Fast algorithm for the 3-D Discrete Hartley Transform

The application of multidimensional fast transforms to solve problems in image processing, motion analysis and multidimensional signal processing is growing. The Discrete Hartley Transform (DHT) is one of the new rods used in many applications including signal and image processing, digital filters, communication etc. This transform is closely related to the Discrete Fourier Transform, but it is a real-to-real transform and it has the same inverse. Many Fast algorithms have been developed for the calculation of one-dimensional DHT. These algorithms are then used for the calculation of multidimensional Hartley transform through an intermediate transform using the row-column approach. However proper multidimensional algorithms can be more efficient and need to be developed. It is the aim of this paper to derive the 3-D vector radix for the 3-D discrete Hartley transform. The arithmetic operations of this algorithm are compared to similar algorithms using the row-column approach.