On Fienup Methods for Sparse Phase Retrieval

Edouard Jean Robert Pauwels*, Amir Beck, Yonina C. Eldar, Shoham Sabach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex priors. In particular, we show that Fienup methods can be viewed as performing alternating minimization on a regularized nonconvex least-squares problem with respect to amplitude measurements. Furthermore, we prove that under mild additional structural assumptions on the prior (semialgebraicity), the sequence of signal estimates has a smooth convergent behavior toward a critical point of the nonconvex regularized least-squares objective. Finally, we propose an extension to Fienup techniques, based on a projected gradient descent interpretation and acceleration using inertial terms. We demonstrate experimentally that this modification combined with an ℓ-1 prior constitutes a competitive approach for sparse phase retrieval.

Original languageEnglish
Article number8141921
Pages (from-to)982-991
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number4
StatePublished - 15 Feb 2018


  • Fourier measurements
  • Non-convex optimization
  • iterative algorithms
  • phase retrieval
  • sparse signal processing

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