Inverse Problems

Inverse problems arise whenever there is a need to infer quantities of interest from indirectly measured data. Inverse problems are ubiquitous in science; they arise in physics, biology, medicine, engineering, finance and computer science (e.g., in machine learning and computer vision). Many imaging problems, such as reconstruction of medical images (computer tomography, magnetic resonance imaging, positron-emission tomography) and deblurring or denoising of microscopy and astronomy images, are also instances of inverse problems. Inverse problems typically share a feature that makes them challenging to solve in practice: they lack continuous dependence on the data and, therefore, small errors in the measurements can lead to large errors in naive reconstructions, making them useless.

In this course we will present the mathematical foundation of inverse problems as well as stable methods for solving  them using regularisation  methods. We will cover both classical approaches as well as modern state-of-the-art methods.