On the MAP estimation in the context of elliptical distributions
Résumé
The purpose of this paper is to study the estimation problem of a multivariate elliptically symmetric random variable corrupted by a multivariate elliptically symmetric noise. In this study, the maximum a posteriori (MAP) approach is presented, extending recent works by Alecu et al. and Selesnick: (i) the estimation is performed in a multivariate context, (ii) the corrupting noise is not limited to be Gaussian. This paper also extends our previous work that dealt with the minimum mean square error (MMSE) approach. The MMSE is briefly recalled and the MAP is derived. Then the practical use of the MAP in a general setting is discussed and compared to that of the MMSE and of the Wiener estimator. Several examples illustrate the behaviors of these estimators and exhibit their performances.