Event Title

Construction of Spline Type Orthogonal Scaling Functions and Wavelets

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

Description

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.