Background: Inverse scattering problems arise when electromagnetic waves are used to image ‘hidden’ objects, e.g., buried landmines, underground oil reserves, or tumours in the body. Practical inverse scattering problems are subject to considerable uncertainty, as the exact location, geometry, physical size and material composition of the objects (and the composition of the surrounding medium) are typically not known a priori. For this reason, analytical inversion techniques applied to electromagnetic imaging often fail for ill-posed scenarios, i.e., when parameters of the problem are uncertain.
Proposal: This PhD project aims to develop new numerical methods for computational electromagnetics where the inputs are probabilistic distributions, instead of ‘exact’ values. These methods can then be used to efficiently solve the forward model over the entire parameter space spanned by the uncertainties to find the most probable set of input variables that would produce the observations (and thereby providing a statistical solution to the inverse problem). To ensure computationally efficient algorithms the uncertainties need to be compactly supported on the parameter space. Accordingly, this project will also focus on sparse orthogonal polynomial and wavelet expansions for the uncertainties.
Applicant: a good background in electromagnetics, programming and numerical analysis is required.
A PhD scholarship is available with a stipend of NZD$ 27,600 p.a. for 3 years, tuition fees are also included.