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Table 2 Extracted variances (\(\lambda\)) and “true” variances (\(\lambda ^*\)) of the noisy and true synthetic dataset

From: Optimal principal component analysis of STEM XEDS spectrum images

Component \(\lambda\) \(\lambda ^*\) \(\frac {\lambda ^*}{\sigma ^2}\) Retrievable
1 1228 1214 43.2
2 938.3 906.4 32.3
3 509.2 482.2 17.2
4 444.7 422.8 15.1
5 273.8 214.6 7.65
6 94.04 40.05 1.43
7 83.53 6.571 0.234
8 81.98 0.5804 0.0207
9 80.61 0.04119 1.47e−3
10 78.30 5.13e−6 2.01e−7
11 78.28 1.63e−6 6.43e−8
  1. The level of homoscedastic noise \(\sigma ^2\) is 28.07. According the Nadler model [33], a component is retrievable if the value in the 4th column exceeds \(\sqrt{\frac {n}{m}}\), which is 0.245 for the number of channels \(n=1200\) and the number of pixels \(m=19920\)