A binary Markov model for the quantized images and its rate/distortion optimization
Zerotree based algorithms represent the state of the art in wavelet based image coding. At a high level, these algorithms can be described as first sending a map of the locations of the zero coefficients (the set of zerotree symbols), and then sending the value of nonzero coefficients. However, the decision of what map to send is typically made using some simplifying assumption on the structure of the map, motivated by some empirically observed property of the data (e.g., that zero coefficients are likely to appear in tree structured sets). In this article, the map of the locations of the zero coefficients is optimally estimated as a hidden binary Markov random field (MRF). Algorithms are presented for the estimation of the hidden field given the observed wavelet coefficients, for encoding the field, and for encoding the data given the field estimate. Simulation results show a very competitive rate/distortion performance of the coding algorithm, equal or superior to any published zerotree based image coder: this fact provides conclusive empirical evidence that the proposed model is appropriate for the data.