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Disentangling orthogonal matrices

Author(s): Zhang, Teng; Singer, Amit

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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 naive 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. (C) 2017 Elsevier Inc. All rights reserved.
Publication Date: 1-Jul-2017
Electronic Publication Date: 9-Mar-2017
Citation: Zhang, Teng, Singer, Amit. (2017). Disentangling orthogonal matrices. LINEAR ALGEBRA AND ITS APPLICATIONS, 524 (159 - 181. doi:10.1016/j.laa.2017.03.002
DOI: doi:10.1016/j.laa.2017.03.002
ISSN: 0024-3795
EISSN: 1873-1856
Pages: 159 - 181
Type of Material: Journal Article
Version: Author's manuscript

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