Constructing MRAs from desired wavelet functions

This paper develops a technique for constructing an orthonormal wavelet that is optimized to a desired signal in the least squares sense, and whose associated scaling function generates an orthonormal multiresolution analysis (MRA). The key development in this paper is a recursive equation for finding the scaling function from a given wavelet, whose closed form solution gives constraints on the wavelet that guarantee an orthonormal scaling function and multiresolution analysis. The matching algorithm uses Lagrangian multipliers to minimize the mean square error between the desired and optimum wavelet power spectra