Mathematics Colloquia and Seminars

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Description

We discuss some of the challenges in orbit recovery, the problem of determining a signal corrupted by an unknown group action in addition to noise. In particular, structure determination in cryogenic electron microscopy represents an orbit recovery problem of particular interest in the biological sciences. Due to structure determination’s difficulty, many simpler models have been developed including multi-reference alignment. Recently, powerful methods from algebraic geometry have given promising results, however many are information theoretic in nature or run with unknown complexity. We give a polynomial-time algorithm that can recover the orbit of a generic signal in dihedral and projected multi-reference alignment when the dimension is a power of two. We’ll spend a significant proportion of the talk discussing the tools developed and context of the problem so it is accessible to a general audience.