3-D vector radix algorithm for the 3-D discrete Hartley transform

The three-dimensional discrete Hartley transform (3-D DHT) has been proposed as an alternative tool to the 3-D discrete Fourier transform (3-D DFT) for 3-D applications when the data is real. The 3-D DHT has been applied in many three-dimensional image and multidimensional signal processing applications. This paper presents a fast three-dimensional algorithm for computing the 3-D DHT. The mathematical development of this algorithm is introduced and the arithmetic complexity is analysed and compared to related algorithms. Based on a single butterfly implementation, this algorithm is found to offer substantial savings in the total number of multiplications and additions over the familiar row-column approach.