Properties of the Multiscale Maxima and Zero-Crossings Representations

Z. Berman and J.S. Baras

Special issue “Wavelets and Signal Processing”  of the IEEE Trans. on Signal Processing, Vol. 41, No. 12, pp. 3212-3231, December 1993.

Abstract

The analysis of a discrete multiscale edge representation is considered. A general signal description, called an inherently bounded adaptive quasi linear representation (AQLR), motivated by two important examples, namely, the wavelet maxima representation, and the wavelet zero-crossings representation, is introduced. This paper mainly addresses the questions of uniqueness and stability. It is shown that the dyadic wavelet maxima (zero-crossings) representations is, in general nonunique. Nevertheless, using idea of the inherently bounded AQLR, two stability results are proven. For a special case, where perturbations are limited to the continious part of the representation, a Lipschitz condition is satisfied.