Dual generators for weighted irregular wavelet frames and reconstruction error

Zuofeng Shang; Xingwei Zhou

doi:10.1016/j.acha.2006.10.001

Dual generators for weighted irregular wavelet frames and reconstruction error

Zuofeng Shang, Xingwei Zhou

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

5 Scopus citations

Abstract

Dual frames are very useful tools to reconstruct a function and have been explored in many different aspects. In this paper, we give the conditions under which a class of special weighted irregular wavelet frames could have a dual generator with a very explicit form. We also prove that when the irregular translations are changed in some admissible range, the reconstruction formula has a very small perturbation. An example is given to show the use of our main results.

Original language	English (US)
Pages (from-to)	356-367
Number of pages	12
Journal	Applied and Computational Harmonic Analysis
Volume	22
Issue number	3
DOIs	https://doi.org/10.1016/j.acha.2006.10.001
State	Published - May 2007
Externally published	Yes

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Dual frames
Dual generator
Weighted irregular wavelet frames
Weighted tight frames

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10.1016/j.acha.2006.10.001

Cite this

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title = "Dual generators for weighted irregular wavelet frames and reconstruction error",

abstract = "Dual frames are very useful tools to reconstruct a function and have been explored in many different aspects. In this paper, we give the conditions under which a class of special weighted irregular wavelet frames could have a dual generator with a very explicit form. We also prove that when the irregular translations are changed in some admissible range, the reconstruction formula has a very small perturbation. An example is given to show the use of our main results.",

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author = "Zuofeng Shang and Xingwei Zhou",

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AU - Shang, Zuofeng

AU - Zhou, Xingwei

PY - 2007/5

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N2 - Dual frames are very useful tools to reconstruct a function and have been explored in many different aspects. In this paper, we give the conditions under which a class of special weighted irregular wavelet frames could have a dual generator with a very explicit form. We also prove that when the irregular translations are changed in some admissible range, the reconstruction formula has a very small perturbation. An example is given to show the use of our main results.

AB - Dual frames are very useful tools to reconstruct a function and have been explored in many different aspects. In this paper, we give the conditions under which a class of special weighted irregular wavelet frames could have a dual generator with a very explicit form. We also prove that when the irregular translations are changed in some admissible range, the reconstruction formula has a very small perturbation. An example is given to show the use of our main results.

KW - Dual frames

KW - Dual generator

KW - Weighted irregular wavelet frames

KW - Weighted tight frames

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M3 - Article

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SN - 1063-5203

VL - 22

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ER -

Dual generators for weighted irregular wavelet frames and reconstruction error

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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