Refining image compression with weighted finite automata

Weighted finite automata (WFA) generalize finite automata by attaching real numbers as weights to states and transitions. As shown by Culik and Kari (1994, 1995) WFA provide a powerful tool for image generation and compression. The inference algorithm for WFA subdivides an image into a set of nonoverlapping range images and then separately approximates each one with a linear combination of the domain images. In the current paper we introduce an improved definition for WFA that increases the approximation quality significantly, clearly outperforming the JPEG image compression standard. This is achieved by the bintree partitioning of the image and by appending not only two adjacent range images but also every single range image to the pool of domain images. Moreover, we present a new lossless entropy coding module that achieves efficient and fast storing and retrieving of the WFA coefficients