Motion correction in low SNR MRI using an approximate rician log-likelihood

Certain MRI acquisitions, such as Sodium imaging, produce data with very low signal-to-noise ratio (SNR). One approach to improve SNR is to acquire several images, each of which takes may take more than a minute, and then average these measurements. A consequence of such a lengthy acquisition procedure is subject motion between each image. This work investigates a solution for retrospective motion correction in this scenario, where the high level of Rician noise renders standard registration tools less effective. We employ a simple generative model for the data based on tissue segmentation maps, and provide a differentiable approximation of the Rician log-likelihood to fit the model to the observations. We find that this approach substantially outperforms a Gaussian log-likelihood baseline on synthetic data that has been corrupted by Rician noise of varying degrees. We also provide results of our approach on real Sodium MRI data, and demonstrate that we can reduce the effects of substantial motion compared to a general purpose registration tool.