Abstract
We derive a direct inversion formula for the exponential Radon transform. Our formula requires only the values of the transform over an 180° range of angles. It is an explicit formula, except that it involves a holomorphic function for which an explicit expression has not been found. In practice, this function can be approximated by an easily computed polynomial of rather low degree.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Kuchment, P. andShneiberg, I., Some inversion formulae in the single photon emission computed tomography,Appl. Anal. 53 (1994), 221–231.
Natterer, F.,The Mathematics of Computerized Tomography, Wiley, Chichester, 1986.
Natterer, F., Inversion of the attenuated Radon transform,Inverse Problems 17 (2001), 113–119.
Noo, F. andWagner, J.-M., Image reconstruction in 2D SPECT with 180° acquisition,Inverse Problems 17 (2001), 1357–1371.
Novikov, R. G., An inversion formula for the attenuated X-ray transformation,Ark. Mat. 40 (2002), 145–167.
Radon, J., Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,Ber. Ver. Sächs. Akad. 69 (1917), 262–277.
Tretiak, O. andMetz, C., The exponential Radon transform,SIAM J. Appl. Math. 39 (1980), 341–354.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rullgård, H. An explicit inversion formula for the exponential Radon transform using data from 180°. Ark. Mat. 42, 353–362 (2004). https://doi.org/10.1007/BF02385485
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02385485