Unbiased Neural Networks for Quantitative MRI Parameter Estimation

Motivation: Neural-network (NN)-based estimators trained with the mean-squared error criterion have a non-negligible bias which impedes inter-method comparability and the clinical adoption of quantitative MRI methods. Goal(s): To develop fast, accurate, precise, and reproducible quantitative MRI estimators that are reliable in the face of pathology. Approach: We explicitly penalize the bias of the NN's estimates during training and study the resulting NN's bias and variance properties for a magnetization transfer model. Results: The proposed method reduces the NN's variable bias throughout parameter space, achieves a variance close to the theoretical minimum, and shows excellent concordance with parameter maps estimated using non-linear least-squares in vivo. Impact: NNs trained with the proposed strategy are approximately minimum variance unbiased estimators and are therefore well-suited for the development, validation, and translation of new quantitative biomarkers, particularly for multi-compartment biophysical models such as magnetization transfer or diffusion in white matter.