Laser-induced plasma spectrum denoising method and system

Abstract

The invention provides a de-noising method and a de-noising system for laser-induced plasma spectroscopy (LIBS), and provides an improved de-noising method aiming at the problem that the analysis accuracy of weak characteristic peaks of the laser-induced plasma spectroscopy (LIBS) is easily interfered by noise. According to a polynomial fitting method, a least square method and a Savitzky-Golay method in a traditional method, effective information in an original signal is easily distorted, so that a weak characteristic peak is lost, and a false peak appears; according to a traditional Fourier transform method, it is assumed that a signal is a global stationary signal, but in practical application, an LIBS signal is usually a non-stationary signal, and the problem of noise and signal confusion occurs. Aiming at the technical problem, the invention provides an improved discrete wavelet transform (DWT) denoising method, which ensures that the peak pattern of a weak characteristic peak is reserved while the noise interference is effectively removed.

Description

Technical Field

[0001] This invention relates to the field of spectral denoising technology, specifically to a laser-induced plasma spectral denoising method and system. Background Technology

[0002] LIBS (Liquid-Induced Spatial Radiation) technology utilizes short-pulse laser focusing to generate high-temperature plasma on the surface of matter. The excited atoms and ions emit plasma emission lines with elemental composition characteristics, which can be used to study the properties of the matter and enable rapid online monitoring of atmospheric aerosols. However, LIBS signals are typically affected by various noise sources, such as electronic circuit noise and optocoupler dark current. This noise and effective signal superimpose each other, leading to a decrease in spectral analysis accuracy. Noise generated by ambient light interference, detector noise, and bremsstrahlung can easily mask weak characteristic peaks in complex spectra. To achieve accurate spectral analysis, denoising becomes a crucial step in spectral preprocessing. Traditional denoising methods have significant shortcomings in handling weak peaks, often resulting in the loss of effective information and causing problems such as distortion of weak peaks and the generation of false peaks after smoothing. Therefore, the key issue in denoising complex spectra is how to effectively remove noise interference while completely preserving the peak value and peak shape parameters of weak characteristic peaks.

[0003] Patent application CN104346516A discloses a method for selecting the optimal number of decomposition layers in wavelet denoising of laser-induced breakdown spectra. This patent, based on a mathematical model of noise energy distribution, calculates the predicted range of noise energy values ​​using wavelet energy entropy and uses this range to determine the optimal number of decomposition layers for wavelet denoising of laser-induced breakdown spectra, thus achieving the goal of denoising spectral data. However, this technique does not consider the maximum number of decomposition layers from the perspective of sampling rate; an inappropriate sampling rate can affect the accuracy of signal reconstruction.

[0004] Patent application CN120929820A discloses a LIBS spectral denoising method, system, device, and storage medium based on adaptive threshold wavelet transform. This patent calculates the standard deviation of noise intensity based on the detail coefficients of the highest decomposition layer; it dynamically determines the optimal value of the adjustment factor using a two-layer optimization strategy combining grid search and the golden section method; and it constructs an adaptive threshold based on the noise intensity standard deviation and the adjustment factor. This adaptive threshold is then used to perform thresholding on high-frequency coefficients, achieving denoising of laser-induced breakdown spectra in complex industrial environments. However, this technique defaults to maximum layer decomposition of the signal, which may lead to over-decomposition and loss of characteristic peaks in low-frequency information. Furthermore, the use of a soft threshold function for spectral processing can cause deviations between the peak values ​​of the denoised spectrum and the original spectrum.

[0005] Patent application CN120870094A discloses a spectral analysis monitoring method for aluminum alloy composition detection. This patent is based on wavelet transform decomposition into signals of different frequency bands, sets a noise threshold of 0.05, sets wavelet coefficients with absolute values ​​below this threshold to zero, and filters out wavelet coefficients below the threshold, thus achieving noise reduction processing of the aluminum alloy spectrum. However, this technology fixes the threshold at 0.05 and cannot automatically adjust according to the noise level, which may lead to signal distortion or residual noise. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a laser-induced plasma spectral denoising method and system.

[0007] The laser-induced plasma spectral noise reduction method provided by the present invention includes:

[0008] Step 1: Obtain the laser-induced plasma spectral signal to be processed, perform frequency analysis on the spectral signal to obtain its frequency characteristic information, and calculate the maximum number of decomposition layers allowed for discrete wavelet transform based on the Nyquist sampling theorem and the frequency characteristic information. Step 2: Based on the maximum decomposition level, perform discrete wavelet transform decomposition on the spectral signal to obtain wavelet coefficients at different decomposition levels; based on the wavelet coefficients, calculate the wavelet energy entropy representing the signal components and the Shannon noise entropy representing the noise components at each decomposition level; determine a decomposition level criterion based on entropy analysis according to the variation law of the ratio of the wavelet energy entropy to the Shannon noise entropy; compare the maximum decomposition level with the decomposition level criterion based on entropy analysis, and select the smaller value as the optimal decomposition level for discrete wavelet transform; Step 3: Using the optimal decomposition level as the actual decomposition termination level of the discrete wavelet transform, the wavelet coefficients of each level from level 1 to the optimal decomposition level are subjected to coefficient shrinkage processing using a preset threshold function to obtain the processed wavelet coefficients of each level; the processed wavelet coefficients of each level are used to reconstruct the signal, and finally the denoised laser-induced plasma spectral signal is output.

[0009] Preferably, step 1 includes: For the original spectral signal Perform a Discrete Fourier Transform and calculate the equivalent value of its highest frequency component. The expression is:

[0010] According to the equivalent value Using the Nyquist sampling theorem, determine the minimum sampling rate of the spectral signal. The expression is:

[0011] Based on the minimum sampling rate Using Discrete Wavelet Transform (DWT) theory, calculate the maximum number of decomposition levels of DWT. The expression is:

[0012] in, Indicates the signal length; Represents discrete frequency variables; Represents discrete-time sampling points; It represents the imaginary unit.

[0013] Preferably, step 2 includes: Based on the maximum number of decomposition levels Perform DWT decomposition on the spectral signal to obtain the number of decomposition layers. wavelet coefficients ; Based on the wavelet coefficients, the number of each decomposition level is calculated. Shannon noise entropy With wavelet energy entropy ; Based on the number of each decomposition layer Shannon noise entropy With wavelet energy entropy The ratio of the two values ​​is used to calculate the entropy analysis ratio. The expression is:

[0014] Calculate the slope of the entropy analysis ratio between adjacent decomposition layers. The expression is:

[0015] in, It is the number of decomposition levels. Entropy analysis ratio below; According to the slope Criterion for determining the number of entropy analysis layers ; The maximum number of decomposition layers With the entropy analysis layer number criterion The smaller value in the equation is determined as the optimal number of decomposition layers. .

[0016] Preferably, the Shannon noise entropy The calculation formula is:

[0017]

[0018] In the formula, For noise variance It is the number of decomposition levels. noise variance For wavelet functions, It is an index of the decomposition level; The wavelet energy entropy The calculation formula is:

[0019] in, Indicates the first The proportion of the energy of the approximation coefficients to the total energy in layer wavelet decomposition; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; This indicates the proportion of energy allocated to the second level detail coefficients in the total energy. This represents the proportion of the energy of the level 1 detail coefficients to the total energy.

[0020] Preferably, step 3 includes: determining the optimal number of decomposition layers. As the termination level of the DWT decomposition; for level 1 to level 2... Wavelet coefficients obtained from layer decomposition The wavelet coefficients are obtained by performing a shrinkage process based on a preset threshold function. ; using the processed wavelet coefficients The denoised spectral signal is reconstructed. ; The first in the preset threshold function Layer threshold The calculation formula is:

[0021] In the formula, For the first Energy required for layer detail factor; The preset threshold function applies to the wavelet coefficients. The shrinkage processing rules are as follows:

[0022] In the formula, Adjusting parameters to control the degree of wavelet coefficient shrinkage under different operating conditions. It is a symbolic function.

[0023] The laser-induced plasma spectral noise reduction system provided by the present invention includes: Module M1: Acquires the laser-induced plasma spectral signal to be processed, performs frequency analysis on the spectral signal to obtain its frequency characteristic information, and calculates the maximum number of decomposition layers allowed for discrete wavelet transform based on the Nyquist sampling theorem and the frequency characteristic information. Module M2: Based on the maximum decomposition level, perform discrete wavelet transform decomposition on the spectral signal to obtain wavelet coefficients at different decomposition levels; based on the wavelet coefficients, calculate the wavelet energy entropy representing the signal components and the Shannon noise entropy representing the noise components at each decomposition level; determine a decomposition level criterion based on entropy analysis according to the variation law of the ratio of the wavelet energy entropy to the Shannon noise entropy; compare the maximum decomposition level with the decomposition level criterion based on entropy analysis, and select the smaller value as the optimal decomposition level for discrete wavelet transform; Module M3: Using the optimal decomposition level as the actual decomposition termination level of the discrete wavelet transform, the wavelet coefficients of each level from the first level to the optimal decomposition level are subjected to coefficient shrinkage processing using a preset threshold function to obtain the processed wavelet coefficients of each level; the processed wavelet coefficients of each level are used to reconstruct the signal, and finally the denoised laser-induced plasma spectral signal is output.

[0024] Preferably, the module M1 includes: For the original spectral signal Perform a Discrete Fourier Transform and calculate the equivalent value of its highest frequency component. The expression is:

[0025] According to the equivalent value Using the Nyquist sampling theorem, determine the minimum sampling rate of the spectral signal. The expression is:

[0026] Based on the minimum sampling rate Using Discrete Wavelet Transform (DWT) theory, calculate the maximum number of decomposition levels of DWT. The expression is:

[0027] in, Indicates the signal length; Represents discrete frequency variables; Represents discrete-time sampling points; It represents the imaginary unit.

[0028] Preferably, the module M2 includes: Based on the maximum number of decomposition levels Perform DWT decomposition on the spectral signal to obtain the number of decomposition layers. wavelet coefficients ; Based on the wavelet coefficients, the number of each decomposition level is calculated. Shannon noise entropy With wavelet energy entropy ; Based on the number of each decomposition layer Shannon noise entropy With wavelet energy entropy The ratio of the two values ​​is used to calculate the entropy analysis ratio. The expression is:

[0029] Calculate the slope of the entropy analysis ratio between adjacent decomposition layers. The expression is:

[0030] in, It is the number of decomposition levels. Entropy analysis ratio below; According to the slope Criterion for determining the number of entropy analysis layers ; The maximum number of decomposition layers With the entropy analysis layer number criterion The smaller value in the equation is determined as the optimal number of decomposition layers. .

[0031] Preferably, the Shannon noise entropy The calculation formula is:

[0032]

[0033] In the formula, For noise variance It is the number of decomposition levels. noise variance For wavelet functions, It is an index of the decomposition level; The wavelet energy entropy The calculation formula is:

[0034] in, Indicates the first The proportion of the energy of the approximation coefficients to the total energy in layer wavelet decomposition; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; This indicates the proportion of energy allocated to the second level detail coefficients in the total energy. This represents the proportion of the energy of the level 1 detail coefficients to the total energy.

[0035] Preferably, module M3 includes: decomposing the optimal number of layers. As the termination level of the DWT decomposition; for level 1 to level 2... Wavelet coefficients obtained from layer decomposition The wavelet coefficients are obtained by performing a shrinkage process based on a preset threshold function. ; using the processed wavelet coefficients The denoised spectral signal is reconstructed. ; The first in the preset threshold function Layer threshold The calculation formula is:

[0036] In the formula, For the first Energy required for layer detail factor; The preset threshold function applies to the wavelet coefficients. The shrinkage processing rules are as follows:

[0037] In the formula, Adjusting parameters to control the degree of wavelet coefficient shrinkage under different operating conditions. It is a symbolic function.

[0038] Compared with the prior art, the present invention has the following beneficial effects: (1) By using the improved DWT to process the spectrum of low-concentration sulfur-containing aerosols, compared with the spectrum processed by the traditional soft and hard threshold functions, the spectrum after denoising by the new threshold function model has less difference in peak value and peak shape compared with the original spectrum, thus solving the problem of weak characteristic peak distortion after denoising by the traditional method. (2) By adopting the improved DWT method, the spectrum of low-concentration sulfur-containing aerosol was processed. Compared with the spectrum processed by traditional soft and hard threshold functions, the SNR of the spectrum after denoising by the new threshold function model was significantly improved, with an average increase of 52% and a maximum increase of 77%; the RMSE was significantly reduced, with an average reduction of 46% and a maximum reduction of 55%, which solved the problem of poor denoising effect and low signal fidelity of traditional methods under weak signal conditions. Attached Figure Description

[0039] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 Criterion for the optimal number of decomposition levels in DWT Calculation flowchart; Figure 2 A comparison of the novel threshold function with soft and hard threshold functions; Figure 3 In the figure, (a)~(e) represent the original signal and the denoised spectrum of the sample at concentrations of 500, 750, 1000, 1250 and 1500 ppm, respectively. Figure 4 (a) and (b) in the figure are comparisons of signal-to-noise ratio and root mean square error for different methods of processing the spectrum. Detailed Implementation

[0040] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0041] Example This invention addresses the problem of noise interference affecting the accuracy of weak characteristic peak analysis in Laser-Induced Plasma Spectroscopy (LIPS). Taking the measurement of weak signals from low-concentration sulfur-containing aerosols in the atmosphere as an example, it proposes an improved denoising method. Traditional methods such as polynomial fitting, least squares, and Savitzky-Golay methods easily distort the effective information in the original signal, leading to the loss of weak characteristic peaks and the appearance of false peaks. Traditional Fourier transform methods assume that the signal is globally stationary, but in practical applications, LIPS signals are usually non-stationary, resulting in noise and signal confusion. To address these technical problems, this invention proposes an improved Discrete Wavelet Transform (DWT) denoising method that ensures effective removal of noise interference while preserving the peak shape of weak characteristic peaks.

[0042] Specifically, the steps include the following: Step 1: Perform a Discrete Fourier Transform on the spectrum to obtain the highest frequency in the spectral information. Calculate the equivalent value of the highest frequency component. Calculate the maximum number of decomposition layers of DWT based on the Nyquist sampling rate. ; Step 1 includes the following steps: Step 1.1: According to the Nyquist sampling theorem, signal reconstruction requires a sampling rate of [missing information]. Greater than or equal to twice the maximum frequency; (1) Considering that the high-frequency spectral components of a signal typically contain a significant amount of noise, which is not the dominant part of the signal, this technique obtains the amplitude of each frequency component in the spectrum by performing a discrete Fourier transform on the spectrum and calculates its average value, which is then used as the equivalent value of the highest frequency component in the signal. ; (2) in, Indicates the signal length; Represents discrete frequency variables; Represents discrete-time sampling points; Represents the imaginary unit; Represents the original signal; Finally, the minimum spectral sampling rate was obtained. As shown in equations (3)-(4): (3) (4) in, This represents the highest frequency in the original signal; Step 1.2: According to the theoretical principle of DWT, as the number of decomposition layers (DL) increases, the sampling frequency of a signal of length N will increase. It decreases exponentially by a factor of 2. Therefore, combined with the minimum sampling rate obtained in step 1.1... The maximum number of DWT decomposition layers in the spectrum can be obtained. : (5) Step 2: Based on the maximum number of decomposition levels DWT decomposition of the spectrum yields the wavelet coefficients of each layer of the spectrum. The wavelet energy entropy and Shannon noise entropy of each wavelet coefficient were calculated, and the ratio of the wavelet energy entropy to the Shannon noise entropy of each DL was used as the entropy analysis ratio. It is used to quantify the relative relationship between signal and noise, subtracting the entropy ratios of adjacent segments as the difference in entropy analysis, quotienting the difference, and calculating the slope between adjacent decomposition layers to measure the relationship. By determining the degree of increase, we can identify the number of layers corresponding to the maximum slope, thus obtaining the entropy analysis layer number criterion. .

[0043] The specific steps in step 2 are as follows: Step 2.1: Calculate the wavelet energy entropy and Shannon noise entropy under different deep learning (DL) conditions using the selected wavelet function. Shannon entropy The calculation results are shown in equations (6) and (7): (6) (7) In the formula, For noise variance For wavelet functions, It is the index of the decomposition layer. Equation (6) shows the noise... Shannon entropy and noise variance The variance is related to DL and wavelet functions. Therefore, functions with the same variance can be used. White noise is used to replace noise in the LIPS signal. White noise variance The estimation method is shown in equation (8): (8) In the formula, Indicates a noisy LIPS signal The median of the wavelet coefficients in the first-level decomposition, Indicates signal High-frequency wavelet coefficients obtained after first-order wavelet decomposition; In wavelet transform, the concept of entropy from information theory is effectively introduced, forming wavelet energy entropy. By integrating the energy distribution and uncertainty of a signal in the wavelet domain, wavelet energy entropy can profoundly reveal the complexity of a signal and provide theoretical support for the rational selection of deep learning (DL) and the effective distinction between useful signals and noise. In the... In the wavelet decomposition of layers, the energy calculation formula for wavelet coefficients is: The probability distribution of the wavelet coefficient energy (P) can be described as follows: , , Therefore, the wavelet energy entropy on the DLj layer. The calculation formula is: (9) in, Indicates the signal at the 1st Approximate coefficients obtained under layer wavelet decomposition; Indicates the signal at the 1st Detail coefficients obtained from layer wavelet decomposition; Indicates the first The proportion of the energy of the approximation coefficients to the total energy in layer wavelet decomposition; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; This represents the proportion of the energy of the detail coefficients in the (j-i+2)th layer to the total energy; This indicates the proportion of energy allocated to the second level detail coefficients in the total energy. This indicates the proportion of energy allocated to the first level detail coefficients in the total energy. Step 2.2: Use the ratio of wavelet energy entropy to Shannon noise entropy for each DL as the entropy analysis ratio. Entropy ratio (DL) is used to quantify the relative relationship between signal and noise. Insufficient DL results in incomplete noise removal, leading to a low signal-to-noise ratio (SNR); excessive DL can cause the loss of useful signals, thus reducing SNR. As DL increases, the difference between noisy LIPS signals and white noise gradually increases, and the two gradually separate. The difference between white noise and the noisy LIPS signal can be quantitatively described by the entropy ratio, specifically expressed as: (10) Step 2.3: Subtract adjacent entropy ratios to obtain the difference in entropy analysis. Calculate the quotient of the difference and compare the results. When the optimal DL is reached, a significant decrease in the noise ratio represents a drastic change in the result; therefore, the largest difference is the optimal DL. When at the optimal DL, the difference between the clean LIPS signal and white noise increases rapidly. This shows a sudden increase. To quantitatively describe this change, it can be measured by calculating the slope between adjacent decomposition layers. The slope of the increased effect is expressed as: (11) In the formula, Indicates the interlayer between adjacent decomposition layers The slope. To achieve optimal DL selection based on entropy ratio, by analyzing... The rate of increase is used to determine this. When the change in slope is most significant, it means... When the growth rate reaches its maximum, the optimal DL selection based on the entropy ratio can be considered achieved. .

[0044] Step 2.4: Take the maximum number of DWT decomposition levels obtained from Steps 1.2 and 2.3. And optimal DL selection based on entropy ratio The minimum value between them is used as the optimal number of decomposition layers. .

[0045] Step 3: Decompose to the optimal number of layers As the DWT decomposition termination layer number for the spectrum, and for 1 to The wavelet coefficients of the layer are shrunk to obtain the processed wavelet coefficients. And reconstruct the denoised spectrum.

[0046] Step 3 includes the following steps: Step 3.1: Calculate the threshold of wavelet coefficients for each layer according to equation (12). : (12) In the formula, For the first Layer detail factor energy, For signal length, The threshold is the number of layers. As the depth (DL) increases, the improved threshold gradually decreases, which is consistent with the characteristics of noise propagation at different scales in wavelet transform, thus ensuring the effectiveness of the denoising effect.

[0047] Step 3.2: Based on the threshold obtained in Step 3.1 Different shrinkage strategies are adopted for wavelet coefficients that are greater than the threshold and those that are less than the threshold, as shown in equation (13): (13) In the formula, These are the wavelet coefficients of each layer of the spectrum obtained by DWT decomposition. Adjust parameters for the degree of wavelet coefficient shrinkage under different operating conditions. Use the shrunken wavelet coefficients. The spectrum is reconstructed to obtain the denoised spectrum. .

[0048] Figure 1 Performing a discrete Fourier transform on the spectrum yields the highest frequency in the spectral information. Calculate the equivalent value of the highest frequency component. Calculate the maximum number of decomposition layers of DWT based on the Nyquist sampling rate. The wavelet coefficients of each layer of the spectrum are obtained by performing DWT decomposition on the spectrum. The wavelet energy entropy and Shannon noise entropy of each wavelet coefficient were calculated, and the ratio of the wavelet energy entropy to the Shannon noise entropy of each DL was used as the entropy analysis ratio. It is used to quantify the relative relationship between signal and noise, subtracting the entropy ratios of adjacent segments as the difference in entropy analysis, quotienting the difference, and calculating the slope between adjacent decomposition layers to measure the relationship. By determining the degree of increase, we can identify the number of layers corresponding to the maximum slope, thus obtaining the entropy analysis layer number criterion. The minimum of the two values ​​is taken as the optimal number of decomposition levels. .

[0049] Figure 2 This is a comparison chart of the new threshold function and the soft and hard threshold functions. The new threshold function... The waveform coefficients exhibit good continuity. For wavelet coefficients below the threshold, traditional soft and hard thresholding functions directly reduce them to zero, while the new thresholding function employs a flexible shrinkage strategy, gradually reducing the coefficients from strong to weak, while introducing a correction factor n to adjust the degree of shrinkage of wavelet coefficients at different decomposition levels. For waveform coefficients exceeding the threshold, the shrinkage increases with the original wavelet coefficients. The increase in threshold value comes from the new threshold function. and the original wavelet coefficients The error between them gradually decreased, and with As an asymptote, it better preserves the low-frequency signal components corresponding to the weak characteristic peaks of the LIPS spectrum. The characteristics of the new threshold function effectively solve the problems of data oscillation and fixed errors encountered when using traditional soft and hard threshold functions in the signal reconstruction stage. These problems stem from the discontinuity and fixed shrinkage characteristics of the threshold function.

[0050] Figure 3 The original signal and denoised spectra of samples at concentrations of 500, 750, 1000, 1250, and 1500 ppm are shown. Figure 3 As shown in (a)-(e), the peak values ​​of the spectral characteristic peaks processed by the new threshold function and the hard threshold function are well preserved. However, there is a fixed error between the peak values ​​of the spectral characteristic peaks processed by the soft threshold function and the peak values ​​of the original spectrum. By comparing and analyzing the peak shapes of the spectral characteristic peaks before and after denoising, it can be seen that the peak shape of the spectral characteristic peaks processed by the new threshold function is most similar to the peak shape of the original spectrum, indicating that it has a good peak shape preservation ability.

[0051] Figure 4 A comparison graph showing the signal-to-noise ratio and root mean square error of different methods for processing the spectrum. (Example) Figure 4As shown in (a), the spectral signal-to-noise ratio (SNR) after processing with the new threshold function is the highest among the three methods. Compared to the hard threshold function, the SNR of the spectral signal-to-noise ratio is improved by 60%, and compared to the soft threshold function, the SNR is improved by 77%. This is because the new threshold function performs shrinkage on coefficients below the threshold, rather than setting them to zero, thus achieving a better balance between preserving signal characteristics and suppressing noise. It can remove noise more effectively without damaging the useful components of the signal, thereby significantly improving the SNR of the denoised signal. Figure 4 As shown in (b), the spectrum processed by the new threshold function has the lowest RMSE. Compared to the hard threshold function, the RMSE of the spectrum processed using the new threshold function is reduced by 44%, and compared to the soft threshold function, it is reduced by 55%. This is because the new threshold function has higher accuracy in restoring the true shape of the signal, reducing the difference between the denoised signal and the original signal, and thus reducing errors, thereby significantly reducing the RMSE.

[0052] The present invention also provides a laser-induced plasma spectral noise reduction system, comprising: Module M1: Acquires the laser-induced plasma spectral signal to be processed, performs frequency analysis on the spectral signal to obtain its frequency characteristic information, and calculates the maximum number of decomposition layers allowed for discrete wavelet transform based on the Nyquist sampling theorem and the frequency characteristic information. Module M2: Based on the maximum decomposition level, perform discrete wavelet transform decomposition on the spectral signal to obtain wavelet coefficients at different decomposition levels; based on the wavelet coefficients, calculate the wavelet energy entropy representing the signal components and the Shannon noise entropy representing the noise components at each decomposition level; determine a decomposition level criterion based on entropy analysis according to the variation law of the ratio of the wavelet energy entropy to the Shannon noise entropy; compare the maximum decomposition level with the decomposition level criterion based on entropy analysis, and select the smaller value as the optimal decomposition level for discrete wavelet transform; Module M3: Using the optimal decomposition level as the actual decomposition termination level of the discrete wavelet transform, the wavelet coefficients of each level from the first level to the optimal decomposition level are subjected to coefficient shrinkage processing using a preset threshold function to obtain the processed wavelet coefficients of each level; the processed wavelet coefficients of each level are used to reconstruct the signal, and finally the denoised laser-induced plasma spectral signal is output.

[0053] The module M1 includes: For the original spectral signal Perform a Discrete Fourier Transform and calculate the equivalent value of its highest frequency component. The expression is:

[0054] According to the equivalent value Using the Nyquist sampling theorem, determine the minimum sampling rate of the spectral signal. The expression is:

[0055] Based on the minimum sampling rate Using Discrete Wavelet Transform (DWT) theory, calculate the maximum number of decomposition levels of DWT. The expression is:

[0056] in, Indicates the signal length; Represents discrete frequency variables; Represents discrete-time sampling points; It represents the imaginary unit.

[0057] The module M2 includes: Based on the maximum number of decomposition levels Perform DWT decomposition on the spectral signal to obtain the number of decomposition layers. wavelet coefficients ; Based on the wavelet coefficients, the number of each decomposition level is calculated. Shannon noise entropy With wavelet energy entropy ; Based on the number of each decomposition layer Shannon noise entropy With wavelet energy entropy The ratio of the two values ​​is used to calculate the entropy analysis ratio. The expression is:

[0058] Calculate the slope of the entropy analysis ratio between adjacent decomposition layers. The expression is:

[0059] in, It is the number of decomposition levels. Entropy analysis ratio below; According to the slope Criterion for determining the number of entropy analysis layers ; The maximum number of decomposition layers With the entropy analysis layer number criterion The smaller value in the equation is determined as the optimal number of decomposition layers. .

[0060] Shannon noise entropy The calculation formula is:

[0061]

[0062] In the formula, For noise variance It is the number of decomposition levels. noise variance For wavelet functions, It is an index of the decomposition level; The wavelet energy entropy The calculation formula is:

[0063] in, Indicates the first The proportion of the energy of the approximation coefficients to the total energy in layer wavelet decomposition; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; This indicates the proportion of energy allocated to the second level detail coefficients in the total energy. This represents the proportion of the energy of the level 1 detail coefficients to the total energy.

[0064] The module M3 includes: determining the optimal decomposition level. As the termination level of the DWT decomposition; for level 1 to level 2... Wavelet coefficients obtained from layer decomposition The wavelet coefficients are obtained by performing a shrinkage process based on a preset threshold function. ; using the processed wavelet coefficients The denoised spectral signal is reconstructed. ; The first in the preset threshold function Layer threshold The calculation formula is:

[0065] In the formula, For the first Energy required for layer detail factor; The preset threshold function applies to the wavelet coefficients. The shrinkage processing rules are as follows:

[0066] In the formula, Adjusting parameters to control the degree of wavelet coefficient shrinkage under different operating conditions. It is a symbolic function.

[0067] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0068] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A laser-induced plasma spectral noise reduction method, characterized in that, include: Step 1: Obtain the laser-induced plasma spectral signal to be processed, perform frequency analysis on the spectral signal to obtain its frequency characteristic information, and calculate the maximum number of decomposition layers allowed for discrete wavelet transform based on the Nyquist sampling theorem and the frequency characteristic information. Step 2: Based on the maximum decomposition level, perform discrete wavelet transform decomposition on the spectral signal to obtain wavelet coefficients at different decomposition levels; based on the wavelet coefficients, calculate the wavelet energy entropy representing the signal components and the Shannon noise entropy representing the noise components at each decomposition level; determine a decomposition level criterion based on entropy analysis according to the variation law of the ratio of the wavelet energy entropy to the Shannon noise entropy; compare the maximum decomposition level with the decomposition level criterion based on entropy analysis, and select the smaller value as the optimal decomposition level for discrete wavelet transform; Step 3: Using the optimal decomposition level as the actual decomposition termination level of the discrete wavelet transform, the wavelet coefficients of each level from level 1 to the optimal decomposition level are subjected to coefficient shrinkage processing using a preset threshold function to obtain the processed wavelet coefficients of each level; the processed wavelet coefficients of each level are used to reconstruct the signal, and finally the denoised laser-induced plasma spectral signal is output.

2. The laser-induced plasma spectral noise reduction method according to claim 1, characterized in that, Step 1 includes: For the original spectral signal Perform a Discrete Fourier Transform and calculate the equivalent value of its highest frequency component. The expression is: According to the equivalent value Using the Nyquist sampling theorem, determine the minimum sampling rate of the spectral signal. The expression is: Based on the minimum sampling rate Using Discrete Wavelet Transform (DWT) theory, calculate the maximum number of decomposition levels of DWT. The expression is: in, Indicates the signal length; Represents discrete frequency variables; Represents discrete-time sampling points; It represents the imaginary unit.

3. The laser-induced plasma spectral noise reduction method according to claim 2, characterized in that, Step 2 includes: Based on the maximum number of decomposition levels Perform DWT decomposition on the spectral signal to obtain the number of decomposition layers. wavelet coefficients ; Based on the wavelet coefficients, the number of each decomposition level is calculated. Shannon noise entropy With wavelet energy entropy ; Based on the number of each decomposition layer Shannon noise entropy With wavelet energy entropy The ratio of the two values ​​is used to calculate the entropy analysis ratio. The expression is: Calculate the slope of the entropy analysis ratio between adjacent decomposition layers. The expression is: in, It is the number of decomposition layers. Entropy analysis ratio below; According to the slope Criterion for determining the number of entropy analysis layers based on changes ; The maximum number of decomposition layers With the entropy analysis layer number criterion The smaller value in the equation is determined as the optimal number of decomposition layers. .

4. The laser-induced plasma spectral noise reduction method according to claim 3, characterized in that, Shannon noise entropy The calculation formula is: In the formula, For noise variance It is the number of decomposition layers. noise variance For wavelet functions, It is an index of the decomposition level; The wavelet energy entropy The calculation formula is: in, Indicates the first The proportion of the energy of the approximation coefficients to the total energy in layer wavelet decomposition; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; This indicates the proportion of energy allocated to the second level detail coefficients in the total energy. This represents the proportion of the energy of the level 1 detail coefficients to the total energy.

5. The laser-induced plasma spectral noise reduction method according to claim 4, characterized in that, Step 3 includes: determining the optimal number of decomposition levels. As the termination level of the DWT decomposition; for level 1 to level 2... Wavelet coefficients obtained from layer decomposition The wavelet coefficients are obtained by performing a shrinkage process based on a preset threshold function. ; using the processed wavelet coefficients The denoised spectral signal is reconstructed. ; The first in the preset threshold function Layer threshold The calculation formula is: In the formula, For the first Energy required for layer detail factor; The preset threshold function applies to the wavelet coefficients. The shrinkage processing rules are as follows: In the formula, Adjusting parameters to control the degree of wavelet coefficient shrinkage under different operating conditions. It is a symbolic function.

6. A laser-induced plasma spectral noise reduction system, characterized in that, include: Module M1: Acquires the laser-induced plasma spectral signal to be processed, performs frequency analysis on the spectral signal to obtain its frequency characteristic information, and calculates the maximum number of decomposition layers allowed for discrete wavelet transform based on the Nyquist sampling theorem and the frequency characteristic information. Module M2: Based on the maximum decomposition level, perform discrete wavelet transform decomposition on the spectral signal to obtain wavelet coefficients at different decomposition levels; based on the wavelet coefficients, calculate the wavelet energy entropy representing the signal components and the Shannon noise entropy representing the noise components at each decomposition level; determine a decomposition level criterion based on entropy analysis according to the variation law of the ratio of the wavelet energy entropy to the Shannon noise entropy; compare the maximum decomposition level with the decomposition level criterion based on entropy analysis, and select the smaller value as the optimal decomposition level for discrete wavelet transform; Module M3: Using the optimal decomposition level as the actual decomposition termination level of the discrete wavelet transform, the wavelet coefficients of each level from the first level to the optimal decomposition level are subjected to coefficient shrinkage processing using a preset threshold function to obtain the processed wavelet coefficients of each level; the processed wavelet coefficients of each level are used to reconstruct the signal, and finally the denoised laser-induced plasma spectral signal is output.

7. The laser-induced plasma spectral noise reduction system according to claim 6, characterized in that, The module M1 includes: For the original spectral signal Perform a Discrete Fourier Transform and calculate the equivalent value of its highest frequency component. The expression is: According to the equivalent value Using the Nyquist sampling theorem, determine the minimum sampling rate of the spectral signal. The expression is: Based on the minimum sampling rate Using Discrete Wavelet Transform (DWT) theory, calculate the maximum number of decomposition levels of DWT. The expression is: in, Indicates the signal length; Represents discrete frequency variables; Represents discrete-time sampling points; It represents the imaginary unit.

8. The laser-induced plasma spectral noise reduction system according to claim 7, characterized in that, The module M2 includes: Based on the maximum number of decomposition levels Perform DWT decomposition on the spectral signal to obtain the number of decomposition layers. wavelet coefficients ; Based on the wavelet coefficients, the number of each decomposition level is calculated. Shannon noise entropy With wavelet energy entropy ; Based on the number of each decomposition layer Shannon noise entropy With wavelet energy entropy The ratio of the two values ​​is used to calculate the entropy analysis ratio. The expression is: Calculate the slope of the entropy analysis ratio between adjacent decomposition layers. The expression is: in, It is the number of decomposition layers. Entropy analysis ratio below; According to the slope Criterion for determining the number of entropy analysis layers based on changes ; The maximum number of decomposition layers With the entropy analysis layer number criterion The smaller value in the equation is determined as the optimal number of decomposition layers. .

9. The laser-induced plasma spectral noise reduction system according to claim 8, characterized in that, Shannon noise entropy The calculation formula is: In the formula, For noise variance It is the number of decomposition layers. noise variance For wavelet functions, It is an index of the decomposition level; The wavelet energy entropy The calculation formula is: in, Indicates the first The proportion of the energy of the approximation coefficients to the total energy in layer wavelet decomposition; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; Indicates the first The proportion of energy allocated to the layer detail factor in the total energy; This indicates the proportion of energy allocated to the second level detail coefficients in the total energy. This represents the proportion of the energy of the level 1 detail coefficients to the total energy.

10. The laser-induced plasma spectral noise reduction system according to claim 9, characterized in that, The module M3 includes: determining the optimal decomposition level. As the termination level of the DWT decomposition; for level 1 to level 2... Wavelet coefficients obtained from layer decomposition The wavelet coefficients are obtained by performing a shrinkage process based on a preset threshold function. ; using the processed wavelet coefficients The denoised spectral signal is reconstructed. ; The first in the preset threshold function Layer threshold The calculation formula is: In the formula, For the first Energy required for layer detail factor; The preset threshold function applies to the wavelet coefficients. The shrinkage processing rules are as follows: In the formula, Adjusting parameters to control the degree of wavelet coefficient shrinkage under different operating conditions. It is a symbolic function.

Images