Disentangling Orthogonal Matrices
Optimization and Control
2017-03-07 v4
Abstract
Motivated by a certain molecular reconstruction methodology in cryo-electron microscopy, we consider the problem of solving a linear system with two unknown orthogonal matrices, which is a generalization of the well-known orthogonal Procrustes problem. We propose an algorithm based on a semi-definite programming (SDP) relaxation, and give a theoretical guarantee for its performance. Both theoretically and empirically, the proposed algorithm performs better than the na\"{i}ve approach of solving the linear system directly without the orthogonal constraints. We also consider the generalization to linear systems with more than two unknown orthogonal matrices.
Cite
@article{arxiv.1506.02217,
title = {Disentangling Orthogonal Matrices},
author = {Teng Zhang and Amit Singer},
journal= {arXiv preprint arXiv:1506.02217},
year = {2017}
}