Autoregressive Image Generative Models with Normal and t-distributed Noise and the Bayes Codes for Them

In this paper, we propose an autoregressive stochastic generative model for images. This model should be one of the most basic models for the new type of lossless image compression which explicitly assume the stochastic generative model. We can easily expand it and theoretically interpret the implicitly assumed stochastic generative models in the various previous predictive coding methods as the expanded versions of our model. Moreover, we can utilize the achievements in the related fields where the linear regression analysis and its expansion are studied to construct the Bayes codes for these generative models. As an example, we expand our generative model from the one with normal noise to the one with the t-distributed noise. Then, we construct the sub-optimal Bayes codes for this generative model by utilizing the variational Bayesian method.