𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The identification problem for the exponential Radon transform

✍ Scribed by Donald C. Solmon

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
446 KB
Volume
18
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The exponential Radon transform, which arises in single photon emission computed tomography, is defined by β„› Ζ’(ΞΌ:Ο‰,s) = ∫~R~Ζ’(__s__Ο‰ + t__omega;^βŸ‚^) e^ΞΌ__t^ d__t__Ζ’. Here Ζ’ is a compactly supported distribution in the plane which represents the location and intensity of a radio‐pharmaceutical in a body of constant, but unknown, attenuation ΞΌ, and Ο‰ is a direction. The identification problem is to determine the attenuation ΞΌ from the data β„›Ζ’ with Ζ’ unknown. We will show that ΞΌ can be determined from the data if and only if Ζ’ is not a radial distribution and give formulae for computing ΞΌ when Ζ’ is not radial.

πŸ“œ SIMILAR VOLUMES

The exponential radon transform and proj
The exponential radon transform and projection filtering in radiotherapy planning
✍ Thomas R. Bortfeld; Arthur L. Boyer πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 936 KB

The mathematical problem of generating a desired dose distribution in a patient who has to undergo external beam radiotherapy is closely related to the problem of reconstructing an image from its projections. Under some simplifying assumptions the theory of the exponential Radon transform as develop

The inversion problem and applications o
The inversion problem and applications of the generalized radon transform
✍ Gregory Beylkin πŸ“‚ Article πŸ“… 1984 πŸ› John Wiley and Sons 🌐 English βš– 708 KB

We prove that under certain conditions the inversion problem for the generalized Radon transform reduces to solvinga Fredholm integral equation and we obtain the asymptoticexpansionof the symbolof the integral operator in this equation. We consider applications of the generalized Radon transform to