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Proceedings Paper

Spectral decomposition of the exponential radon transform
Author(s): Grant T. Gullberg; Gengsheng Larry Zeng
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Paper Abstract

The attenuated Radon transform mathematically represents the measured projections in single photon emission computed tomography (SPECT) for an ideal detector with a delta geometric response function and no detected scattered photons. As a special case of the attenuated Radon transform, the exponential Radon transform is defined for a constant attenuator by modifying the measured projections through a transformation which places the detector at the center of rotation. Several papers have presented analytical spectral decompositions of the Radon transform; however, no analytical decomposition of the exponential or the attenuated Radon transform has been derived. Here an eigenanalysis of the exponential Radon transform is compared with that of the Radon transform using the Galerkin approximation to estimate the spectral decomposition. The condition number of the spectrum increases with increased attenuation coefficient which correlates with the increase in statistical error propagation seen in clinical images obtained with low energy radionuclides.

Paper Details

Date Published: 1 November 1990
PDF: 12 pages
Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990); doi: 10.1117/12.23641
Show Author Affiliations
Grant T. Gullberg, Univ. of Utah (United States)
Gengsheng Larry Zeng, Univ. of Utah (United States)

Published in SPIE Proceedings Vol. 1351:
Digital Image Synthesis and Inverse Optics
Arthur F. Gmitro; Paul S. Idell; Ivan J. LaHaie, Editor(s)

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