Symmetry-preserving reversible integer-to-integer wavelet transforms

Studied are two lifting-based families of symmetry-preserving reversible integer-to-integer wavelet transforms. The transforms from both of these families are shown to be compatible with symmetric extension, which permits the treatment of arbitrary length signals in a nonexpansive manner. Throughout this work, particularly close attention is paid to rounding functions, and the properties that they must possess in various instances. Symmetric extension is also shown to be equivalent to constant per-lifting-step extension in certain circumstances.