Zerotree Coding of DCT Coefficients

We show that an efficient quantizer originally developed for wavelet compression can be applied to DCT coding with excellent results. We have implemented a system for block-based, embedded, progressive, DCT image compression which makes use of the embedded zerotree wavelet (EZW) algorithm of Shapiro. The image is partitioned into a number of distinct square blocks and the DCT applied to each of these individually. The coefficients are then rearranged into a sub-band structure which outwardly resembles a wavelet transformed image, with the number of sub-bands being related to the size of DCT used. The zerotee coding algorithm is then employed to quantize the coefficients. The system outperforms the embedded zerotree wavelet scheme in a rate-distortion sense, with good performance from lossless (to the fixed point DCT precision) to high compression. The system gives the best trade between accuracy and high frequency ringing with a DCT block size of 16 x 16, corresponding to four sub-band scales. The JPEG baseline method for still image coding uses the Discrete Cosine Transform (DCT) in a fixed 8x8 pixel partition [1, 2]. A linear quantization table and zigzag scanning of DCT coefficients exploits the redundancy and bandwidth characteristics of the DCT over a range of compressions. However the JPEG system is not effective at high compression ratios, and other methods such as wavelets have produced better results while having the advantage of being fully embedded and progressive [3, 4]. Recently some fully embedded DCT methods have been reported [5, 6, 7]. In this work, we modify Shapiro's Embedded Zerotree Wavelet (EZW) algorithm [3] to use the DCT instead of the Discrete Wavelet Transform, combining the near optimum decorrelation of the DCT with the efficient significance map coding of the zerotree data structure. A similar result using Said and Perlman's SPIHT quantizer [4] has been obtained by Ziong et al [7], but evaluated only for 8x8 DCT blocks. Here we consider the best block size to use and also evaluate the near-lossless performance of the method. The Discrete Cosine Transform [1] is widely used in image coding because of its near optimum ability to decorrelate signals with Gauss-Markov-1 statistics. Many existing DCT based systems are simply enhancements of the basic JPEG system using more appropriate quantization schemes [8, 9] or adaptive segmentation strategies. We use the same coefficient normalization as JPEG coders, so that the MSE significance of all coefficients is equal, and a compromise …