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Robust estimation analysis for signal and image processing

Abstract : One of the main challenges in radar processing is to identify a target hidden in a disturbance environment. To this end, the noise statistical properties, especially the ones of the disturbance covariance matrix, need to be determined. Under the Gaussian assumption, the latter is estimated by the sample covariance matrix (SCM) whose behavior is perfectly known. However, in many applications, such as, for instance, the modern high resolution radar systems, collected data exhibit a heterogeneous nature that cannot be adequately described by a Gaussian process. To overcome this problem, Complex Elliptically Symmetric distributions have been proposed since they can correctly model these data behavior. In this case, the SCM performs very poorly and M-estimators appear as a good alternative, 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. In this context, the contributions of this thesis are multiple. First, an original approach to analyze the statistical properties of M-estimators is proposed, revealing that the statistical properties of M-estimators can be approximately well described by a Wishart distribution. Thanks to these results, we go further and analyze the eigendecomposition of the covariance matrix. Depending on the application, the covariance matrix can exhibit a particular structure involving multiple eigenvalues containing the information of interest. We thus address various scenarios met in practice and propose robust procedures based on M- estimators. Furthermore, we study the robust signal detection problem. The statistical properties of various adaptive detection statistics built with M-estimators are analyzed. Finally, the last part deals with polarimetric synthetic aperture radar (PolSAR) image processing. In PolSAR imaging, a particular effect called speckle significantly degrades the image quality. In this thesis, we demonstrate how the new statistical properties of M-estimators can be exploited in order to build new despeckling techniques.
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Contributor : Frédéric Pascal <>
Submitted on : Saturday, February 29, 2020 - 12:08:55 PM
Last modification on : Friday, April 10, 2020 - 2:11:43 AM
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Gordana Draskovic. Robust estimation analysis for signal and image processing. Signal and Image Processing. Université Paris-Saclay - CentraleSupélec, 2019. English. ⟨tel-02494757⟩



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