  In this paper, we propose the use of Recurrent Inference Machines (RIMs) to
perform T1 and T2 mapping. The RIM is a neural network framework that learns an
iterative inference process based on the signal model, similar to conventional
statistical methods for quantitative MRI (QMRI), such as the Maximum Likelihood
Estimator (MLE). This framework combines the advantages of both data-driven and
model-based methods, and, we hypothesize, is a promising tool for QMRI.
Previously, RIMs were used to solve linear inverse reconstruction problems.
Here, we show that they can also be used to optimize non-linear problems and
estimate relaxometry maps with high precision and accuracy. The developed RIM
framework is evaluated in terms of accuracy and precision and compared to an
MLE method and an implementation of the ResNet. The results show that the RIM
improves the quality of estimates compared to the other techniques in Monte
Carlo experiments with simulated data, test-retest analysis of a system
phantom, and in-vivo scans. Additionally, inference with the RIM is 150 times
faster than the MLE, and robustness to (slight) variations of scanning
parameters is demonstrated. Hence, the RIM is a promising and flexible method
for QMRI. Coupled with an open-source training data generation tool, it
presents a compelling alternative to previous methods.
