Pixel-pyramid model for divergent projection geometry

Zikuan Chen; Ruola Ning

doi:10.1117/1.1844531

1 February 2005 Pixel-pyramid model for divergent projection geometry

Zikuan Chen, Ruola Ning

Author Affiliations +

Optical Engineering, Vol. 44, Issue 2, 027002 (February 2005). https://doi.org/10.1117/1.1844531

Abstract

Divergent projection refers to fan-beam or cone-beam projection originating from a point source, which is commonly seen in x-ray imaging. Conventionally, the divergent projection calculation is carried out using a ray model, in which each detector pixel (cell) receives radiations emanating from a point source, in a form of straight-line ray. The finite dimension of the detector pixel develops a zero-width ray into a nonzero-width strip, with its cross section assuming the effective aperture of a detector pixel facet. In the pursuit of accuracy, we portray the divergent projection from the point source radiation on a detector cell by a pyramidal element (pyrel), which is formed by a pyramidal base (detector pixel facet) and an apex (point source). A pyrel intersects the object and circumscribes a trapezoidal zone for fan-beam projection (a frustum volume for cone-beam projection), wherein the object voxels are accumulated (appropriately weighted) to produce the detector cell's signal. In addition to the forward divergent projection calculation, the pyrel model can be used for iterative object reconstruction by repeating the backprojection and reprojection. Since the pyrel model portrays more naturally the divergent projection geometry, it maximizes the calculation accuracy, though at the cost of more computations. This model may be rewarding in certain situations: (1) when the detector resolution is unacceptably low, (2) when the projection data set is severely incomplete (for example, the number of projections <100), and (3) when the projection-beam angle is too large (say, >40 deg). Simulations on an iterative fan-beam tomographic reconstruction, using the pyrel model, the ray model, and the voxel-splatting model, are demonstrated.

©(2005) Society of Photo-Optical Instrumentation Engineers (SPIE)

Citation Download Citation

Zikuan Chen and Ruola Ning "Pixel-pyramid model for divergent projection geometry," Optical Engineering 44(2), 027002 (1 February 2005). https://doi.org/10.1117/1.1844531

Published: 1 February 2005

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