Choice of training label matters: how to best use deep learning for quantitative MRI parameter estimation

TL;DR

This work addresses the bias-variance tension in DL-based qMRI parameter estimation by introducing SupervisedMLE, a supervised framework that trains on non-groundtruth MLE labels $y_{MLE}$ in the parameter space $Y$ and can be blended with groundtruth-based supervision. By incorporating $W$-weighted parameter losses and explicit Rician noise modelling, SupervisedMLE reproduces the low-bias behavior associated with self-supervised methods while maintaining controlled variance, and it remains compatible with complex or non-differentiable signal models. The authors demonstrate, through synthetic and clinical data, that a tunable hybrid loss can interpolate between low-bias and low-variance regimes, offering near-MLE performance with accelerated inference and strong practical relevance for real-time qMRI parameter estimation. This unifying approach enables task-driven design of DL estimators, with potential extensions to patch-based or spatially structured models and broader adoption in clinical qMRI pipelines.

Abstract

Deep learning (DL) is gaining popularity as a parameter estimation method for quantitative MRI. A range of competing implementations have been proposed, relying on either supervised or self-supervised learning. Self-supervised approaches, sometimes referred to as unsupervised, have been loosely based on auto-encoders, whereas supervised methods have, to date, been trained on groundtruth labels. These two learning paradigms have been shown to have distinct strengths. Notably, self-supervised approaches have offered lower-bias parameter estimates than their supervised alternatives. This result is counterintuitive - incorporating prior knowledge with supervised labels should, in theory, lead to improved accuracy. In this work, we show that this apparent limitation of supervised approaches stems from the naive choice of groundtruth training labels. By training on labels which are deliberately not groundtruth, we show that the low-bias parameter estimation previously associated with self-supervised methods can be replicated - and improved on - within a supervised learning framework. This approach sets the stage for a single, unifying, deep learning parameter estimation framework, based on supervised learning, where trade-offs between bias and variance are made by careful adjustment of training label.

Figures (12)

• Figure 1: Comparison between our proposed method (SupervisedMLE) and existing supervised and self-supervised approaches.
• Figure 2: Parameter estimation performance at low SNR (15) as a function of groundtruth parameter $Y$. Performance summarised by bias & RMSE with respect to groundtruth and standard deviation with respect to noise repetition. Conventional MLE fitting is provided as a non-DNN reference standard. For the sake of visualisation, each plotted point represents marginalisation over all non-specified ${Y}$ dimensions.
• Figure 3: Parameter estimation performance, visualised as in Figure \ref{['fig:lowsnr']}, but for high SNR (30) data.
• Figure 4: Comparison between SupervisedGT and reference conventional MLE fitting, expressed in terms of estimation bias and information compression at low SNR (15). Arrows represent the mean mapping from $Y$ to $\hat{Y}$, averaged over noise, as a function of parameter space $Y$. For the sake of visualisation, each plotted point represents marginalisation over all non-specified ${Y}$ dimensions.
• Figure 5: In vivo parameter estimation performance of networks trained on low SNR (15) synthetic data, as a function of supersampling-derived reference parameter values. The first three rows summarise performance by showing bias & RMSE with respect to reference value and standard deviation with respect to noise repetition, marginalised over all non-specified ${Y}$ dimensions. The bottom row shows the distribution of reference parameter values across the parameter range being visualised.