2016Ye Cohomology

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Ye, K. & Lim, L. H. Cohomology of cryo-electron Microscopy Arxiv, 2016


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)-coe�cients. 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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