id: 06003184
dt: j
an: 06003184
au: Hadani, Ronny; Singer, Amit
ti: Representation theoretic patterns in three-dimensional cryo-electron
    microscopy. II: The class averaging problem.
so: Found. Comput. Math. 11, No. 5, 589-616 (2011).
py: 2011
pu: Springer-Verlag, New York, NY
la: EN
cc: 
ut: differential geometry; spectral theory; optimization theory; mathematical
    biology; 3D cryo-electron microscopy
ci: Zbl 1216.92046; Zbl 1227.92036
li: doi:10.1007/s10208-011-9095-3
ab: Summary: We study the formal algebraic structure underlying the intrinsic
    classification algorithm, recently introduced by {\it A. Singer} et al.
    [SIAM J. Imaging Sci. 4, No. 2, 723‒759 (2011; Zbl 1216.92046)], 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 that way, we continue to develop the representation
    theoretic set-up for three-dimensional cryo-EM that was initiated by
    the authors in part I of this paper [Ann. Math. (2) 174, No. 2,
    1219‒1241 (2011; Zbl 1227.92036)].
rv: