Smoothing transforms for wavelet approximation of piecewise smooth functions

M. Aslam, S. D. Riemenschneider, L. Shen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Multi-resolution analysis with high vanishing moment wavelets provides a framework to efficiently approximate smooth functions. However, it is a well-known fact that wavelet approximation usually cannot achieve the same order of approximation in the vicinity of discontinuous points of functions as that in the smooth regions. Ringing artefacts in the reconstructed functions inevitably appear around discontinuous points. To reduce these artefacts, the authors propose to locally smooth piecewise smooth functions at the discontinuous points, prior to applying the wavelet transform, via a smoothing transform. The numerical experiments for one- and two-dimensional signals show the effectiveness of the proposed strategy.

Original languageEnglish (US)
Pages (from-to)239-248
Number of pages10
JournalIET Image Processing
Volume2
Issue number5
DOIs
StatePublished - Nov 19 2008

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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