Disentangling Orthogonal Matrices

Keywords

Cryo-EM; Orthogonal Procrustes problem; SDP relaxation

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 naïve 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.

Publication Date

7-1-2017

Publication Title

Linear Algebra and Its Applications

Volume

524

Number of Pages

159-181

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.laa.2017.03.002

Socpus ID

85015645786 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85015645786

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