The problem of averaging symmetric positive-definite (SPD) matrices arises for example in medical imaging (denoising and segmentation tasks in Diffusion Tensor Imaging), mechanics (elasticity tensor computation), and in video tracking and radar detection tasks. We will review recent advances in iterative methods that converge to the SPD geometric mean (namely the least-squares mean in the sense of the so-called affine-invariant metric), and in methods that approach it using limited resources.

This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .

Authors:

Pierre-Antoine Absil (University of Louvain)

Yuan Xinru (Florida State University)

Kyle Gallivan (Florida State University)

Estelle Massart (UCLouvain)

Julien Hendrickx (UCLouvain)

Keywords:

nonlinear optimization, numerical linear algebra