Quantifying the Coding Performance of Zerotrees of Wavelet Coefficients: Degree-k Zerotree

Locating zerotrees in a wavelet transform allows encoding of sets of coefficients with a single symbol. It is an efficient means of coding if the overhead to identify the locations is small compared to the size of the zerotree sets on the average. It is advantageous in this regard to define classes of zerotrees according to the levels from the root until the remainder of the tree contains all zeroes. We call a tree with all zeroes except for the top levels 0 (root) through k a degree-k zerotree. A degree-k zerotree coder is one that can encode degree-0 through degreek zerotrees. We quantify the bit savings of a degree-k2 over a degree-k1, k2 > k1, coder. Because SPIHT is a degree-2 zerotree coder and EZW a degree-0 zerotree coder, we are able to explain the superior efficiency of SPIHT. Finally, we gather statistics of degree-k zerotrees for different values of k in the bitplanes of several image wavelet transforms to support our analysis of the coding performance of degree-k zerotree coders.