Spectral decomposition of the exponential radon transform

Grant T. Gullberg; Gengsheng Larry Zeng

doi:10.1117/12.23641

1 November 1990 Spectral decomposition of the exponential radon transform

Grant T. Gullberg, Gengsheng Larry Zeng

Proceedings Volume 1351, Digital Image Synthesis and Inverse Optics; (1990) https://doi.org/10.1117/12.23641
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

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.

Citation Download Citation

Grant T. Gullberg and Gengsheng Larry Zeng "Spectral decomposition of the exponential radon transform", Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990); https://doi.org/10.1117/12.23641

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