Construction of Spline Type Orthogonal Scaling Functions and Wavelets
Tung Lam Nguyen · Digital Commons at Illinois Wesleyan University (Illinois Wesleyan University) · 2014
In this talk, we present a method to construct orthogonal spline-type wavelet. B-spline functions have several useful properties such as compactly support and refinement relationship. However, except for the case of the first order, B-splines of order greater than one are not orthogonal. To induce the orthogonality while keeping the properties of B-splines, we use a class of polynomial function factors to transform the original B-splines to a spline-type orthogonal compactly-supported and refinable scaling functions in L2. In this paper we establish the existence of this class of polynomial factors and their construction. In addition, the corresponding spline-type wavelets and the decomposition and reconstruction formulas for their Multi-Resolution Analysis (MRA) are given.