CUQI – Computational Uncertainty Quantification for Inverse Problems

Mathematics and AI for Imaging Seminars I

Organizer：

Chenglong Bao

Speaker：

Per Christian Hansen, Technical University of Denmark

Time：

Wednesday, 15:00-16:00

Oct. 23, 2024

Venue：

A04, the 8th Floor

Shuangqing Complex Building

双清综合楼8楼A04

Title：

CUQI – Computational Uncertainty Quantification for Inverse Problems

Abstract:

Since 2019 we have worked on developing a practical framework for applying uncertainty quantification to inverse problems.

Our work contributes to the basis for UQ studies of a range of linear and nonlinear inverse problems with different priors and noise models. Specifically, building on the Bayesian framework we develop a modeling and computational platform, including an abstraction layer aimed at non-experts, which is implemented in the python software package CUQIpy.

In this talk I highlight some of our results and methods, with examples from X-ray computed tomography (CT). I describe how we handle uncertain projection angles, how we include structural priors tailored to the geometry of the scanned object, and how we use a goal-oriented approach to compute inclusion boundaries and their roughness. I also briefly describe our software package.

This is joint work with all the members of the CUQI project:

https://sites.dtu.dk/cuqi

The work is supported by a grant from the Villum Foundation.