CN114077852A - Intelligent denoising method for strong noise spectrum signal - Google Patents

Intelligent denoising method for strong noise spectrum signal Download PDF

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CN114077852A
CN114077852A CN202111391714.6A CN202111391714A CN114077852A CN 114077852 A CN114077852 A CN 114077852A CN 202111391714 A CN202111391714 A CN 202111391714A CN 114077852 A CN114077852 A CN 114077852A
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范国刚
凌梦旋
邵英杰
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Sichuan Sfitek Scientific Instrument Co ltd
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Abstract

The invention relates to an intelligent denoising method of a strong noise spectrum signal, which mainly comprises the following steps: carrying out variation modal decomposition on the spectral signal x containing strong noise to obtain a series of ukA component; calculating the energy entropy of each component to find the corresponding modal component u when the first energy entropy gets the local maximumiRetention of u1‑ui‑1A component; for u under reservation1‑ui‑1And respectively denoising the components by using wavelet soft thresholds, and reconstructing the components into denoised spectral signals. The invention can effectively remove the noise in the spectrum by the variable mode decomposition and the dual denoising of the wavelet soft threshold, and can effectively find the demarcation point of the noise component and the non-noise component by calculating the energy entropy. The invention is suitable for denoising signals of ultraviolet-visible spectrum, fluorescence spectrum, infrared spectrum, near infrared spectrum and Raman spectrum which contain strong noise.

Description

Intelligent denoising method for strong noise spectrum signal
Technical Field
The invention belongs to the field of analytical chemistry signal processing, and particularly relates to an intelligent denoising method for a strong noise spectrum signal.
Background
The spectral instrument is influenced by factors such as humidity, temperature, dark current and the like in the measurement process, so that noise exists in the acquired signals. Noise not only reduces the resolution of the signal but also limits the extraction of useful information in the spectrum. It is often necessary to de-noise the spectral signal prior to spectral analysis.
Wavelet transform (Wavelet transform) has the advantage of multi-resolution, and has been widely used for signal denoising (Da Chen, XG Shao, B Hu, QD Su, A Background and noise ionization method for quadratic denoising of near isolated spectra, analytical chip Acta,2004,511, 37-45). But the rich wavelet basis functions and decomposition scales of wavelet transforms pose difficulties for parameter selection. Empirical Mode Decomposition (EMD) with adaptive decomposition overcomes the disadvantages of wavelet transform and is also applied to spectral signal denoising (benhui, lumin, zucchini, weijunfu, li shujuan, zhao jun, a spectral signal denoising method based on hilbert-yellow transform, 2018, ZL 2015105816608). But empirical modal decomposition has modal aliasing and end-point effects. Local Mean Decomposition (LMD) can mitigate the degree of modal aliasing, but does not completely eliminate modal aliasing and still has end-point effects (performance comparison studies, mechanical design and studies, 2012,28,38-40, of zhang qiang, yanglido, li jian army, Local mean decomposition and empirical modal decomposition).
The variable mode decomposition (Variational mode decomposition) is a self-adaptive and completely non-recursive spectral denoising method, which can decompose a spectral Signal into a series of modal functions at the same time and solve modal aliasing and end-point effect by applying mathematical Variational problem (K dragomirtsky, D Zosso, Variational mode decomposition, IEEE Transactions on Signal Processing,2014,62, 531-544). Signal denoising has been studied by applying a method of variational modal decomposition (von jun, liu, zhou li, lei rui, li xiao qin, liu cheng zhi, lei dian, li xin, zhou chun.) a method of denoising seismic data of low rank tensor based on variational modal decomposition, a patent published in china, 2021, CN 113204051A). However, some instruments collect weaker spectrum signals, such as Raman spectrum. Although there are various signal enhancement techniques (R Pilot, rsignorii, C dual, L Orian, M bhamidipiti, L Fabris, a review on surface-enhanced Raman scattering, Biosensors-Basel,2019,9,57), the finally acquired spectrum still has strong noise, so that the noise cannot be completely removed by using only the variational modal decomposition. In addition, a plurality of frequency components are obtained through variation modal decomposition, and because the noise components and the effective information components are sometimes difficult to distinguish through observation, the intelligent determination of the demarcation points of the noise components and the effective information components is also a difficult problem.
Disclosure of Invention
The invention aims to solve the existing problems and provides a method for removing the noise of the strong noise spectrum signal, which combines the advantages of the variational modal decomposition, the energy entropy and the wavelet soft threshold, and the energy entropy is used for determining the boundary point of the noise and the effective signal by combining the variational modal decomposition and the wavelet soft threshold, so that the strong noise in the spectrum signal can be effectively removed.
The technical scheme provided for realizing the invention comprises the following steps:
1) decomposing the strong noise spectrum signal x by using Variational Modal Decomposition (VMD) to obtain a certain number ukA component;
the variational modal decomposition is realized by the following steps:
firstly, initializing modal components
Figure BDA0003364591350000021
Center frequency of the mode
Figure BDA0003364591350000022
Lagrange penalty operator
Figure BDA0003364591350000023
Enabling the iteration number n;
introducing a secondary penalty factor alpha, and iteratively updating u according to a formulakAnd ωk；
Figure BDA0003364591350000024
Figure BDA0003364591350000025
Iteratively updating Lagrange penalty operator lambda according to a formula;
Figure BDA0003364591350000026
given an error e, if
Figure BDA0003364591350000031
Stopping iteration, otherwise repeating the steps (c) and (d).
2) Calculate each ukEnergy entropy H of a componentk；
The calculation of the energy entropy is realized by the following steps:
computing the energy E of the k componentk
Figure BDA0003364591350000032
② total energy E
Figure BDA0003364591350000033
Thirdly, calculating the proportion P of the kth component in the total energyk
Pk＝Ek*E
Fourthly, calculating each ukEnergy entropy H of a componentk
Hk＝-PklgPk
3) Searching the first energy entropy to obtain the corresponding modal component ui(ii) a The modal components after i and i are noise components and are directly deleted;
4) for modal components u containing useful information1，u2……ui-1Respectively performing wavelet soft threshold reductionNoise is generated;
the specific flow of wavelet soft threshold denoising is as follows:
selecting proper wavelet basis function, wavelet decomposition layer number and wavelet threshold;
performing wavelet transformation on the modal component according to the selected wavelet basis to obtain a wavelet coefficient corresponding to the decomposition layer number;
comparing the wavelet coefficient obtained by decomposition with the threshold value;
and fourthly, reserving the mode with the wavelet coefficient larger than the threshold value.
5) And reconstructing the denoised modal component of the wavelet soft threshold to obtain a denoised spectral signal.
The invention has the advantages that: the denoising method combines a wavelet soft threshold value method through variational modal decomposition, and the spectral noise is removed more thoroughly; the energy entropy is used as an index, and the noise component and the non-noise component are intelligently and effectively distinguished.
Drawings
The invention is further described below with reference to the accompanying drawings;
FIG. 1 is a Raman spectrum signal containing strong noise information;
FIG. 2 is the result of a Raman spectral signal variational modal decomposition;
FIG. 3 is an energy entropy distribution for each modal component;
FIG. 4 is a decomposition result of a non-noise modal component passing through a wavelet soft threshold;
FIG. 5 is a denoised Raman spectrum signal.
Detailed Description
The present invention will be further described in detail with reference to the following examples for better understanding, but the scope of the present invention as claimed is not limited to the scope shown in the examples.
Example 1:
this example implements denoising of raman spectral signals of cobalt monatomic catalysts supported on carbon and nitrogen carriers. The signal is measured by an XploRA PLUS laser confocal Raman spectrometer, and the sampling wave number range is 2600--1At an interval of 2.6cm-1And comprises 715 variables. Fig. 1 is a raw spectrum containing strong noise. It can be seen from the figure that the raman spectrum signal contains strong noise.
1) Decomposing the original strong noise spectrum by adopting a variational modal decomposition method to obtain u1-u6A total of 6 modal components, as shown in fig. 2.
The variational modal decomposition is realized by the following steps:
firstly, initializing modal components
Figure BDA0003364591350000041
Center frequency of the mode
Figure BDA0003364591350000042
Lagrange penalty operator
Figure BDA0003364591350000043
Enabling the iteration number n;
introducing a secondary penalty factor alpha, and iteratively updating u according to a formulakAnd ωk；
Figure BDA0003364591350000044
Figure BDA0003364591350000051
Iteratively updating Lagrange penalty operator lambda according to a formula;
Figure BDA0003364591350000052
given an error e, if
Figure BDA0003364591350000053
Stopping iteration, otherwise repeating the steps (c) and (d).
It can be seen from fig. 2 that as the order of u becomes larger, the oscillation frequency becomes gradually smaller. And it is obvious that u4-u6Is obviously a noise component, u1And u2Clearly non-noise components, but no u can be determined3Whether or not it is a noise component.
2) Calculating the energy entropy of each modal component;
the calculation of the energy entropy is realized by the following steps:
computing the energy E of the k componentk
Figure BDA0003364591350000054
② total energy E
Figure BDA0003364591350000055
Thirdly, calculating the proportion P of the kth component in the total energyk
Pk＝Ek/E
Fourthly, calculating each ukEnergy entropy H of a componentk
H＝-PklgPk
Fig. 3 shows the energy entropy of the modal components, with the abscissa being the order of u and the ordinate being the energy entropy of each modal component. As can be seen from the figure, u1-u4The energy entropy is increased and then decreased, wherein u3The modal energy entropy is highest; u. of4-u6The energy entropy is also increased and then decreased, where u5The energy entropy of (a) is highest.
3) It can be seen from fig. 3 that the first energy entropy takes the local maximum and the corresponding modal component is u3Thus, u can be determined3-u6Directly deleting the noise modal component and reserving the non-noise modal component u1And u2。
4) For modal components u containing useful information1And u2And respectively carrying out wavelet soft threshold denoising treatment. The wavelet basis function was chosen to be db8 with a wavelet decomposition level of 5 levels.
The specific flow of wavelet soft threshold denoising is as follows:
selecting proper wavelet basis function, wavelet decomposition layer number and wavelet threshold;
performing wavelet transformation on the modal component according to the selected wavelet basis to obtain a wavelet coefficient corresponding to the decomposition layer number;
comparing the wavelet coefficient obtained by decomposition with a threshold value, and judging the comparison between the wavelet coefficient and the threshold value;
and fourthly, reserving the mode with the wavelet coefficient larger than the threshold value.
FIG. 4 shows u after wavelet soft threshold denoising1And u2The modal components, both of which are seen to be almost noise free.
5) And reconstructing two modal components retained after the wavelet soft threshold is denoised into a denoised spectral signal. Fig. 5 shows the denoised spectral signal. It can be seen that the combination of the variational modal decomposition and the wavelet soft threshold removes a significant amount of noise.

Claims (6)

1. An intelligent denoising method for a strong noise spectrum signal is characterized by comprising the following steps: carrying out variation modal decomposition on an original spectrum signal x containing strong noise to obtain a series of ukA component; calculating the energy entropy of each component to find the corresponding modal component u when the first energy entropy gets the local maximumiRetention of u1-ui-1A component; for u under reservation1-ui-1Respectively carrying out wavelet soft threshold denoising processing on the components; will u1-ui-1The components are reconstructed into denoised spectral signals.
2. The intelligent denoising method of a strong noise spectrum signal according to claim 1, wherein the decomposition step of the variational modal decomposition is:
firstly, initializing modal components
Figure FDA0003364591340000011
Center frequency of the mode
Figure FDA0003364591340000012
Lagrange penalty operator
Figure FDA0003364591340000013
Enabling the iteration number n;
introducing a secondary penalty factor alpha, and iteratively updating u according to a formulakAnd ωk；
Figure FDA0003364591340000014
Figure FDA0003364591340000015
Iteratively updating Lagrange penalty operator lambda according to a formula;
Figure FDA0003364591340000016
given an error e, if
Figure FDA0003364591340000017
Stopping iteration, otherwise repeating the steps (c) and (d).
3. The intelligent denoising method of a strong noise spectrum signal according to claim 1, wherein: the energy entropy is calculated by the following steps:
computing the energy E of the k componentk
Figure FDA0003364591340000021
② total energy E
Figure FDA0003364591340000022
Thirdly, calculating the proportion P of the kth component in the total energyk
Pk＝Ek/E
Fourthly, calculating each ukEnergy entropy H of a componentk
Hk＝-Pklg Pk。
4. The intelligent denoising method of a strong noise spectrum signal according to claim 1, wherein: searching the first energy entropy to obtain the corresponding modal component uiDeleting i and the modal component after i, and keeping u1-ui-1And (4) components.
5. The intelligent denoising method of a strong noise spectrum signal according to claim 1, wherein: respectively carrying out wavelet soft threshold denoising treatment on the reserved modes, wherein the wavelet soft threshold denoising step comprises the following steps:
selecting proper wavelet basis function, wavelet decomposition layer number and wavelet threshold;
performing wavelet transformation on the modal component according to the selected wavelet basis to obtain a wavelet coefficient corresponding to the decomposition layer number;
comparing the wavelet coefficient obtained by decomposition with a threshold value, and judging the comparison between the wavelet coefficient and the threshold value;
and fourthly, reserving the mode with the wavelet coefficient larger than the threshold value.
6. The intelligent denoising method of a strong noise spectrum signal according to claim 1, wherein: the spectrum signals comprise ultraviolet-visible spectrum, fluorescence spectrum, infrared spectrum, near infrared spectrum and Raman spectrum signals.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114624271A (en) * 2022-03-25 2022-06-14 电子科技大学 X-ray fluorescence spectrum background deduction method based on variational modal decomposition

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114624271A (en) * 2022-03-25 2022-06-14 电子科技大学 X-ray fluorescence spectrum background deduction method based on variational modal decomposition
CN114624271B (en) * 2022-03-25 2023-08-25 电子科技大学 X-ray fluorescence spectrum background subtraction method based on variation modal decomposition

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