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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 3 — Mar. 1, 2006
  • pp: 550–556

Simple constraint for phase retrieval with high efficiency

Haifeng He  »View Author Affiliations

JOSA A, Vol. 23, Issue 3, pp. 550-556 (2006)

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I propose the use of a simple real space constraint for iterative phase retrieval intended for diffractive imaging. The proposed constraint is a single parameter equal to the number of nonzero pixels in the image. This greatly simplifies the procedure to determine the constraint. A series of algorithms using this constraint can be easily deduced from existing algorithms, such as hybrid-input–output and difference map algorithms. The high efficiency of these algorithms is largely preserved, as confirmed by numerical studies. A concept widely used in control system theory, proportional-integral–derivative control, is shown to increase the execution speed of the proposed constraint significantly.

© 2006 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval

ToC Category:
Image Processing

Original Manuscript: May 6, 2005
Revised Manuscript: July 12, 2005
Manuscript Accepted: July 13, 2005

Haifeng He, "Simple constraint for phase retrieval with high efficiency," J. Opt. Soc. Am. A 23, 550-556 (2006)

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  15. In reality, the histogram relies on a comparison operation. Ambiguity arises for comparison between complex values. This is the fundamental reason why histogram constraint or any constraint that relies on comparison is best suited for real-valued problems. For more information, see Section and Appendix .
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