Interpolation and denoising of nonuniformly sampled data using wavelet-domain processing

Hyeokho Choi, Richard Baraniuk

Research output: Chapter in Book/Report/Conference proceedingChapter

20 Scopus citations

Abstract

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space B q α (L p), the optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space W α(L 2), the optimization reduces to a simple weighted least-squares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.

Original languageEnglish (US)
Title of host publicationICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1645-1648
Number of pages4
Volume3
StatePublished - 1999
EventProceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99) - Phoenix, AZ, USA
Duration: Mar 15 1999Mar 19 1999

Other

OtherProceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99)
CityPhoenix, AZ, USA
Period3/15/993/19/99

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Acoustics and Ultrasonics

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