seminarios en cmat.edu.uy seminarios en cmat.edu.uy
Jue Dic 13 21:00:25 -03 2018


Viernes 14 de diciembre, de 10:30 AM a 11:30 AM, Salón de Seminario - Centro de Matemática

Expositor: Gordana Drasković, Université Paris-Sud

Título: New insights into the statistical properties of M-estimators with application to signal detection and PolSAR image denoising.

Resumen: In signal processing applications, the knowledge of scatter matrix is of crucial importance. It arises in diverse applications such as filtering, detection, estimation or classification. Generally, in most of signal processing methods the data can be locally modelled by a multivariate zero-mean circular Gaussian stochastic process, which is completely determined by its covariance matrix. In that case, the classical covariance matrix estimator is the sample covariance matrix (SCM) whose behavior is perfectly known. Indeed, it follows the well-known Wishart distribution. Nevertheless, the complex normality sometimes presents a poor approximation of underlying physics. An alternative has been proposed by introducing elliptical distributions, namely the Complex Elliptically Symmetric distributions. In this context the SCM can perform very poorly and M-estimators appear as very interesting candidates, mainly due to their flexibility to the statistical model and their robustness to outliers and/or missing data. However, the behavior of such estimators still remains unclear and not well understood since they are described by fixed-point equations that make their statistical analysis very difficult. To fill this gap, the main contribution of this work is to prove that these estimators distribution is more accurately described by a Wishart distribution than by the classical asymptotic Gaussian approximation. These results can be of great interest in a wide range of signal processing problems such as adaptive detection problems, polarimetric SAR images restoration, target detection, clustering etc.


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