Recovering exponential accuracy from non-harmonic Fourier data through spectral reprojection

Anne Gelb, Taylor Hines

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Spectral reprojection techniques make possible the recovery of exponential accuracy from the partial Fourier sum of a piecewise-analytic function, essentially conquering the Gibbs phenomenon for this class of functions. This paper extends this result to non-harmonic partial sums, proving that spectral reprojection can reduce the Gibbs phenomenon in non-harmonic reconstruction as well as remove reconstruction artifacts due to erratic sampling. We are particularly interested in the case where the Fourier samples form a frame. These techniques are motivated by a desire to improve the quality of images reconstructed from non-uniform Fourier data, such as magnetic resonance (MR) images.

Original languageEnglish (US)
Pages (from-to)158-182
Number of pages25
JournalJournal of Scientific Computing
Volume51
Issue number1
DOIs
StatePublished - Apr 1 2012

Keywords

  • Fourier frames
  • Gegenbauer reconstruction
  • Gibbs phenomenon
  • Non-harmonic reconstruction
  • Piecewise-analytic functions

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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