Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior

TL;DR

This paper introduces a linearised deep image prior method to accurately estimate pixel-wise uncertainty in computed tomography reconstructions, enhancing reliability for real-world applications.

Contribution

It develops a conjugate Gaussian-linear model approach for uncertainty estimation in DIP with TV regularisation, including a Gaussian surrogate for TV.

Findings

Provides pixel-wise uncertainty estimates with superior calibration.

Demonstrates effectiveness on synthetic and real high-resolution μCT data.

Offers a marginal likelihood objective for hyperparameter tuning.

Abstract

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 $\mu$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.