A two-dimensional translation invariant wavelet representation and its applications

Addresses the problem of the sensitivity of wavelet representations to translations for two-dimensional signals. The authors describe a fast algorithm to calculate the two-dimensional wavelet transforms for all the circular translates of an input image. They select the optimal translate for the decomposition using a quadtree search algorithm. The resulted wavelet representation is invariant under translations measured by an additive cost criterion. The complexity of the whole algorithm is O(N² log N) for a N×N input block. They apply this translation invariant wavelet transform to data compression. The results show that by taking into account the effect of translations, additional compression can be achieved beyond that achieved by a standard wavelet transform