Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior
This work addresses uncertainty estimation for computed tomography reconstructions, which is crucial for real-world deployment in medical or industrial imaging, but it is incremental as it builds on existing deep image prior methods.
The paper tackled the lack of accurate uncertainty estimates in deep-learning based tomographic image reconstruction by developing a linearised deep image prior method, which provided superior calibration of uncertainty estimates on synthetic and real 2D μCT data compared to previous probabilistic formulations.
Existing deep-learning based tomographic image reconstruction methods do not provide accurate estimates of reconstruction uncertainty, hindering their real-world deployment. This paper develops a method, termed as the linearised deep image prior (DIP), to estimate the uncertainty associated with reconstructions produced by the DIP with total variation regularisation (TV). Specifically, 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 $μ$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.