Erich Kobler

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 motioncorrupted 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.

State-of-the-art image reconstruction often relies on complex, highly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a sequence of quadratic problems. These updates have two key components: (i) learned filters to extract salient image features, and (ii) an attention mechanism that locally adjusts the penalty of filter responses. Our method achieves performance on par with leading plug-and-play and learned regularizer approaches while offering interpretability, robustness, and convergent behavior. In effect, we bridge traditional regularization and deep learning with a principled reconstruction approach.

In cardiac cine magnetic resonance imaging (MRI), the heart is repeatedly imaged at numerous time points during the cardiac cycle. Frequently, the temporal evolution of a certain region of interest such as the ventricles or the atria is highly relevant for clinical diagnosis. In this paper, we devise a novel approach that allows for an automatized propagation of an arbitrary region of interest (ROI) along the cardiac cycle from respective annotated ROIs provided by medical experts at two different points in time, most frequently at the end-systolic (ES) and the end-diastolic (ED) cardiac phases. At its core, a 3D TV-L1-based optical flow algorithm computes the apparent motion of consecutive MRI images in forward and backward directions. Subsequently, the given terminal annotated masks are propagated by this bidirectional optical flow in 3D, which results, however, in improper initial estimates of the segmentation masks due to numerical inaccuracies. These initially propagated segmentation masks are then refined by a 3D U-Net-based convolutional neural network (CNN), which was trained to enforce consistency with the forward and backward warped masks using a novel loss function. Moreover, a penalization term in the loss function controls large deviations from the initial segmentation masks. This method is benchmarked both on a new dataset with annotated single ventricles containing patients with severe heart diseases and on a publicly available dataset with different annotated ROIs. We emphasize that our novel loss function enables fine-tuning the CNN on a single patient, thereby yielding state-of-the-art results along the complete cardiac cycle.