Volume 31, Issue 2
Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

Anal. Theory Appl., 31 (2015), pp. 109-122.

Published online: 2017-04

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• Abstract

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for $L^2(\mathbb{R}^d)$ by replacing some mother framelets.

• Keywords

Wavelet, tight frame, framelet packet, matrix dilation, extension principle, Fourier transform.

42C40, 42C15, 65T60

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@Article{ATA-31-109, author = {}, title = {Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {2}, pages = {109--122}, abstract = {

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for $L^2(\mathbb{R}^d)$ by replacing some mother framelets.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n2.2}, url = {http://global-sci.org/intro/article_detail/ata/4627.html} }
TY - JOUR T1 - Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix JO - Analysis in Theory and Applications VL - 2 SP - 109 EP - 122 PY - 2017 DA - 2017/04 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n2.2 UR - https://global-sci.org/intro/article_detail/ata/4627.html KW - Wavelet, tight frame, framelet packet, matrix dilation, extension principle, Fourier transform. AB -

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for $L^2(\mathbb{R}^d)$ by replacing some mother framelets.

F. A. Shah & Abdullah. (1970). Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix. Analysis in Theory and Applications. 31 (2). 109-122. doi:10.4208/ata.2015.v31.n2.2
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