Convergence Rates for Hölder-Windows in Filtered Back Projection

In this paper we consider the approximation of bivariate functions by using the well-established filtered back projection (FBP) formula from computerized tomography. We establish error estimates and convergence rates for the FBP reconstruction method for target functions f from a Sobolev space H
^α
(ℝ
²
) of fractional order α > 0, where we bound the FBP reconstruction error with respect to the weaker norms of the Sobolev spaces H
^σ
(ℝ
²
), for 0 ≤ σ ≤ α. By only assuming Hölder continuity of the low-pass filter's window function, the results of this paper generalize previous of our findings in [2]-[4].