A Library-Based Approach To Design Of Smooth Orthonormal Wavelets

Abstract

Recently we addressed the question of using comprehensive libraries of smooth orthonormal wavelets for signalbased wavelet design. Here we present the details of the algorithm for assembling a wavelet library from the continuum of compactly-supported orthonormal wavelets. The algorithm is based on a multi-level minimization, with local variation serving as the smoothness measure and the discrete inner product as the measure used to discriminate between wavelet shapes. An example library is provided. 1. INTRODUCTION An orthonormal (ON) wavelet library is a set of wavelets selected from the continuum of compactly-supported ON wavelets, such that they satisfy one or more criteria. Examples are the libraries formed by the Daubechies wavelets (for which the objective is the maximum number of vanishing wavelet moments), nearly-symmetric wavelets (filters closest to linear phase), and Coiflets (scaling function and wavelet have the same number of vanishing moments). Each of these libraries p..