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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: Franco Gori
  • Vol. 28, Iss. 10 — Oct. 1, 2011
  • pp: 2124–2131

Approximate Fourier phase information in the phase retrieval problem: what it gives and how to use it

Eliyahu Osherovich, Michael Zibulevsky, and Irad Yavneh  »View Author Affiliations


JOSA A, Vol. 28, Issue 10, pp. 2124-2131 (2011)
http://dx.doi.org/10.1364/JOSAA.28.002124


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Abstract

This work evaluates the importance of approximate Fourier phase information in the phase retrieval problem. The main discovery is that a rough phase estimate (up to π / 2 rad ) allows development of very efficient algorithms whose reconstruction time is an order of magnitude faster than that of the current method of choice—the hybrid input–output (HIO) algorithm. Moreover, a heuristic explanation is provided of why continuous optimization methods like gradient descent or Newton-type algorithms fail when applied to the phase retrieval problem and how the approximate phase information can remedy this situation. Numerical simulations are presented to demonstrate the validity of our analysis and success of our reconstruction method even in cases where the HIO algorithm fails, namely, complex-valued signals without tight support information.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(100.5070) Image processing : Phase retrieval

ToC Category:
Image Processing

History
Original Manuscript: July 14, 2011
Manuscript Accepted: August 17, 2011
Published: September 21, 2011

Virtual Issues
November 23, 2011 Spotlight on Optics

Citation
Eliyahu Osherovich, Michael Zibulevsky, and Irad Yavneh, "Approximate Fourier phase information in the phase retrieval problem: what it gives and how to use it," J. Opt. Soc. Am. A 28, 2124-2131 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-10-2124


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References

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