Finding the optimal wavelet functions for image representation
David Stanhill, Yehoshua Y. Josh Zeevi · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
A complete and unique parametrization is given for all compactly supported, orthogonal, two dimensional wavelet functions for the case of the quincunx decimation matrix. Once we have a complete parametrization we search for optimal wavelet functions. Here we concentrate on the task of image representation and compression. We suggest three different criterions for measuring optimality. The first is tailored for each specific image, the second measures optimality in a more statistical sense and the third uses the general quality of vanishing moments. We compare between the three criterions which seem at first very different in nature, and show that they give very similar results.