Scalable methods for robust uncertainty quantification

This PhD project will investigate novel statistical methods combining the Bayesian formalism with high-dimensional optimization tools to infer parameters and associated uncertainty in large-scale (imaging) problems.

Future defence applications will involve challenges such as: the imaging, monitoring and analysis of underwater terrain and assets from heterogenous data: e.g. sonar and underwater Lidar; or the quantification of radioactive sources or pollutants from event-data, time-of-flight (ToF) data and spectral measurements. These are examples of severely ill-posed inverse problems with potentially multi-modal data where advanced signal models coupled with quantification of uncertainty will be instrumental in aiding signal and image recovery. This project will focus on solving such inverse problems, enhancing optimisation with post-optimisation confidence estimates. Among the different applications mentioned above, the proposed methodologies will be applied in particular to imaging and sensing applications in complex environments.

Convex and non-convex optimisation tools offer the potential to enable fast scalable robust Bayesian inference in high dimensions. Proximal calculus algorithms rooted in optimisation as well as random data selection approaches and approximate Bayesian computation (ABC) to accelerate Monte Carlo sampling will be the focus of this work. Using proximal optimisation algorithms and ABC to explore the confidence region defined by Bayesian models around initial point estimates offers a route to scalable uncertainty quantification for large scale inverse problems but work is required to achieve this and to expand it to deal with multi-modal data. The issues of parallelisation and distribution functionalities, as well as the convergence properties of these proximal methods must also be addressed to enable scalable solutions to be developed.

The University Defence Research Collaboration are pleased to invite applications for PhD studentships to work as part of a leading team of experts in signal processing. The project will be hosted by Heriot-Watt University and the student will work on the University Defence Research Collaboration (UDRC). The UDRC is a leading research partnership for signal processing for defence and develops new techniques to better transform data across many domains into actionable information, and meet the requirements for improved situational awareness, information superiority, and autonomy. This collaboration, sponsored by Dstl and the EPSRC, is academia-led and has commenced its third phase of research focusing on "Signal Processing in the Information Age". The Consortium is made up of the University of Edinburgh, Heriot-Watt University, Queen’s University Belfast and University of Strathclyde and there are currently PhD opportunities available across the four universities to work on diverse topics in signal processing, as part of a collaborative team. The work will involve strong links with industry and the UK defence sector. The PhD student will be expected to work closely with other research team members and to attend regular meetings to present project updates to the sponsors and partners of this project.