Image Coding Using Multiplier-Free Filter Banks

Subband coding is now one of the most important techniques for image compression. It was originally introduced by Crochiere in 1976, as a method for speech coding [CWF76]. Approximately a decade later it was extended to image coding by Woods and O’Neil [WO86] and has been gaining momentum ever since. There are two distinct components in subband coding: the analysis/synthesis section, in which filter banks are used to decompose the image into subband images; and the coding system, where the subband images are quantized and coded. A wide variety of filter banks and subband decompositions have been considered for subband image coding. Among the earliest and most popular were uniformband decompositions and octave-band decompositions [GT86, GT88, WBBW88, WO86, KSM89, JS90, Woo91]. But many alternate tree-structured filter banks were considered in the mid 1980s as well [Wes89, Vet84]. Concomitant with the investigation of filter banks was the study of coding strategies. There is great variation among subband coder methods and implementations. Common to all, however, is the notion of splitting the input image into subbands and coding these subbands at a target bit rate. The general improvements obtained by subband coding may be attributed largely to several characteristics—notably the effective exploitation of correlation within subbands, the exploitation of statistical dependencies among the subbands, and the use of efficient quantizers and entropy coders [Hus91, JS90, Sha92]. The particular subband coder that is the topic of discussion in this chapter was introduced by the authors in [KCS95] and embodies all the aforementioned attributes. In particular, intra-subband and inter-band statistical dependencies are exploited by a finite state prediction model. Quantization and entropy coding are performed jointly using multistage residual quantizers and arithmetic coders. But perhaps most important and uniquely characteristic of this particular system is that all components are designed together to optimize ratedistortion performance, subject to fixed constraints on computational complexity. High performance in compression is clearly an important measure of overall value,