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IMA Data Science Seminar - Tamir Bendory
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.

Feb 7, 2023 01:25 PM in Central Time (US and Canada)

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Speakers

Tamir Bendory
Assistant Professor @Tel Aviv University
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.