caa a22 4500 445331666 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10208-011-9095-3 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9095-3 Representation Theoretic Patterns in Three-Dimensional Cryo-Electron Microscopy II—The Class Averaging Problem [Elektronische Daten] [Ronny Hadani, Amit Singer] In this paper we study the formal algebraic structure underlying the intrinsic classification algorithm, recently introduced in Singer et al. (SIAM J. Imaging Sci. 2011, accepted), for classifying noisy projection images of similar viewing directions in three-dimensional cryo-electron microscopy (cryo-EM). This preliminary classification is of fundamental importance in determining the three-dimensional structure of macromolecules from cryo-EM images. Inspecting this algebraic structure we obtain a conceptual explanation for the admissibility (correctness) of the algorithm and a proof of its numerical stability. The proof relies on studying the spectral properties of an integral operator of geometric origin on the two-dimensional sphere, called the localized parallel transport operator. Along the way, we continue to develop the representation theoretic set-up for three-dimensional cryo-EM that was initiated in Hadani and Singer (Ann. Math. 2010, accepted). SFoCM, 2011 Representation theory nationallicence Differential geometry nationallicence Spectral theory nationallicence Optimization theory nationallicence Mathematical biology nationallicence 3D cryo-electron microscopy nationallicence Hadani Ronny Department of Mathematics, University of Texas at Austin, C1200, Austin, USA aut Singer Amit Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, 08544-1000, Princeton, NJ, USA aut Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 589-616 1615-3375 11:5<589 2011 11 10208 https://doi.org/10.1007/s10208-011-9095-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9095-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hadani Ronny Department of Mathematics, University of Texas at Austin, C1200, Austin, USA aut NATIONALLICENCE 700 1- Singer Amit Department of Mathematics and PACM, Princeton University, Fine Hall, Washington Road, 08544-1000, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 589-616 1615-3375 11:5<589 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer