Discrete tomography focuses on the reconstruction of functions f:A→R from their line sums in a finite number d of directions, where A is a finite subset of Z2. 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.