Two-dimensional Autoregressive Model with Time-varying Parameters and the Bayes Codes

This paper proposes a two-dimensional autoregressive model with time-varying parameters as a stochastic image generative model and a lossless image compression algorithm using the Bayes codes. Most studies have relied on Markov chain Monte Carlo methods for Bayesian estimation of autoregressive models with time-varying parameters. However, such a sampling method is not suitable to lossless image compression. Therefore, we propose a Bayes coding algorithm that incorporates image characteristics as hyperparameter settings of an independent conjugate prior distribution. That enables handling the time-varying parameters without any sampling methods. We confirm the properties of the algorithm by numerical experiments.