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arXiv · 1604.01319

Cohomology of Cryo-Electron Microscopy

Ke Ye·Lek-Heng Lim
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Abstract

The goal of cryo-electron microscopy (EM) is to reconstruct the 3-dimensional structure of a molecule from a collection of its 2-dimensional projected images. In this article, we show that the basic premise of cryo-EM --- patching together 2-dimensional projections to reconstruct a 3-dimensional object --- is naturally one of Cech cohomology with SO(2)-coefficients. We deduce that every cryo-EM reconstruction problem corresponds to an oriented circle bundle on a simplicial complex, allowing us to classify cryo-EM problems via principal bundles. In practice, the 2-dimensional images are noisy and a main task in cryo-EM is to denoise them. We will see how the aforementioned insights can be used towards this end.

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Ke Ye, Lek-Heng Lim. 2016-04-05. Cohomology of Cryo-Electron Microscopy. https://arxiv.org/abs/1604.01319

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