Tamir Bendory: Group orbit recovery: Theory, algorithms, and applications

Abstract: The group orbit recovery problem seeks to estimate the orbit of a signal from multiple noisy observations, each transformed by a random group element. These models can be viewed as Gaussian mixture models whose centers are structured by group actions. Motivated by applications in modern structural biology, particularly single-particle cryo-electron microscopy (cryo-EM), we focus on the notoriously challenging high-noise regime.

The talk will cover two complementary aspects of orbit recovery:

1. Fundamental limits. We analyze the sample complexity and stability of orbit recovery, revealing deep connections between information-theoretic limits and the underlying algebraic structure of the group action.
2. Algorithms in the high-noise regime. We study the behavior of the expectation-maximization algorithm under high noise, explaining why it can become exceedingly slow, even in the vicinity of the true solution. We then present new algorithms that achieve the maximum-likelihood estimator significantly faster than EM, making large-scale orbit recovery problems substantially more practical.