Abstract
Deep learning (DL) has shown great potential in medical image enhancement
problems, such as super-resolution or image synthesis. However, to date, little
consideration has been given to uncertainty quantification over the output
image. Here we introduce methods to characterise different components of
uncertainty in such problems and demonstrate the ideas using diffusion MRI
super-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 to
quantify $predictive$ uncertainty over the output image. Moreover, we introduce
a method to propagate the predictive uncertainty on a multi-channelled image to
derived scalar parameters, and separately quantify the effects of intrinsic and
parameter uncertainty therein. The methods are evaluated for super-resolution
of two different signal representations of diffusion MR images---DTIs and Mean
Apparent Propagator MRI---and their derived quantities such as MD and FA, on
multiple datasets of both healthy and pathological human brains. Results
highlight three key benefits of uncertainty modelling for improving the safety
of DL-based image enhancement systems. Firstly, incorporating uncertainty
improves the predictive performance even when test data departs from training
data. Secondly, the predictive uncertainty highly correlates with errors, and
is therefore capable of detecting predictive "failures". Results demonstrate
that such an uncertainty measure enables subject-specific and voxel-wise risk
assessment of the output images. Thirdly, we show that the method for
decomposing predictive uncertainty into its independent sources provides
high-level "explanations" for the performance by quantifying how much
uncertainty arises from the inherent difficulty of the task or the limited
training examples.
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