Mathematical Programming Computation

, Volume 8, Issue 3, pp 311–335 | Cite as

Phase retrieval for imaging problems

  • Fajwel Fogel
  • Irène Waldspurger
  • Alexandre d’AspremontEmail author
Full Length Paper


We study convex relaxation algorithms for phase retrieval on imaging problems. We show that exploiting structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can significantly speed-up convergence and improve recovery performance. We detail numerical results in molecular imaging experiments simulated using data from the Protein Data Bank.


Phase recovery Semidefinite programming X-ray diffraction Molecular imaging Fourier optics 

Mathematics Subject Classification

94A12 90C22 90C27 



AA and FF would like to acknowledge support from a starting grant from the European Research Council (project SIPA).


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Copyright information

© Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society 2016

Authors and Affiliations

  • Fajwel Fogel
    • 1
  • Irène Waldspurger
    • 2
  • Alexandre d’Aspremont
    • 3
    Email author
  1. 1.C.M.A.P., École Polytechnique, UMR CNRS 7641Palaiseau CedexFrance
  2. 2.D.I., École Normale SupérieureParisFrance
  3. 3.CNRS & D.I., UMR 8548, École Normale SupérieureParisFrance

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