Computational Uncertainty Quantification for Inverse ProblemsCUQI

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

The CUQI team as of Nov. 24, 2021

The CUQI Team as of Nov. 23, 2021.


Photo: Per Christian Hansen Click on the picture to see a brief introduction to inverse problems and UQ.

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 platform for modeling and computations, suited for non-experts, which can be used in many different industrial and academic inverse problems.

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.

For more details about the CUQI research initiative see the slides from the inauguration in Nov. 2019 (to see the animation on slide 4 you need to show the pdf-file in Acrobat).

The Villum Investigator

Photo: Joachim Rode

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.


A brief introduction to the CUQI research initiative. The video is in Danish only.