A common architecture, which is based on the Cooley-Tukey[1] algorithm, is developed for the Fourier, Hadamard, and forward and inverse Cosine transforms. The theory to implement the first three transforms in this architecture is well known. However, the existing algorithms for the inverse Cosine transform (IDCT) would disqualify it from the unified architecture and this led us to develop a new IDCT algorithm which falls within the unified architecture if we allow ourselves the luxury of double length processing. Details of the unified architecture and the new algorithm for the IDCT will be given in this paper.

The concept of fast KL transform coding introduced earlier [7], [8] for first-order Markov processes and certain random fields has been extended to higher order autoregressive (AR) sequences and practical images yielding what we call recursive block coding (RBC) algorithms. In general, the rate-distortion performance for these algorithms is significantly superior to that of the conventional block KL transform algorithm. Moreover, these algorithms permit the use of small size transforms, thereby removing the need for fast transforms and making the hardware implementation of such coders more appealing. This improved performance has been verified for practical image data and results in suppression of the block-boundary effect commonly observed in traditional transform coding techniques. This is illustrated by comparing RBC with cosine transform coding using both one- and twodimensional algorithms. Examples of RBC encoded images at various rates are given.