On Parent-Child Coding Gain in Zero-Tree Based Coders

We attempt to quantify the coding gain due to parent-child dependencies in subband transforms. These dependencies are generally credited for the excellent MSE performances of zero-tree based compression algorithms such as EZW and SPIHT. It is a simple matter to devise an experiment to remov e the ability of zero-tree coders to exploit the parent-child dependence. The goal is to prevent the treestructures from exhibiting spatial coherence, without disturbing the decaying spectrum property of the transform. T oachieve this goal, subbands are rotated b y 90 degrees with respect to the previous scale prior to zero-tree coding. Once zero-tree encoding and zero-tree decoding are performed, the subbands are rotated back to achieve the original orientation of each subband, prior to the inverse wav elettransform. This operation essentially destroys the parent-child dependencies in the treestructures. Thus, the resulting compression performance must be largely independent of parent-child relationships. We refer to the di erence between the \normal" and \rotated" compression performance as the parent-child coding gain, GPC . The av erageparent-child coding gain is plotted as a function of encoding rate for a set of 18 512 512 natural images in Figure 1. Results for both SPIHT with arithmetic coding (SPIHT-AC) and SPIHT without arithmetic coding (SPIHT-NC) are included. Results indicate that, for natural images, the parent-child coding gain is typically around 0.40 dB for SPIHT-NC, and 0.25 dB for SPIHT-AC. These numbers are substantially smaller than what is widely believed. Similarly, we hav e observed that if the rotation experiment is performed using integer wav elet transforms to enable lossless decompression, the lossless le sizes are largely unchanged.