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Conference Papers Year : 2022

A Convex Formulation for the Robust Estimation of Multivariate Exponential Power Models

Abstract

The multivariate power exponential (MEP) distribution can model a broad range of signals. In noisy scenarios, the robust estimation of the MEP parameters has been traditionally addressed by a fixed-point approach associated with a nonconvex optimization problem. Establishing convergence properties for this approach when the distribution mean is unknown is still an open problem. As an alternative, this paper presents a novel convex formulation for robustly estimating MEP parameters in the presence of multiplicative perturbations. The proposed approach is grounded on a re-parametrization of the original likelihood function in a way that ensures convexity. We also show that this property is preserved for several typical regularization functions. Compared with the robust Tyler’s estimator, the proposed method shows a more accurate precision matrix estimation, with similar mean and covariance estimation performance.
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Dates and versions

hal-03763278 , version 1 (29-08-2022)

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Nora Leïla Ouzir, Jean-Christophe Pesquet, Frédéric Pascal. A Convex Formulation for the Robust Estimation of Multivariate Exponential Power Models. 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022), May 2022, Singapore, France. pp.5772-5776, ⟨10.1109/ICASSP43922.2022.9747354⟩. ⟨hal-03763278⟩
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