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Proceedings Paper

Reconstruction of the image on the Cartesian lattice from a finite number of projections in computed-tomographic imaging
Author(s): Nan Du; Yusheng Feng; Artyom M. Grigoryan
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Paper Abstract

The reconstruction of the image f(x, y) is from a finite number of projections on the discrete Cartesian lattice N × N is described. The reconstruction is exact in the framework of the model, when image is considered as the set of N2 cells, or image elements with constant intensity each. Such reconstruction is achieved because of the following two facts. Each basis function of the tensor transformation is determined by the set of parallel rays, and, therefore, the components of the tensor transform can be calculated by ray-sums. These sums can be determined from the ray-integrals, and we introduce here the concept of geometrical, or G-rays to solve this problem. The examples of image reconstruction by the proposed method are given, and the reconstruction on the Cartesian lattice 7 × 7 is described in detail.

Paper Details

Date Published: 7 March 2013
PDF: 15 pages
Proc. SPIE 8667, Multimedia Content and Mobile Devices, 866718 (7 March 2013); doi: 10.1117/12.2000152
Show Author Affiliations
Nan Du, The Univ. of Texas at San Antonio (United States)
Yusheng Feng, The Univ. of Texas at San Antonio (United States)
Artyom M. Grigoryan, The Univ. of Texas at San Antonio (United States)


Published in SPIE Proceedings Vol. 8667:
Multimedia Content and Mobile Devices
Reiner Creutzburg; Todor G. Georgiev; Dietmar Wüller; Cees G. M. Snoek; Kevin J. Matherson; David Akopian; Andrew Lumsdaine; Lyndon S. Kennedy, Editor(s)

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