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Directional Tight Framelet Filter Bank Design

  • Author / Creator
    Che, Menglu
  • 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.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3WX1M
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Wong, Yau Shu(Mathematical and Statistical Sciences)
    • Han, Bin(Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Bowman, John C(Mathematical and Statistical Sciences)
    • Han, Bin(Mathematical and Statistical Sciences)
    • Wong, Yau Shu(Mathematical and Statistical Sciences)
    • Kong, Linglong(Mathematical and Statistical Sciences)