<title>Recursive scaled DCT</title>

Abstract

Among the various image data compression methods, the discrete cosine transform (DCT) has become the most popular in performing gray-scale image compression and decomposition. However, the computational burden in performing a DCT is heavy. For example, in a regular DCT, at least 11 multiplications are required for processing an 8 X 1 image block. The idea of the scaled-DCT is that more than half the multiplications in a regular DCT are unnecessary, because they can be formulated as scaling factors of the DCT coefficients, and these coefficients may be scaled back in the quantization process. A fast recursive algorithm for computing the scaled-DCT is presented in this paper. The formulations are derived based on practical considerations of applying the scaled-DCT algorithm to image data compression and decompression. These include the considerations of flexibility of processing different sizes of DCT blocks and the actual savings of the required number of arithmetic operations. Due to the recursive nature of this algorithm, a higher-order scaled-DCT can be obtained from two lower-order scaled DCTs. Thus, a scaled-DCT VLSI chip designed according to this algorithm may process different sizes of DCT under software control. To illustrate the unique properties of this recursive scaled-DCT algorithm, the one-dimensional formulations are presented with several examples exhibited in signal flow-graph forms.