Title :
Radix-2 × 2 × 2 algorithm for the 3-D discrete Hartley transform
Author :
Boussakta, Said ; Alshibami, Osama Hamoud ; Aziz, Mohammed Yunis
Author_Institution :
Inst. of Integrated Inf. Syst., Leeds Univ., UK
fDate :
12/1/2001 12:00:00 AM
Abstract :
The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 × 2 × 2 algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms
Keywords :
communication complexity; discrete Hartley transforms; image processing; multidimensional signal processing; 1D DHT; 2D DHT; 3D discrete Hartley transform; 3D radix; arithmetic complexity; butterfly structure; digital signal processing; divide-and-conquer approach; fast algorithms; image processing; multidimensional Hartley transform; multidimensional algorithms; multidimensional applications; multidimensional signal processing; row-column approach; Discrete Fourier transforms; Discrete transforms; Filtering; Image analysis; Image processing; Multidimensional signal processing; Multidimensional systems; Signal processing; Signal processing algorithms; Two dimensional displays;
Journal_Title :
Signal Processing, IEEE Transactions on