# On Fienup Methods for Regularized Phase Retrieval

arXiv: https://arxiv.org/abs/1702.08339 · HTML: https://mlsanity.com/paper/1702.08339/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2017.

## Built on by (most cited first, 3 of 3)

- [Misspecified Phase Retrieval with Generative Priors](https://mlsanity.com/paper/2210.05571/) (2022)
- [Unique Bispectrum Inversion for Signals with Finite Spectral/Temporal Support](https://mlsanity.com/paper/2111.06479/) (2021)
- [Low Complexity Regularized Phase Retrieval](https://mlsanity.com/paper/2407.16413/) (2024)

## Abstract (arXiv)

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. We then prove that under mild additional structural assumptions on the prior (semi-algebraicity), the sequence of signal estimates has a smooth convergent behaviour towards 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 ℓ1 prior constitutes a competitive approach for sparse phase retrieval.