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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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OPED reconstruction algorithm for limited angle problem

Y. Xu
  • Department of Mathematics, University of Oregon Eugene, Oregon 97403-1222, USA. Email:
/ O. Tischenko
  • Institute of Radiation Protection, Helmholtz Zentrum München GmbH, German Research Center for Environmental Health, 85764 Neuherberg, Germany. Email:
Published Online: 2009-11-25 | DOI: https://doi.org/10.1515/JIIP.2009.047


The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems. In stead of completing the set of data, the set of discrete sine transforms of the data is completed. This is achieved by solving systems of linear equations that have, upon choosing appropriate parameters, positive definite coefficient matrices. Numerical examples are presented.

Key words.: Reconstruction of images; algorithms; limited angle problem

Received: 2008-11-04

Published Online: 2009-11-25

Published in Print: 2009-11-01

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 8, Pages 795–813, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2009.047, November 2009

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