Welcome to the research group Inverse Problems
Inverse problems consist in reconstructing causes from observed effects.
For example, in magnetic resonance imaging (MRI) one has to reconstruct
the proton density in a human or animal body which gave rise to a measured magnetic signal.
In coherent x-ray imaging, one tries to reconstruct the refractive index of a sample
which causes a measured diffraction pattern.
The basic difficulty in the numerical solution of inverse problems consists in the ill-posedness of most of
in the sense that arbitrarily small measurement errors may
cause large errors in the reconstruction. Therefore, naive approaches fail.
A remedy against ill-posedness is regularization. Here a-priori information about
the solution are incorporated into the reconstruction procedure. In more mathematical
terms, instead of the discontinuous inverse of the forward operator, which maps the unknown to
the data, a continuous approximation of this inverse is applied to the data to obtain a
In particular, we work on inverse problems in the following fields: