Model-based Dynamic 3D MRI Reconstructions using Neural Fields and Tensor Product Expansions

MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions. This ambiguity becomes more severe under high acceleration, where pixel-domain continuous predictors tend to average over feasible reconstructions and suppress high-frequency anatomy. We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction. Leveraging discrete priors proven effective in visual autoregressive modeling, our method restricts the solution to compact sequences of codebook tokens, enabling sharp reconstructions even from extremely sparse measurements. This discrete autoregressive formulation also aligns naturally with modern large language model post-training techniques. Building on this observation, we introduce on-policy privileged information distillation for visual autoregressive modeling, where a teacher is provided training only privileged context that is unavailable at inference, in our case fully sampled acquisitions, and supervises a student trained on its own rollouts, leading to consistent reconstruction gains. Through extensive experiments on the fastMRI benchmark, we show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling. Project website is \href{https://yilmazkorkmaz1.github.io/discrete-mri-reconstruction-opd/}{here}.

Prospective reconstruction is crucial in many clinical applications such as MRI-guided radiotherapy, which demands accurate image reconstruction and fast motion estimation from currently acquired measurements. However, prospective reconstruction remains challenging due to ultra-sparse sampling and stringent latency requirements. In this work, we propose PDMR, a Prospective Dynamic 3D MRI Reconstruction framework with latent-space motion tracking. Our core idea is to learn an efficient and generalizable latent manifold of motion fields offline, enabling rapid online adaptation for prospective reconstruction. Specifically, we parameterize the deformation vector fields (DVFs) on a low-dimensional manifold, effectively reducing the search space for fast online adaptation, and employ a tri-plane representation to achieve geometry-aware and memory-efficient encoding of 3D motion. Experiments on both XCAT digital phantoms and in-house abdominal MRI datasets demonstrate that PDMR achieves high-fidelity and temporally consistent reconstruction across multiple prospective scenarios (Immediate and After-2min), outperforming state-of-the-art retrospective and online methods. Our results suggest a promising pathway toward ultra-fast, motion-aware prospective MRI reconstruction in clinical practice.

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.