Estimation From Quantized Gaussian Measurements: When and How to Use Dither
Estimation From Quantized Gaussian Measurements: When and How to Use Dither
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DOI：
10.1109/tsp.2019.2916046
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发表时间：
2018-11
影响因子：
5.4
通讯作者：
Joshua Rapp;R. Dawson;Vivek K Goyal
中科院分区：
文献类型：
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作者：
Joshua Rapp;R. Dawson;Vivek K Goyal
减法抖动是去除粗量化信号的量化噪声对信号的依赖性的一种有效方法。然而，从抖动测量的估计通常天真地应用样本均值或中值，即使当总噪声不能很好地用高斯分布或均匀分布描述时。我们表明，广义高斯分布近似描述减法抖动，量化的高斯信号的样本。此外，广义高斯拟合导致简单的估计顺序统计量的基础上，更复杂的最大似然估计，需要迭代求解器的性能相匹配。对于高斯和均匀噪声的非平凡和，基于阶矩的估计优于样本均值和中值。广义高斯近似的附加分析产生用于确定何时以及如何将抖动应用于量化测量的经验法则。具体来说，我们发现减法抖动是有益的高斯标准偏差和量化间隔长度之间的比率大致小于三分之一。当该比率也大于0.822/$K^{{\text{0.930}$的测量数$K>\text{20}$时，我们提出的估计量比中间值更有效。
Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than one-third. When that ratio is also greater than 0.822/$K^{{\text{0.930}}}$ for the number of measurements $K>\text{20}$, estimators we present are more efficient than the midrange.