EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium.
Ultramicroscopy. 2013 Feb;125:35-42. doi: 10.1016/j.ultramic.2012.10.001. Epub 2012 Oct 27.
Principal component analysis (PCA) noise filtering is a popular method to remove noise from experimental electron energy loss (EELS) spectrum images. Here, we investigate the statistical behaviour of this method by applying it on a simulated data set with realistic noise levels. This phantom data set provides access to the true values contained in the data set as well as to many different realizations of the noise. Using least squares fitting and parameter estimation theory, we demonstrate that even though the precision on the estimated parameters can be better as the Cramér-Rao lower bound, a significant bias is introduced which can alter the conclusions drawn from experimental data sets. The origin of this bias is in the incorrect retrieval of the principal loadings for noisy data. Using an expression for the bias and precision of the singular values from literature, we present an evaluation criterion for these singular values based on the noise level and the amount of information present in the data set. This criterion can help to judge when to avoid PCA noise filtering in practical situations. Further we show that constructing elemental maps of PCA noise filtered data using the background subtraction method, does not guarantee an increase in the signal to noise ratio due to correlation of the spectral data as a result of the filtering process.
主成分分析（PCA）噪声滤波是一种从实验电子能量损失（EELS）谱图像中去除噪声的常用方法。在这里，我们通过将其应用于具有真实噪声水平的模拟数据集来研究该方法的统计行为。该幻影数据集提供了对数据集内真实值的访问，以及对噪声的许多不同实现的访问。使用最小二乘拟合和参数估计理论，我们证明，即使估计参数的精度可以优于克拉美-罗下限，也会引入显著的偏差，从而改变从实验数据集得出的结论。这种偏差的来源在于对噪声数据的主载荷的不正确检索。使用文献中关于奇异值的偏差和精度的表达式，我们提出了一种基于噪声水平和数据集内信息量的这些奇异值的评估标准。该标准可以帮助判断在实际情况下何时避免 PCA 噪声滤波。此外，我们还表明，由于滤波过程中谱数据的相关性，使用背景扣除法构建 PCA 噪声滤波数据的元素图并不能保证信噪比的提高。
