Recent advances in weighted finite automata fractals

A recent method in fractal compression is weighted finite automata (WFA) which are used for the approximation and subsequent compression of two-dimensional discrete functions such as images. Traditional fractal based methods look for similarities at two fixed levels of resolutions (or scales). Every block of the image (range) is approximated by a scaled version of other regions, called domains. The WFA tree structure permits the usage of domains at any scale, allowing a larger domain pool. Ranges are approximated by a linear combination of domains. In this work, an additional image-independent domain pool is used to further enhance compression, and similarities at different scales are exploited using a quadrature mirror filter (QMF) decomposition instead of the image itself. Our algorithm achieved (as an example) a very good quality (34.6 dB PSNR) at 14.4:1 compression.