A high-dimensional inverse frame operator approximation technique

Guohui Song, Jacqueline Davis, Anne Gelb

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

The ability to efficiently and accurately approximate an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame operators for one-dimensional problems. Using the admissible frame approach, it is possible to project the corresponding frame data onto a more suitable (admissible) frame, even when the sampling frame is only weakly localized. As a result, a target function may be approximated as a finite frame expansion with its asymptotic convergence solely dependent on its smoothness. In this investigation, we seek to expand the admissible frame approach to higher dimensions, which requires some additional constraints. We prove that the admissible frame technique converges and then demonstrate its usefulness with some numerical experiments that use two-dimensional sampling patterns inspired by applications that acquire data nonuniformly in the Fourier domain.

Original languageEnglish (US)
Pages (from-to)2282-2301
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Fourier frames
  • High-dimensional frames
  • Inverse frame operator
  • Localized frames
  • Nonuniform fourier data
  • Numerical frame approximation

ASJC Scopus subject areas

  • Numerical Analysis

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