Rate-distorsion efficiency of zerotree coders

Although zerotree coders are extremely simple in terms of algorithmic complexity and structure, their rate-distortion tradeoff is among the best known in the literature. This paper intends to provide an explanation to this phenomenon, by explicitly showing which part of the algorithm is at its origin. This is somewhat proved by introducing the same mechanism in other type of algorithms, which in turn show a similar rate/distortion performance. More specifically, we compare three coders: The first one is the original zerotree coder, the other ones are two “zerotree-like” coders, where coefficient significance is determined by thresholding (first coder) and by by rate-distortion optimization (second coder). These coders exhibit similar behaviour and performances. Thresholding seems to corresponds to a rate-distortion optimal way of isolating significant data. We show the impact that this procedure has on the distribution of the quantization noise. In particular, thresholding removes the coefficients responsible for the non-uniformity of the quantization noise. The significance map is encoded using classical lossless techniques. All three coders are shown to have (almost) equal rate-distortion characteristics