Unbiased Neural Networks for Parameter Estimation in Quantitative MRI

Purpose: To develop neural-network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the theoretical minimum, the Cram\'er-Rao bound. Theory and Methods: We explicitly penalize the bias of the NN's estimates during training, which involves averaging over multiple noise realizations of the same measurements. Bias and variance properties of the resulting NNs are studied for two quantitative neuroimaging applications. Results: In simulation, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cram\'er-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as non-linear least-squares fitting, while state-of-the-art NNs show larger deviations. Conclusion: NNs trained with the proposed strategy are approximately minimum variance unbiased estimators and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.