Katrine Ottesen Bangsgaard: Quantifying the eliability of computed tomography and inverse problems in general
Imagine that a long underwater pipe has an internal damage and you need to locate it without stopping the flow and opening the pipe. How can we obtain knowledge about the location and extent of the damage without direct inspection? X-ray imaging – based on measurements of the attenuation of X-rays passing through the pipe – presents a solution to this problem.
X-ray imaging, seismic imaging and ultrasound inspection are examples of inverse problems, where we use a mathematical model to compute information about hidden internal structure from exterior measurements. But the computations are inherently very sensitive to small errors in the measurements and the models – so a pressing challenge is: to what extent can we trust the computed images?
Uncertainty Quantification (UQ) is a mathematical tool which takes errors and inaccuracies in the data, models, algorithms, etc. into account. UQ allows us to rigorously characterize and study the sensitivity and reliability of the computed result – in this case the 3D images. Ultimately this leads to lower risks and more correct decisions based on the images.
The goal of this PhD project is twofold. As an outset we develop mathematical UQ-models and computational methods for X-ray and neutron tomography that allow us to incorporate model uncertainties and thus quantify the uncertainties in the computed images. We will then use our experience from these use-cases to develop a general approach to handling and quantifying the influence of model uncertainties.
This is an important ingredient of the CUQI research initiative that funds this PhD project, and whose ultimate goal is to develop a framework, including UQ models and software, aimed at non-experts.