A Tyler-Type Estimator of Location and Scatter Leveraging Riemannian Optimization

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...

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Bibliographic Details
Published inICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 5160 - 5164
Main Authors Collas, A., Bouchard, F., Breloy, A., Ren, C., Ginolhac, G., Ovarlez, J.-P.
Format Conference Proceeding
LanguageEnglish
Published IEEE 06.06.2021
Subjects
Compound Gaussian
Compounds
Gaussian distribution
Manifolds
Maximum likelihood estimation
Numerical simulation
Riemannian optimization
Robust location and scatter estimation
Signal processing
Signal processing algorithms
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Summary: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.
ISSN:2379-190X
DOI:10.1109/ICASSP39728.2021.9414974