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.
