The Resource Highly Symmetric Multiple Bi-Frames for Curve and Surface Multiresolution Processing, Khulud Saeed Ziadi

Highly Symmetric Multiple Bi-Frames for Curve and Surface Multiresolution Processing, Khulud Saeed Ziadi

Label
Highly Symmetric Multiple Bi-Frames for Curve and Surface Multiresolution Processing
Title
Highly Symmetric Multiple Bi-Frames for Curve and Surface Multiresolution Processing
Statement of responsibility
Khulud Saeed Ziadi
Creator
Subject
Genre
Language
eng
Summary
Wavelets and wavelet frames are important and useful mathematical tools in numerous applications, such as signal and image processing, and numerical analysis. Recently, the theory of wavelet frames plays an essential role in signal processing, image processing, sampling theory, and harmonic analysis. However, multiwavelets and multiple frames are more flexible and have more freedom in their construction which can provide more desired properties than the scalar case, such as short compact support, orthogonality, high approximation order, and symmetry. These properties are useful in several applications, such as curve and surface noise-removing as studied in this dissertation. Thus, the study of multiwavelets and multiple frames construction has more advantages for many applications. Recently, the construction of highly symmetric bi-frames for curve and surface multiresolution processing has been investigated. The 6-fold symmetric bi-frames, which lead to highly symmetric analysis and synthesis bi-frame algorithms, have been introduced. Moreover, these multiple bi-frame algorithms play an important role on curve and surface multiresolution processing. This dissertation is an extension of the study of construction of univariate biorthogonal wavelet frames (bi-frames for short) or dual wavelet frames with each framelet being symmetric in the scalar case. We will expand the study of biorthogonal wavelets and bi-frames construction from the scalar case to the vector case to construct biorthogonal multiwavelets and multiple bi-frames in one-dimension. In addition, we will extend the study of highly symmetric bi-frames for triangle surface multiresolution processing from the scalar case to the vector case. More precisely, the objective of this research is to construct highly symmetric biorthogonal multiwavelets and multiple bi-frames in one and two dimensions for curve and surface multiresolution processing. It runs in parallel with the scalar case. We mainly present the methods of constructing biorthogonal multiwavelets and multiple bi-frames in both dimensions by using the idea of lifting scheme. On the whole, we discuss several topics include a brief introduction and discussion of multiwavelets theory, multiresolution analysis, scalar wavelet frames, multiple frames, and the lifting scheme. Then, we present and discuss some results of one-dimensional biorthogonal multiwavelets and multiple bi-frames for curve multiresolution processing with uniform symmetry: type I and type II along with biorthogonality, sum rule orders, vanishing moments, and uniform symmetry for both types. In addition, we present and discuss some results of two-dimensional biorthogonal multiwavelets and multiple bi-frames and the multiresolution algorithms for surface multiresolution processing. Finally, we show experimental results on curve and surface noise-removing by applying our multiple bi-frame algorithms
Member of
Cataloging source
UMS
http://library.link/vocab/creatorName
Ziadi, Khulus Saeed
Degree
Ph.D.
Dissertation year
2018
Granting institution
University of Missouri--St. Louis
Illustrations
illustrations
Index
no index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
  • theses
http://library.link/vocab/subjectName
  • Wavelets (Mathematics)
  • Signal processing
  • Image processing
  • Sampling (Statistics)
  • Harmonic analysis
  • Symmetric functions
Label
Highly Symmetric Multiple Bi-Frames for Curve and Surface Multiresolution Processing, Khulud Saeed Ziadi
Instantiates
Publication
Note
Title from title page of PDF (University of Missouri--St. Louis, viewed September 3, 2018)
Bibliography note
Includes bibliographical references (pages 143-149)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
1055555652
Extent
1 online resource (149 pages)
Form of item
online
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color)
Specific material designation
remote
System control number
(OCoLC)1055555652
Label
Highly Symmetric Multiple Bi-Frames for Curve and Surface Multiresolution Processing, Khulud Saeed Ziadi
Publication
Note
Title from title page of PDF (University of Missouri--St. Louis, viewed September 3, 2018)
Bibliography note
Includes bibliographical references (pages 143-149)
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
1055555652
Extent
1 online resource (149 pages)
Form of item
online
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color)
Specific material designation
remote
System control number
(OCoLC)1055555652

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