Adaptation criterions for wavelet filter banks with variable zero moments

In this paper, we compare different adaptation criteria in the proposed two-channel wavelet filter bank with variable number of zero moments. Generally, filters with more zero moments are more appropriate for representing smooth parts of the analyzed signal, while shorter filters are better for transients and singularities. Depending on the criterion, filter banks that change number of zero moments at each step of decomposition can outperform fixed banks in a number of applications. When applied to signals, variable zero moment wavelets result in low ripple on edges and good concentration of wavelet coefficients in smooth parts. An error signal is formed from filtered wavelet coefficients and therefore available on the reconstruction side. We discuss different adaptation algorithms based on spectral properties, adaptation interval and causality. The chosen criterion determines decomposition properties, as well as its reproducibility on the reconstruction side. Results on synthetic and real signals are presented.