# Research on an Ultraviolet Spectral Denoising Algorithm Based on the Improved SVD Method
## 4 Experimentation and Evaluation
### Denoising Experiments for Each Concentration Gradient of \(So_{2}\)  
To further validate the denoising effectiveness of the algorithm on measured spectra, a UV absorption spectroscopy-based SO\({}_{2}\) detection platform was established. This platform was equipped with a setup designed for SO\({}_{2}\) analysis. We meticulously prepared five sets of SO\({}_{2}\) test samples, each with concentrations of 1, 2, 5, 10, and 20 \(\mu\)L/L. A schematic of the experimental testing platform is depicted in Figure 8.  
Figure 8: Testing platform.  
Figure 7: RMSE after denoising.  
In the course of the experiments, a Bwtek Quest X-ray spectrometer and a HAMMA-MATSU L9455-11 scintillation xenon lamp were utilized. Single-mode optical fibers, selected for their optical transmission efficiency of at least 80% within the 200 nm to 400 nm wavelength range, were employed for optical transmission. The gas absorption cell, featuring an optical path length of 0.85 m, incorporated several concave mirrors coated with a high-reflectivity aluminum film. The inner wall of the cell was lined with a Teflon film to effectively mitigate gas adsorption effects. The UV light emitted by the xenon lamp was guided through the single-mode optical fiber and directed into the gas absorber cell using the collimating mirror. Within the gas absorption cell, the UV light thoroughly interacted with the SO\({}_{2}\) gas before being directed to the spectrometer via the focusing mirror. The spectrometer was connected to a computer, which further analyzed and processed the acquired spectral data. The high-reflectivity concave mirrors used in the experiments were integrated into the back of the flange, and the microspectrometer, xenon lamp, single-mode fiber optic, and PC processing terminal were integrated into the portable toolbox, as illustrated in Figure 9.  
Figure 9: Hardware equipment used in the experiment. (**a**) Gas absorption cells and portable spectral data acquisition box; (**b**) Highly reflective concave mirrors; (**c**) Internal optical pathway schematic.  
Spectral data for SO\({}_{2}\) at five different concentrations were subjected to noise reduction using three distinct methods: the algorithm proposed in this paper, wavelet transform, and SVDS. Following the Beer-Lambert law, absorbance is directly proportional to gas concentration, taking into account the absorption coefficient and optical path length. Similarly, in the frequency domain, attributes such as the maximum magnitude following FFT are also proportionate to gas concentration. Figure 10 illustrates that the UV absorption spectra of SO\({}_{2}\) at varying concentrations, after processing with the algorithm presented in this paper, display a well-defined distribution of absorption peaks and consistent frequency domain characteristics.  
To compare the performance difference between the improved SVD denoising algorithm proposed in this paper and other denoising methods, line curves depicting the relationship between the FFT values of the UV differential spectra and the SO\({}_{2}\) gas concentration after various denoising methods were fitted, as illustrated in Figure 11.  
Figure 11: Goodness of the linear regression fits. (**a**) Original signal: 0.936; (**b**) Improved SVD: 0.997; (**c**) Wavelet transform: 0.995; (**d**) SVDS: 0.956.  
Figure 10: UV difference spectra of SO\({}_{2}\) concentration after denoising.  
The figure above illustrates that, following the improved SVD processing, the line fit of concentration to the FFT eigenvalues surpasses the performance of both the wavelet transform denoising algorithm and the singular value difference spectral denoising algorithm processing. Moreover, the determination coefficient is enhanced from 0.93627 to 0.99735 for the original data.