Abstract

The attenuated Radon transform is the mathematical basis of single-photon emission-computed tomography. The case of constant attenuation is reviewed, and a new proof of the Tretiak–Metz algorithm is presented. A space-domain version of the inverse attenuated Radon transform is derived. A special case of this transform that is applicable when the object is rotationally symmetric, the attenuated Abel transform, is derived, and its inverse is found.

© 1983 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Formation of images from projections: Radon and Abel transforms*

C. M. Vest
J. Opt. Soc. Am. 64(9) 1215-1218 (1974)

Recursive methods for computing the Abel transform and its inverse

Eric W. Hansen and Phaih-Lan Law
J. Opt. Soc. Am. A 2(4) 510-520 (1985)

Radon transform and bandwidth compression

Warren E. Smith and Harrison H. Barrett
Opt. Lett. 8(7) 395-397 (1983)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (1)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (42)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription