article

Wavelets for multichannel signals

Authors:

Silvia Bacchelli,

Mariantonia Cotronei,

Thomas SauerAuthors Info & Claims

Advances in Applied Mathematics, Volume 29, Issue 4

Pages 581 - 598

https://doi.org/10.1016/S0196-8858(02)00033-7

Published: 01 November 2002 Publication History

Abstract

In this paper, we introduce and investigate multichannel wavelets, which are wavelets for vector fields, based on the concept of full rank subdivision operators. We prove that, like in the scalar and multiwavelet case, the existence of a scaling function with orthogonal integer translates guarantees the existence of a wavelet function, also with orthonormal integer translates. In this context, however, scaling functions as well as wavelets turn out to be matrix-valued functions.

References

[1]

Bacchelli, S., Cotronei, M. and Sauer, T., Multifilters with and without prefilters. BIT. v42. 231-261.

Google Scholar

[2]

Micchelli, C.A. and Sauer, T., Regularity of multiwavelets. Adv. Comput. Math. v7. 455-545.

Crossref

Google Scholar

[3]

Micchelli, C.A. and Sauer, T., On vector subdivision. Math. Z. v229. 621-674.

Google Scholar

[4]

Skrandies, W. and Jedynak, A., Associative learning in human brains¿conditioning of sensory-evoked brain activity. Behavioural Brain Res. v107. 1-8.

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Cited By

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Cotronei MHolschneider M(2013)Partial parameterization of orthogonal wavelet matrix filtersJournal of Computational and Applied Mathematics10.1016/j.cam.2012.11.016243(113-125)Online publication date: 1-May-2013
https://dl.acm.org/doi/10.1016/j.cam.2012.11.016
Conti CCotronei MSauer T(2010)Full rank interpolatory subdivisionJournal of Approximation Theory10.1016/j.jat.2009.08.008162:3(559-575)Online publication date: 1-Mar-2010
https://dl.acm.org/doi/10.1016/j.jat.2009.08.008
Conti CCotronei MSauer T(2010)Full rank interpolatory subdivision schemesJournal of Computational and Applied Mathematics10.1016/j.cam.2009.02.016233:7(1649-1659)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.1016/j.cam.2009.02.016
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Index Terms

Wavelets for multichannel signals
1. Hardware
  1. Communication hardware, interfaces and storage
    1. Signal processing systems

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cover image Advances in Applied Mathematics

Advances in Applied Mathematics Volume 29, Issue 4

November 2002

166 pages

ISSN:0196-8858

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Academic Press, Inc.

United States

Publication History

Published: 01 November 2002

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Cotronei MHolschneider M(2013)Partial parameterization of orthogonal wavelet matrix filtersJournal of Computational and Applied Mathematics10.1016/j.cam.2012.11.016243(113-125)Online publication date: 1-May-2013
https://dl.acm.org/doi/10.1016/j.cam.2012.11.016
Conti CCotronei MSauer T(2010)Full rank interpolatory subdivisionJournal of Approximation Theory10.1016/j.jat.2009.08.008162:3(559-575)Online publication date: 1-Mar-2010
https://dl.acm.org/doi/10.1016/j.jat.2009.08.008
Conti CCotronei MSauer T(2010)Full rank interpolatory subdivision schemesJournal of Computational and Applied Mathematics10.1016/j.cam.2009.02.016233:7(1649-1659)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.1016/j.cam.2009.02.016
Conti CCotronei MSauer T(2008)Full rank positive matrix symbols: interpolation and orthogonality BIT10.1007/s10543-008-0162-348:1(5-27)Online publication date: 1-Mar-2008
https://dl.acm.org/doi/10.1007/s10543-008-0162-3

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A multivariate thresholding technique for image denoising using multiwavelets

Generalized Discrete Multiwavelet Transform With Embedded Orthogonal Symmetric Prefilter Bank

Separable and nonseparable multiwavelets in multiple dimensions

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