Data driven design of an orthogonal wavelet with vanishing moments

Ralf Peeters; Joël Karel

Data driven design of an orthogonal wavelet with vanishing moments

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

We present a framework to design an orthogonal wavelet with compact support and vanishing moments, tuned to a given application. This is achieved by optimizing a criterion, such that a prototype signal, which is characteristic for the application, becomes sparse in the wavelet domain. This approach is beneficial for compression and detection purposes. A parameterization is developed for which orthogonality and compact support are built in, and in terms of which we can express the vanishing moment conditions conveniently. The ap- proach is developed for critically sampled wavelet transforms as well as for the stationary wavelet transform. Several examples illustrate the methods.

Original language	English
Title of host publication	21st International Symposium on Mathematical Theory of Networks and Systems
Pages	1665-1672
ISBN (Electronic)	978-90-367-6321-9
Publication status	Published - 11 Jul 2014

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Cite this

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abstract = "We present a framework to design an orthogonal wavelet with compact support and vanishing moments, tuned to a given application. This is achieved by optimizing a criterion, such that a prototype signal, which is characteristic for the application, becomes sparse in the wavelet domain. This approach is beneficial for compression and detection purposes. A parameterization is developed for which orthogonality and compact support are built in, and in terms of which we can express the vanishing moment conditions conveniently. The ap- proach is developed for critically sampled wavelet transforms as well as for the stationary wavelet transform. Several examples illustrate the methods.",

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N2 - We present a framework to design an orthogonal wavelet with compact support and vanishing moments, tuned to a given application. This is achieved by optimizing a criterion, such that a prototype signal, which is characteristic for the application, becomes sparse in the wavelet domain. This approach is beneficial for compression and detection purposes. A parameterization is developed for which orthogonality and compact support are built in, and in terms of which we can express the vanishing moment conditions conveniently. The ap- proach is developed for critically sampled wavelet transforms as well as for the stationary wavelet transform. Several examples illustrate the methods.

AB - We present a framework to design an orthogonal wavelet with compact support and vanishing moments, tuned to a given application. This is achieved by optimizing a criterion, such that a prototype signal, which is characteristic for the application, becomes sparse in the wavelet domain. This approach is beneficial for compression and detection purposes. A parameterization is developed for which orthogonality and compact support are built in, and in terms of which we can express the vanishing moment conditions conveniently. The ap- proach is developed for critically sampled wavelet transforms as well as for the stationary wavelet transform. Several examples illustrate the methods.

M3 - Conference article in proceeding

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EP - 1672

BT - 21st International Symposium on Mathematical Theory of Networks and Systems

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