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Feeding Genetic Heterogeneity via a Smart Mutation Operator in the Memetic Phase Retrieval Approach

  • Marta Mauri
  • Davide Emilio Galli
  • Alessandro Colombo
Conference paper

Abstract

A memetic algorithm is a stochastic optimization method obtained by hybridizing an evolutionary approach with common deterministic optimization procedures. The recently introduced Memetic Phase Retrieval (MPR) approach exploits this synergy to face the so-called phase retrieval problem in Coherent Diffraction Imaging (CDI). Here we focus on the development of a smart mutation genetic operator; our aim is the improvement of MPR performance by continually feeding with relevant information the genetic heritage of the population of candidate solutions. Remarkably, statistical tests on synthetic CDI data performed using MPR enhanced via a smart mutation operator reveal a smaller reconstruction error with respect to an MPR implementation supplied with a blind random mutation only.

Keywords

Coherent diffraction imaging Memetic algorithms Phase retrieval problem Computational intelligence 

Notes

Acknowledgements

We acknowledge L. De Caro, E. Carlino and F. Scattarella for useful discussions. This work was supported by the NOXSS PRIN (2012Z3N9R9) project. We acknowledge the CINECA and Regione Lombardia LISA award LI05p-PUMAS, the CINECA ISCRA–C award IMAGES and the CINECA ISCRA–B award MEMETICO for the availability of high performance computing resources and support.

References

  1. 1.
    D. Sayre, Some implications of a theorem due to Shannon. Acta Crystallogr. 5(6), 843 (1952)Google Scholar
  2. 2.
    C. Fienup, J. Dainty, Phase retrieval and image reconstruction for astronomy. in Image Recovery: Theory and Application (1987), pp. 231–275Google Scholar
  3. 3.
    L. De Caro, E. Carlino, F.A. Vittoria, D. Siliqi, C. Giannini, Keyhole electron diffractive imaging (KEDI). Acta Crystallogr. Sect. A 68, 687–7026 (2012)Google Scholar
  4. 4.
    Y. Shechtman, Y.C. Eldar, O. Cohen, H.N. Chapman, J. Miao, M. Segev, Phase retrieval with application to optical imaging: a contemporary overview. IEEE Signal Process. Mag. 32(3), 87–109 (2015)Google Scholar
  5. 5.
    L. De Caro, E. Carlino, D. Siliqi, C. Giannini, Coherent diffractive imaging: from nanometric down to picometric resolution, in Handbook of Coherent-Domain Optical Methods (Springer, 2013), pp. 291–314Google Scholar
  6. 6.
    M. Altarelli, R. Brinkmann, M. Chergui, W. Decking, B. Dobson, S. Düsterer, G. Grübel, W. Graeff, H. Graafsma, J. Hajdu et al., The European X-ray free-electron laser, in Technical Design Report, DESY 97 (2006), pp. 1–26Google Scholar
  7. 7.
    S. Marchesini, Invited article: a unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instrum. 78(1), 011301 (2007)Google Scholar
  8. 8.
    J.R. Fienup, Phase retrieval algorithms: a comparison. Appl. Opt. 21(15), 2758–2769 (1982)Google Scholar
  9. 9.
    J.R. Fienup, C.C. Wackerman, Phase-retrieval stagnation problems and solutions. J. Opt. Soc. Am. A 3(11), 1897–1907 (1986)Google Scholar
  10. 10.
    A. Colombo, D.E. Galli, L. De Caro, F. Scattarella, E. Carlino, Facing the phase problem in coherent diffractive imaging via memetic algorithms. Sci. Rep. 7(42236) (2017)Google Scholar
  11. 11.
    D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. (Addison-Wesley Longman Publishing Co. Inc., Boston, MA, USA, 1989). ISBN: 0201157675Google Scholar
  12. 12.
    P. Moscato et al., On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms, in Caltech Concurrent Computation Program, C3P Report (1989), p. 826Google Scholar
  13. 13.
    R. Storn, K. Price, Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Marta Mauri
    • 1
  • Davide Emilio Galli
    • 1
  • Alessandro Colombo
    • 1
  1. 1.Dipartimento di Fisica “Aldo Pontremoli”Università degli Studi di MilanoMilanItaly

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