The generalized method of moments for multi-reference alignment

This paper studies the application of generalized method moments (GMM) to multi-reference alignment (MRA): problem estimating a signal from its circularly-translated and noisy copies. We begin by proving that GMM estimator maintains asymptotic optimality for statistical models with group symmetry, including MRA. Then, we conduct comprehensive numerical study show substantially outperforms classical moments, whose MRA has been studied thoroughly in literature. also formulate estimate three-dimensional molecular structure using cryo-electron microscopy present results on simulated data.