Interpolation and Denoising of Piecewise Smooth Signals by Wavelet Regularization

Hyeokho Choi, Richard Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of finding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p α(L p), p ≥ 1, the optimization corresponds to convex programming in the wavelet domain. The algorithm simultaneously achieves signal interpolation and wavelet denoising, which makes it particularly suitable for noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsM.A. Unser, A. Aldroubi, A.F. Laine
Pages16-27
Number of pages12
Volume5207
Edition1
StatePublished - 2003
EventWavelets: Applications in Signal and Image Processing X - San Diego, CA, United States
Duration: Aug 4 2003Aug 8 2003

Other

OtherWavelets: Applications in Signal and Image Processing X
CountryUnited States
CitySan Diego, CA
Period8/4/038/8/03

Keywords

  • Besov
  • Denoising
  • Interpolation
  • Regularization
  • Wavelet

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

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