Numerische Mathematik

, Volume 56, Issue 4, pp 371–383

Incomplete data problems in X-ray computerized tomography

II. Truncated projections and region-of-interest tomography
  • Alfred K. Louis
  • Andreas Rieder

DOI: 10.1007/BF01396611

Cite this article as:
Louis, A.K. & Rieder, A. Numer. Math. (1989) 56: 371. doi:10.1007/BF01396611


In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.

Subject Classifications

AMS(MOS): 65 R 10CR: 61.2

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Alfred K. Louis
    • 1
  • Andreas Rieder
    • 1
  1. 1.Fachbereich Mathematik, MA 6-1Technische Universität BerlinBerlin 12