Statistically Adaptive Wavelet Image Coding

In the mid-1980's, wavelet theory was developed in applied mathematics [1, 2, 3]. Soon, subband coding [4], which has been a very active research area for image and video compression, was identi ed as wavelet's discrete cousin. Furthermore, a fundamental insight into the structure of subband lters was developed from wavelet theory that led to a more productive approach to designing the lters [1, 5, 6]. Thus subband and wavelet are often used interchangeably in the literature. Two types of subband decomposition are commonly used in image compression, i.e., uniform and pyramidal decomposition. Uniform decomposition [7] divides an image into equal-sized subbands (Fig. 1a). By contrast, pyramidal decomposition represents an octave-band (dyadic) decomposition, o ering a multiresolution representation of the image as illustrated in Fig. 1b. Most of the subband image coders published recently are based on pyramidal decomposition. Conventional wavelet or subband image coders [5, 8] mainly exploit the energy compaction property of subband decomposition by using optimal bit allocation strategies. The drawback is apparent in that all zero-valued wavelet coe cients, which convey little information, must be represented and encoded, biting away a signi cant portion of the bit budget. Although this type of wavelet coders provide superior visual quality by eliminating the blocking e ect in comparison to block-based image coders such as JPEG [9], their objective performance measured by peak signal-to-noise ratio (PSNR, eq. (1)) increases only moderately.