Statistical Modelling and Imaging from Electromagnetic Measurements

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.

The project is aimed at solving the forward and inverse problems in electromagnetic imaging based on time-harmonic Maxwell's equations. These problems find numerous applications in geophysical exploration, medical imaging and non-destructing testing of synthetic materials and structures. For the forward problem, numerical finite element methods are sought for computing the likelihood of the electric field measurements in terms of its expectation and covariance when the electrical properties are modeled as lognormal random fields with prescribed covariance. The focus of this work is on developing appropriate algorithms based on model reduction that approximate the solution of the model equations efficiently. This process yields a deterministic, parametric form of the posterior distribution for the sought electrical parameters, which allows us to cast the inverse problem as a high-dimensional integration problem for a variety of desirable posterior estimators. To compute these integrals and quantify their uncertainty efficient collocation schemes will be investigated.

Further Information: 

This research is aimed to extend our group's framework on uncertainty quantification (UQ) for Maxwell's equations in the quasi-magnetostatic regime for the controlled source electromagnetic imaging application. More details in the technical reports

  1. D. Kamilis, Forward modelling in electromagnetism with the finite element method, Technical report, University of Edinburgh, 2016.
  2. D. Kamilis, Stochastic forward modelling for time-harmonic Maxwell's equations, Technical report, University of Edinburgh, 2016.

Closing Date: 

Sunday, December 31, 2017
Figure: Electrical field simulation from electrical dipole source submerged in seawater
Figure: Electrical field simulation from electrical dipole source submerged in seawater

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