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Parameter estimation for multivariate generalized Gaussian distributions

Pascal, Frédéric and Bombrun, Lionel and Tourneret, Jean-Yves and Berthoumieu, Yannick Parameter estimation for multivariate generalized Gaussian distributions. (2013) IEEE Transactions on Signal Processing, vol. 61 (n° 23). pp. 5960-5971. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2013.2282909

Abstract

Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention in signal and image processing applications. Considering the estimation issue of the MGGD parameters, the main contribution of this paper is to prove that the maximum likelihood estimator (MLE) of the scatter matrix exists and is unique up to a scalar factor, for a given shape parameter belonging to the interval [0,1]. Moreover, an estimation algorithm based on a Newton-Raphson recursion is proposed for computing the MLE of MGGD parameters. Various experiments conducted on synthetic and real data are presented to illustrate the theoretical derivations in terms of number of iterations and number of samples for different values of the shape parameter. The main conclusion of this work is that the parameters ofMGGDs can be estimated using the maximum likelihood principle with good performance.

Item Type:Article
Additional Information:Thanks to Institute of Electrical and Electronics Engineers editor. The definitive version is available at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6605599
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Nationale Supérieure d’Electronique, Informatique et Radiocommunications de Bordeaux - ENSEIRB (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Other partners > Ecole Supérieure d'Electricité - SUPELEC (FRANCE)
Other partners > Université de Bordeaux 1 (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
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Deposited By: Jean-yves TOURNERET
Deposited On:14 Apr 2014 12:49

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