Fan-beam reconstruction methods
- 1 January 1979
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 67 (12) , 1616-1623
- https://doi.org/10.1109/proc.1979.11542
Abstract
In a previous paper a technique was developed for finding reconstruction algorithms for arbitrary ray-sampling schemes. The resulting algorithms use a general linear operator, the kernel of which depends on the details of the scanning geometry. Here this method is applied to the problem of reconstructing density distributions from arbitrary fan-beam data. The general fan-beam method is then specialized to a number of scanning geometries of practical importance. Included are two cases where the kernel of the general linear operator can be factored and rewritten as a function of the difference of coordinates only and the superposition integral consequently simplifies into a convolution integral. Algorithms for these special cases of the fan-beam problem have been developed previously by others. In the general case, however, Fourier transforms and convolutions do not apply, and linear space-variant operators must be used. As a demonstration, details of a fan-beam method for data obtained with uniform ray-sampling density are developed.Keywords
This publication has 3 references indexed in Scilit:
- Density reconstruction using arbitrary ray-sampling schemesProceedings of the IEEE, 1978
- Fast Image Reconstruction Based on a Radon Inversion Formula Appropriate for Rapidly Collected DataSIAM Journal on Applied Mathematics, 1977
- The Fourier reconstruction of a head sectionIEEE Transactions on Nuclear Science, 1974