Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev SpacesCP2

The filtered back projection formula allows to reconstruct bivariate functions from given Radon samples, where low-pass filters of finite bandwidth are employed to stabilize the reconstruction. Our aim is to analyze the inherent approximation error incurred by the low-pass filter. We prove error estimates in fractional Sobolev spaces along with asymptotic convergence rates as the bandwidth goes to infinity, where we observe saturation at fractional order depending on smoothness properties of the filter's window function.

This presentation is part of Contributed Presentation “CP2 - Contributed session 2

Matthias Beckmann (University of Hamburg)
Armin Iske (Dept. Mathematics, University of Hamburg)
computed tomography, image reconstruction