# On recovery guarantees for angular synchronization

arXiv: https://arxiv.org/abs/2005.02032 · HTML: https://mlsanity.com/paper/2005.02032/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2020.

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

- [Optimal Orthogonal Group Synchronization and Rotation Group Synchronization](https://mlsanity.com/paper/2109.13491/) (2021)
- [Robust Angular Synchronization via Directed Graph Neural Networks](https://mlsanity.com/paper/2310.05842/) (2023)
- [Generalized Orthogonal Procrustes Problem under Arbitrary Adversaries](https://mlsanity.com/paper/2106.15493/) (2021)

## Abstract (arXiv)

The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as a optimization problem on graphs involving the graph Laplacian matrix. We consider a general, weighted version of this problem, where the impact of the noise differs between different pairs of entries and some of the differences are erased completely; this version arises for example in ptychography. We study two common approaches for solving this problem, namely eigenvector relaxation and semidefinite convex relaxation. Although some recovery guarantees are available for both methods, their performance is either unsatisfying or restricted to the unweighted graphs. We close this gap, deriving recovery guarantees for the weighted problem that are completely analogous to the unweighted version.