Linear parameterization of orthogonal wavelets

Abstract

This paper describes a new method for the parameterization of compactly supported orthogonal wavelet filters. The well-known Daubechies (1988) orthogonal wavelets can be viewed as a subset in the parameterized orthogonal wavelet class, which processes a maximum number of vanishing moments for a given filter length. Unlike the existing parameterizations of orthogonal wavelets, the proposed method does the parameterization through a linear characterization of all halfband filters. The paper also includes examples of optimal designs of orthogonal wavelets obtained using this parameterization technique in conjunction with efficient linear programming or quadratic programming, and application of these wavelets to signal compression and signal denoising.