Title of Presentation

Construction of Spline Type Orthogonal Scaling Functions and Wavelets

Type of Submission

Event

Graduation Year

2015

Location

Room E102, Center for Natural Sciences, Illinois Wesleyan University

Start Date

12-4-2014 10:00 AM

End Date

12-4-2014 11:00 AM

Disciplines

Applied Mathematics

Abstract

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.

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Apr 12th, 10:00 AM Apr 12th, 11:00 AM

Construction of Spline Type Orthogonal Scaling Functions and Wavelets

Room E102, Center for Natural Sciences, Illinois Wesleyan University

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.