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Adaptive undersampling for spectro-microscopy: exploring new mathematical properties and enhancing performance

Project Description

This is a collaborative project between the University of Bath and Diamond Light Source, the national synchrotron science facility located at the Harwell Science and Innovation Campus near Oxford


Lead supervisor: Dr Silvia Gazzola, Department of Mathematical Sciences, University of Bath
Co-supervisor (Bath): Dr Sergey Dolgov, Department of Mathematical Sciences, University of Bath
Co-supervisor (Diamond Light): Dr Paul Quinn, Diamond Light Source


Spectro-microscopy is a powerful technique that can be used to obtain information about the spatial distribution of chemical states in a sample by combining imaging and X-ray absorption spectroscopy. Unfortunately, its uptake is limited by factors such as the speed of measurement, dilute concentrations, and radiation damage. Many applications in material sciences will benefit from new methods that can accelerate accurate data collection in spectro-microscopy.

This project aims to develop, implement, analyse, and validate novel techniques to reduce the time and dose needed to acquire spectro-microscopy data. The central focus is on adaptive reduced sampling methods for synchrotron scans, with the goal of obtaining high-quality full reconstructions from a much smaller subset of the measurements than presently required.

Since spectro-microscopy performs spatial scans of a sample at different energy levels, undersampling in both space and energy is possible. We propose performing the former by randomly acquiring image rows, and by developing reconstruction methods using matrix completion techniques. Undersampling in energy will be achieved by applying the Discrete Empirical Interpolation Method. Joint undersampling in space and energy will be also explored. Optimal undersampling strategies will be formulated as bi-level optimisation problems, taking into account the constraints of real experimental acquisitions.


The student will develop expertise in X-ray microscopy experiments (acquisition and analysis), and design novel methods for undersampling (requiring innovative compressive sensing and analysis techniques). The successful student will be given privileged access to the training activities of the ``SAMBa’’ EPSRC Centre for Doctoral Training (such as optional courses in a variety of statistical and applied mathematics topics, research seminars, biannual workshops with industry; see: Diamond Light Source will provide the required training in experimental scanning methods, X-ray physics, and analysis methods.


Applicants should hold, or expect to receive, a First Class or high Upper Second Class UK Honours degree (or the equivalent qualification gained outside the UK) in a Mathematics- or Physics-based discipline, with experience of Numerical Analysis and Scientific Computing. A master’s level qualification would also be advantageous. Non-UK applicants must meet our English language entry requirement


Informal enquiries are welcomed and should be addressed to Dr Silvia Gazzola, .

Formal applications should be made via the University of Bath’s online application form for a PhD in Mathematics:

Please ensure that you quote the supervisor’s name and project title in the ‘Your research interests’ section.

More information about applying for a PhD at Bath may be found here:

Anticipated start date: 28 September 2020.

Funding Notes

UK and EU candidates applying for this project will be considered for a studentship funded by the University of Bath and Diamond Light Source Limited. The studentship will be tenable for up to 3.5 years and will cover UK/EU tuition fees, an enhanced stipend (£17,246 in year 1, increasing annually) and a budget for travel and conference attendance.

Unfortunately, applicants who are classed as Overseas for fee-paying purposes are not eligible for the funding.

How good is research at University of Bath in Mathematical Sciences?

FTE Category A staff submitted: 44.40

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

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