Image reconstruction via the Hartley transform

Abstract

The continuous and discrete Hartley transforms are real valued transforms that have similar properties to the continuous and discrete Fourier transforms. In addition, a fast algorithm exists for computing the discrete Hartley transform which is faster than the fast Fourier transform, even when the fast Fourier transform is optimized for dealing with real data. In this paper the authors apply the Hartley transform to the problem of image reconstruction. The authors will show that the projection-slice theorem and the filtered back-projection algorithm can be derived using the Hartley transform and that the filter part of the filtered back-projection algorithm can be implemented using Bracewell's fast Hartley transform.