Uncertainty Quantification in Astro-Imaging by Optimisation

In our recent work [1], we proposed a Bayesian uncertainty quantification method for large scale imaging inverse problems. It aims to analyse the confidence in specific structures observed in maximum a posteriori (MAP) estimates (e.g., lesions in medical imaging, celestial sources in astronomical imaging), assuming a log-concave Bayesian model. This information can subsequently be used as evidence to inform decisions and conclusions. We propose to perform a hypothesis test on the structures of interest, to assert their uncertainty. The test is formulated as a convex minimisation problem, enabling the use of advanced optimisation algorithms. In this abstract we summarise the proposed Bayesian Uncertainty Quantification by Optimisation (BUQO) method and we provide results obtained on real data in the context of radio-astronomical imaging.