MRI Reconstruction with Fourier-Constrained Diffusion Bridges

Abstract

Diffusion-based image priors have gained recent traction in MRI reconstruction. Common diffusion priors use a multi-step transformation to map Gaussian noise onto fully-sampled MRI data. However, this transformation diverges from the desired reconstruction transformation from undersampled to fully-sampled data, yielding suboptimal results. To overcome this limitation, we introduce Fourier-constrained diffusion bridges (FDB; https://github.com/icon-lab/FDB) for accelerated MRI reconstruction. FDB learns a multi-step transformation from undersampled to fully-sampled data guided by two degradation operators: random noise addition and random frequency removal. Unlike common diffusion priors that use an asymptotic endpoint (e.g., Gaussian noise), FDB performs a finite transformation with an endpoint based on moderately degraded data. Unlike common diffusion bridges that assume learnable forward and backward processes, FDB improves learning by injecting a task-relevant Fourier-domain constraint via its frequency removal operator. Demonstrations on brain MRI show that FDB outperforms state-of-the-art reconstruction methods including previous diffusion priors.

Usama Mirza

Ph.D. Student in Electrical and Electronics Engineering

My research focuses on generative models (diffusion models, GANs) for computational imaging, particularly accelerated MRI reconstruction and multi-contrast MRI synthesis.