Image recovery using deep end-to-end posterior networks

Motivation: End-to-End (E2E) trained unrolled algorithms recover MR images with high quality. However, they have large memory demands during training. In addition, these maximum a posteriori methods cannot provide uncertainty estimates. Goal(s): To develop a memory-efficient framework for E2E learning of the posterior probability distribution. Approach: We model the posterior distribution as a combination of the data-consistent-determined likelihood term and the prior, represented using a Convolutional Neural Network whose weights are learned in an E2E fashion using maximum likelihood optimization. Results: The proposed E2E training strategy requires significantly less memory than unrolling. In addition, the model facilitates sampling and provides uncertainty estimates. Impact: The higher memory efficiency of the proposed E2E scheme makes it an attractive option for image reconstruction problems of large dimensions. The learned posterior model provides a minimum mean square estimate and uncertainty maps, which unrolled approaches cannot offer.