论文标题
向量泊松通道：条件平均估计器的线性
The Vector Poisson Channel: On the Linearity of the Conditional Mean Estimator
论文作者
论文摘要
这项工作研究了矢量泊松噪声中条件平均估计器的特性。主要重点是研究诱导条件平均估计量线性的先前分布条件。本文由两个主要结果组成。第一个结果表明，诱导条件均值估计器线性的唯一分布是产品伽马分布。此外，结果表明，当泊松噪声的暗电流参数非零时，条件均值估计器不能是线性的。第二个结果对第一个结果产生了定量的完善。具体而言，可以表明，如果条件平均值估计器在平方误差方面接近线性，则先前的分布必须以其特征函数的范围接近乘积伽马分布。最后，将结果与其高斯对应物进行比较。
This work studies properties of the conditional mean estimator in vector Poisson noise. The main emphasis is to study conditions on prior distributions that induce linearity of the conditional mean estimator. The paper consists of two main results. The first result shows that the only distribution that induces the linearity of the conditional mean estimator is a product gamma distribution. Moreover, it is shown that the conditional mean estimator cannot be linear when the dark current parameter of the Poisson noise is non-zero. The second result produces a quantitative refinement of the first result. Specifically, it is shown that if the conditional mean estimator is close to linear in a mean squared error sense, then the prior distribution must be close to a product gamma distribution in terms of their characteristic functions. Finally, the results are compared to their Gaussian counterparts.
