Adaptive sensing for NMR measurements

This paper addresses the challenge of estimating T₁-T₂ distributions from NMR measurements in well-logging applications, where the number of measurements is constrained by associated costs. Adaptive sensing is incorporated into the NMR inverse problem framework to improve estimation accuracy under experimental constraints, with a focus on two-dimensional T₁-T₂ experiments. This work proposes two adaptive measurement systems that dynamically select measurements to perform. For the case of T₁-T₂ experiments, it is the set of wait times (T_W) that is chosen. The proposed adaptive measurements use the mutual information between the observations and the unknown relaxation time distribution to prioritize those measurements that are expected to yield the highest information gain. The proposed adaptive measurement system is evaluated by comparing its performance with a fixed measurement system that comprises a complete set of measured data, using the mean root mean square error (MRMSE) as the evaluation metric. It is demonstrated through experimental results that improved estimation accuracy is achieved with a reduced number of measurements, and hence measurement cost is reduced.