Radix-2 x 2 x 2 algorithm for the 3-D discrete hartley transform

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 2X 2X 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

Transform coding of pictorial data

By using transform coding, image transmission rates as low as 0.5 bit/pel can be achieved. Generally, the bit rate reduction is achieved by allocating fewer bits to low energy high order coefficients, However, to ensure reasonably good picture quality, a large number of bits has to be allocated to high energy dc coefficients for both fine quantization and good channel error immunity, A technique has been developed that, in some cases, allows the de coefficients to be estimated at the receiver, thus eliminating a major source of difficulty with respect to channel errors. [Continues.