Accelerated motion correction with deep generative diffusion models

Abstract Purpose The aim of this work is to develop a method to solve the ill‐posed inverse problem of accelerated image reconstruction while correcting forward model imperfections in the context of subject motion during MRI examinations. Methods The proposed solution uses a Bayesian framework based on deep generative diffusion models to jointly estimate a motion‐free image and rigid motion estimates from subsampled and motion‐corrupt two‐dimensional (2D) k‐space data. Results We demonstrate the ability to reconstruct motion‐free images from accelerated two‐dimensional (2D) Cartesian and non‐Cartesian scans without any external reference signal. We show that our method improves over existing correction techniques on both simulated and prospectively accelerated data. Conclusion We propose a flexible framework for retrospective motion correction of accelerated MRI based on deep generative diffusion models, with potential application to other forward model corruptions.