Résumé : How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts ? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. 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.
Joint work with Afonso Bandeira and Philippe Rigollet.
Lieu : Bâtiment 1R3, salle de conférence du premier étage (MIP)