Emanuel Ström: Multi-Reference alignment with Moment Constraints

Abstract:

Multi-reference alignment (MRA) is a statistical model for inference of an unknown signal given noisy, randomly shifted meaurements. A naive maximum likelihood approach typically does not preserve the power spectrum of the signal. In this project together with Vahid Shahverdi, we introduce a simple correction to the power spectrum. This results in a constrained maximum likelihood formulation, which we show is smooth in the infinite data limit, and whose critical points are analytically known. We compare this method to recently proposed alternatives, and show that it is competitive.