Abstract
Image reconstruction from conebeam projections is required for both xray computed tomography (CT) and single photon emission computed tomography (SPECT). Grangeat's algorithm accurately performs conebeam reconstruction provided that Tuy's data sufficiency condition is satisfied and projections are complete. The algorithm consists of three stage: (a) Forming weighted plane integrals by calculating the line integrals on the conebeam detector, and obtaining the first derivative of the plane integrals (3D Radon transform) by taking the derivative of the weighted plane integrals. (b) Rebinning the data and calculating the second derivative with respect to the normal to the plane. (c) Reconstructing the image using the 3D Radon backprojection. A new method for implementing the first stage of Grangeat's algorithm was developed using spherical harmonics. The method assumes that the detector is large enough to image the whole object without truncation. Computer simulations show that if the trajectory of the cone vertex satisfies Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction.
Original language  English (US) 

Pages (fromto)  N127N138 
Journal  Physics in medicine and biology 
Volume  46 
Issue number  6 
DOIs 

State  Published  2001 
Externally published  Yes 
ASJC Scopus subject areas
 Radiological and Ultrasound Technology
 Radiology Nuclear Medicine and imaging