An axiomatic approach to multiresolution signal decomposition

We have been developing general multiresolution signal decomposition schemes that unify traditional (linear) approaches and allow use of nonlinear filtering techniques in the decomposition. This paper summarizes our approach and provides several simple examples. Some of these examples are known in the literature (e.g., Haar pyramid and wavelet) and some of them are new (e.g., morphological Haar pyramid and wavelet).