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

Sean C. Epstein, Timothy Bray+2 more|arXiv (Cornell University)|May 11, 2022

Non-Destructive Testing Techniques20 references4 citations

TL;DR

This paper demonstrates that supervised deep learning for quantitative MRI parameter estimation can achieve low-bias performance—previously only attainable via self-supervised methods—by replacing standard groundtruth labels with maximum likelihood estimates (MLEs) computed independently from the data. The proposed method unifies low-bias and low-variance estimation within a single supervised framework, enabling tunable trade-offs between bias and variance through label selection.

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.

Motivation & Objective

• To address the counterintuitive finding that supervised deep learning methods for qMRI parameter estimation produce higher bias than self-supervised alternatives despite having access to more information.
• To investigate whether the high bias in supervised learning stems from the choice of training labels rather than the learning paradigm itself.
• To develop a new supervised deep learning framework that replicates and improves upon the low-bias performance of self-supervised methods.
• To unify bias and variance control in qMRI parameter estimation under a single supervised learning framework through strategic label selection.
• To enable flexible, task-specific optimization of deep learning models for qMRI by decoupling signal model fitting from training loss.

Proposed method

• The authors replace standard groundtruth labels in supervised training with maximum likelihood estimates (MLEs) of qMRI parameters, computed independently from the same noisy input data.
• These MLEs serve as training labels for a deep neural network (DNN), which learns to map noisy qMRI signal curves to parameter estimates.
• The method preserves the computational efficiency and scalability of supervised learning while reducing bias by avoiding the noise-induced bias inherent in groundtruth labels.
• The approach allows for flexible loss weighting across parameters, enabling prioritization of clinically relevant parameters.
• It incorporates Rician noise modeling into the training process, improving performance at low signal-to-noise ratios (SNR).
• The framework supports non-differentiable signal models by separating the signal model from the training loss function.

Experimental results

Research questions

• RQ1 Why do supervised deep learning methods for qMRI parameter estimation produce higher bias than self-supervised methods, despite having access to more information?
• RQ2 Can the low-bias performance of self-supervised methods be replicated within a supervised learning framework?
• RQ3 Does replacing groundtruth labels with MLE-derived labels improve the bias characteristics of supervised deep learning in qMRI?
• RQ4 Can a unified supervised learning framework enable tunable trade-offs between bias and variance in qMRI parameter estimation?
• RQ5 What are the advantages of using MLE-based labels over groundtruth labels in terms of model flexibility, noise modeling, and parameter prioritization?

Key findings

• Using MLE-derived labels instead of groundtruth labels in supervised training reduces bias to levels comparable with or better than self-supervised methods, particularly at low SNR (e.g., SNR = 15).
• The proposed method achieves lower bias and similar or better root mean square error (RMSE) than both supervised groundtruth and self-supervised approaches across multiple parameter values and noise levels.
• At low SNR (15), the MLE-trained supervised model shows significantly reduced bias compared to the groundtruth-supervised model, especially for extreme parameter values (e.g., D_slow = 0.69 and D_slow = 2.71).
• The method enables flexible loss weighting, allowing the network to prioritize estimation accuracy for specific qMRI parameters of clinical interest.
• Incorporating Rician noise modeling into the training process improves parameter estimation performance at low SNR, particularly for the slow diffusion coefficient (D_slow).
• The framework allows for the estimation of non-differentiable signal models by decoupling the signal model from the training loss, expanding the range of applicable qMRI models.