Two Families of Symmetry-preserving Reversible Integer-to-integer Wavelet Transforms

Two families of symmetry-preserving reversible integer-to-integer wavelet transforms are introduced. Briefly, we explain how transforms from these families can be used in conjunction with symmetric extension in order to handle signals of arbitrary length in a nonexpansive manner (which is often a desirable attribute in signal coding applications). The characteristics of the two transform families and their constituent transforms are then studied. For the more constrained of the two families, we identify precisely which transforms belong to the family (by specifying properties and conditions for membership). Such results might be exploited in the filter bank design process in order to find new symmetry-preserving reversible integer-to-integer wavelet transforms for signal coding applications.