<title>Cone-beam image reconstruction from equiangular sampling using spherical harmonics</title>

Abstract

All of the exact cone-beam reconstruction algorithms for so called long-object problem do not use equi-angular sampling but use equi-space sampling. However, cylindrical detectors (equi-angular sampling in xy and equi-spatial in z) have advantage in their compact design. Therefore, toward the long-object problem with equi-angular sampling, the purpose of this study is to develop a cone-beam reconstruction algorithm using equi-angular sampling for short-object problem. A novel implementation of Grangeat's algorithm using equi-angular sampling has been developed for short- object problem with and without detector truncation. First, both cone-beam projection g(Psi )((Theta) ,(phi) ) and the first derivative of plane integral (3D Radon transform) p(Psi )((Theta) ,(phi) ) are described using spherical harmonics with equi-angular sampling. Then, using Grangeat's formula, relationship between coefficients of spherical harmonics for g(Psi )((Theta) ,(phi) ) and p(Psi )((Theta) ,(phi) ) are found. Finally, a method has been developed to obtain p(Psi )((Theta) ,(phi) ) from cone- beam projection data in which the object is partially scanned. Images are reconstructed using the 3D Radon backprojection with rebinning. Computer simulations were performed in order to verify this approach: Isolated (axially bounded) objects were scanned both with circular and helical orbits. Wen the orbit of the cone vertex does not satisfy Tuy's data sufficiency conditions, strong oblique shadows and blurring in the axial direction were shown in reconstructed coronal images. ON the other hand, if the trajectory satisfied Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction. In conclusion, a novel implementation of the Grangeat's algorithm for cone-beam image reconstruction using equi-angular sampling has been developed.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.