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Variational Bayesian Inversion Approaches for Ultrasonic Tomography

Department of Mathematics & Statistics

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Dr Katherine Tant , Dr M Foondun , Dr V Dolean Maini No more applications being accepted Funded PhD Project (European/UK Students Only)

About the Project

A fully-funded four year PhD studentship is available, starting on or after 1st October 2020. The intra-disciplinary research will be supervised by Dr Katherine Tant and undertaken primarily within the Continuum Mechanics and Industrial Mathematics group in the Department of Mathematics and Statistics at the University of Strathclyde. Please see https://www.strath.ac.uk/research/subjects/mathematicsstatistics/continuummechanicsindustrialmathematics/ for details of the group’s research. The student will also have the opportunity to interact with the Stochastic Analysis group and the Numerical Analysis and Scientific Computing group, facilitated by their second supervisors, Dr Mohammud Foondun and Professor Victorita Dolean Maini.

Ultrasonic non-destructive evaluation (NDE) is critical for the structural assessment of the UK’s aging industrial infrastructure, as well as for the monitoring and quality control of modern additive manufacturing methods. It concerns the practice of transmitting mechanical waves through a solid object and subsequently using the reflected wave data collected on its surface to ‘see the unseen’; that is to create an image of the object’s interior which highlights any embedded defects. Mathematically, this is known as an inverse problem. This project will focus on developing new ultrasonic tomography techniques for NDE based on the principles of Bayesian inference, which provide a convenient mathematical framework to estimate the joint conditional probability distribution of the spatially varying material properties of an object given some observed boundary measurement data (this is the posterior distribution). Typically, Markov chain Monte Carlo sampling methods are used to obtain numerical approximations of the true posterior distribution, but these approaches are often computationally intractable for high-dimensional parameter spaces (such as those present in ultrasonic tomography problems). This project will examine Variational Bayesian (VB) approaches instead, where the Bayesian inverse problem is reformulated as a more computationally efficient deterministic optimisation problem. Although the project will focus primarily on NDE applications, the techniques developed will be applicable across many sectors, including medical imaging and seismology.

This is a very exciting project which will allow the student to work at the interface between mathematics and industry. The student will attend regular research seminars and events within the Mathematics and Statistics department and the Centre of Ultrasonic Engineering at Strathclyde, and so will have many opportunities to interact with a multi-disciplinary team and develop both technically and professionally.

Applicants should have, or be expecting to obtain in the near future, a first class or good 2.1 honours degree (or equivalent) in mathematics or a mathematical science.

Funding Notes

The studentship covers full tuition fees and a tax-free stipend for four years starting in October 2020. Funding is only available to UK nationals and to EU nationals who have lived in the UK for three years prior to the start of the studentship.
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