Perfect Reconstructing Nonlinear Filter Banks

Perfect reconstruction (PR) filter banks have found numerous applications, and have received much attention in the literature. For linear filter banks, necessary and sufficient conditions for PR have been established for most practical situations. Recently, nonlinear filter banks have been proposed for image coding applications. These filters are generally simple, and produce better results than linear filters of same complexity. Nevertheless, the lack of general PR conditions limits these filters to cases where one of the filters is the identity. In this paper, we present a framework that allows, for the first time, the design of PR nonlinear filter banks including (non-trivial) filters on all channels. Although the framework does not include all nonlinear PR filter banks, it does include all previously published nonlinear filter banks, as well as all linear ones. This framework suggest new possibilities for the design of nonlinear PR filter banks.