Exponential x-ray transform
Thesis/Dissertation
·
OSTI ID:6519429
In emission computed tomography one wants to determine the location and intensity of radiation emitted by sources in the presence of an attenuating medium. If the attenuation is known everywhere and equals a constant ..cap alpha.. in a convex neighborhood of the support of f, then the problem reduces to that of inverting the exponential x-ray transform P/sub ..cap alpha../. The exponential x-ray transform P/sub ..mu../ with the attenuation ..mu.. variable, is of interest mathematically. For the exponential x-ray transform in two dimensions, it is shown that for a large class of approximate delta functions E, convolution kernels K exist for use in the convolution backprojection algorithm. For the case where the attenuation is constant, exact formulas are derived for calculating the convolution kernels from radial point spread functions. From these an exact inversion formula for the constantly attenuated transform is obtained.
- Research Organization:
- Oregon State Univ., Corvallis (USA)
- OSTI ID:
- 6519429
- Country of Publication:
- United States
- Language:
- English
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