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Deep generative models have gained recent traction in accelerated MRI reconstruction. Diffusion priors are particularly promising given their representational fidelity. Instead of the target transformation from undersampled to fully-sampled data required for MRI reconstruction, common diffusion priors are trained to learn a task-agnostic transformation from an asymptotic start-point of Gaussian noise onto the finite end-point of fully-sampled data. During inference, data-consistency projections are injected in between reverse diffusion steps to reach a compromise solution within the span of both the trained diffusion prior and the imaging operator for an accelerated MRI acquisition. Unfortunately, performance losses can occur due to the discrepancy between target and learned transformations given the asymptotic normality assumption in diffusion priors. To address this discrepancy, here we introduce a novel Fourier-constrained diffusion bridge (FDB) for MRI reconstruction that transforms between a finite start-point of moderately undersampled data and an end-point of fully-sampled data. We derive the theoretical formulation of FDB as a generalized diffusion process based on a stochastic degradation operator that performs random spatial-frequency removal. We propose an enhanced sampling algorithm with a learned correction term for soft dealiasing across reverse diffusion steps. Demonstrations on brain MRI indicate that FDB outperforms state-of-the-art methods including non-diffusion and diffusion priors.

Deep MRI reconstruction is commonly performed with conditional models that de-alias undersampled acquisitions to recover images consistent with fully-sampled data. Since conditional models are trained with knowledge of the imaging operator, they can show poor generalization across variable operators. Unconditional models instead learn generative image priors decoupled from the operator to improve reliability against domain shifts related to the imaging operator. Recent diffusion models are particularly promising given their high sample fidelity. Nevertheless, inference with a static image prior can perform suboptimally. Here we propose the first adaptive diffusion prior for MRI reconstruction, AdaDiff, to improve performance and reliability against domain shifts. AdaDiff leverages an efficient diffusion prior trained via adversarial mapping over large reverse diffusion steps. A two-phase reconstruction is executed following training: a rapid-diffusion phase that produces an initial reconstruction with the trained prior, and an adaptation phase that further refines the result by updating the prior to minimize data-consistency loss. Demonstrations on multi-contrast brain MRI clearly indicate that AdaDiff outperforms competing conditional and unconditional methods under domain shifts, and achieves superior or on par within-domain performance.

Multi-institutional efforts can facilitate training of deep MRI reconstruction models, albeit privacy risks arise during cross-site sharing of imaging data. Federated learning (FL) has recently been introduced to address privacy concerns by enabling distributed training without transfer of imaging data. Existing FL methods for MRI reconstruction employ conditional models to map from undersampled to fully-sampled acquisitions via explicit knowledge of the imaging operator. Since conditional models generalize poorly across different acceleration rates or sampling densities, imaging operators must be fixed between training and testing, and they are typically matched across sites. To improve generalization and flexibility in multi-institutional collaborations, here we introduce a novel method for MRI reconstruction based on Federated learning of Generative IMage Priors (FedGIMP). FedGIMP leverages a two-stage approach: cross-site learning of a generative MRI prior, and subject-specific injection of the imaging operator. The global MRI prior is learned via an unconditional adversarial model that synthesizes high-quality MR images based on latent variables. Specificity in the prior is preserved via a mapper subnetwork that produces site-specific latents. During inference, the prior is combined with subject-specific imaging operators to enable reconstruction, and further adapted to individual test samples by minimizing data-consistency loss. Comprehensive experiments on multi-institutional datasets clearly demonstrate enhanced generalization performance of FedGIMP against site-specific and federated methods based on conditional models, as well as traditional reconstruction methods.