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Journal of Fourier Analysis and Applications

, Volume 17, Issue 6, pp 1152–1179 | Cite as

Detection of Edges from Nonuniform Fourier Data

  • Anne GelbEmail author
  • Taylor Hines
Article

Abstract

Edge detection is important in a variety of applications. While there are many algorithms available for detecting edges from pixelated images or equispaced Fourier data, much less attention has been given to determining edges from nonuniform Fourier data. There are applications in sensing (e.g. MRI) where the data is given in this way, however. This paper introduces a method for determining the locations of jump discontinuities, or edges, in a one-dimensional periodic piecewise-smooth function from nonuniform Fourier coefficients. The technique employs the use of Fourier frames. Numerical examples are provided.

Keywords

Fourier frames Nonuniform Fourier data Piecewise-analytic functions Edge detection 

Mathematics Subject Classification

42C15 42A50 65T40 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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