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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 2 — Feb. 1, 2006
  • pp: 279–287

Multiresolution phase retrieval in the Fresnel region by use of wavelet transform

Alexei Souvorov, Tetsuya Ishikawa, and Armen Kuyumchyan  »View Author Affiliations


JOSA A, Vol. 23, Issue 2, pp. 279-287 (2006)
http://dx.doi.org/10.1364/JOSAA.23.000279


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Abstract

A multiresolution (multiscale) analysis based on wavelet transform is applied to the problem of optical phase retrieval from the intensity measured in the in-line geometry (lens-free). The transport-of-intensity equation and the Fresnel diffraction integral are approximated in terms of a wavelet basis. A solution to the phase retrieval problem can be efficiently found in both cases using the multiresolution concept. Due to the hierarchical nature of wavelet spaces, wavelets are well suited to multiresolution methods that contain multigrid algorithms. Appropriate wavelet bases for the best solution approximation are discussed. The proposed approach reduces the computational complexity and accelerates the convergence of the solution. It is robust and reliable, and successful on both simulated and experimental images obtained with hard x rays.

© 2006 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets
(110.7440) Imaging systems : X-ray imaging

ToC Category:
Image Processing

History
Original Manuscript: March 11, 2005
Manuscript Accepted: May 31, 2005

Citation
Alexei Souvorov, Tetsuya Ishikawa, and Armen Kuyumchyan, "Multiresolution phase retrieval in the Fresnel region by use of wavelet transform," J. Opt. Soc. Am. A 23, 279-287 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-2-279

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