# Uncertainty-Aware Self-supervised Neural Network for Liver T1ρ Mapping with Relaxation Constraint

arXiv: https://arxiv.org/abs/2207.03105 · HTML: https://mlsanity.com/paper/2207.03105/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 62 references that are in the map.
- First posted on arXiv 7 Jul 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Domain Adaptation for Medical Image Analysis: A Survey](https://mlsanity.com/paper/2102.09508/) (2021)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Association of genomic subtypes of lower-grade gliomas with shape features automatically extracted by a deep learning algorithm](https://mlsanity.com/paper/1906.03720/) (2019)
- [Semi-Supervised Medical Image Segmentation via Learning Consistency under Transformations](https://mlsanity.com/paper/1911.01218/) (2019)
- [Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2004.12573/) (2020)

## Built on by (most cited first, 5 of 5)

- [An Uncertainty Aided Framework for Learning based Liver T1ρ Mapping and Analysis](https://mlsanity.com/paper/2307.02736/) (2023)
- [Guiding Quantitative MRI Reconstruction with Phase-wise Uncertainty](https://mlsanity.com/paper/2502.20877/) (2025)
- [Chemical Shift Encoding based Double Bonds Quantification in Triglycerides using Deep Image Prior](https://mlsanity.com/paper/2407.01926/) (2024)
- [Quantitative mapping from conventional MRI using self-supervised physics-guided deep learning: applications to a large-scale, clinically heterogeneous dataset](https://mlsanity.com/paper/2601.05063/) (2026)
- [Multiparameter Uncertainty Mapping in Quantitative Molecular MRI using a Physics-Structured Variational Autoencoder (PS-VAE)](https://mlsanity.com/paper/2602.03317/) (2026)

## Abstract (arXiv)

T1ρ mapping is a promising quantitative MRI technique for the non-invasive assessment of tissue properties. Learning-based approaches can map T1ρ from a reduced number of T1ρ weighted images, but requires significant amounts of high quality training data. Moreover, existing methods do not provide the confidence level of the T1ρ estimation. To address these problems, we proposed a self-supervised learning neural network that learns a T1ρ mapping using the relaxation constraint in the learning process. Epistemic uncertainty and aleatoric uncertainty are modelled for the T1ρ quantification network to provide a Bayesian confidence estimation of the T1ρ mapping. The uncertainty estimation can also regularize the model to prevent it from learning imperfect data. We conducted experiments on T1ρ data collected from 52 patients with non-alcoholic fatty liver disease. The results showed that our method outperformed the existing methods for T1ρ quantification of the liver using as few as two T1ρ-weighted images. Our uncertainty estimation provided a feasible way of modelling the confidence of the self-supervised learning based T1ρ estimation, which is consistent with the reality in liver T1ρ imaging.