Shift-invariant Gibbs-free denoising algorithm based on wavelet transform footprints

Pier Luigi Dragotti; Martin Vetterli

doi:10.1117/12.408672

4 December 2000 Shift-invariant Gibbs-free denoising algorithm based on wavelet transform footprints

Pier Luigi Dragotti, Martin Vetterli

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408672
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

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.

Citation Download Citation

Pier Luigi Dragotti and Martin Vetterli "Shift-invariant Gibbs-free denoising algorithm based on wavelet transform footprints", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408672

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