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

doi:10.1117/12.2662881

4 April 2023 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

Author Affiliations +

Proceedings Volume 12617, Ninth Symposium on Novel Photoelectronic Detection Technology and Applications; 1261703 (2023) https://doi.org/10.1117/12.2662881
Event: 9th Symposium on Novel Photoelectronic Detection Technology and Applications (NDTA 2022), 2022, Hefei, China

Abstract

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.

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Zheng Li, Bo Hou, Yuchen Cai, Sheng Zhou, Yuanqin Yu, and Jingsong Li "Research on singular value decomposition denoising algorithm based on a genetic algorithm and FFT and its application", Proc. SPIE 12617, Ninth Symposium on Novel Photoelectronic Detection Technology and Applications, 1261703 (4 April 2023); https://doi.org/10.1117/12.2662881

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KEYWORDS

Denoising

Signal to noise ratio

Electronic filtering

Genetic algorithms

Interference (communication)

Optical filters

Oxygen

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