Research

My research focuses on the intersection of applied analysis and data science, particularly image processing and machine learning. My specialism is in graph-based learning methods for image processing, e.g. for image segmentation and joint reconstruction-segmentation.

Ongoing research

The spline theory of sparse autoencoders. Collaborators: Prof. Randall Balestriero, Dr. Keith Duggar, Dr. Chris Wendler, Javier Ideami, Benjamin Macdowall Rynne, Can Rager

Joint reconstruction-segmentation with graph-based methods and with Bhattacharyya methods. Collaborators: Prof. Franca Hoffmann, Prof. Carola-Bibiane Schönlieb, Prof. Allen Tannenbaum, Dr. Ricardo Baptista, Dr. Yves van Gennip, Dr. Jonas Latz, John Cao.

Properties of continuum limits of graph-based processes with respect to kernel density estimates. Collaborators: Prof. Franca Hoffmann, Prof. Bamdad Hosseini, Dr. Yifan Chen.

Learned graph Merriman–Bence–Osher image segmentation. Collaborators: Dr. Martin Benning, Dr. Moshe Eliasof, Dr. Jonas Latz, Dr. Lisa Kreusser, James Rowbottom.

Preconditioned non-equispaced fast Fourier transform (NFFT) methods for matrix exponentials and graph diffusion. Collaborators: Dr Jonas Latz, Dr. John Pearson, Andrés Miniguano-Trujillo.

Graph-Laplacian-based multi-fidelity modelling. Collaborators: Prof. Franca Hoffmann, Prof. Assad Oberai, Dr. Oscar Pinti.