Hierarchical modeling via optimal context quantization

Alexandre Krivoulets, Xiaolin Wu

Abstract: Optimal context quantization with respect to the minimum conditional entropy (MCECQ) is proven to be an efficient way for high order statistical modeling and model complexity reduction in data compression systems. The MCECQ merges together contexts that have similar statistics to reduce the size of the original model. In this technique, the number of output clusters (the model size) must be set before quantization. Optimal model size for the given data is not usually known in advance. We extend the MCECQ technique to a multi-model approach for context modeling, which overcomes this problem and gives the possibilities for better fitting the model to the actual data. The method is primarily intended for image compression algorithms. In our experiments, we applied the proposed technique to embedded conditional bit-plane entropy coding of wavelet transform coefficients. We show that the performance of the proposed modeling achieves the performance of the optimal model of fixed size found individually for given data using MCECQ (and in most cases it is even slightly better).