Picture reconstruction from projections in restricted range

Abstract

In order to reduce scanning time modern x-ray scanners provide projections only in a restricted range [O, &Phi;] with &Phi;< &pi;. We consider the reconstruction of pictures from p+1 complete projections in [O, &Phi;]. An extrapolation procedure is given to achieve approximations gp of the data in the whole range. We show that the L2-error of the corresponding picture is of order p- &alpha; if the original belongs to the SOBOLEV space H o &alpha;. The validity of our error estimate is investigeted by numerical experiments.