Fast adaptive wavelet packets using interscale embedding of decomposition structures

The most widely used basis selection algorithm for adaptive wavelet packets is the optimal basis selection method, which first grows a full wavelet packet tree and then prunes it into the optimal tree that gives the minimum cost. We observed that there exists the interscale embedding property in wavelet packet decomposition structures between interscale subbands along the same orientation. Based on this observation, we propose a fast basis selection algorithm by first decomposing a dyadic wavelet subband with the decomposition structure of its parent subband, before applying the optimal basis selection method for further decomposition. Experiments show that the proposed algorithm generates almost the same wavelet packet decomposition structures as the optimal basis selection method while significantly reducing the computational complexity for some image classes.