Fast Inversion of the Radon Transform Using Log-polar Coordinates and Partial Back-Projections

In this paper a novel filtered back-projection algorithm for inversion of a discretized Radon transform is presented. It makes use of invariance properties possessed by both the Radon transform its dual. By switching to log-polar coordinates, both operators can be expressed in a displacement invariant manner. Explicit expressions for the corresponding transfer functions are calculated. Furthermore, by dividing the back-projection into several partial back-projections, it can be performed by means of finite convolutions, and hence implemented by an FFT-algorithm. In this way, a fast and accurate reconstruction method is obtained.