Title of Presentation

Frames and Spline Framelets

Type of Submission

Event

Graduation Year

2015

Location

Atrium, Center for Natural Sciences, Illinois Wesleyan University

Start Date

20-4-2013 9:00 AM

End Date

20-4-2013 10:00 AM

Disciplines

Mathematics

Abstract

Frames can be seen as a generalization of orthonormal bases, which not only maintain useful characteristics of orthonormal bases but also allow more flexibility in applications. The applications of frames include communication and image processing, as its characteristic inherited from orthonormal bases helps speed up the transmitting and processing time while its additional flexibility adds to frames the ability to reconstruct lost information. In this project, we study the construction of a class of tight frames in Euclidean spaces. Also, we use Fourier transforms and the techniques of Multi-Resolution Analysis (MRA) in wavelet analysis to investigate a class of tight spline framelets.

Included in

Mathematics Commons

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Apr 20th, 9:00 AM Apr 20th, 10:00 AM

Frames and Spline Framelets

Atrium, Center for Natural Sciences, Illinois Wesleyan University

Frames can be seen as a generalization of orthonormal bases, which not only maintain useful characteristics of orthonormal bases but also allow more flexibility in applications. The applications of frames include communication and image processing, as its characteristic inherited from orthonormal bases helps speed up the transmitting and processing time while its additional flexibility adds to frames the ability to reconstruct lost information. In this project, we study the construction of a class of tight frames in Euclidean spaces. Also, we use Fourier transforms and the techniques of Multi-Resolution Analysis (MRA) in wavelet analysis to investigate a class of tight spline framelets.

 

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