Variational Diffusion Models for Blind MRI Inverse Problems

Abstract

Diffusion models have demonstrated state-of-the-art results in solving inverse problems in various domains including medical imaging. However, existing works generally consider the cases where the forward operator is fully known. Therefore, blind inverse problems with unknown forward operator parameters require modifications on existing methods. In this work, we present an extension of the recently developed regularization by denoising diffusion process (RED-diff) algorithm to blind inverse problems. Similarly to RED-diff, our method can reconstruct images without model re-training or fine-tuning for arbitrary acquisition settings. Tested in fieldmap-corrected MR image reconstruction, our blind RED-diff framework can successfully approximate the unknown forward model parameters and produce fieldmap-corrected reconstructions accurately.