# On phase retrieval via matrix completion and the estimation of low rank PSD matrices

arXiv: https://arxiv.org/abs/1907.09537 · HTML: https://mlsanity.com/paper/1907.09537/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Phase retrieval with rank d measurements -- descending algorithms phase transitions](https://mlsanity.com/paper/2506.18282/) (2025)

## Abstract (arXiv)

Given underdetermined measurements of a Positive Semi-Definite (PSD) matrix X of known low rank K, we present a new algorithm to estimate X based on recent advances in non-convex optimization schemes. We apply this in particular to the phase retrieval problem for Fourier data, which can be formulated as a rank 1 PSD matrix recovery problem. Moreover, we provide theory for how oversampling affects the stability of the lifted inverse problem.