Adaptation of a 2-d Nonseparable Wavelet Filter Bank with Variable Number of Zero Moments

In this paper, we compare different adaptation criterions of the proposed two dimensional wavelet filter bank with a variable number of zero moments. Twodimensional generalization of the previously reported 1D algorithm is based on nonseparable quincunx scheme. 2-D filters were designed directly, rather then obtained from 1-D filters using pyramid scheme. Filter banks with more zero moments are better for representing smooth parts of the analyzed signal, while shorter filters are more suitable for edges and singularities. When applied to images, variable zero moment 2-D wavelets result in low ripple on edges and good concentration of wavelet coefficients in smooth parts. We discuss different adaptation algorithms based on the size of adaptation area. Chosen criterion determines decomposition properties and robustness. Results on synthetic and real images are presented.