Angular Synchronization by Eigenvectors and Semidefinite Programming: Analysis and Application to Class Averaging in Cryo-Electron Microscopy
Year: 2009
Type: preprint
Abstract: . The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles θ1,..., θn from m noisy measurements of their offsets θi − θj mod 2π. Of particular interest is angle recovery in the presence of many outlier measurements that are uniformly distributed in [0,2π) and carry no information on the true offsets. We introduce an efficient recovery algorithm for the unknown angles from the top eigenvector of a specially designed Hermitian matrix. The eigenvector method is extremely stable and succeeds even when the number of outliers is exceedingly large. For example, we successfully estimate n = 400 angles from a full set of m = `400 ´ offset measurements of which 90 % are outliers in less than a second 2 on a commercial laptop. We use random matrix theory to prove that the eigenvector method q gives
Source: arXiv (Cornell University)
Authors: Amit Singer, Yoel Shkolnisky
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2981311553