Margaret Duff

Margaret graduated from the University of Cambridge with a BA and MMath in Mathematics in 2018.

Margaret graduated from the University of Cambridge with a BA and MMath in Mathematics in 2018. During this time, she completed summer projects in the Cambridge Image Analysis group and with GSK in Stevenage. Both projects focused on image classification, applying a mixture of computer vision and machine learning techniques to classify images. Her Master’s Essay was on “Time Reversal Imaging in Inhomogeneous Media” which has applications to everything from earthquakes to brain tumours! She is excited to explore interesting applications of image analysis and mathematical biology. Outside of Maths, Margaret is a Cub and Guide leader and volunteers with the Hosanna House and Children’s Pilgrimage Trust. She enjoys walking, swimming, reading and travelling.

Research project title:
Generative Models Applied to Inverse Problems

Matthias Ehrhardt, Neill Campbell

Project description:
An inverse problem is the process of calculating from a set of observations, the data, the causal factors that produced them, the model parameters. Inverse problems that are interesting are nearly always ill-posed, meaning that small errors in the data may lead to large errors in the model parameter and there are several possible model parameter values that are consistent with the observations. Addressing this ill-posedness is critical in applications where decision making is based on the recovered model parameter, such as for medical imaging. Medical images remain the gold standard for diagnostics of many conditions. However, analysis of medical images raises fundamental issues with the standard “deep learning” approach of training a multi-layer neural network on hundreds of thousands of images. Such algorithms cannot accurately quantify their uncertainty, nor describe the reasoning that led to a given classification for an image. Generative models provide a promising avenue to solve the aforementioned problems. They implicitly model high-dimensional distributions of data from noisy indirect observations. From this, new samples from the distribution could be generated and estimators calculated. However, in pushing the boundaries of computer science, fundamental mathematics has somewhat been left behind and this threatens the ability to exploit the many applications of these methods. Margaret’s project aims to fill some of these mathematical gaps.

Fun fact(s):
● I volunteer as a Guide and Cub Scout Leader.
● I am always cold and rarely seen without multiple jumpers.
● I can’t survive without multiple cups of tea!
● I know some sign language, primarily Makaton, and want to learn more.