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Permanent link (DOI): https://doi.org/10.7939/R3WX1M

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Directional Tight Framelet Filter Bank Design Open Access

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Other title
Subject/Keyword
tight framelet filter bank
tensor product
image processing
directionality
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Che, Menglu
Supervisor and department
Han, Bin(Mathematical and Statistical Sciences)
Wong, Yau Shu(Mathematical and Statistical Sciences)
Examining committee member and department
Han, Bin(Mathematical and Statistical Sciences)
Bowman, John C(Mathematical and Statistical Sciences)
Wong, Yau Shu(Mathematical and Statistical Sciences)
Kong, Linglong(Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Applied Mathematics
Date accepted
2013-07-16T15:57:05Z
Graduation date
2013-11
Degree
Master of Science
Degree level
Master's
Abstract
It is well known that most information of an image is contained in its edges. Therefore capturing edges in an image is of fundamental importance in image processing. Tensor product real-valued wavelets only capture edges along the horizontal and vertical direc- tions. Hence they are only suboptimal for handling high-dimensional problems. In this thesis we use a framelet-based approach to enhance the performance of tensor product real-valued wavelets. By employing an additional high-pass filter, we construct finitely supported complex-valued tight framelet filter banks {a;b1,b2} such that their tensor products in dimension two offer four directions along 0◦(horizontal), 45◦, 90◦(vertical) and 135◦. We propose a simple and effective algorithm to construct such directional tight framelet filter banks, and provide a necessary and sufficient condition for their existence. Finally, several concrete examples of such directional tight framelet filter banks are given.
Language
English
DOI
doi:10.7939/R3WX1M
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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