离散参数随机过程非线性滤波的稳健性及其应用(一)

ROBUSTNESS OF NONLINEAR FILTERING FOR DISCRETE PARAMETER STOCHASTIC PROCESSES AND ITS APPLICATIONS(Ⅰ)

离散参数随机过程非线性滤波的一种重要类型是次序统计滤波器 (OSF) ,而研究次序统计滤波器的有效途径则是考察次序统计量的稳健性性质 .作者通过概率分布距离空间上统计量泛函的弱连续性及统计量泛函的影响函数 ,研究次序统计量的稳健性性质 ,考察在各种概率分布类型下中值滤波器与最大值滤波器的低通、带通特性 。

The Order Statistic Filter (OSF) is a basic class of nonlinear filtering for discrete parameter stochastic processes. Its robustness has important applications in image processing. The authors study robustness of order statistic using weak continuity and influence function of statistic functional which is defined on the probability distribution distance space, and apply the properties of lowpass and bandpass to document image processing for the Median Order Statistic Filter (MedOSF) and the Maximum Order Statistic Filter (MaxOSF) respectively.