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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 \(m=19920\)
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