A derivative-free noncircular fan-beam reconstruction formula

Author

Wang, Ge ; Lin, Tein-hsiang ; Cheng, Ping-Chin

Author_Institution

Mallinckrodt Inst. of Radiol., Washington Univ., St. Louis, MO, USA

Volume

2

Issue

4

fYear

1993

fDate

10/1/1993 12:00:00 AM

Firstpage

543

Lastpage

547

Abstract

In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given

Keywords

image reconstruction; circular equispatial fan-beam reconstruction formula; derivative-free formula; fan-beam reconstruction formula; image reconstruction; noncircular scanning locus; reconstruction coordinate system; rotation angle; source-to-origin distance; Biological materials; Biomedical engineering; Biomedical materials; Detectors; Image reconstruction; Laboratories; Radiology; Real time systems; Sensor arrays; Synchrotron radiation;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.242365

Filename

242365