Inverse problems, meaning the recovery of parameters or states in a mathematcial model that best match some observed data, are ubiquitous in applied sciences. This course will provide an introduction to the deterministic (variational) and stochastic (Bayesian) theories of inverse problems in function spaces.
Contents:
- Examples of inverse problems in mathematics and physical sciences
- Preliminaries from functional analysis
- Preliminaries from probability theory
- Linear inverse problems and variational regularisation
- Bayesian regularisation of inverse problems
- Monte Carlo methods for Bayesian problems