Sebastian J. Scott

ACADEMIC BACKGROUND

I graduated from the University of Bath in summer 2020 with a first-class honours Master of Mathematics. Currently I am doing an Integrated PhD in Statistical Applied Mathematics at the University of Bath, as part of the 7th cohort of the EPSRC SAMBa CDT. Having finished the MRes year, I am now in my second year of PhD research.

My undergraduate Masters dissertation on "efficient priorconditioning for edge enhancement in imaging" was supervised by Dr Silvia Gazzola and Professor Alastair Spence. The project involved the regularization of discrete ill-posed linear inverse problems and employing Krylov subspace methods that adaptively define edge-enhancing encodings between iterates.

Now, my PhD topic on "learned regularisation for inverse problems" concerns how one can use machine learning techniques when solving inverse problems. It is being supervised by Dr Matthias J. Ehrhardt and Dr Silvia Gazzola.

RESEARCH

My mathematical interests primarily lie in numerical analysis, with inverse problems being a particular focus. Inverse problems arise naturally in various applications such as medical imaging, wherin one has a quantity of interest (e.g. brain scan) but only has access to an indirect measurement (e.g. sinogram/output of a medical device) and an understanding of how these quantities are related (e.g. radon transform). The task is then: given this indirect measurement, what is associated quantity of interest that gives rise to said measurement?

Due to noise in the measurement data, directly solving this problem often leads to a meaningless reconstruction of the quantity of interest. Instead, one considers a "nearby" problem that is less sensitive to noise, but still representative of the orginal problem - a technqiue called variational regularisation. How "nearby" you are is controlled by a non-negative number called the regularisation parameter. My PhD concerns how one can use machine learning techniques, with mathematical guarantees, to solve variationally regularised problems, with a focus determining the choice of the regularisation parameter.

During my MRes year of the Integrated PhD, I took the following modules:

Year-long:: MA50264: Inter-disciplinary Research Project (IRP) concerning numerical methods for proton therapy treatment planning; MA50246: Student-led symposia and integrative think tanks
Semester 1:: MA40198: Applied Statistical Inference; MA50263: Mathematics of machine learning; MA50183: Reading course on edge-enhancing regularisation methods in imaging
Semester 2:: MA50250: Inverse problems, data assimilation and filtering; MA50251: Applied stochastic differential equations; MA50215: Reading course on spectral theory and its applications

During my first year of research, the following taught modules were also taken:

Semester 1:: MA50183: Reading course on the mathematics of deep learning
Semester 2:: MA50215: Reading course on biomedical denoising

PUBLICATIONS

Benfenati, A; Chouzenoux, E; Franchini, G; Latva-Aijo, S; Narnhofer, D; Pesquet, J-C; Scott, S.J.; Yousefi, M. Majorization-Minimization for sparse SVMs. arXiv preprint: arXiv:2308.16858, 2023

Ehrhardt, M.J.; Gazzola, S.; Scott, S.J. On Optimal Regularization Parameters via Bilevel Learning. arXiv preprint: arXiv:2305.18394, 2023

Gazzola, S.; Scott, S.J.; Spence, A. Flexible Krylov Methods for Edge Enhancement in Imaging. J. Imaging 2021, 7, 216. Available online: doi.org/10.3390/jimaging7100216

NEWS

September 2024

Attended the 4th IMA Conference on Inverse Problems: from theory to application. and presented at the minisymposium Attendance was in part funded by the IMA Small Grant Scheme.
Began a 2 month research visit at TU/e, hosted by Remco Duits. This visit was possible thanks to the REMODEL staff exchange project.

June 2024

Attended the University of Bath Doctoral Celebration Evening where I recieved a Doctoral Recognition Award.

May 2024

Gave a talk at the Pint of Science Festival about how one how one formulates and solves an inverse problem, with a focus on computerised tomography.
Attended IPMS24 and presented at the minisymposium for Inverse and Control Problems for Evolution Equations and Variational Inequalities. Attendance was in part funded by the QJMAM Fund for Applied Mathematics .

October 2023

Gave a talk at the University of Bath Postgraduate Seminar Series (PSS) on "What makes a regulariser good?". This is based on our recent work "On Optimal Regualrization Parameters via Bilevel Learning".
Attended the Ada Lovelace day at the University of Bath where I gave a lightning talk about Emilie du Chatelet

September 2023

Our preprint "Majorization-Minimization for sparse SVMs" is now available on arXiv! This is work started at the ATOMI workshop in June 2022.

August 2023

Attended ICIAM 2023 and presented at the minisymposium for Recent advances in deep learning-based inverse and imaging problems.

July 2023

Gave a talk at TU Graz to the Vision, Learning and Optimization Group about Optimal Regularization Parameters via Bilevel Learning
Started a 6 week research visit hosted by Thomas Pock at the Institute for Computer Graphs and Vision, TU Graz, Austria. This visit was possible thanks to the SAMBa internationalisation fund and the LMS Travel Grants for Early Career Researchers.

May 2023

Attended and gave a talk at the 2023 SIAM Conference on Optimization, Seattle, about Learning the Regularization Parameter for Inverse Problems. Attendance was possible thanks to the SIAM Student Travel Award, and the IMA Small Grant Scheme.
Our preprint "On Optimal Regularization Parameters via Bilevel Learning" is now available on arXiv!

January 2023

Gave a talk at the SAMBa Ethics in Maths Reading and Discussion Group about AI Generated Art

December 2022

Attended the Deep learning for industry workshop, Maths4DL, Unviersity of Bath

November 2022

Gave a talk at the Bath Imaging Group seminar about my current research

October 2022

Gave a talk at the University of Bath Postgraduate Seminar Series about my current research

September 2022

Became secretary for the Bath SIAM-IMA student chapter
Attended and gave a talk at the Post-graduate Researchers in Inverse Problems, Machine Learning, and Optimization (PRIMO) workshop

July 2022

Organised and attended the Statistical Applied Mathematics at Bath (SAMBa) CDT conference, University of Bath
Attended the LMS Mathematics Communication workshop (beginner session)
Attended the Analytic and Geometric Approaches to Machine Learning, University of Bath

June 2022

Invited to speak at the Post-graduate Researchers in Inverse Problems, Machine Learning, and Optimization (PRIMO) workshop
Attended and gave a lightning talk at Advanced Techniques in Optimization for Machine learning and Imaging (ATOMI), INdAM workshop, Rome, Italy

May 2022

Presented a poster at the 3rd IMA Conference for Inverse Problems from Theory to Application in Edinburgh, United Kingdom

April 2022

Attended and presented at the Recent advances in computational inverse problems workshop, University of Bath
Attended the Mathematics for deep learning opening workshop, University of Bath
Invited to speak at the Recent advances in computational inverse problems workshop in Bath
Co-organiser of the 2022 SAMBa Summer Conference which will take place July 2022

March 2022

Attended the SIAM Imaging conference (IS22)

February 2022

Gave a talk at the University of Bath Postgraduate Seminar Series about using Wolfe conditions to choose the step length of a gradient-based iterative solver

January 2022

Gave a talk at the SAMBa Ethics in Maths Reading and Discussion Group about Cookies and Targeted Advertising

December 2021

Attended the Interpretability, safety, and security in AI event by the Alan Turing Institute

October 2021

Gave a talk at the University of Bath Postgraduate Seminar Seriers on parameter choice rules for choosing the regularisation parameter when solving inverse problems
Became an organiser of the University of Bath Postgraduate Seminar Seriers (PSS), alongside Ed Gallagher, for the 2021-22 academic year

November 2021