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Averaging Symmetric Positive-Definite Matrices

In: Handbook of Variational Methods for Nonlinear Geometric Data

Author

Listed:
  • Xinru Yuan

    (Florida State University, Department of Mathematics)

  • Wen Huang

    (Xiamen University, School of Mathematical Sciences)

  • Pierre-Antoine Absil

    (Université catholique de Louvain, Department of Mathematical Engineering, ICTEAM Institute)

  • Kyle A. Gallivan

    (Florida State University, Department of Mathematics)

Abstract

Symmetric positive definite (SPD) matrices have become fundamental computational objects in many areas, such as medical imaging, radar signal processing, and mechanics. For the purpose of denoising, resampling, clustering or classifying data, it is often of interest to average a collection of symmetric positive definite matrices. This paper reviews and proposes different averaging techniques for symmetric positive definite matrices that are based on Riemannian optimization concepts.

Suggested Citation

  • Xinru Yuan & Wen Huang & Pierre-Antoine Absil & Kyle A. Gallivan, 2020. "Averaging Symmetric Positive-Definite Matrices," Springer Books, in: Philipp Grohs & Martin Holler & Andreas Weinmann (ed.), Handbook of Variational Methods for Nonlinear Geometric Data, chapter 0, pages 555-575, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-31351-7_20
    DOI: 10.1007/978-3-030-31351-7_20
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