Geometric Tomography Algorithms with Partial Data Sets

Applications are invited for a postgraduate research position leading to a PhD degree in Electrical Engineering in the Institute for Digital Communications within the School of Engineering at the University of Edinburgh.

X-ray computed tomography (X-ray CT) has been one of the century's greater scientific innovations and has revolutionised diagnostics in various sectors including biomedical imaging and material non-destructing testing. A fundamental bottleneck of this technology is that it does not scale well with the dimensions of the targeted body in the sense that a small target requires a small (in area) detector while a big target needs a proportionally large detector. In essence this places the whole of the target within the X-ray projection field of view, a necessary requirement for the formation of the Radon data and its inversion. This project is to explore alternative image reconstruction approaches that are suitable in the cases where the detector covers only an interior region insider the target, resulting in truncated projection data. It has since been proven that such partial data cannot resolve the image uniquely using conventional Fourier-based signal back projection algorithms. One way to compensate for this loss of information is by introducing a priori assumptions about the sought target and thereafter recover an approximated image by Bayesian estimation. This approach can also incorporate some recent results in geometric tomography for recovering piecewise constant images with convex boundaries, when such priors are available. The project will see the development of new image reconstruction algorithms for the interior problem in linear attenuation models such as that of Xray CT, inclusive of coding, testing and analysis. This has multiple potential applications in various domains such as medical imaging for obese people, micro-tomography for material testing, as well as non-destructing testing of large infrastructures.

Further Information: 

The project will benefit from the collaboration with the university's medical school and colleagues from the X-ray scanner manufacturing industry. More information on the interior tomography problem and the principles of geometric tomography can be found in:

  1. G. Van Gompel et al., Reconstruction of a uniform star object from interior X-ray data: uniqueness, stability, algorithm, Inverse Problems, 25, 2009
  2. R. J. Gardner, Geometric tomography, 2nd ed., Cambridge University Press, 2006
  3. F. Natterer, The mathematics of computerised tomography, SIAM, 2001

Closing Date: 

Sunday, December 31, 2017
Geometric Tomography Algorithms with Partial Data Sets
Geometric Tomography Algorithms with Partial Data Sets

Principal Supervisor: 

Eligibility: 

A first class Honours degree (or International equivalent) in engineering, physics, informatics or applied mathematics, ideally supplemented by an MSc Degree.

Further information on English language requirements for EU/Overseas applicants.

Funding: 

Competitive funding subject to availability.

Further information and other funding options.

Informal Enquiries: 

Nick Polydorides, Agile Tomography Group Leader, n.polydorides@ed.ac.uk