  Discrete tomography focuses on the reconstruction of functions $f: A \to
\mathbb{R}$ from their line sums in a finite number $d$ of directions, where
$A$ is a finite subset of $\mathbb{Z}^2$. Consequently, the techniques of
discrete tomography often find application in areas where only a small number
of projections are available. In 1978 M.B. Katz gave a necessary and sufficient
condition for the uniqueness of the solution. Since then, several
reconstruction methods have been introduced. Recently Pagani and Tijdeman
developed a fast method to reconstruct $f$ if it is uniquely determined.
Subsequently Ceko, Pagani and Tijdeman extended the method to the
reconstruction of a function with the same line sums of $f$ in the general
case. Up to here we assumed that the line sums are exact. In this paper we
investigate the case where a small number of line sums are incorrect as may
happen when discrete tomography is applied for data storage or transmission. We
show how less than $d/2$ errors can be corrected and that this bound is the
best possible.
