Seminar: Machine Learning Seminar
Multi-reference alignment: Representation theory perspective, sparsity, and projection-based algorithms
The problem of multi-reference alignment (MRA) involves retrieving a signal from multiple copies that have been corrupted by noise and transformed by a random group element. MRA is of particular interest in the context of single-particle cryo-electron microscopy (cryo-EM), a prominent technique used to reconstruct biological molecular structures. During this talk, I will examine the second moment of both MRA and cryo-EM models. Firstly, I will demonstrate that the second moment can determine the signal up to a set of unitary matrices, which depend on the decomposition of the signal space into irreducible representations of the group. Secondly, I will outline the conditions of sparsity that enable a signal to 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 also introduce a novel computational framework for cryo-EM that utilizes a sparse representation of the molecule along with projection-based methods.
Tamir Bendory is an Assistant Professor of Electrical Engineering at Tel Aviv University. His current research interests include theoretical and computational aspects of data science and developing computational methods for structural biology.