Denoising method based on an improved discrete wavelet transform

Laser-induced breakdown spectroscopy (LIBS) is susceptible to interference from factors such as ambient light, detector noise, and bremsstrahlung radiation, which can compromise the accurate identification of weak signals and reduce analytical accuracy. To mitigate the impact of noise, this study proposes a criterion for determining the optimal decomposition level of discrete wavelet transform (DWT) based on wavelet transform, Nyquist sampling rate, and entropy theory. A novel thresholding function, to our knowledge, and a threshold correction model, which is dependent on the decomposition level (DL), are developed. Denoising experiments were performed on the measured weak signal spectra of sulfur-containing aerosols. The results demonstrate that, compared to traditional soft and hard thresholding methods, the use of the proposed thresholding function yields a maximum improvement in signal-to-noise ratio (SNR) by 77%, while the root-mean-square error (RMSE) has been reduced by up to 55%. After applying this method, the limit of detection (LOD), mean average error (MAE), and linear correlation coefficient (<i>R</i>²) of the spectral calibration curves were all improved compared with those obtained from the original spectra. This study provides effective technical support for the denoising of LIBS spectra.