Research on singular value decomposition denoising algorithm based on a genetic algorithm and FFT and its application
Zheng Li, Bo Hou, Yuchen Cai, Sheng Zhou, Yuanqin Yu, Jingsong Li · 2023
To address the impact of noise in spectral signals on gas detection accuracy and sensitivity, this paper carries out a study of a singular value decomposition denoising algorithm based on a genetic algorithm and fast Fourier transform. Aiming at the optimization problem of two key parameters (structure of Toeplitz matrix and effective singular value order) in the smooth filtering algorithm of singular value decomposition, this paper uses a genetic algorithm to optimize the number of rows of the reconstructed Toeplitz matrix and determines the effective singular value order by performing fast Fourier transform on the constructed differential spectral signal. To test the effectiveness of the self-established singular value decomposition denoising algorithm, a detailed filtering and noise reduction analysis study is carried out on the simulated spectrum and experimentally measured signals with the absorption spectrum of atmospheric oxygen molecules as the analysis object, and compared with the traditional S-G filtering algorithm, wavelet transform denoising and principal component analysis denoising algorithm. The results show that the singular value decomposition denoising algorithm established in this paper has obvious superiority in suppressing noise, which can more effectively improve the signal-to-noise ratio and reduce the root-mean-square error of the spectral signal, thus improving the gas detection accuracy and sensitivity of the spectral experimental system.