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On the Method of Logarithmic Cumulants for Parametric Probability Density Function Estimation

Vladimir Krylov 1 Gabriele Moser 2 Sebastiano B. Serpico 2 Josiane Zerubia 1 
1 ARIANA - Inverse problems in earth monitoring
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : Parameter estimation of probability density functions is one of the major steps in the mainframe of statistical image and signal processing. In this report we explore the properties and limitations of the recently proposed method of logarithmic cumulants (MoLC) parameter estimation approach which is an alternative to the classical maximum likelihood (ML) and method of moments (MoM) approaches. We derive the general sufficient condition of strong consistency of MoLC estimates which represents an important asymptotic property of any statistical estimator. With its help we demonstrate the strong consistency of MoLC estimates for a selection of widely used distribution families originating (but not restricted to) synthetic aperture radar (SAR) image processing. We then derive the analytical conditions of applicability of MoLC to samples generated from several distribution families in our selection. Finally, we conduct various synthetic and real data experiments to assess the comparative properties, applicability and small sample performance of MoLC notably for the generalized gamma and K family of distributions. Supervised image classification experiments are considered for medical ultrasound and remote sensing SAR imagery. The obtained results suggest MoLC to be a feasible yet not universally applicable alternative to MoM that can be considered when the direct ML approach turns out to be unfeasible.
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https://hal.inria.fr/inria-00605274
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Submitted on : Tuesday, August 16, 2011 - 4:43:16 PM
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Vladimir Krylov, Gabriele Moser, Sebastiano B. Serpico, Josiane Zerubia. On the Method of Logarithmic Cumulants for Parametric Probability Density Function Estimation. [Research Report] RR-7666, INRIA. 2011. ⟨inria-00605274v2⟩

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