Title :
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
fDate :
10/1/1993 12:00:00 AM
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;
Journal_Title :
Image Processing, IEEE Transactions on
