Recent Developments in Inverse Problems - Abstract

König, Claudia

Error estimates for exponentially ill-posed problems with impulsive noise

We consider exponentially ill-posed equations where the data is perturbed by impulsive noise, i.e. the perturbation is large on a small part. Following Hohage, Werner ( SINUM 52(3), 2014 ), we prove error estimates for the Bregman distance in terms of the regularization and noise parameters, assuming a variational source condition and smoothing properties of the forward operator. The latter assumption is verified for real analytic functions in the range of the forward operator. The error estimates are applied to the Backward Heat Equation and to Satellite Gradiometry. Numerical simulations show the superior behaviour of $L^1$-data fitting.
(joint work with Hohage & Werner)