Harmonic Analysis and Signal Processing Seminar
Reference Free Cryo-EM Structure Determination
through Eigenvectors of
Department of Mathematics
Wednesday, March 25, 2009, 3:30pm, WWH 201
The goal in Cryo-EM structure determination is to reconstruct 3D
macromolecular structures from their noisy projections, taken by an
microscope at unknown random orientations. Resolving the Cryo-EM problem
of great scientific importance, as the method is applicable to essentially
all macromolecules, as opposed to other existing methods such as
crystallography. Since almost all large proteins have not yet been
crystallized for 3D X-ray crystallography, Cryo-EM seems the most
alternative, once its associated mathematical challenges are solved.
In this talk, we present an extremely efficient and robust algorithm that
successfully recovers the projection angles in a globally consistent
The key idea of the algorithm is designing a sparse operator defined on
projection data, whose eigenvectors reveal the orientation of each
projection. Such an operator is constructed by utilizing the geometry
induced on Fourier space by the projection-slice theorem. The presented
algorithm is direct (as opposed to iterative refinement schemes), does not
require any prior model for the reconstructed object, and shown to have
favorable computational and numerical properties. Moreover, our algorithm
does not impose any assumption on the distribution of the projection
orientations. Physically, this means that the algorithm successfully
reconstructs molecules that have unknown spatial preference.
No prior knowledge of tomography, electron microscopy, or spectral graph
theory is assumed.
Joint work with Amit Singer, Ronald Coifman and Fred Sigworth.