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

— Locating zerotrees in a wavelet transform allows encoding of sets of coef cients with a single symbol. It is an ef cient 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 de ne 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 k levels a degree-k zerotree. A degree-k zerotree coder is one that can encode degree-0 through degree-k 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 ef ciency 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. Index Terms— zerotree, zerotree coder, SPIHT, EZW, wavelet image compression.