Inverse problems – indirect measurements, detection and reconstruction in problems from the natural sciences

Inverse problems are ubiquitous in nature, in medical, scientific and engineering applications and in our daily lives. In all of these problems it is the objective to recover properties of the underlying (physical) system by means of indirect measurements. As these problems are typically in a mathematically precise sense "ill-posed", this turns out to be a difficult task in general. In this article some of the main challenges are introduced by discussing prototypical problems which are investigated at the MPI MiS.