IDeAS Seminar: Optimal rates of estimation for the multi-reference alignment problem

How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal. These bounds show a striking dependence on the signal-to-noise ratio of the problem. If time permits, efficient recovery algorithms will also be shown.