# Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI

arXiv: https://arxiv.org/abs/2312.11468 · HTML: https://mlsanity.com/paper/2312.11468/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [MR fingerprinting Deep RecOnstruction NEtwork (DRONE)](https://mlsanity.com/paper/1710.05267/) (2017)
- [Learning to Estimate Without Bias](https://mlsanity.com/paper/2110.12403/) (2021)
- [Artificial neural network for myelin water imaging](https://mlsanity.com/paper/1904.12522/) (2019)
- [Bias in parametric estimation: reduction and useful side-effects](https://mlsanity.com/paper/1311.6311/) (2013)
- [Cram'er-Rao bound-informed training of neural networks for quantitative MRI](https://mlsanity.com/paper/2109.10535/) (2021)

## Abstract (arXiv)

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.