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Proceedings Paper

Shift-invariant Gibbs-free denoising algorithm based on wavelet transform footprints
Author(s): Pier Luigi Dragotti; Martin Vetterli
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Paper Abstract

In recent years wavelet have had an important impact on signal processing theory and practice. The effectiveness of wavelets is mainly due to their capability of representing piecewise smooth signals with few non-zero coefficients. Away from discontinuities, the inner product between a wavelet and a smooth function will be either zero or very small. At singular points, a finite number of wavelets concentrated around the discontinuity lead to non-zero inner products. This ability of wavelet transform to pack the main signal information in few large coefficients is behind the success of wavelet based denoising algorithms. Indeed, traditional approaches simply consist in thresholding the noisy wavelet coefficients, so the few large coefficients carrying the essential information are usually kept while small coefficients mainly containing, so the few large coefficients carrying the essential information are usually kept while small coefficients mainly containing noise are canceled. However, wavelet denoising suffers of two main drawbacks: it is not shift-invariant and it exhibits pseudo Gibbs phenomenon around discontinuities.

Paper Details

Date Published: 4 December 2000
PDF: 10 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408672
Show Author Affiliations
Pier Luigi Dragotti, Swiss Federal Institute of Technology Lausanne (Switzerland)
Martin Vetterli, Swiss Federal Institute of Technology Lausanne and Univ. of California/Berkeley (Switzerland)


Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)

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