A novel method of splitting the 3D discrete Hartley transform

A method of the vectorial representation for splitting the calculation of the nonseparable three-dimensional discrete Hartley transform (3D DHT) into a set of one-dimensional (1D) DHTs is presented. The method is based on the vectorial, or tensor form of representation of a 3D image and can be applied to any orders of the transform. The case of the N/spl times/N&N-point DHT, for N=2/sup r/ (r>1), is considered in detail. The number of multiplications required for calculating the 3D DHT by the method of vectorial representation equals 7[8/sup r-1/(r-3)+4/sup r-1/] that is the best estimate of all existent algorithms. The improvement of this method, the recurrent algorithm, that reduces about 1.6 times the number of multiplications is also described.