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Deep learning (DL) has shown great potential in medical image enhancementproblems, such as super-resolution or image synthesis. However, to date, littleconsideration has been given to uncertainty quantification over the outputimage. Here we introduce methods to characterise different components ofuncertainty in such problems and demonstrate the ideas using diffusion MRIsuper-resolution. Specifically, we propose to account for $intrinsic$uncertainty through a heteroscedastic noise model and for $parameter$uncertainty through approximate Bayesian inference, and integrate the two toquantify $predictive$ uncertainty over the output image. Moreover, we introducea method to propagate the predictive uncertainty on a multi-channelled image toderived scalar parameters, and separately quantify the effects of intrinsic andparameter uncertainty therein. The methods are evaluated for super-resolutionof two different signal representations of diffusion MR images---DTIs and MeanApparent Propagator MRI---and their derived quantities such as MD and FA, onmultiple datasets of both healthy and pathological human brains. Resultshighlight three key benefits of uncertainty modelling for improving the safetyof DL-based image enhancement systems. Firstly, incorporating uncertaintyimproves the predictive performance even when test data departs from trainingdata. Secondly, the predictive uncertainty highly correlates with errors, andis therefore capable of detecting predictive "failures". Results demonstratethat such an uncertainty measure enables subject-specific and voxel-wise riskassessment of the output images. Thirdly, we show that the method fordecomposing predictive uncertainty into its independent sources provideshigh-level "explanations" for the performance by quantifying how muchuncertainty arises from the inherent difficulty of the task or the limitedtraining examples.

Uncertainty Quantification in Deep Learning for Safer Neuroimage Enhancement