Approximating the inverse frame operator from localized frames

Guohui Song, Anne Gelb

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that sampling with well-localized frames improves both the accuracy of the numerical frame approximation as well as the robustness and efficiency of the (finite) frame operator inversion. Moreover, in applications such as magnetic resonance imaging, where the given data often may not constitute a well-localized frame, a technique is devised to project the corresponding frame data onto a more suitable frame. As a result, the target function may be approximated as a finite expansion with its asymptotic convergence solely dependent on its smoothness. Numerical examples are provided.

Original languageEnglish (US)
Pages (from-to)94-110
Number of pages17
JournalApplied and Computational Harmonic Analysis
Volume35
Issue number1
DOIs
StatePublished - Jul 2013

Keywords

  • Fourier frames
  • Inverse frame operator
  • Localized frames
  • Numerical frame approximation

ASJC Scopus subject areas

  • Applied Mathematics

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