Silja Westphal Christensen: How much can we trust tomographic reconstructions?
What do you see when you look at an image from an X-ray scan? The true interior of the scanned object? No, in fact you see a reconstruction which can contain errors and uncertainty for numerous reasons. Many people are aware that measurements are uncertain, but assumptions and simplifications in mathematical models and reconstruction algorithms can also give rise to significant uncertainty and errors. So when you look at an X-ray scan, you should not interpret it as the true interior, but rather a best guess. In this project we study how good this guess is by quantifying the uncertainty.
This PhD project considers uncertainty quantification in X-ray computed tomography (CT). CT reconstructions can be categorized as inverse problems. That means we infer information about internal defining characteristics of a system based on external observations of that system. In CT we infer information about internal material densities and structures based on external observations of X-ray attenuation. The project will focus on materials research and the use of so-called micro-CT scanners. One example is examining samples from wind turbine blades, where an understanding of the glass fiber microstructure gives information about strength, durability, etc.
Traditionally tomographic reconstructions are computed using the filtered back projection (FBP) method, but when data quality is limited, FBP fails to produce useful images. So-called regularization techniques can help compensate by incorporating a-priori information and an improved reconstruction can be obtained by formulating and solving a convex optimization problem. However, this only provides one particular estimate and does not express how (un-)reliable the reconstruction is. In this project we will create a Bayesian inversion framework and software for the CT community. In this framework we do not infer a single reconstruction based on measured data and a-priori information, but rather a full probability distribution of the reconstruction. From this probability distribution we can provide the most likely reconstruction, but we can also quantify the uncertainty.
This project is part of the research initiative CUQI (Computational Uncertainty Quantification for Inverse problems) funded by Villum Fonden (https://www.compute.dtu.dk/english/cuqi). The goal of CUQI is to make uncertainty quantification (UQ) for inverse problems readily available for non-experts.