Probability Distribution Estimation for Autoregressive Pixel-Predictive Image Coding

Pixelwise linear prediction using backward-adaptive least-squares or weighted least-squares estimation of prediction coefficients is currently among the state-of-the-art methods for lossless image compression. While current research is focused on mean intensity prediction of the pixel to be transmitted, best compression requires occurrence probability estimates for all possible intensity values. Apart from common heuristic approaches, we show how prediction error variance estimates can be derived from the (weighted) least-squares training region and how a complete probability distribution can be built based on an autoregressive image model. The analysis of image stationarity properties further allows deriving a novel formula for weight computation in weighted least-squares proofing and generalizing ad hoc equations from the literature. For sparse intensity distributions in non-natural images, a modified image model is presented. Evaluations were done in the newly developed C++ framework volumetric, artificial, and natural image lossless coder (Vanilc), which can compress a wide range of images, including 16-bit medical 3D volumes or multichannel data. A comparison with several of the best available lossless image codecs proofs that the method can achieve very competitive compression ratios. In terms of reproducible research, the source code of Vanilc has been made public.