Robust Group Synchronization via Quadratic Programming

TL;DR

This paper introduces DESC, a quadratic programming approach for robust group synchronization that accurately estimates corruption levels, tolerates high corruption, and does not need good initializations, demonstrated on rotation averaging tasks.

Contribution

The paper presents a novel quadratic programming formulation for estimating corruption in group synchronization, extending to other algebraic structures and achieving exact recovery under mild conditions.

Findings

Tolerates corruption up to the information-theoretic limit

Does not require good initial estimates

Achieves exact recovery of corruption levels under mild conditions

Abstract

We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem. Our objective function exploits the cycle consistency of the group and we thus refer to our method as detection and estimation of structural consistency (DESC). This general framework can be extended to other algebraic and geometric structures. Our formulation has the following advantages: it can tolerate corruption as high as the information-theoretic bound, it does not require a good initialization for the estimates of group elements, it has a simple interpretation, and under some mild conditions the global minimum of our objective function exactly recovers the corruption levels. We demonstrate the competitive accuracy of our approach on both synthetic and real data experiments of rotation averaging.