Picture reconstruction from projections in restricted range

摘要

AbstractIn order to reduce scanning time modernx‐ray scanners provide projections only in a restricted range 0, ϕ with ϕ<π. We consider the reconstruction of pictures fromp+ 1 complete projections in 0, ϕ. An extrapolation procedure is given to achieve approximationsgpof the data in the whole range. We show that theL2‐error of the corresponding picture is of orderp−αif the original belongs to the Sobolev spaceHoα.The validity of our error estimate is investigated by numerical