# Phase retrieval using alternating minimization in a batch setting

arXiv: https://arxiv.org/abs/1706.08167 · HTML: https://mlsanity.com/paper/1706.08167/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2017.

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

- [Sharp global convergence guarantees for iterative nonconvex optimization: A Gaussian process perspective](https://mlsanity.com/paper/2109.09859/) (2021)
- [Asymptotic Dynamics of Alternating Minimization for Bilinear Regression](https://mlsanity.com/paper/2402.04751/) (2024)
- [Compressing Sign Information in DCT-based Image Coding via Deep Sign Retrieval](https://mlsanity.com/paper/2209.10712/) (2022)

## Abstract (arXiv)

This paper considers the problem of phase retrieval, where the goal is to recover a signal z∈ Cn from the observations yi=|ai^* z|, i=1,2,cdots,m. While many algorithms have been proposed, the alternating minimization algorithm has been one of the most commonly used methods, and it is very simple to implement. Current work has proved that when the observation vectors aii=1m are sampled from a complex Gaussian distribution N(0, I), it recovers the underlying signal with a good initialization when m=O(n), or with random initialization when m=O(n2), and it conjectured that random initialization succeeds with m=O(n). This work proposes a modified alternating minimization method in a batch setting, and proves that when m=O(nlog3n), the proposed algorithm with random initialization recovers the underlying signal with high probability. The proof is based on the observation that after each iteration of alternating minimization, with high probability, the angle between the estimated signal and the underlying signal is reduced.