# Kolloquiumsvortrag, Prof. Armin Iske, Universität Hamburg / am 12.05.2017

12.05.2017 von 14:15 bis 15:45

Institut für Informatik, Ludewig-Meyn-Straße 2, 24118 Kiel, Raum: Übungsraum 2/K

Titel: Error Estimates and Convergence Rates for Filtered Back Projection.

Abstract: We consider the approximation of target functions from fractional Sobolev spaces by the method of filtered back projection (FBP), which gives an inversion of the Radon transform. To this end, we analyze the intrinsic FBP approximation error which is incurred by the use of a low-pass filter with finite bandwidth, before we prove $L^2$-error estimates on Sobolev spaces of fractional order. The obtained error bounds are affine-linear with respect to the distance between the filter's window function and the constant function $1$ in the $L^\infty$-norm. With assuming more regularity for the window function, we refine the error estimates to prove convergence for the FBP approximation in the $L^2$-norm as the filter's bandwidth goes to infinity. We finally give asymptotic convergence rates in terms of the bandwidth of the low-pass filter and the smoothness of the target function.