Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI

TL;DR

This paper introduces bias-reduced neural networks for quantitative MRI parameter estimation, achieving near-Cramér-Rao bound variance and reduced bias, with improved efficiency and accuracy over traditional methods.

Contribution

It generalizes the loss function to control bias and variance, resulting in neural networks that outperform standard estimators in MRI parameter estimation.

Findings

Bias is significantly reduced across parameter space.

Variance approaches the Cramér-Rao bound.

Neural networks show good agreement with traditional estimators.

Abstract

Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. Results: In simulations, 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: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.