Equivariant Bootstrapping for Uncertainty Quantification in Imaging Inverse Problems

Julián Tachella, Marcelo Pereyra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Scientific imaging problems are often severely ill-posed and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of experimental results as well as for reliably using the reconstructed images as scientific evidence. Unfortunately, existing imaging methods are unable to quantify the uncertainty in the reconstructed images in a way that is robust to experiment replications. This paper presents a new uncertainty quantification methodology based on an equivariant formulation of the parametric bootstrap algorithm that leverages symmetries and invariance properties commonly encountered in imaging problems. Additionally, the proposed methodology is general and can be easily applied with any image reconstruction technique, including unsupervised training strategies that can be trained from observed data alone, thus enabling uncertainty quantification in situations where there is no ground truth data available. We demonstrate the proposed approach with a series of experiments and comparisons with alternative state-of-the-art uncertainty quantification strategies. In all our experiments, the proposed equivariant bootstrap delivers remarkably accurate high-dimensional confidence regions and outperforms the competing approaches in terms of estimation accuracy, uncertainty quantification accuracy, and computing time. These empirical findings are supported by a detailed theoretical analysis of equivariant bootstrap for linear estimators.
Original languageEnglish
Title of host publicationProceedings of Machine Learning Research
Pages4141-4149
Number of pages9
Volume238
Publication statusPublished - 18 Apr 2024
Event27th International Conference on Artificial Intelligence and Statistics 2024 - Valencia, Spain
Duration: 2 May 20244 May 2024

Conference

Conference27th International Conference on Artificial Intelligence and Statistics 2024
Abbreviated titleAISTATS 2024
Country/TerritorySpain
CityValencia
Period2/05/244/05/24

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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