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arXiv · 1506.02217

Disentangling Orthogonal Matrices

Teng Zhang·Amit Singer
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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.

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Teng Zhang, Amit Singer. 2015-06-07. Disentangling Orthogonal Matrices. https://arxiv.org/abs/1506.02217

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