# Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior

arXiv: https://arxiv.org/abs/2203.00479 · HTML: https://mlsanity.com/paper/2203.00479/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 88 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 30 of 41)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [Bayesian Deep Convolutional Networks with Many Channels are Gaussian Processes](https://mlsanity.com/paper/1810.05148/) (2018)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty](https://mlsanity.com/paper/2011.07586/) (2020)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks](https://mlsanity.com/paper/1810.03982/) (2018)
- [Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning](https://mlsanity.com/paper/2104.04975/) (2021)
- [Getting a CLUE: A Method for Explaining Uncertainty Estimates](https://mlsanity.com/paper/2006.06848/) (2020)
- [Approximate Inference Turns Deep Networks into Gaussian Processes](https://mlsanity.com/paper/1906.01930/) (2019)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Depth Uncertainty in Neural Networks](https://mlsanity.com/paper/2006.08437/) (2020)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Early Stopping for Deep Image Prior](https://mlsanity.com/paper/2112.06074/) (2021)

## Built on by (most cited first, 10 of 10)

- [UnCRtainTS: Uncertainty Quantification for Cloud Removal in Optical Satellite Time Series](https://mlsanity.com/paper/2304.05464/) (2023)
- [Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent](https://mlsanity.com/paper/2306.11589/) (2023)
- [Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems](https://mlsanity.com/paper/2310.11838/) (2023)
- [Nonlinear Assimilation via Score-based Sequential Langevin Sampling](https://mlsanity.com/paper/2411.13443/) (2024)
- [Improving Linear System Solvers for Hyperparameter Optimisation in Iterative Gaussian Processes](https://mlsanity.com/paper/2405.18457/) (2024)
- [Diffusion Active Learning: Towards Data-Driven Experimental Design in Computed Tomography](https://mlsanity.com/paper/2504.03491/) (2025)
- [DM4CT: Benchmarking Diffusion Models for Computed Tomography Reconstruction](https://mlsanity.com/paper/2602.18589/) (2026)
- [One-Dimensional Deep Image Prior for Curve Fitting of S-Parameters from Electromagnetic Solvers](https://mlsanity.com/paper/2306.04001/) (2023)
- [Principled Confidence Estimation for Deep Computed Tomography](https://mlsanity.com/paper/2602.05812/) (2026)
- [Conditional Diffusion Posterior Alignment for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2604.21960/) (2026)

## Abstract (arXiv)

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 μCT 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/bayesdip.