Proper quaternion Gaussian graphical models

Alba Sloin*, Ami Wiesel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this paper, we extend Gaussian graphical models to proper quaternion Gaussian distributions. The properness assumption reduces the number of unknowns by a factor of four while graphical models reduce the number of degrees of freedom via sparsity. Each of the methods allows accurate estimation using a small number of samples. To enjoy both gains, we show that the proper quaternion Gaussian inverse covariance estimation problem is convex and has a closed form solution. We proceed to demonstrate that the additional sparsity constraints on the inverse covariance matrix also lead to a convex problem, and the optimizations can be efficiently solved by standard numerical methods. In the special but practical case of a chordal graph, we provide a closed form solution. We demonstrate the improved performance of our suggested estimators on both synthetic and real data.

Original languageAmerican English
Article number6880839
Pages (from-to)5487-5496
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number20
StatePublished - 15 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


  • Quaternions
  • chordal graphs
  • covariance estimation
  • graphical models


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