Abstract
Image reconstruction from cone-beam projections is required for both x-raycomputed tomography (CT) and single photon emission computed tomography(SPECT). Grangeat's algorithm accurately performs cone-beam reconstructionprovided that Tuy's data sufficiency condition is satisfied and projectionsare complete. The algorithm consists of three stages:(a) Forming weighted plane integrals by calculating the line integralson the cone-beam detector, and obtaining the first derivative of the planeintegrals (3D Radon transform) by taking the derivative of the weighted planeintegrals.(b) Rebinning the data and calculating the second derivative withrespect 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'salgorithm was developed using spherical harmonics. The method assumes that thedetector is large enough to image the whole object without truncation.Computer simulations show that if the trajectory of the cone vertex satisfiesTuy's data sufficiency condition, the proposed algorithm provides an exactreconstruction.
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