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Mathematical Problems in Engineering
Volume 2015, Article ID 268295, 10 pages
Research Article

Approximate Image Reconstruction in Landscape Reflection Imaging

1Laboratoire Equipes de Traitement de l’Information et Systèmes (ETIS), ENSEA/Université de Cergy-Pontoise/CNRS UMR 8051, 95302 Cergy-Pontoise, France
2Institute of Applied Mathematics, University of Saarland, 66041 Saarbrücken, Germany

Received 8 February 2015; Accepted 24 June 2015

Academic Editor: Franklin A. Mendivil

Copyright © 2015 Rémi Régnier et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Simple reflection imaging of landscape (scenery or extended objects) poses the inverse problem of reconstructing the landscape reflectivity function from its integrals on some particular family of spheres. Such data acquisition is encoded in the framework of a Radon transform on this family of spheres. In spite of the existence of an exact inversion formula, the numerical landscape reflectivity function reconstitution is best obtained with an approximate but judiciously chosen reconstruction kernel. We describe the working of this reflection imaging modality and its theoretical handling, introduce an efficient and stable image reconstruction algorithm, and present simulation results to prove the validity of this choice as well as to demonstrate the feasibility of this imaging process.