Ruud B. van Heeswijk

Jaume Banus, Augustin C. Ogier, Roger Hullin et al.

We present a probabilistic framework for modeling structured spatiotemporal dynamics from sparse observations, focusing on cardiac motion. Our approach integrates neural ordinary differential equations (NODEs), graph neural networks (GNNs), and neural processes into a unified model that captures uncertainty, temporal continuity, and anatomical structure. We represent dynamic systems as spatiotemporal multiplex graphs and model their latent trajectories using a GNN-parameterized vector field. Given the sparse context observations at node and edge levels, the model infers a distribution over latent initial states and control variables, enabling both interpolation and extrapolation of trajectories. We validate the method on three synthetic dynamical systems (coupled pendulum, Lorenz attractor, and Kuramoto oscillators) and two real-world cardiac imaging datasets - ACDC (N=150) and UK Biobank (N=526) - demonstrating accurate reconstruction, extrapolation, and disease classification capabilities. The model accurately reconstructs trajectories and extrapolates future cardiac cycles from a single observed cycle. It achieves state-of-the-art results on the ACDC classification task (up to 99% accuracy), and detects atrial fibrillation in UK Biobank subjects with competitive performance (up to 67% accuracy). This work introduces a flexible approach for analyzing cardiac motion and offers a foundation for graph-based learning in structured biomedical spatiotemporal time-series data.

Yiwei Chen, Amir Aghabiglou, Shijie Chen et al.

We introduce the R2D2 Deep Neural Network (DNN) series paradigm for fast and scalable image reconstruction from highly-accelerated non-Cartesian k-space acquisitions in Magnetic Resonance Imaging (MRI). While unrolled DNN architectures provide a robust image formation approach via data-consistency layers, embedding non-uniform fast Fourier transform operators in a DNN can become impractical to train at large scale, e.g in 2D MRI with a large number of coils, or for higher-dimensional imaging. Plug-and-play approaches that alternate a learned denoiser blind to the measurement setting with a data-consistency step are not affected by this limitation but their highly iterative nature implies slow reconstruction. To address this scalability challenge, we leverage the R2D2 paradigm that was recently introduced to enable ultra-fast reconstruction for large-scale Fourier imaging in radio astronomy. R2D2's reconstruction is formed as a series of residual images iteratively estimated as outputs of DNN modules taking the previous iteration's data residual as input. The method can be interpreted as a learned version of the Matching Pursuit algorithm. A series of R2D2 DNN modules were sequentially trained in a supervised manner on the fastMRI dataset and validated for 2D multi-coil MRI in simulation and on real data, targeting highly under-sampled radial k-space sampling. Results suggest that a series with only few DNNs achieves superior reconstruction quality over its unrolled incarnation R2D2-Net (whose training is also much less scalable), and over the state-of-the-art diffusion-based "Decomposed Diffusion Sampler" approach (also characterised by a slower reconstruction process).

Thomas Sanchez, Baran Gözcü, Ruud B. van Heeswijk et al.

Compressed sensing applied to magnetic resonance imaging (MRI) allows to reduce the scanning time by enabling images to be reconstructed from highly undersampled data. In this paper, we tackle the problem of designing a sampling mask for an arbitrary reconstruction method and a limited acquisition budget. Namely, we look for an optimal probability distribution from which a mask with a fixed cardinality is drawn. We demonstrate that this problem admits a compactly supported solution, which leads to a deterministic optimal sampling mask. We then propose a stochastic greedy algorithm that (i) provides an approximate solution to this problem, and (ii) resolves the scaling issues of [1,2]. We validate its performance on in vivo dynamic MRI with retrospective undersampling, showing that our method preserves the performance of [1,2] while reducing the computational burden by a factor close to 200.