Bayes Code for 2-dimensional Auto-regressive Hidden Markov Model and Its Application to Lossless Image Compression

For general lossless data compression in information theory, researchers have repeated expansion of stochastic models to express target data and design of codes for the expanded models. In this paper, we apply this approach to lossless image compression. We expand an auto-regressive hidden Markov model to a 2-dimensional model to express images containing single diagonal edge. Then, we design a Bayes code with an approximative parameter estimation by variational Bayesian methods. Experimental results for synthetic images show that the proposed model is sufficiently flexible for the target images and the parameter estimation is accurate enough. We also confirm the behavior of the proposed method on real images.