Ye, Ke; Lim, Lek-Heng Cohomology of cryo-electron microscopy. (English) Zbl 1377.92054 SIAM J. Appl. Algebra Geom. 1, No. 1, 507-535 (2017). Summary: 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 paper, we show that the basic premise of cryo-EM – patching together 2-dimensional projections to reconstruct a 3-dimensional object – is naturally one of Čech 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. Cited in 3 Documents MSC: 92C55 Biomedical imaging and signal processing 55N05 Čech types Keywords:oriented circle bundle; flat oriented circle bundle; co-cycle condition; impossible figure; classifying space; principal bundle; circular Radon transform PDFBibTeX XMLCite \textit{K. Ye} and \textit{L.-H. Lim}, SIAM J. Appl. Algebra Geom. 1, No. 1, 507--535 (2017; Zbl 1377.92054) Full Text: DOI arXiv References: [1] G. Ambartsoumian and P. Kuchment, {\it A range description for the planar circular Radon transform}, SIAM J. Math. Anal., 38 (2006), pp. 681-692, . · Zbl 1120.44003 [2] G. Ambartsoumian and P. Kuchment, {\it On the injectivity of the circular Radon transform arising in thermoacoustic tomography}, Inverse Problems, 21 (2005), pp. 473-485, . · Zbl 1072.44001 [3] S. R. Arridge, {\it Optical tomography in medical imaging}, Inverse Problems, 15 (1999), pp. R41-R93, . · Zbl 0926.35155 [4] S. R. Arridge and J. C. Hebbden, {\it Optical imaging in medicine: II. 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