Graduate Student Seminar: S^1 synchronization on grids, Speaker: Shuangping Li

Abstract: Group synchronization is a set of problems where the goal is to estimate unknown group elements (\theta_v)_{v\in V} associated to the vertices of a graph G=(V,E), given noisy relative observations on edges of the graph. This model has various applications in computer vision, community detection and other fields. We focus on the case when the group is the 2D rotation group S^1 and the graph is the 3 dimensional lattice, and consider the weak recovery problem: for two far away vertices u and v, can we estimate \theta_v^{-1}\theta_u better than random guessing? Prior methods solve this problem for large enough signal-to-noise ratio (SNR) under perfect knowledge of the SNR. We present a more robust multi-scale algorithm that establishes similar results without knowledge of the SNR. This is joint work with Allan Sly.