Award Date
1-1-2003
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
First Committee Member
David G. Costa
Number of Pages
126
Abstract
In the last two decades plenty of research has been carried out in the field of Wavelet theory and it is well known that wavelets can efficiently deal with point-like singularities. Unfortunately, such is not the case for higher dimensions singularities. To overcome this weakness of the Wavelet transform E. Candes and D. Donoho [4] introduced a new wavelet-like transform that can effectively deal with linear singularities in two dimensions, namely the Ridgelet transform. This new representation tool exploits the ability of wavelets to deal with point singularities. In fact, the Ridgelet transform is equivalent to a one-dimensional wavelet transform in the Radon domain. By doing so, a line singularity is transformed into a point singularity (by means of the Radon transform) which can then be efficiently analyzed by the wavelet transform; This thesis presents the Ridgelet transform, its properties and connections to the Radon and Wavelet transform. Also, the reader is presented with practical results that allow us to see how the Ridgelet transform is much better suited than the Wavelet transform for representing images with straight edges (linear singularities).
Keywords
Linear; Objects; Promising; Represent; Ridgelets; Singularities; Transforms; Wavelet
Controlled Subject
Mathematics
File Format
File Size
2437.12 KB
Degree Grantor
University of Nevada, Las Vegas
Language
English
Permissions
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Repository Citation
Teruel, Maria Beatriz, "Ridgelets: A promising new wavelet-like transform to represent objects with linear singularities" (2003). UNLV Retrospective Theses & Dissertations. 1513.
http://dx.doi.org/10.25669/kj0a-yj6p
Rights
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