J. Eur. Opt. Society-Rapid Publ. 21, 13( 2025) 149
Fig
. 8.( a) Recovered noisy spectrogram;( b) Spectrogram obtained by PCA method;( c) Spectrogram processed by PCA-NLM method;( d) Relationship between current magnitude and signal intensity.
signal in the third principal component was caused mainly by the difference in the intensity from the two characteristic peaks of the potassium signals under different current intensities. The fourth to sixth principal components corresponded to random noise, and their contribution rates were even lower; thus, they were not considered in the potassium spectral analysis.
To analyse the intensity relationship of the extracted signals, the noise signals and the potassium signals in the six groups of hybrid data needed to be separated and restored using the specific principal components and their corresponding projection values for linear superposition. Figure 8a shows the noise spectrum of the potassium lamp recovered by the first, fourth, fifth, and sixth principal components at 6 mA. Figure 8b displays the potassium lamp spectrum recovered through PCA method under a current condition of 6 mA. The analysis results indicate that the PCA method can effectively isolate the potassium lamp signal from complex background signals, but the extracted spectral components still contain a certain amount of residual noise. Based on this, Figure 8c presents the potassium lamp spectrum further recovered by the PCA combined with NLM denoising algorithm. The results demonstrate that the PCA-NLM method can significantly further reduce the noise components in the potassium lamp spectrum, enhancing the purity of the spectrum and improving the signal-to-noise ratio( SNR).
To illustrate the effectiveness of the PCA-NLM algorithm for signal extraction, the SNR of the potassium spectrum was defined as follows:
SNR ¼ S N; ð10Þ
where S is the potassium signal intensity and N is the atmospheric background intensity. Based on the restored potassium spectral intensity at 6 mA shown in Figure 8c and compared with the data in Figure 6, the SNR of the potassium signal in the original measurement results was 0.1310; these results indicated that a weak potassium signal was successfully extracted at this low SNR. The SNR of the restored potassium spectrum in Figure 8c was 16.9019; these results further illustrated the effectiveness of the PCA-NLM method.
Although the second principal component and the third principal component both contained potassium signals, since the contribution rates of the two were different by an order of magnitude, the projection value of the second principal component S 2j( j = 1,2,3... 6) could be used to characterize the intensities of the potassium signals in the six groups of mixed data. Linear regression was performed on S 2j and the potassium lamp current, and the results are shown in Figure 8c. The intensity of the restored potassium lamp signal was linearly related to the corresponding current; here, the correlation coefficient was