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