Extended Wedgelets — Geometrical Wavelets in Efficient Image Coding

In modern world image coding and especially image compression plays a very important role. There are well known and recognized theories concerning this topic such as, for example, Fourier and wavelets theories. Both of these theories allow for representation of images in a sparse way. Unfortunately wavelets, hence very good in catching point discontinuities, cannot properly catch line discontinuities present often in images, that is edges. As the remedy for this problem the new theory of geometrical wavelets has arisen. In the paper there is presented the new and modern, hence known, theory of geometrical wavelets called wedgelets, which allows to code images with edges in very efficient way. Moreover it is presented the new improvement of the theory of wedgelets. This improvement — the theory of extended wedgelets — allows to represent images in more sparse and efficient way then in the case of the known wedgelets. Such representation allows to get higher compression ratio, together with better visual effects. Furthermore the application to image coding also has been presented. The performance of the improvement has been confirmed both theoretically as well as experimentally.