Robert originally graduated with a Mathematical Physics degree from the University of Nottingham in 2023. During the summer at the end of his 2nd year, he did a 6-week internship at the UK Centre for Ecology & Hydrology (UKCEH) looking at bias-correcting river streamflow prediction data using quantile mapping. During this internship he really enjoyed working with the streamflow data, and along with his enjoyment of programming modules decided to continue along this route and study a Master’s degree in Data Science at York straight after graduating from Nottingham. His final master’s project was looking at applying Machine Learning to virtually decouple split peaks in hydrogen Nuclear Magnetic Resonance (NMR) spectrum. In general, his Mathematical interests are in applied mathematics and applications of Machine Learning in mathematics.

Outside of maths he enjoys singing (was very excited to find out there was a maths choir), playing video games, playing board/card games and ringing church bells.

Project title:
Mathematical Methods for Ptychography Imaging

Supervisor(s):
Sergey Dolgov, Mohammad Golbabaee (University of Bristol), Darren Batey (Diamond Light Source), Margaret Duff (STFC)

Project description:
Ptychography is a method of recovering the phase and amplitude of an image via an inverse Fourier transform problem. The method can be used to reconstruct images that are noisy and have low resolution. The Ptychographical Iterative Engine (PIE) is a phase retrieval algorithm that can perform this method. There are several different iterations of this algorithm such as parallel PIE (pPIE), extended PIE (ePIE), regularized PIE (rPIE) and momentum-accelerated PIE (mPIE).

My aim is to develop, test and analyse algorithms for recovering full ptychography images from undersampled data, particularly in tomography, which consists of many similar images at slightly different angles, and/or spectral ptychography at multiple beam energies.  Further aims will be looking at regularisation and relaxation techniques when applied to the optimisation problems underlying ptychography and tomography. In particular, similar images in (spectral) tomography can be approximated by a low-rank matrix or tensor. If time permits, the project will consider uncertainty quantification (such as Bayesian inference) if the noise in the image is large, for example, in the case of low photon counts.