Field reconstruction from single scale continuous wavelet coefficients

Jacques Lewalle

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

The redundancy of continuous wavelet transforms implies that the wavelet coefficients are not independent of each other. This interdependence allows the reconstruction or approximation of the wavelet transform, and of the original field, from a subset of the wavelet coefficients. Contrasting with lines of modulus maxima, known to provide useful partition functions and some data compaction, the reconstruction from single-scale coefficients is derived for the Hermitian family of wavelets. The formula is exact in the continuum for d-dimensional fields, and its limitations under discretization are illustrated.

Original languageEnglish (US)
Pages (from-to)131-142
Number of pages12
JournalInternational Journal of Wavelets, Multiresolution and Information Processing
Volume7
Issue number1
DOIs
StatePublished - May 7 2009

Keywords

  • Continuous wavelets
  • Inverse transform
  • Mexican hat

ASJC Scopus subject areas

  • Signal Processing
  • Information Systems
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Field reconstruction from single scale continuous wavelet coefficients'. Together they form a unique fingerprint.

  • Cite this