# Convex recovery from interferometric measurements

arXiv: https://arxiv.org/abs/1307.6864 · HTML: https://mlsanity.com/paper/1307.6864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2013.

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

- [Tractable Gaussian Phase Retrieval with Heavy Tails and Adversarial Corruption with Near-Linear Sample Complexity](https://mlsanity.com/paper/2601.18245/) (2026)

## Abstract (arXiv)

This note formulates a deterministic recovery result for vectors x from quadratic measurements of the form (Ax)i overline(Ax)j for some left-invertible A. Recovery is exact, or stable in the noisy case, when the couples (i,j) are chosen as edges of a well-connected graph. One possible way of obtaining the solution is as a feasible point of a simple semidefinite program. Furthermore, we show how the proportionality constant in the error estimate depends on the spectral gap of a data-weighted graph Laplacian. Such quadratic measurements have found applications in phase retrieval, angular synchronization, and more recently interferometric waveform inversion.