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
Main Authors: Collas, A., Bouchard, F., Breloy, A., Ren, C., Ginolhac, G., Ovarlez, J.-P.
Format: Conference Proceeding
Language:English
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