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Review of Scientific Instruments / Volume 78 / Issue 1 / INVITED ARTICLE

Rev. Sci. Instrum. 78, 011301 (2007); http://dx.doi.org/10.1063/1.2403783 (10 pages)

Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval

S. Marchesini

Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550-9234 and Center for Biophotonics Science and Technology, University of California, Davis, 2700 Stockton Boulevard, Suite 1400, Sacramento, California 95817

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(Received 28 March 2006; accepted 5 November 2006; published online 25 January 2007; publisher error corrected 19 April 2007)

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and the possibility of using radiation for which no lenses exist. The challenge of this imaging technique is transferred from the lenses to the algorithms. We evaluate these new computational “instruments” developed for the phase-retrieval problem, and discuss acceleration strategies.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE PHASE PROBLEM
  3. SETS, PROJECTORS AND METRICS
  4. ITERATIVE PROJECTION ALGORITHMS
    1. Positivity
  5. STEEPEST DESCENT, CONJUGATE GRADIENT, AND MIN-MAX ALGORITHMS
    1. Feedback and the saddle-point problem
  6. CONCLUSIONS

EDITORIALLY RELATED

  1. Publisher's Note: “Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval” [Rev. Sci. Instrum. 78, 011301 (2007)]
    S. Marchesini
    Rev. Sci. Instrum. 78, 049901 (2007)RSINAK000078000004049901000001

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KEYWORDS and PACS

Keywords

iterative methods, image reconstruction, light scattering, light diffraction

PACS

  • 42.30.Wb

    Image reconstruction; tomography

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2403783

PUBLICATION DATA

ISSN

0034-6748 (print)  
1089-7623 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    J. C. H. Spence and R. B. Doak, Phys. Rev. Lett. 92, 198102 (2004).

    J. Miao et al., Phys. Rev. Lett. 89, 088303 (2002).

    W. McBride, N. L. O'Leary, and L. J. Allen, Phys. Rev. Lett. 93, 233902 (2004).

    S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, . A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, Phys. Rev. B 68, 140101(R) (2003).

    R. Barakat and G. Newsam, J. Math. Phys. 25, 3190 (1984)JMAPAQ000025000011003190000001.


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