Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction

Recent years have witnessed a surge in deep generative models for accelerated MRI reconstruction. Diffusion priors in particular have gained traction with their superior representational fidelity and diversity. Instead of the target transformation from undersampled to fully-sampled data, common diffusion priors are trained to learn a multi-step transformation from Gaussian noise onto fully-sampled data. During inference, data-fidelity projections are injected in between reverse diffusion steps to reach a compromise solution within the span of both the diffusion prior and the imaging operator. Unfortunately, suboptimal solutions can arise as the normality assumption of the diffusion prior causes divergence between learned and target transformations. To address this limitation, here we introduce the first diffusion bridge for accelerated MRI reconstruction. The proposed Fourier-constrained diffusion bridge (FDB) leverages a generalized process to transform between undersampled and fully-sampled data via random noise addition and random frequency removal as degradation operators. Unlike common diffusion priors that use an asymptotic endpoint based on Gaussian noise, FDB captures a transformation between finite endpoints where the initial endpoint is based on moderate degradation of fully-sampled data. Demonstrations on brain MRI indicate that FDB outperforms state-of-the-art reconstruction methods including conventional diffusion priors.

Adaptive Diffusion Priors for Accelerated MRI Reconstruction

Deep MRI reconstruction is commonly performed with conditional models that map undersampled data as input onto fully-sampled data as output. Conditional models perform de-aliasing under knowledge of the accelerated imaging operator, so they poorly generalize under domain shifts in the operator. Unconditional models are a powerful alternative that instead learn generative image priors to improve reliability against domain shifts. Recent diffusion models are particularly promising given their high representational diversity and sample quality. Nevertheless, projections through a static image prior can lead to suboptimal performance. Here we propose a novel MRI reconstruction, AdaDiff, based on an adaptive diffusion prior. To enable efficient image sampling, an adversarial mapper is introduced that enables use of large diffusion steps. A two-phase reconstruction is performed with the trained prior: a rapid-diffusion phase that produces an initial reconstruction, and an adaptation phase where the diffusion prior is updated to minimize reconstruction loss on acquired k-space data. Demonstrations on multi-contrast brain MRI clearly indicate that AdaDiff achieves superior performance to competing models in cross-domain tasks, and superior or on par performance in within-domain tasks.

Federated Learning of Generative Image Priors for MRI Reconstruction

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.