Abstract
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 Hα(ℝ2) of fractional order α > 0, where we bound the FBP reconstruction error with respect to the weaker norms of the Sobolev spaces Hσ(ℝ2), for 0 ≤ σ ≤ α. By only assuming Holder continuity of the low-pass filter’s window function, the results of this paper generalize previous of our findings in [2]–[4].
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