ReSync: Riemannian Subgradient-based Robust Rotation Synchronization

TL;DR

ReSync is a novel Riemannian subgradient algorithm designed for robust rotation synchronization, providing strong theoretical guarantees and demonstrating effective convergence and performance in practical scenarios.

Contribution

This paper introduces ReSync, a new algorithm with theoretical convergence guarantees for robust rotation synchronization on the rotation group.

Findings

ReSync converges linearly to the ground-truth rotations.

The initialization procedure effectively starts within a local region around the true rotations.

Experimental results confirm the effectiveness of ReSync.

Abstract

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims at recovering the underlying rotations directly. We provide strong theoretical guarantees for ReSync under the random corruption setting. Specifically, we first show that the initialization procedure of ReSync yields a proper initial point that lies in a local region around the ground-truth rotations. We next establish the weak sharpness property of the aforementioned formulation and then utilize this property to derive the local linear convergence of ReSync to the ground-truth rotations. By combining these guarantees, we conclude that ReSync converges linearly to the ground-truth rotations under appropriate conditions. Experiment results demonstrate the effectiveness of ReSync.