Computed Tomography for Region-of-Interest Problems with Limited Data

AbstractIn this thesis the mathematical model for reconstructing cross-sectional images of deep sea oil pipes is studied for limited region-of-interest X-ray measurement data. This is motivated by a research and development project in collaboration with the Digital X-ray inspection division within the company FORCE Technology. The images are used to detect defects in the pipes such as cracks and corrosion.

The first part of the thesis provides insight into a mathematical model describing region-of-interest X-ray tomography. For this model it is shown exactly which singularities of a measured object are (or are not) visible in the data using a framework derived from microlocal analysis. This provides an expectation of the challenges in reconstructions from limited data.

The second part of the thesis studies reconstruction algorithms for the region-of-interest model. Firstly, the expected challenges of reconstructing using this model are verified numerically and additional challenges, when using standard algorithms, are shown. With the aim of overcoming these challenges a weighted frame-based sparsity penalty in a variational formulation is used to incorporate prior knowledge of the measurement geometry and object. This method is shown to include only significant details of the object that are visible in the data and is well-represented by the frame.

In the third and last part of the thesis this insight is used on real measurement data provided by FORCE from a prototype set-up. The expected challenges of ROI are shown to hold for real data. Hence, an exterior measurement geometry is proposed as an alternative to ROI yielding more singularities of the object in the data. The weighted frame-based methods are shown to provide reliable reconstructions on this type of data.
TypeMaster's thesis [Industrial collaboration]
PublisherTechnical University of Denmark, Department of Applied Mathematics and Computer Science
AddressRichard Petersens Plads, Building 324, DK-2800 Kgs. Lyngby, Denmark,
SeriesDTU Compute M.Sc.-2017
NoteDTU supervisors: Per Christian Hansen,, DTU Compute, and Yiqiu Dong,, DTU Compute
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IMM Group(s)Scientific Computing