Picture reconstruction from projections in restricted range

In order to reduce scanning time modern x-ray scanners provide projections only in a restricted range 0, ?] with ? < π. We consider the reconstruction of pictures from p + 1 complete projections in 0, ?]. An extrapolation procedure is given to achieve approximations g_p of the data in the whole range. We show that the L₂-error of the corresponding picture is of order p^?α if the original belongs to the Sobolev space H_o^α. The validity of our error estimate is investigated by numerical experiments.