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, ϕ] with ϕ < π. We consider the reconstruction of pictures from p + 1 complete projections in [0, ϕ]. An extrapolation procedure is given to achieve approximations g p of the data in the whole range. We show that the L 2 ‐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.