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Optics Letters

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  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 23 — Dec. 1, 2006
  • pp: 3432–3434

Symplectic wavelet transformation

Hong-yi Fan and Hai-liang Lu  »View Author Affiliations


Optics Letters, Vol. 31, Issue 23, pp. 3432-3434 (2006)
http://dx.doi.org/10.1364/OL.31.003432


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Abstract

Usually a wavelet transform is based on dilated–translated wavelets. We propose a symplectic-transformed–translated wavelet family ψ r , s * ( z κ ) ( r , s are the symplectic transform parameters, s 2 r 2 = 1 , κ is a translation parameter) generated from the mother wavelet ψ and the corresponding wavelet transformation W ψ f ( r , s ; κ ) = ( d 2 z π ) f ( z ) ψ r , s * ( z κ ) . This new transform possesses well-behaved properties and is related to the optical Fresnel transform in quantum mechanical version.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing

ToC Category:
Fourier Optics and Optical Signal Processing

History
Original Manuscript: July 21, 2006
Revised Manuscript: September 4, 2006
Manuscript Accepted: September 4, 2006
Published: November 9, 2006

Citation
Hong-yi Fan and Hai-liang Lu, "Symplectic wavelet transformation," Opt. Lett. 31, 3432-3434 (2006)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-23-3432


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References

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