Nonseparable radial frame multiresolution analysis in multidimensions

Manos Papadakis; G. Gogoshin; I. A. Kakadiaris; D. J. Kouri; D. K. Hoffman

doi:10.1081/NFA-120026385

Nonseparable radial frame multiresolution analysis in multidimensions

Manos Papadakis, G. Gogoshin, I. A. Kakadiaris, D. J. Kouri, D. K. Hoffman

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.

Original language	English (US)
Pages (from-to)	907-928
Number of pages	22
Journal	Numerical Functional Analysis and Optimization
Volume	24
Issue number	7-8
DOIs	https://doi.org/10.1081/NFA-120026385
State	Published - 2003

Keywords

Frames
Nonseparable multiresolution analysis
Wavelets

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1081/NFA-120026385

Cite this

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title = "Nonseparable radial frame multiresolution analysis in multidimensions",

abstract = "In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.",

keywords = "Frames, Nonseparable multiresolution analysis, Wavelets",

author = "Manos Papadakis and G. Gogoshin and Kakadiaris, \{I. A.\} and Kouri, \{D. J.\} and Hoffman, \{D. K.\}",

note = "Funding Information: This research was partially supported by the following grants: University of Houston TLCC funds, NSF-DMS 0070376, NSF Career Award CISE-9985482, NSF-CHE-0074311, by Texas Higher Education Coordinating Board ARP-003652-0071-2001 and R. A. Welch Foundation E-0608. We would also like to thank the anonymous referee for his suggestions.",

year = "2003",

doi = "10.1081/NFA-120026385",

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T1 - Nonseparable radial frame multiresolution analysis in multidimensions

AU - Papadakis, Manos

AU - Gogoshin, G.

AU - Kakadiaris, I. A.

AU - Kouri, D. J.

AU - Hoffman, D. K.

N1 - Funding Information: This research was partially supported by the following grants: University of Houston TLCC funds, NSF-DMS 0070376, NSF Career Award CISE-9985482, NSF-CHE-0074311, by Texas Higher Education Coordinating Board ARP-003652-0071-2001 and R. A. Welch Foundation E-0608. We would also like to thank the anonymous referee for his suggestions.

PY - 2003

Y1 - 2003

N2 - In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.

AB - In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.

KW - Frames

KW - Nonseparable multiresolution analysis

KW - Wavelets

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JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 7-8

ER -

Nonseparable radial frame multiresolution analysis in multidimensions

Abstract

Keywords

ASJC Scopus subject areas

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