# Multi-Frequency Phase Synchronization

arXiv: https://arxiv.org/abs/1901.08235 · HTML: https://mlsanity.com/paper/1901.08235/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2019.

## Built on by (most cited first, 7 of 7)

- [Joint Community Detection and Rotational Synchronization via Semidefinite Programming](https://mlsanity.com/paper/2105.06031/) (2021)
- [SDP Achieves Exact Minimax Optimality in Phase Synchronization](https://mlsanity.com/paper/2101.02347/) (2021)
- [A Spectral Method for Joint Community Detection and Orthogonal Group Synchronization](https://mlsanity.com/paper/2112.13199/) (2021)
- [ReSync: Riemannian Subgradient-based Robust Rotation Synchronization](https://mlsanity.com/paper/2305.15136/) (2023)
- [Robust Angular Synchronization via Directed Graph Neural Networks](https://mlsanity.com/paper/2310.05842/) (2023)
- [Multi-Frequency Joint Community Detection and Phase Synchronization](https://mlsanity.com/paper/2206.12276/) (2022)
- [Multi-Irreducible Spectral Synchronization for Robust Rotation Averaging](https://mlsanity.com/paper/2311.16544/) (2023)

## Abstract (arXiv)

We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise comparisons in multiple frequency channels. Inspired by harmonic retrieval in signal processing, we develop a simple yet efficient two-stage algorithm that leverages the multi-frequency information. We demonstrate in theory and practice that the proposed algorithm significantly outperforms state-of-the-art phase synchronization algorithms, at a mild computational costs incurred by using the extra frequency channels. We also extend our algorithmic framework to general synchronization problems over compact Lie groups.