M-band nonlinear subband decompositions with perfect reconstruction

We investigate nonlinear multirate filterbanks with maximal decimation and perfect reconstruction. Definitions of the desired properties of such structures are given for general nonlinear filterbanks. We then consider a triangular representation of linear filterbanks and see that it may be easily extended to the nonlinear case. Furthermore, general nonlinear filterbanks are presented, for which perfect reconstruction is either inherently guaranteed or ensured subject to an easily verified condition. Extensions to bidimensional filters are also discussed and an application for nonlinear multiresolution schemes to feature sieves is shown.