Nonlinear frame-like decompositions

In this paper, we revisit a number of concepts which have recently proven to be useful in multiscale signal analysis, specifically by replacing the now classical linear scale transition operators by nonlinear ones. Connections between nonlinear perfect reconstruction filter banks and PDE operators used in scale-space theory are established. An application of the proposed nonlinear tools is then given for extracting a signal embedded in noise. We also develop the important case of time invariant nonlinear representations.