PROPERTIES OF THE MULTISCALE MAXIMA AND ZERO-CROSSINGS REPRESENTATIONS

The analysis of a discrete multiscale edge representation is considere d. A general signal description, called an inherently bounded adaptive quasi linear representation (AQLR), motivated by two important exampl es, namely, the wavelet maxima representation, and the wavelet zero-cr ossings representation, is introduced. This paper mainly addresses the questions of uniqueness and stability. It is shown, that the dyadic w avelet maxima (zero-crossings) representation is, in general, nonuniqu e. Nevertheless, using the idea of the inherently bounded AQLR, two st ability results are proven. For a general perturbation, a global BIBO stability is shown. For a special case, where perturbations are limite d to the continuous part of the representation, a Lipschitz condition is satisfied.