A maximum a posteriori method for quantitative $$$T_1$$$ mapping with uncertainty using MP2RAGE

Motivation: The MP2RAGE sequence allows for quantitative MRI imaging of $$$T_1$$$ in the brain, but current methods do not provide a way to measure uncertainty in this mapping. Goal(s): We introduce a probabilistic signal representation to allow for $$$T_1$$$ mapping with uncertainty maps. Approach: Using a Monte Carlo simulation, we generate a probability distribution for the MP2RAGE images that allows us to map the posterior distribution of $$$T_1$$$ and generate a measure of uncertainty. Results: Our $$$T_1$$$ map numerically agrees with previous single-echo MP2RAGE methods with limited data while providing a way to map statistical measures like expected value or standard deviation. Impact: Our posterior distribution allows for uncertainty quantification in $$$T_1$$$ mapping with MP2RAGE, and it opens up the possibility for other probabilistic methods. The proposed method allows for a better quantitative understanding with only a minor modification to the acquisition sequence.