MRI Reconstruction Risk Estimation from Inference Dynamics

Diffusion models have achieved strong performance in imaging inverse problems, but typically rely on domain-matched pretrained models and external training data. Moreover, errors introduced at intermediate reverse-sampling steps can accumulate and degrade the final reconstruction, with their propagation strongly influenced by how successive states are related. We propose TRACE, a training-free TRAjectory-Constrained rEconstruction framework for imaging inverse problems. TRACE replaces the pretrained diffusion model with an untrained overparameterized network optimized directly from the observed measurements and organizes reconstruction as a sequence of intermediate states. At each step, TRACE enforces stochastic proximal consistency (SPC) by inferring each reconstruction from a stochastically perturbed predecessor under measurement consistency, while proximally constraining the resulting estimate to its corresponding unperturbed state. This formulation admits a proximal interpretation, from which we derive stability bounds characterizing the variation between consecutive states under approximate network updates. A local Jacobian analysis further characterizes how SPC regularizes the network-parameterized reconstruction. Experiments on natural-image restoration and CT reconstruction demonstrate competitive performance against both untrained and pretrained neural-prior methods. We further show that the proposed trajectory constraint can be incorporated into existing diffusion-based inverse solvers to improve reconstruction performance.

MRI reconstruction methods for undersampled k-space data naturally utilize complex-valued measurements. Parallel developments in sparse phase retrieval have shown that magnitude-only measurements may provide complementary information for signal recovery. However, their use in MRI reconstruction remains largely unexplored, due to lack of practical settings where informative magnitude measurements can be obtained without additional scan time. In this work, we investigate the use of auxiliary k-space magnitude information for accelerated steady-state dynamic MRI reconstruction, and demonstrate strong consistency of k-space magnitudes across time-frames. Building on this observation, we propose $\mathbb{C}+\text{Mag}$, a magnitude-informed physics-driven deep learning reconstruction method. The proposed method employs an ADMM-based unrolling framework with a novel magnitude-aware data-fidelity formulation, where quadratically smoothed optimization and momentum-based updates are introduced to address the non-differentiability and non-convexity of the magnitude constraints. Experiments on retrospectively undersampled cine MRI and phase-contrast flow MRI datasets, as well as prospectively undersampled real-time cine MRI acquisitions, demonstrate improved artifact suppression, sharper anatomical recovery, and better preservation of phase information compared to conventional PD-DL methods, which is further supported through blinded expert reader evaluations.

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 here.