A Tyler-Type Estimator of Location and Scatter Leveraging Riemannian Optimization
Antoine Collas, Florent Bouchard, Arnaud Breloy, Chenfang Ren, Guillaume Ginolhac, Jean Philippe Ovarlez
Abstract
We consider the problem of jointly estimating the location and scatter matrix of a Compound Gaussian distribution with unknown deterministic texture parameters. When the location is known, the Maximum Likelihood Estimator (MLE) of the scatter matrix corresponds to Tyler’s M-estimator, which can be computed using fixed point iterations. However, when the location is unknown, the joint estimation problem remains challenging since the associated standard fixed-point procedure to evaluate the solution may often diverge. In this paper, we propose a stable algorithm based on Riemannian optimization for this problem. Finally, numerical simulations show the good performance and usefulness of the proposed algorithm.
BibTeX
@inproceedings{icassp2021_atylertypeestima,
title = {A Tyler-Type Estimator of Location and Scatter Leveraging Riemannian Optimization},
author = {Antoine Collas and Florent Bouchard and Arnaud Breloy and Chenfang Ren and Guillaume Ginolhac and Jean Philippe Ovarlez},
booktitle = {ICASSP 2021},
year = {2021}
}