Inverse Problems Research Group
Many inverse problems arise from a practical need to literally see beyond the surface. What treasures does the Earth’s crust hold? How fares the patient’s heart? What lies inside a faraway galaxy?
Inverse problems form a subfield of applied mathematics that seeks to answer such questions. Inverse problems utilise diverse subfields of mathematics, like theory of partial differential equations, functional analysis, complex analysis, and Fourier analysis. In practical problems also numerical analysis and probability theory are used. People interested in inverse problems run into applications of diverse mathematical objects, like Dirac’s delta, Brownian motion and Riemannian manifolds. Related fields of science include especially different subfields of physics but even bio and environmental sciences are not uncommon working fields for inverse problems researchers.
Inverse problems are encountered in various applications, like
- medical imaging: CT, MR, and ultrasound scans
- geological surveys: acoustic or electric exploration for e.g. oil or valuable minerals
- non-destructive testing, quality control in industrial manufacturing
- remote sensing, including satellite and radar observations
A common feature for the applications is that it either is not possible or practical to make direct (in situ) observations of the target. In inverse problems, the task is to get information about an unknown structure from indirect and even possibly imprecise observations of the unknown structure. Below is a presentation of our research given to students 21.1.2015 (in Finnish).