Frames in two dimensions arising from wavelet transforms

Research output: Contribution to journalArticle

Abstract

A mathematical scheme for generating functions spanning the Hilbert space L2(R2, (dτ ds/s2) is advanced. The completeness condition is guaranteed by the fact that the proposed functions constitute a frame for L2(R2, (dτ ds/s2)). Such functions are built up out of the following ingredients: (i) the wavelet transform, and (ii) a frame for L2(R, dt).

Original languageEnglish
Pages (from-to)2079-2091
Number of pages13
JournalProceedings of the Royal Society of London A
Volume457
Issue number2013
DOIs
Publication statusPublished - 8 Sep 2001

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wavelet analysis
Wavelet transforms
Wavelet Transform
Two Dimensions
Generating Function
Completeness
Hilbert space
Hilbert spaces
completeness
ingredients

Keywords

  • Frame representation
  • Time frequency time-scale representation
  • Two-dimensional frames
  • Wavelet transform
  • Wide-band Doppler imaging
  • Wide-band remote sensing

Cite this

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Frames in two dimensions arising from wavelet transforms. / Rebollo-Neira, L.

In: Proceedings of the Royal Society of London A, Vol. 457, No. 2013, 08.09.2001, p. 2079-2091.

Research output: Contribution to journalArticle

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