11:00 am Wednesday, November 3, 2010
Mathematical Physics Seminar : Representation theoretic patterns in three dimensional cryo-electron microscopy: generalized paradigm by Ronny Hadani (UT Austin) in RLM 12.166
Three dimensional cryo-electron microscopy (3D cryo-EM, for short) is the problem of determining the three dimensional structure of a large molecule from the set of images, taken by an electron microscope, of randomly oriented and positioned identical molecular particles which are frozen in a thin layer of ice. A solution to this problem is of particular interest, since it promises to be an entirely general technique which does not require crystallization or other special preparation stages. Present approaches to the problem fail with particles that are too small, cryo-EM images that are too noisy or at resolutions where the signal-to-noise ratio becomes too small. In my talk, I will describe an algorithm for the solution of the 3D cryo-EM problem, generalizing and improving upon the intrinsic reconstitution algorithm, described in my previous talk on this subject. The algorithm uses a novel non-linear optimization paradigm, based on representation theory, that exhibits remarkable stability to noise and is general enough to account for the case of molecules with symmetries. My main goal is to explain the underlying mathematical structures behind this new paradigm and to give a conceptual explanation for the admissibility (correctness) and the numerical stability of the algorithm. If time permits, I will explain a generalization of the algorithm to the case of molecules with symmetries, using invariant theory with respect to finite subgroups in SO(3). THE TALK WILL BE COMPLETELY SELF CONTAINED. This work is part of a joint project with Amit Singer (Princeton), Shamgar Gurevich (Wisconsin Madison), Yoel Shkolnisky (Tel-Aviv University) and Fred Sigworth (Yale).
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