Mathematical Colloquium: Carola-Bibiane Schönlieb (University of Cambridge)

Title

Mathematical imaging: from partial differential equations to deep learning for images

Abstract

Images are a rich source of beautiful mathematical formalism and analysis. Associated mathematical problems arise in functional and non-smooth analysis, the theory and numerical analysis of nonlinear partial differential equations, inverse problems, harmonic, stochastic, and statistical analysis, and optimization, just to name a few. Applications of mathematical imaging are profound and arise in biomedicine, material sciences, astronomy, digital humanities, as well as many technological developments such as autonomous driving, facial screening and many more. 

In this talk I will discuss my perspective on mathematical imaging, share my fascination and vision for the subject. I will then zoom into one research problem that I am currently most excited about and that we helped make first advances on: the mathematical formalisation of machine learned approaches for solving inverse imaging problems.