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This paper concerns the approximation of bivariate functions by using the well-known filtered back projection (FBP) formula from computerized tomography. We prove error estimates and convergence rates for the FBP approximation of target functions from Sobolev spaces $$\mathrm H^\alpha ({\mathbb {R}}^2)$$ of fractional order $$\alpha >0$$, where we bound the FBP approximation error, which is incurred by the application of a low-pass filter, with respect to the weaker norms of the rougher Sobolev spaces $$\mathrm H^\sigma ({\mathbb {R}}^2)$$, for $${0 \le \sigma \le \alpha }$$. In particular, we generalize our previous results to non band-limited filter functions and show that the decay rate of the error saturates at fractional order depending on smoothness properties of the filter’s window function at the origin. The theoretical results are supported by numerical simulations.

Saturation rates of filtered back projection approximations