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

  • Image processing
  • Tensor product
  • Directionality
  • Tight framelet filter bank

• Graduation date

  Fall 2013

• 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.