Mathematical properties of four wavelet filters and their performance in embedded image coders

This paper analyses the mathematical properties of four famous wavelets and evaluates their coding performance for different kinds of images in EZW image coders. It can be found that although the 9/7 biorthogonal wavelets, which obtain better tradeoff among incompatible mathematical properties, give the best performance. But it still can´t code edges and textures efficiently due to existing ringing and smearing artifacts at low bit rates. The harmonic decomposition must follow the uncertainty principle that prevents any atom perfectly, which is well localized in the space domain to retain frequency localization. It gives an opportunity to develop new paradigms to efficiently representing and coding structures very well localized in the space domain, but with large frequency band such as edges and textures.