On Computation of Approximate Joint Block-Diagonalization Using Ordinary AJD

  • Petr Tichavský
  • Arie Yeredor
  • Zbyněk Koldovský
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7191)

Abstract

Approximate joint block diagonalization (AJBD) of a set of matrices has applications in blind source separation, e.g., when the signal mixtures contain mutually independent subspaces of dimension higher than one. The main message of this paper is that certain ordinary approximate joint diagonalization (AJD) methods (which were originally derived for “degenerate” subspaces of dimension 1) can also be used successfully for AJBD, but not all are suitable equally well. In particular, we prove that when the set is exactly jointly block-diagonalizable, perfect block-diagonalization is attainable by the recently proposed AJD algorithm “U-WEDGE” (uniformly weighted exhaustive diagonalization with Gaussian iteration) - but this basic consistency property is not shared by some other popular AJD algorithms. In addition, we show using simulation, that in the more general noisy case, the subspace identification accuracy of U-WEDGE compares favorably to competitors.

Keywords

Blind Source Separation Angular Error Blind Separation Unperturbed Case Average Angular Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Petr Tichavský
    • 1
    • 3
  • Arie Yeredor
    • 2
  • Zbyněk Koldovský
    • 1
    • 3
  1. 1.Institute of Information Theory and AutomationPraha 8Czech Republic
  2. 2.Dept. of Electrical Engineering - Systems, School of Electrical EngineeringTel-Aviv UniversityTel-AvivIsrael
  3. 3.Faculty of Mechatronic and Interdisciplinary StudiesTechnical University of LiberecLiberecCzech Republic

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