  Filtered back projection (FBP) methods are the most widely used
reconstruction algorithms in computerized tomography (CT). The ill-posedness of
this inverse problem allows only an approximate reconstruction for given noisy
data. Studying the resulting reconstruction error has been a most active field
of research in the 1990s and has recently been revived in terms of optimal
filter design and estimating the FBP approximation errors in general Sobolev
spaces.
  However, the choice of Sobolev spaces is suboptimal for characterizing
typical CT reconstructions. A widely used model are sums of characteristic
functions, which are better modelled in terms of Besov spaces
$\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$. In particular
$\mathrm{B}^{\alpha,1}_1(\mathbb{R}^2)$ with $\alpha \approx 1$ is a preferred
model in image analysis for describing natural images.
  In case of noisy Radon data the total FBP reconstruction error
$$\|f-f_L^\delta\| \le \|f-f_L\|+ \|f_L - f_L^\delta\|$$ splits into an
approximation error and a data error, where $L$ serves as regularization
parameter. In this paper, we study the approximation error of FBP
reconstructions for target functions $f \in \mathrm{L}^1(\mathbb{R}^2) \cap
\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$ with positive $\alpha \not\in
\mathbb{N}$ and $1 \leq p,q \leq \infty$. We prove that the $\mathrm{L}^p$-norm
of the inherent FBP approximation error $f-f_L$ can be bounded above by
\begin{equation*} \|f - f_L\|_{\mathrm{L}^p(\mathbb{R}^2)} \leq c_{\alpha,q,W}
\, L^{-\alpha} \, |f|_{\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)} \end{equation*}
under suitable assumptions on the utilized low-pass filter's window function
$W$. This then extends by classical methods to estimates for the total
reconstruction error.
