1:15 pm Wednesday, May 30, 2012
CVC Seminar: Orientation Determination by Categorical Optimization by
Itamar Gal (UT Austin) in ACE 4.304
Cryo-electron microscopy (cryo-EM) refers to a procedure in which the potential function of a molecule must be computed from a large set of extremely noisy X-Ray images which are taken from random, unknown viewing orientations. Orientation determination (i.e. the problem of determining these viewing orientations directly from the X-Ray data) is a fundamental problem in cryo-EM. Orientation determination can be formulated as a high-dimensional, non-convex optimization problem. Recently a new approach to solving the orientation determination problem was introduced by Singer and Shkolnisky, which has several advantages over the methods which are currently being used. This approach relies on the utilization of a certain geometric integral operator, called the common lines operator. The common lines operator provides a solution in the case where the potential function of the molecule is sufficiently generic, but cannot be applied to a molecule whose potential function admits symmetries. The operator approach was generalized to the case of symmetries by Gurevich, Hadani and Singer. This generalization leads to a re-characterization of the problem in terms of a certain algebra and canonically associated characters, or equivalently in terms of a certain algebraic variety with an associated set of points. This talk will give a brief review of cryo-EM and orientation determination, and then describe the mathematical framework in which the operator approach can be understood; first in the generic case, then in the case of symmetries. Submitted by
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