ReSync: Riemannian Subgradient-based Robust Rotation Synchronization
This work addresses a specific problem in engineering applications, offering incremental improvements with theoretical backing.
The paper tackles the robust rotation synchronization problem by proposing ReSync, a Riemannian subgradient-based algorithm that recovers underlying rotations with strong theoretical guarantees, including local linear convergence to ground-truth rotations under random corruption settings.
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.