The circular harmonic Radon transform

Abstract

The circular harmonic decomposition method for evaluating the inverse Radon transform is investigated. A discrete, finite set of projection data may be aliased and its interpretation is inevitably non-unique. When the inverse Radon transform is approximated by a summation, the filtered back projection, it is shown that as well as being non-unique, the reconstruction is inconsistent with the data. By contrast, the circular harmonic decomposition produces a consistent image. The stable form of the method is used to develop a simple and efficient numerical algorithm. This is illustrated with various simple examples and head phantoms.