Solving a Nonlinear Blind Inverse Problem for Tagged MRI with Physics and Deep Generative Priors

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.

This work introduces MedForj, a suite of 3D foundational generative priors based on diffusion models. The MedForj models were trained on $72{,}659$ 1~mm isotropic 3D $T_1$-weighted MRI human brain image volumes from $38{,}174$ subjects, drawn from a curated corpus of $80{,}675$ volumes from $42{,}506$ subjects spanning $38$ publicly available datasets. These training images were manually inspected to exclude those with poor quality and excessive pathology, and otherwise were minimally processed. The models include six different diffusion training strategies: rectified flow, latent diffusion rectified flow, flow matching, velocity prediction, clean prediction, and noise prediction. Image samples produced by each of these models were compared to each other and against real, ground truth data under downstream segmentation distributions, FID, five inverse problems, and blind human inspection in an observer study. Flow matching was the strongest strategy overall, achieving the best inverse problem solving results at $28.80$~dB PSNR and $0.874$ SSIM averaged over the five forward problems, the highest rate of reconstructions judged real by blind human raters at $72.6\%$, and the closest per-structure match to real segmented anatomy in a permutation test. It was not best everywhere: rectified flow produced the most convincing unconditional samples in the observer study and the best FID, and the latent rectified-flow model achieved the smallest joint distributional distance to real anatomy. No other strategy, however, performed consistently well across all four evaluations. We therefore recommend flow matching as the default MedForj prior, while releasing every strategy so that the choice can be revisited per application. All model weights and corresponding code are publicly available at https://github.com/piksl-research/medforj.

MRI sequence synthesis aims to recover missing image contrast while preserving patient-specific anatomy. The choice of generation mechanism affects both optimization and the way source information reaches the synthesized image. In this study, we propose SRUG, a supervised standalone fusion-driven generator that learns a deterministic source-to-target mapping for paired MRI synthesis. Its direct reconstruction formulation removes generator-discriminator competition and requires neither variational latent sampling nor iterative diffusion denoising. To support structural fidelity within this formulation, SRUG uses a residual encoder adapted for image reconstruction, with a full-resolution convolutional stem, pooling-separated feature stages, and channel recalibration embedded in the residual branches. A nested multi-scale decoder (NMD) repeatedly fuses the resulting spatial features and predicts the target sequence through a single output head. L1 loss and Multi-Scale Structural Loss (MSS loss) jointly supervise the prediction, connecting the direct generation objective to anatomical detail recovery. Experiments on BraTS 2023 show competitive reconstruction fidelity and structural consistency across three MRI translation tasks. Architecture ablations assess the effects of channel recalibration, NMD, and structural supervision within the same generator framework. Additional evaluation on IXI supports applicability to another dataset and modality pair, while zero-shot testing on BraTS 2019 provides preliminary evidence of cross-dataset transferability. These results support direct supervised generation as a practical approach to paired MRI sequence synthesis, with the adapted encoding and reconstruction pathway providing the basis for structural preservation. The SRUG implementation is publicly available at https://github.com/RisingRich/SRUG.