On the Method of Logarithmic Cumulants for Parametric Probability Density Function Estimation
On the Method of Logarithmic Cumulants for Parametric Probability Density Function Estimation
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DOI：
10.1109/tip.2013.2262285
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发表时间：
2013-10-01
影响因子：
10.6
通讯作者：
Zerubia, Josiane
中科院分区：
文献类型：
--
作者：
Krylov, Vladimir A.;Moser, Gabriele;Zerubia, Josiane
概率密度函数的参数估计是统计图像和信号处理区域中的主要步骤之一。在本文中，我们探讨了最近提出的对数累积物（MOLC）参数估计方法的几种属性和局限性，这是经典最大可能性（ML）和矩（MOM）方法的替代方法。我们为MOLC估计值的强一致性提供了一般条件，该估计代表了任何统计估计量的重要渐近特性。该结果可以证明MOLC估计值的强度一致性，以选择源自（但不限于）合成孔径雷达图像处理的广泛使用的分布家族。然后，我们得出了MOLC对我们选择中分布家族的样品适用性的分析条件。最后，我们进行了各种合成和真实的数据实验，以评估MOLC的比较性能，适用性和较小的样本性能，特别是对广义分布的γ和K家族。监督的图像分类实验被考虑用于医学超声和遥感SAR图像。获得的结果表明，MOLC是可行的，计算快速但不是普遍适用于MOM的替代品。当直接ML进近是不可行时，Molc变得特别有用。
Parameter estimation of probability density functions is one of the major steps in the area of statistical image and signal processing. In this paper we explore several 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 for a strong consistency of the MoLC estimates which represents an important asymptotic property of any statistical estimator. This result enables the demonstration of the strong consistency of MoLC estimates for a selection of widely used distribution families originating from (but not restricted to) synthetic aperture radar image processing. We then derive the analytical conditions of applicability of MoLC to samples for the 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 families of distributions. Supervised image classification experiments are considered for medical ultrasound and remote-sensing SAR imagery. The obtained results suggest that MoLC is a feasible and computationally fast yet not universally applicable alternative to MoM. MoLC becomes especially useful when the direct ML approach turns out to be unfeasible.