Sobolev error estimates for filtered back projection reconstructions

This paper concerns the approximation of bivariate functions using the filtered back projection (FBP) formula from computerized tomography. To this end, we prove 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 (rougher) Sobolev spaces H
^σ
(ℝ
²
), for 0 ≤ σ ≤ α. The results of this paper generalize previous of our findings in [2]-[4] for L
²
-error estimates, i.e., for the case σ = 0, to Sobolev error estimates for all fractional orders σ ∈ [0, α] and provide criteria to assess the performance of the utilized low-pass filter by means of its window function.