Submission Type
Event
Expected Graduation Date
2015
Location
Atrium, Center for Natural Sciences, Illinois Wesleyan University
Start Date
4-20-2013 9:00 AM
End Date
4-20-2013 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
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.