New extended fan-beam reconstruction formula

Ge Wang; T. H. Lin; Ping Chin Cheng

doi:10.1117/12.59612

26 June 1992 New extended fan-beam reconstruction formula

Ge Wang, T. H. Lin, Ping Chin Cheng

Proceedings Volume 1660, Biomedical Image Processing and Three-Dimensional Microscopy; (1992) https://doi.org/10.1117/12.59612
Event: SPIE/IS&T 1992 Symposium on Electronic Imaging: Science and Technology, 1992, San Jose, CA, United States

Abstract

Because of its high imaging efficiency, fan-beam reconstruction approach has been very popular in recent years. However, fan-beam reconstruction formula had been restricted to a circular scanning locus until an extended fan-beam reconstruction formula was presented by D. B. Smith. Actually, non-circular scanning loci are not only academically interesting, but also practically significant. Smith's extended fan-beam reconstruction formula requires a scanning locus satisfying some nontrivial conditions, contains the derivative of the scanning locus, and in general a spatially variant convolution. In addition, Smith's formula must be specifically discretized for each kind of scanning loci. In this paper, we propose a new extended fan-beam reconstruction formula, which is obtained based on geometrical intuition and is then validated by a strict mathematical proof. The new fan-beam reconstruction formula is the same as the conventional equispatial one, except that the source-to-origin distance depends on the rotation angle, and thus gets rid of the derivative of a locus and always requires a spatially invariant convolution. Furthermore, due to its simple form, the new formula naturally results in a unified discrete version. The new formula requires that the source-to-origin distance be differentiable almost everywhere with respect to the rotation angle and be symmetric with respect to the origin of the reconstruction coordinate system. The numerical simulation results of the new fan-beam formula are also presented.

Citation Download Citation

Ge Wang, T. H. Lin, and Ping Chin Cheng "New extended fan-beam reconstruction formula", Proc. SPIE 1660, Biomedical Image Processing and Three-Dimensional Microscopy, (26 June 1992); https://doi.org/10.1117/12.59612

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available