The Parametric Wavelet Maxima Representation

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 presents a new reconstruction scheme based on the minimization of an appropriate cost function. The convergence of two described algorithms is guaranteed for all inherently bounded AQLR. As a consequence, we describe possible modifications in the basic multiscale maxima representations.