I will be talking about the recent paper https://arxiv.org/abs/1710.02793 which considers the problem of multireference alignment.
Multireference alignment refers to the problem of estimating a signal from its circularly translated copies in the presence of noise. Previous papers showed that if the translations are drawn from the uniform distribution, then the sample complexity of the problem scales as 1/SNR^3 in the low SNR regime. In the paper we show that the sample complexity for any aperiodic translation distribution scales as 1/SNR^2 in the low SNR regime. This rate is achieved by a simple spectral algorithm. I will explain how this algorithm works and how we guarantee this achieves the optimal rate of estimation using tools from information theory.