Inverse problems are a branch of exact mathematics, pure and
applied, where the goal is to find unknown parameters or
structures by indirect measurements.
A typical inverse problem is the inverse conductivity problem,
called in medical imaging the Electrical Impedance Tomography.
Its practical setting is the following: Assume that you want to find the inner
structure of your torso by doing resistivity measurements at your skin.
In mathematical terms, this means the problem of
finding
of the unknown parameter functions of a partial differential
equation
from the knowledge of the boundary values of the solutions.
The inverse problems are studied all around Finland and we have
founded the
Finnish Inverse Problems Society which promotes the research
on the area.