Cone beam tomography with circular, elliptical and spiral orbits

Abstract

A general formula for image reconstruction from cone beam data is described. Applying this formula to various cone beam geometries results in a class of filtered backprojection algorithms. This formula is known to lead to exact reconstructions in cases in which the cone vertices form certain unbounded curves. An example of such a curve is an infinite straight line. In the case where the curve is a circle, this formula leads to the well-known Feldkamp algorithm, for which the reconstructions are only approximations to the true image. The authors apply this general formula to the cases where the curve is an ellipse and a sprial, and new algorithms are derived. The properties of these algorithms are investigated through studies of the point spread function and reconstructions of computer generated phantom data.