Bias‐reduced neural networks for parameter estimation in quantitative MRI

Abstract

PurposeTo develop neural network (NN)‐based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér–Rao bound.Theory and MethodsWe 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.ResultsIn simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér–Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least‐squares fitting, while state‐of‐the‐art NNs show larger deviations.ConclusionThe 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.

Sensitivity of unconstrained quantitative magnetization transfer MRI to Amyloid burden in preclinical Alzheimer's disease

“…Zhang et al (2022): 11 fully connected layers with batch normalization and skip connections with a maximum layer width of 1024. The network incorporated a data-driven correction for B 0 and B + 1 inhomogeneities as described in (Assländer, Gultekin, et al, 2024), and was trained explicitly to minimize the bias that is typically introduced when assuming a distribution for the simulated training data (Mao et al, 2024). Example parameter maps for an Aβ+ subject are shown in Figure 2.…”