Convolutional reconstruction algorithm for fan beam concave and convex circular detectors

A modified convolution-backprojection reconstruction algorithm for a circular detector with an arbitrary radius of curvature has been derived for fan-beam geometries. The algorithm reduces to conventional fan-beam algorithms for flat detectors and for curved detectors having whose radii of curvature coincident with the X-ray tube focal spot. The algorithm substitutes a power series of convolution integrals in place of a single convolution integral. Computer simulations have verified the validity of the algorithm for a detector that curves away from the X-ray source. In this case, it has been demonstrated that good reconstructions are obtained when only a few of the terms of the power series are retained. The development of this algorithm represents a first step toward a cone-beam reconstruction algorithm that eventually will be used for an image-intensifier-based computerized-tomography volume imager being developed in the authors´ laboratory