Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior

Abstract

Existing deep-learning based tomographic image reconstruction methods do not provide accurate uncertainty estimates of their reconstructions, hindering their real-world deployment. This paper develops a method, termed as linearised deep image prior (DIP), to estimate the uncertainty associated with reconstructions produced by the DIP with total variation (TV) regularisation. We endow the DIP with conjugate Gaussian-linear model type error-bars computed from a local linearisation of the neural network around its optimised parameters. To preserve conjugacy, we approximate the TV regulariser with a Gaussian surrogate. This approach provides pixel-wise uncertainty estimates and a marginal likelihood objective for hyperparameter optimisation. We demonstrate the method on synthetic data and real-measured high-resolution 2D $\mu$CT data, and show that it provides superior calibration of uncertainty estimates relative to previous probabilistic formulations of the~DIP. Our code is available at https://github.com/educating-dip/bayes_dip.