Detection of Edges from Nonuniform Fourier Data

Anne Gelb, Taylor Hines

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1152-1179
Number of pages28
JournalJournal of Fourier Analysis and Applications
Volume17
Issue number6
DOIs
StatePublished - Dec 1 2011

Keywords

  • Edge detection
  • Fourier frames
  • Nonuniform Fourier data
  • Piecewise-analytic functions

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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