A flexible zerotree coding with low entropy

We introduce a new zerotree scheme that effectively exploits the inter-scale self-similarities found in the octave decomposition by a wavelet transform. A zerotree is useful to code wavelet coefficients and its effectiveness was proved by Shapiro´s (1993) EZW (embedded zerotree wavelet). In the coding scheme, wavelet coefficients are symbolized and then entropy-coded. The entropy per symbol is determined from the produced symbols and the final coded size is calculated by multiplying the entropy and the total number of symbols. We analyze symbols produced from the EZW and discuss the entropy per symbol. Since the entropy depends on the produced symbols, we modify the procedure of symbol generation. First, we extend the relation between a parent and children used in the EZW to raise the probability such that a significant parent has significant children. The proposed relation is flexibly extended according to the fact that a significant coefficient is likely to have significant coefficients in its neighborhood. Our coding results are compared with the published results of Shapiro and improvements come from the use of lower entropy per symbol. We also give a comparison of the number of produced symbols