivo ChoCo acquisition, was applied to the matching S3 no-motion reference slice. (a) Simulated corrupted image and MoSAIK motion-corrected reconstructions. (b) Ground-truth and MoSAIK-estimated motion trajectories.

Panel of Figure 10 — Figure 10: In-vivo free-motion ChoCo acquisition. (a) Motion-corrupted image and MoSAIK motion-corrected reconstructions obtained with Tikhonov and TV regularization. (b) Post-processed MoSAIK-estimated motion trajectory during the free-motion scan.

Panel of Figure 11 — Figure 11: In-vivo free-motion ChoCo acquisition. (a) Corrupted and MoSAIK-corrected images for a slice with residual artefacts. (b) Post-processed MoSAIK-estimated motion trajectory.

Panel of Figure 12 — Figure 12: Motion-free reference slices for: (a) Figure 8 and Figure 9 , (b) Figure 10 , (c) Figure 11 .

Panel of Figure 13 — Figure 13: PhRUITS: phantom and fruits trainingset and in vivo brain scans as a validation set.

Figure 14: Ablation tests performed on $64\times 64$ cropped k-space dataset showing severe overfitting when convolutional embedding layer is removed. Intermediate generalization performance is exhibited by the model when a small number of convolutional layers is preserved.

Figure 15: Preliminary results obtained with classical CNN and LSTM models were presented at the Alpine Brain Imaging Meeting (ABIM) 2024. These models were able to learn and generalize in the presence of a single random motion event, which corresponds to the experimental setting shown in the plots presented here. However, performance was significantly reduced when multiple motion events were introduced, suggesting that their limited ability to capture long-range dependencies across k-space lines prevents them from accurately modeling more complex motion trajectories.

Panel of Figure 16 — Figure 16: Validation-set mean squared error (MSE) plots between predicted and ground-truth motion parameters for MoSAIK models trained with different hyperparameter configurations. The lowest MSEs were achieved using a 192-line crop along the frequency-encoding direction and a dropout rate of 0.2.

Panel of Figure 17 — Figure 17: Validation-set mean absolute error (MAE) plots between predicted and ground-truth motion parameters for MoSAIK models trained with different hyperparameter configurations. The lowest MAEs were achieved using a 192-line crop along the frequency-encoding direction and a dropout rate of 0.2.

Panel of Figure 18 — Figure 18: Validation-set correlation plots between predicted and ground-truth motion parameters for MoSAIK models trained with different hyperparameter configurations. The highest correlations were achieved using a 192-line crop along the frequency-encoding direction and a dropout rate of 0.2.

Magnetic Resonance Imaging

Magnetic resonance imaging uses magnetic fields and radio waves to create images of anatomy and tissue function for research and clinical care.

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Magnetic resonance imaging (MRI) is highly susceptible to patient motion due to its relatively long acquisition times and the fact that data are acquired sequentially in k-space. Even small patient movements introduce phase inconsistencies across measurements, leading to severe artifacts such as blurring, ghosting, and geometric distortions that can compromise diagnostic quality. Retrospective motion compensation remains challenging, particularly in accelerated acquisitions, due to the ill-posed nature of the joint reconstruction and motion estimation problem. In this work, we propose a unified Bayesian framework for motion-compensated 3D MRI that jointly estimates the anatomical image, rigid-body motion parameters, and coil sensitivity maps directly from motion-corrupted k-space data. Our approach integrates pretrained 3D complex-valued score-based diffusion models as expressive anatomical image priors within a physics-based forward model. Inference is performed by alternating diffusion posterior image updates with efficient proximal optimization steps for motion and coil sensitivity estimation, enabling fully unsupervised reconstruction without the need for paired motion-free training data. Experiments on simulated and real-motion brain MRI datasets demonstrate that the proposed method achieves improved image quality and motion robustness compared to state-of-the-art classical and learning-based motion correction techniques, particularly in the presence of severe motion and high acceleration.

Abstract

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