INVERSE PROBLEMS

Inverse problems appear in several fields, including medical imaging, image processing, mathematical finance, astronomy, geophysics, nondestructive material testing and sub-surface prospecting. Typical inverse problems arise from asking simple questions "backwards". For instance, the simple question might be "If we know precisely the structure of the inner organs of a patient, what kind of X-ray images would we get from her?" The same question backwards is "Given a set of X-ray images of a patient, what is the three-dimensional structure of her inner organs?" This is the inverse problem of Computerized Tomography, or CT imaging.

Usually the inverse problem is more difficult than the simple question that it reverses. For example, even though the Earth's gravitational field is governed by Newton's law of gravitation, the inverse problem of finding sub-surface structures from minor variations of the gravitational field on the surface is extremely hard. Successful solution of inverse problems requires specially designed algorithms that can tolerate errors in measured data.

CENTRE OF EXCELLENCE The Finnish Centre of Excellence in Inverse Problems Research is a network comprising research groups in the following institutions: University of Helsinki, Department of Mathematics and Statistics, Rolf Nevanlinna Institute, Helsinki University of Technology, Institute of Mathematics, University of Kuopio, Department of Applied Physics, Lappeenranta University of Technology, Institute of Information Technology, University of Oulu, Department of Mathematical Sciences, University of Oulu, Sodankylä Geophysical Observatory, Tampere University of Technology, Institute of Mathematics. Director in charge of research is professor Lassi Päivärinta from University of Helsinki. The Finnish Inverse Problems Society is an active scientific organization.