Speaker: Tamir Bendory
Title: Multi-reference alignment: Representation theory perspective, sparsity, and projection-based algorithms
Abstract: Multi-reference alignment (MRA) is the problem of recovering a signal from its multiple noisy copies, each acted upon by a random group element. MRA is mainly motivated by single-particle cryo-electron microscopy (cryo-EM): a leading technology to reconstruct biological molecular structures. In this talk, I will analyze the second moment of the MRA and cryo-EM models. First, I will show that in both models the second moment determines the signal up to a set of unitary matrices, whose dimension is governed by the decomposition of the space of signals into irreducible representations of the group. Second, I will present sparsity conditions under which a signal can be recovered from the second moment, implying that the sample complexity is proportional to the square of the variance of the noise. If time permits, I will introduce a new computational framework for cryo-EM that combines a sparse representation of the molecule with projection-based techniques used for phase retrieval in X-ray crystallography.