Disentangling orthogonal matrices

Teng Zhang, Amit Singer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)159-181
Number of pages23
JournalLinear Algebra and Its Applications
StatePublished - Jul 1 2017

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis
  • Algebra and Number Theory


  • Cryo-EM
  • Orthogonal Procrustes problem
  • SDP relaxation


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