Approach to wavelet multiresolution analysis using Coiflets and a two-wave mixing arrangement

Ángel Salazar; Héctor Lorduy G.

doi:10.1016/j.optcom.2008.01.059

Approach to wavelet multiresolution analysis using Coiflets and a two-wave mixing arrangement

Research output: Contribution to scientific journal › Article in an indexed scientific journal › peer-review

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Abstract

An approach to the wavelet multiresolution analysis is realized using Coiflet wavelets and a two-wave mixing arrangement via transmission gratings in a bismuth silicon oxide (BSO) crystal. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. 2-D wavelet bases are generated by a tensorial product of the 1-D Coiflet bases and are separable in x and y. Therefore, the 1-D band-pass property produces direction ability in the 2-D tensorial products. In this way, unlike the Mexican hat-based filters, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of an original image. The decomposition of a signal in two levels of multiresolution is experimentally demonstrated in this scheme. The original image is discomposed in an average image and several detail images depending on the level of multiresolution. Coif12 wavelets are used to achieve the multiresolution analysis. The photorefractive implementation of the wavelet analysis is numerically simulated and experimentally performed. An agreement between numerical and experimental results is obtained.

Original language	English
Pages (from-to)	3091-3098
Number of pages	8
Journal	Optics Communications
Volume	281
Issue number	11
DOIs	https://doi.org/10.1016/j.optcom.2008.01.059
State	Published - 1 Jun 2008

Bibliographical note

Funding Information:
A. Salazar and H. Lorduy acknowledge the financial support of the Universidad Pontificia Bolivariana, Medellín-Colombia, its Centro de Ciencia Básica and the Centro Integrado para el Desarrollo de la Investigación, CIDI, throughout the research 890-05/06-27. Equally, A. Salazar and H. Lorduy, acknowledge the important and constructive remarks of the reviewers of this paper.

Keywords

Coiflets
Photorefractive BSO crystal
Wavelet multiresolution analysis

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10.1016/j.optcom.2008.01.059

Cite this

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title = "Approach to wavelet multiresolution analysis using Coiflets and a two-wave mixing arrangement",

abstract = "An approach to the wavelet multiresolution analysis is realized using Coiflet wavelets and a two-wave mixing arrangement via transmission gratings in a bismuth silicon oxide (BSO) crystal. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. 2-D wavelet bases are generated by a tensorial product of the 1-D Coiflet bases and are separable in x and y. Therefore, the 1-D band-pass property produces direction ability in the 2-D tensorial products. In this way, unlike the Mexican hat-based filters, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of an original image. The decomposition of a signal in two levels of multiresolution is experimentally demonstrated in this scheme. The original image is discomposed in an average image and several detail images depending on the level of multiresolution. Coif12 wavelets are used to achieve the multiresolution analysis. The photorefractive implementation of the wavelet analysis is numerically simulated and experimentally performed. An agreement between numerical and experimental results is obtained.",

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author = "{\'A}ngel Salazar and \{Lorduy G.\}, H{\'e}ctor",

note = "Funding Information: A. Salazar and H. Lorduy acknowledge the financial support of the Universidad Pontificia Bolivariana, Medell{\'i}n-Colombia, its Centro de Ciencia B{\'a}sica and the Centro Integrado para el Desarrollo de la Investigaci{\'o}n, CIDI, throughout the research 890-05/06-27. Equally, A. Salazar and H. Lorduy, acknowledge the important and constructive remarks of the reviewers of this paper. ",

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N2 - An approach to the wavelet multiresolution analysis is realized using Coiflet wavelets and a two-wave mixing arrangement via transmission gratings in a bismuth silicon oxide (BSO) crystal. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. 2-D wavelet bases are generated by a tensorial product of the 1-D Coiflet bases and are separable in x and y. Therefore, the 1-D band-pass property produces direction ability in the 2-D tensorial products. In this way, unlike the Mexican hat-based filters, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of an original image. The decomposition of a signal in two levels of multiresolution is experimentally demonstrated in this scheme. The original image is discomposed in an average image and several detail images depending on the level of multiresolution. Coif12 wavelets are used to achieve the multiresolution analysis. The photorefractive implementation of the wavelet analysis is numerically simulated and experimentally performed. An agreement between numerical and experimental results is obtained.

AB - An approach to the wavelet multiresolution analysis is realized using Coiflet wavelets and a two-wave mixing arrangement via transmission gratings in a bismuth silicon oxide (BSO) crystal. A Coiflet filter acts not only as a band-pass filter but as a high-pass or low-pass filter. 2-D wavelet bases are generated by a tensorial product of the 1-D Coiflet bases and are separable in x and y. Therefore, the 1-D band-pass property produces direction ability in the 2-D tensorial products. In this way, unlike the Mexican hat-based filters, the Coiflet-based filters allow selecting horizontal, vertical or diagonals details of an original image. The decomposition of a signal in two levels of multiresolution is experimentally demonstrated in this scheme. The original image is discomposed in an average image and several detail images depending on the level of multiresolution. Coif12 wavelets are used to achieve the multiresolution analysis. The photorefractive implementation of the wavelet analysis is numerically simulated and experimentally performed. An agreement between numerical and experimental results is obtained.

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KW - Wavelet multiresolution analysis

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DO - 10.1016/j.optcom.2008.01.059

M3 - Artículo en revista científica indexada

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SN - 0030-4018

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JO - Optics Communications

JF - Optics Communications

IS - 11

ER -

Approach to wavelet multiresolution analysis using Coiflets and a two-wave mixing arrangement

Abstract

Bibliographical note

Keywords

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