Computational Uncertainty Quantification for Inverse ProblemsCUQI

A research initiative sponsored by Villum Fonden (the Villum Foundation)

Uncertainty
Picture taken by Per Christian Hansen in the garden of the Heian Shrine in Kyoto, Japan.

Aim

Uncertainty Quantification (UQ) is a branch of scientific computing where we characterize and study the sensitivity of a solution taking into account errors and inaccuracies in the data, models, algorithms, etc. We develop the mathematical, statistical and computational framework for applying UQ to inverse problems such as deconvolution, image deblurring, tomographic imaging, source reconstruction, and fault inspection. The goal is to create a computational platform, suited for non-experts, which can be used by many different industrial and academic end users.

To give just one example, engineers who use X-ray imaging to inspect an object for defects will be able to characterize the reliability of every detail in the image – thus aiding the interpretation and the decision whether a crack is actually present.

The Villum Investigator

Per Christian Hansen

The project is headed by Prof. Per Christian Hansen who specializes in numerical analysis, matrix computations, iterative algorithms and computational algorithms for inverse problems. His recent research projects were High-Definition Tomography (HD-Tomo) funded by an ERC Advanced Research grant, and Improved Impedance Tomography with Hybrid Data, together with Assoc. Prof. Kim Knudsen, funded by the Danish Council for Independent Research.

Per Christian Hansen is an author of four books, 100+ papers and seven software packages, and he has made major contributions in computational algorithms, e.g., for regularization methods, imaging, tomography, and subspace methods for signal processing. All his activities comprise a combination of theoretical insights and computational algorithms.

DTU Compute is Denmark´s largest environment for mathematics and computer science. The department encompasses both in-depth theory and practical applications which allows converting new ideas into innovative products and provide public sector consultancy - to the benefit of both the business community and public sector institutions.

Villum Fonden

Villum Fonden (the Villum Foundation) is one of Denmark's largest research funding foundations with annual grants of approx. DKK 500 million. The aim is to foster research at the highest international level platformed at Danish universities and research institutions.