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  1. KEEP
  2. Theses and Dissertations
  3. Barrett, The Honors College Thesis/Creative Project Collection
  4. Designing concentration factors to detect jump discontinuities from non-uniform Fourier data
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Designing concentration factors to detect jump discontinuities from non-uniform Fourier data

Full metadata

Description

Edge detection plays a significant role in signal processing and image reconstruction applications where it is used to identify important features in the underlying signal or image. In some of these applications, such as magnetic resonance imaging (MRI), data are sampled in the Fourier domain. When the data are sampled uniformly, a variety of algorithms can be used to efficiently extract the edges of the underlying images. However, in cases where the data are sampled non-uniformly, such as in non-Cartesian MRI, standard inverse Fourier transformation techniques are no longer suitable. Methods exist for handling these types of sampling patterns, but are often ill-equipped for cases where data are highly non-uniform. This thesis further develops an existing approach to discontinuity detection, the use of concentration factors. Previous research shows that the concentration factor technique can successfully determine jump discontinuities in non-uniform data. However, as the distribution diverges further away from uniformity so does the efficacy of the identification. This thesis proposes a method for reverse-engineering concentration factors specifically tailored to non-uniform data by employing the finite Fourier frame approximation. Numerical results indicate that this design method produces concentration factors which can more precisely identify jump locations than those previously developed.

Date Created
2015-05
Contributors
  • Moore, Rachael (Author)
  • Gelb, Anne (Thesis director)
  • Davis, Jacueline (Committee member)
  • Barrett, The Honors College (Contributor)
Topical Subject
  • Applied Mathematics
  • Signal Processing
  • Edge Detection
  • Nonuniform Fourier Data
  • Fourier Frames
Resource Type
Text
Extent
23 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Barrett, The Honors College Thesis/Creative Project Collection
Series
Academic Year 2014-2015
Handle
https://hdl.handle.net/2286/R.I.35287
Level of coding
minimal
Cataloging Standards
asu1
Note
A copy of this thesis/creative project may be available at Barrett, the Honors College at Arizona State University. If you would like to access the printed copy, please email thesis@asu.edu, opens in a new window.
System Created
  • 2017-10-30 02:50:57
System Modified
  • 2021-07-16 10:38:41
  •     
  • 1 year 6 months ago
Additional Formats
  • OAI Dublin Core
  • MODS XML

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