Software Implementation of the Algorithm for Processing Wavelet Coefficients in Problems of Experimental Data Analysis
https://doi.org/10.1134/S2304487X21010120
Abstract
A modern method based on the wavelet transform has been proposed to clean diffractometric measurement data from noise. This method involves a multilevel one-dimensional discrete wavelet decomposition of the diffraction pattern and allows decomposing the source signal into approximating and detailing coefficients containing information with useful and noise components. The noise component of the diffraction pattern is mainly manifested in the detail coefficients obtained at the lowest decomposition level, to which threshold processing must be applied. This removes sufficiently small coefficients that are considered noise. The reconstruction of the diffraction pattern from the detail coefficients that have passed this processing will significantly reduce the noise level and, as a result, the localization error of the diffraction maxima. In order to obtain the best picture, it is necessary to use certain parameters for wavelet processing. In this work, the multilevel wavelet transform of the original diffraction pattern has been performed using real wavelets of various families with further analysis of the dependence of the processing quality on the choice of a basis. The efficiency of various algorithms for automatic threshold processing of decomposition coefficients in the MatLab software environment and the influence of the choice of thresholding parameters on the quality of cleaning are investigated. The results obtained are evaluated by comparing the standard deviation of the reconstructed and original diffraction patterns, as well as by comparing them visually. Examples of filtering diffraction patterns by the proposed method are given. In conclusion, the optimal parameters of thresholding for
processing diffraction patterns are given. The analysis of the displacement of the location of peaks on the processed diffraction pattern is performed. The detected peaks, which could not be localized on the original spectra, have been interpreted.
About the Authors
S. B. Moskovsky
Yaroslavl State University
Russian Federation
Russian Federation
150000
Yaroslavl
A. N. Sergeev
Yaroslavl State University
Russian Federation
Russian Federation
150000
Yaroslavl
E. I. Sidorova
Yaroslavl State University
Russian Federation
Russian Federation
150000
Yaroslavl
А. A. Marudov
Yaroslavl State University
Russian Federation
Russian Federation
150000
Yaroslavl
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Review
For citations:
Moskovsky S.B., Sergeev A.N., Sidorova E.I., Marudov А.A. Software Implementation of the Algorithm for Processing Wavelet Coefficients in Problems of Experimental Data Analysis. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(1):77-84. (In Russ.) https://doi.org/10.1134/S2304487X21010120
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