Speaker
Description
In 1980, Zvi Kam introduced an autocorrelation-based approach to cryo-electron microscopy (cryo-EM) single particle reconstruction, in which moments of the 2D images are computed and the 3D molecule is recovered by solving a polynomial system of equations. Recently, the method has also been used in X-ray free electron laser (XFEL) imaging.
This talk addresses important challenges in applying Kam’s method. Drawing on invariant theory and tensor decomposition, we find the first provable solver for recovering the 3D molecule from the moments of the 2D images, for the setting of uniformly-distributed viewing angles. In XFEL (where the uniformity assumption holds), experiments show numerical stability and a speed-up over existing solvers by orders of magnitude. Additionally, we extend autocorrelation analysis to include an unknown, non-uniform distribution of viewing angles, which is the relevant case for cryo-EM. Rather unexpectedly, for referred orientations in cryo-EM, significantly fewer images are required than for the uniform distribution case in XFEL. A covariance-based non-convex optimization scheme for cryo-EM reconstruction is presented.
