Double Density Complex Wavelet Based Image Cartoon-Texture Decomposition

Both the Kingsbury dual-tree and the subsequent Selesnick double-density dual-tree complex wavelet transform approximate an analytic function. The classification of the phase dependency across scales is largely unexplored except by Romberg et al. Here we characterize the subband dependency of the orientation of phase gradients by applying the Morel-Helmholtz principle to bivariate histograms to locate meaningful modes. A further characterization using the Earth mover's Distance with the fundamental Rudin-Osher-Meyer Banach space decomposition into cartoon and texture elements is presented. Possible applications include image compression and invariant descriptor selection for image matching.