Properties of the Conditional Mean Estimator in Poisson Noise
Properties of the Conditional Mean Estimator in Poisson Noise
复制标题
泊松噪声条件均值估计器的性质
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
H. Poor
中科院分区：
文献类型：
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作者：
Alex Dytso;H. Poor
本文考虑泊松噪声中随机变量的估计问题。具体地说，本文研究了条件均值估计量随尺度系数、暗电流参数、输入随机变量分布和信道实现的变化特性，建立了关于尺度系数和暗电流的几个导数恒等式。例如，它示出的条件均值估计相对于暗电流参数的导数是成比例的条件方差。在此基础上，提出了一种评分函数，得到了条件期望的Tweedy型公式，并给出了条件期望分布的几个正则性条件。例如，它表明，条件均值估计唯一地确定输入分布。此外，它表明，如果条件期望是接近于一个线性函数的均方误差，那么输入分布是近似伽玛的Lévy度量。
This paper considers estimation of a random variable in Poisson noise. Specifically, the paper focuses on properties of the conditional mean estimator as a function of the scaling coefficient, the dark current parameter, the distribution of the input random variable and channel realizations.With respect to the scaling coefficient and the dark current, several identities in terms of derivatives are established. For example, it is shown that the derivative of the conditional mean estimator with respect to the dark current parameter is proportional to the conditional variance. Moreover, a version of score function is proposed and a Tweedy-like formula for the conditional expectation is recovered.With respect to the distribution, several regularity conditions are shown. For instance, it is shown that the conditional mean estimator uniquely determines the input distribution. Moreover, it is shown that if the conditional expectation is close to a linear function in the mean squared error, then the input distribution is approximately gamma in the Lévy metric.
泊松噪声的估计：条件均值估计器的属性
影响因子：
2.5
作者：
Dytso, Alex;Vincent Poor, H.
通讯作者：
Vincent Poor, H.
影响因子：
2.5
作者：
Calmon, Flavio du Pin;Polyanskiy, Yury;Wu, Yihong
通讯作者：
Wu, Yihong