Roadside infrared spectrum remote sensing monitoring method and system based on VDL-DTCWT

Abstract

The present invention provides a roadside infrared spectroscopy remote sensing monitoring method and system based on VDL-DTCWT. The method comprises: in the process of background spectrum estimation, spectral bands with different characteristics are processed by variational decomposition layers; nonlinear compression is performed by nonlinear least squares analysis; high-frequency coefficients are processed by L1 regularization, NLLS is used to iteratively calculate the spectrum, fit the measured spectrum, compare the calculated spectrum with the original measured spectrum, until the residual between the calculated spectrum and the measured spectrum converges to a stable solution; and the applicable background spectrum is applied to nonlinear least squares concentration inversion. The present invention solves the technical problem that it is difficult to collect background spectrum data in real time in a scene with an open optical path, which restricts the adaptability and accuracy of OP-FTIR technology under complex environmental conditions, resulting in low characterization accuracy of characterizing gaseous pollutants.

Description

Technical Field

[0001] The present invention relates to the field of atmospheric pollutant detection based on active remote sensing, and in particular to a roadside infrared spectrum remote sensing monitoring method and system based on VDL-DTCWT. Background Art

[0002] Infrared spectroscopy remote sensing technology has become one of the core tools for environmental monitoring and atmospheric science research, especially showing its unique advantages in the identification and quantitative analysis of atmospheric pollutants. Among them, FTIR (Fourier transform infrared) technology, with its wide band coverage and high spectral resolution, provides the possibility for accurate identification and quantification of multi-component atmospheric pollutants. Specific references: Ju W, Lu C, Liu C, et al. Rapid identification of atmospheric gaseous pollutants using Fourier-transform infrared spectroscopy combined with independent component analysis[J]. Journal of Spectroscopy,2020, 2020: 1-14); Fourier transform infrared spectroscopy for measurements of vehicle exhaust emissions: A review[J]. Applied Sciences,2021, 11(16): 7416; From ground-based FTIR (Fourier transform infrared) Retrieval of tropospheric and stratospheric NO from ground-based Fourier-transform infrared (FTIR) measurements[J]. Atmospheric Measurement Techniques, 2021, 14(9):6233-6247。

[0003] Accurate acquisition of the background spectrum is crucial to ensure measurement accuracy, as it is used for calibration and reference and is key to identifying and quantifying atmospheric components. Specific references: A retrieval ofxCO2 from ground-based mid-infrared NDACC solar absorption spectra and comparison to TCCON (Chiarella R, Buschmann M, Laughner J, et al. A retrieval ofxCO2 from ground-based mid-infrared NDACC solar absorption spectra and comparison to TCCON[J]. Atmospheric Measurement Techniques Discussions, 2023,2023: 1-31); Yamanouchi S, Conway S, Strong K, et al. NDACC FTIR trace gas measurementsat the University of Toronto Atmospheric Observatory from 2002 to 2020[J].Earth System Science Data Discussions, 2023, 2023: 1-73); Quantifying the impact of solar spectra on the inter-calibration of satellite instruments (Bhatt R, Doelling DR, Coddington O, et al. Quantifying the impact of solar spectra on the inter-calibration of satellite instruments[J]. Remote Sensing, 2021, 13(8): 1438).

[0004] However, the complexity of the natural environment and the changes in atmospheric conditions pose challenges to the acquisition of background spectra. Traditional background spectrum acquisition methods, such as short-range background spectroscopy, upwind background spectroscopy and synthetic background spectroscopy, have their own advantages, but they also have shortcomings. For example, the short-range background spectroscopy method disclosed in the literature: Increasing the quantitative credibility of open-path Fourier transform infrared (FT-IR) spectroscopic data, with focus on several properties of the background spectrum [J]. Applied Spectroscopy, 2013, 67(3): 335-341 can effectively reduce the interference of target gases, but may cause detector saturation due to excessive light flux; although the upwind background spectroscopy method can reflect the uncontaminated background state, its effectiveness is limited by changes in wind direction.

[0005] In order to solve these problems, the brightness temperature spectrum is used to convert the radiation into a temperature spectrum in the literature: Research on Intelligent Inspection Technology for Gas Leakage (Yue Z, Fengxiang M, Anjing W, et al. Research on Intelligent Inspection Technology for GasLeakage[C] / / 2023 IEEE International Conference on Image Processing andComputer Applications (ICIPCA). IEEE, 2023: 156-162) and Remote sense for environment pollutiongases in wide infrared spectral range (Yang Z, Yu C, Zhang W, et al. Remote sense for environment pollutiongases in wide infrared spectral range[C] / / AOPC 2019: Optical Spectroscopy andImaging. SPIE, 2019, 11337: 299-309), where the background object appears as a slowly changing baseline in the brightness temperature spectrum, and the gas characteristic line is linearly superimposed on this baseline. The regression coefficient is obtained by fitting a single measured spectrum to reconstruct and remove the background spectrum. However, this method assumes that all gas features are linearly superimposed, which is only applicable to thin cloud conditions and may cause errors for thick cloud conditions. In addition, if the reference spectrum does not match the actual situation, the fitting result will have a large residual, which will affect the target feature extraction and identification. In the literature: CM Gittins, “Detection and characterization of chemical vapor fugitive emissions by nonlinear optimalestimation: Theory and simulation,” Appl. Opt, vol. 48, no. 23, pp. 4545–4561, Aug. 2009), the brightness temperature spectrum theory was improved to deal with the nonlinear transmission problem in thick cloud conditions. It is assumed that the shape of the synthetic thin cloud transmission spectrum is the same as that of the thick cloud, but there is a difference in the scaling value. The thick cloud situation is handled by linear approximation. However, this existing method relies on the identification of the initial target cloud and requires prior information to generate a synthetic reference spectrum. Otherwise, the initial guess error may be amplified, and the computational complexity is high, which limits real-time applications.In the literature: Adaptive Detection Algorithm for Hazardous Clouds Based on Infrared Remote Sensing Spectroscopy and the LASSO Method (Li D, Cui F, Wang A, et al. Adaptive Detection Algorithm for Hazardous Clouds Based on Infrared Remote Sensing Spectroscopy and the LASSO Method [J]. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58 (12): 8649-8664), the most suitable reference spectrum is automatically selected from the predefined reference spectrum through the variable selection function, the residual is reduced and better spectral fitting is achieved, and the background is adaptively reconstructed and removed. However, the effect of the LASSO method depends on the quality and quantity of the pre-generated reference spectra. If the reference spectrum cannot cover all possible situations or is not representative enough, residuals may occur in the fitting results. The deviation introduced in the variable selection process may also affect the final target feature extraction and recognition accuracy. The truncated background method is a commonly used method for estimating background spectra. A straight line is drawn between two selected points, and any spectral contribution below the straight line is removed or truncated to obtain the background spectrum. For details, see the literature: Application of open-path Fourier transform infrared spectroscopy (OP-FTIR) to measure greenhouse gas concentrations from agricultural fields [J]. Atmospheric Measurement Techniques, 2019, 12 (6): 3403-3415). The truncated background method is based on the assumption that the background signal is linear between two selected points, which may not always be true in actual situations.

[0006] The existing invention patent application document "A method and system for improving voiceprint recognition accuracy" with publication number CN106971736A, the existing method includes: obtaining voiceprints of the same user in different states, constructing multiple background recognition models corresponding to the voiceprints, the background voiceprint features include multiple background voiceprint feature vectors; constructing a standard recognition model according to the background recognition model, and dividing the recognition priority; obtaining unrecognized voiceprint features in unrecognized voiceprints, the unrecognized voiceprint features at least include wavelet elements of the unrecognized voiceprints; processing the unrecognized voiceprint features and the standard voiceprint features in the voiceprint recognition model according to the priority to obtain the recognition degree corresponding to the unrecognized voiceprint, judging whether the recognition degree is greater than a preset standard threshold, when the recognition degree is greater than the standard threshold, identifying the unrecognized voiceprint as a locked voiceprint, and exiting. From the specific implementation content of the existing document, it can be seen that the existing technology performs at least one of the following wavelet transforms on the normalized sample vector of the predetermined length: performing a real wavelet transform on the normalized sample vector of the predetermined length to obtain the real coefficient of the first predetermined frequency band, and selecting a frequency band that meets the first predetermined condition in the first predetermined frequency band for sampling to obtain the real wavelet element in the unrecognized voiceprint feature; performing a double-tree complex wavelet transform on the normalized sample vector of the predetermined length to obtain the real coefficient and imaginary coefficient of the second predetermined frequency band, and selecting a frequency band that meets the second predetermined condition in the second predetermined frequency band for sampling to obtain the complex wavelet element in the unrecognized voiceprint feature. The prior art solution disclosed in the aforementioned CN106971736A focuses on improving the accuracy of voiceprint recognition and is mainly used to process voice signals. From the specific implementation content of the solution, it can be seen that the spectral analysis and voiceprint recognition method of the aforementioned prior art processes voice signals and relies on wavelet transform to optimize voiceprint recognition. The specific principle of the existing solution to achieve sparse optimization is: optimization through comparison of priority and feature vectors. The effectiveness of the existing solution in removing useless signals and noise needs to be improved. In terms of background correction and model adjustment, the aforementioned prior art adjusts the background recognition model to adapt to different voiceprint features and improve recognition efficiency. The accuracy of the spectral data output by the existing method needs to be improved. The aforementioned existing solution mainly deals with the impact of environmental noise on speech recognition, and mainly focuses on speech signal processing. It is difficult to eliminate the impact of noise on spectral data, which restricts the accuracy of spectral analysis. At the same time, the aforementioned prior art mainly relies on vector distance optimization and has no iterative convergence mechanism. It is difficult to ensure the stability and accuracy of spectral data, and it is difficult to apply to complex remote sensing environments.

[0007] The existing invention patent application document "Feature-level fusion method of infrared and visible light sequence images based on target detection" with publication number CN1932882A, the existing method includes: using the region growing method to segment each frame of the source image, automatically obtaining the background area and the target area according to the effective measurement calculation, and transforming the segmented source image sequence using the dual-tree complex wavelet transform method; after obtaining the transformed wavelet coefficients, applying different fusion rules to the target and background areas respectively to achieve feature-level sequence image fusion; after obtaining the wavelet fusion coefficients of different areas, using the dual-tree complex wavelet inverse transform to obtain the fused sequence image. The existing solution disclosed in the aforementioned CN1932882A focuses on voiceprint recognition. In this existing technology, the dual-tree complex wavelet transform (DTCWT, Dual-Tree Complex Wavelet Transform) is used to enhance the feature stability of infrared and visible light sequence images, which is mainly used for target detection and image feature fusion. From the specific implementation content of the solution, it can be seen that the core of the solution is to improve the robustness of target detection and maintain a high resolution in complex environments. This prior art focuses on feature enhancement and target detection of image sequences, time-frequency positioning and artifact reduction of images, and focuses on improving the accuracy and stability of image processing, without involving correction and sparse optimization of background spectra. It is impossible to collect and correct background spectral data in real time in complex environments. The accuracy of the spectral signal of this existing solution makes it difficult to ensure the operational stability of background spectrum estimation. The aforementioned existing solutions can improve the accuracy of image sequence feature processing to a certain extent, but do not solve the problem of difficulty in real-time collection of background spectral data under an open optical path. The signal restoration capability needs to be improved, and it is difficult to adjust and correct background spectral data in real time. The difficulty of background spectrum collection of OP-FTIR technology in complex environments cannot be overcome, which restricts the accuracy of pollutant characterization.

[0008] The existing invention patent application document "Image Preprocessing Method and Device in Low-light Illumination Environment" with publication number CN110717858A, the existing method includes: for the original image with a strong noise background obtained in the low-light illumination environment, the approximate value K of the ambient light is obtained by dual-tree complex wavelet transform, and the approximate value of the ambient light is used to defog the image after two-dimensional separable wavelet transform, complex wavelet operation and super-resolution reconstruction. Then, the image data obtained after defogging is fused, peeled according to the target features, and finally the target area that can be used for image recognition is output. In the existing scheme disclosed in the aforementioned CN110717858A, for image preprocessing in low-light illumination environment, dual-tree complex wavelet transform and super-resolution reconstruction are used to remove environmental influences such as noise and haze, extract the target area in the image, and finally improve the accuracy and speed of image recognition. From the specific implementation content of the scheme, it can be seen that the existing scheme processes images in low-light environments, removes image noise, and improves resolution to obtain clear target areas that can be used for recognition. The existing solution uses dual-tree complex wavelet and super-resolution reconstruction technology, focusing on image enhancement, defogging, and de-noising, and ultimately improving the accuracy of image recognition. However, the existing technology cannot correct the background spectrum in real time, it is difficult to ensure the accuracy of gas pollutant detection, and it is difficult to obtain accurate background spectra in real time in complex environments.

[0009] In the existing open document "Multi-scale Remote Sensing Image Denoising Method Based on Dual-tree Complex Wavelet", cloud noise is the main source of interference in the process of ground remote sensing imaging. The superposition of cloud noise of different frequencies makes the remote sensing image very easy to have low contrast, poor readability, unclear scenery and other phenomena. This existing document proposes a visible light remote sensing image denoising method that combines dual-tree complex wavelet analysis technology with Laplace filtering. The remote sensing image containing cloud noise is decomposed at multiple scales by using dual-tree complex wavelet, and the optimal filter combination and optimal decomposition scale are tested by aliasing energy ratio. The low-frequency subbands and high-frequency subbands at different scales are obtained accordingly, and Laplace filtering is used to denoise the subbands with strong cloud noise interference, and then the reconstructed image is obtained by inverse dual-tree complex wavelet transform. The aforementioned existing document performs multi-scale remote sensing image denoising based on dual-tree complex wavelet: mainly for the cloud noise problem in remote sensing images, dual-tree complex wavelet transform combined with Laplace filtering technology is used to denoise the high and low frequency subbands of different scales, and reconstruct the image to improve its contrast and detail retention effect. This existing solution is mainly used for remote sensing image processing, especially to remove noise such as clouds and fog, and to improve image clarity and readability. It cannot be directly applied to spectral analysis application scenarios. From the specific implementation content of this solution, it can be seen that this existing technology uses a dual-tree complex wavelet denoising method to process noise in remote sensing images, especially cloud and fog noise, to improve image contrast and details. Laplace filtering and multi-scale analysis are used to remove noise in the image by processing high and low frequency sub-bands. However, it is impossible to accurately correct the background spectrum in a complex environment, and it is difficult to ensure the stability and accuracy of data acquisition under open optical path conditions. The real-time performance and ability to adapt to complex environments of this existing solution need to be improved.

[0010] In summary, the existing technology is difficult to collect background spectral data in real time when the optical path is open, which restricts the adaptability and accuracy of OP-FTIR technology under complex environmental conditions, resulting in the technical problem of low characterization accuracy of gaseous pollutants. Summary of the invention

[0011] The technical problem to be solved by the present invention is: how to solve the technical problem that the existing technology is difficult to collect background spectral data in real time under the scenario of open light path, which restricts the adaptability and accuracy of OP-FTIR technology under complex environmental conditions, resulting in low characterization accuracy of gaseous pollutants.

[0012] The present invention adopts the following technical solutions to solve the above technical problems: The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT includes:

[0013] S1. Read the measured spectrum of the incident spectrum ;

[0014] S2, preset the number of decomposition layers and the maximum number of iterations for different wave number bands;

[0015] S3. Measure the spectrum Applying the dual-tree complex wavelet transform DTCWT, by using the first independent wavelet filter tree and the second independent wavelet filter tree, processing to obtain real components and imaginary components, performing basic wavelet transform enhancement operations on the real components and the imaginary components, and obtaining a dual-tree complex wavelet transform signal;

[0016] S4. Decompose the dual-tree complex wavelet transform signal into n layer, and obtain the double-tree complex wavelet decomposition spectral signal I(W) , observe the double-tree complex wavelet decomposition spectral signal I(W) Different frequency band coefficients;

[0017] S5, performing sparse optimization operation on high-frequency components in coefficients of different frequency bands to obtain sparse optimized high-frequency components;

[0018] S6. Decompose the spectral signal by double-tree complex wavelet according to the sparse optimization of high-frequency components I(W) Perform signal restoration operation to obtain a restored background spectrum;

[0019] S7, performing a background correction operation on the restored background spectrum to obtain a corrected reconstructed background spectrum signal;

[0020] S8, obtaining a calculated spectrum according to the corrected reconstructed background spectrum signal, and judging whether the residual between the calculated spectrum and the measured spectrum has reached the convergence of a stable solution, or whether the iterative update operation has reached the maximum number of iterations;

[0021] S9, if yes, then output the corrected reconstructed background spectrum signal ;

[0022] S10, if not, performing an iterative update operation until an applicable background spectrum is estimated;

[0023] S11. Perform a nonlinear least squares concentration inversion operation based on the applicable background spectrum.

[0024] The present invention can collect and correct the background spectrum in real time in an open optical path environment through the variable decomposition level dual-tree complex wavelet transform (VDL-DTCWT). The dual-tree complex wavelet transform adopted by the present invention provides an efficient signal processing framework, which captures the details and smooth parts in the data through two orthogonal wavelet tree structures. This structure can effectively separate and represent the multi-scale features in the spectral data, and dynamically adjust the number of DTCWT decomposition levels according to the absorption characteristics, signal-to-noise ratio differences and spectral complexity in different wavenumber ranges, so as to capture different scale features. The present invention improves the ability to identify the characteristics of polluted gases by improving the acquisition accuracy of the background spectrum, can better cope with rapidly changing environmental conditions, and provides strong adaptability.

[0025] The present invention uses the variable decomposition layer dual tree complex wavelet transform VDL-DTCWT for roadside infrared spectrum remote sensing monitoring. Specifically, the variable decomposition layer dual tree complex wavelet transform VDL-DTCWT used in the present invention mainly processes infrared spectrum data, performs spectrum decomposition and optimization through DTCWT, and at the same time, the present invention performs sparse optimization on high-frequency components through the VDL-DTCWT method to remove useless signals and noise.

[0026] The present invention uses a variable decomposition layer dual tree complex wavelet transform VDL-DTCWT to iteratively correct the background spectrum to ensure that the spectral data finally output is more accurate. The VDL-DTCWT method provided by the present invention iteratively updates the background spectrum until convergence is reached, thereby ensuring the stability and accuracy of the spectral data obtained by gas pollutant detection, and is particularly suitable for complex remote sensing environments. At the same time, the variable decomposition layer dual tree complex wavelet transform VDL-DTCWT is specially designed and suitable for complex infrared spectral remote sensing monitoring scenarios.

[0027] In a more specific technical solution, in S2, the following logic is used to preset the number of decomposition layers: :

[0028] (13)

[0029] Use the following logic to preset the maximum number of iterations N :

[0030] (14)

[0031] Among them, the function Indicated in wave number The absorption peak characteristics at P Indicates the absorption peak characteristics, For the wave number The signal-to-noise ratio at Indicated in wave number The spectral complexity at C Indicates spectral complexity, wave number The wide band is , v1 represents the minimum wave number in a wide band, v2 Broadband maximum wave number, is the proportionality constant.

[0032] In a more specific technical solution, in S3, the following logic is used to process the measured spectrum using the dual-tree complex wavelet transform DTCWT: :

[0033]

[0034] in, Represents the low-frequency part of the signal after decomposition, represents the high-frequency part of the signal after decomposition, l Indicates low frequency, h Indicates high frequency;

[0035] According to the following logic, with the first independent wavelet filter tree, use the first group k Wavelet filter Transform to get the real part:

[0036] (7)

[0037] in, represents matrix multiplication, are the wavelet coefficients obtained by the first independent wavelet filter tree A, represents the original signal, t Indicates time, g represents the filters of the first independent wavelet filter tree;

[0038] According to the following logic, with the second independent wavelet filter tree, using the second group k Wavelet filter Continue the transformation to generate the imaginary component:

[0039] (8)

[0040] Among them, * represents the convolution operation, are the wavelet coefficients obtained by the second independent wavelet filter tree B, h A filter representing a second independent wavelet filter tree;

[0041] Using the following logic, the first group k Wavelet filter , Group 2 k Wavelet filter Designed to be Hilbert pairs:

[0042] (9)

[0043] in, For the first group k Wavelet filter Perform the Hilbert transform operation, H represents the Hilbert transform;

[0044] The real and imaginary components are combined to obtain the complex wavelet coefficients. The dual-tree complex wavelet transform is used for analytical operation to obtain the phase and amplitude information of the complex wavelet coefficients. The signal analysis is performed based on the phase and amplitude information to obtain the dual-tree complex wavelet transform signal. The complex wavelet coefficients are expressed using the following logic:

[0045] (10)

[0046] in, represents the dual-tree complex wavelet transform signal obtained by performing a dual-tree complex wavelet transform operation on the real component and the imaginary component, represents the real part, represents the imaginary part, W represents the frequency domain, R represents the real part, I represents the imaginary part, i Represents the imaginary unit.

[0047] In a more specific technical solution, in S4, the following logic is used to decompose the dual-tree complex wavelet decomposition spectral signal: I(W) :

[0048]

[0049] In the formula, represents the frequency domain, Represents the low frequency part, Represents the high frequency part, k Indicates the decomposition level, n Indicates the current iteration number, represents the sum of the low-frequency parts, Represents the sum of high frequency parts.

[0050] In a more specific technical solution, in S5, the following formula is used to perform sparse optimization operation:

[0051]

[0052] In the formula, represents the high frequency component, Indicates Gas, h Indicates high frequency, represents the sparsely optimized high-frequency component, Represents a sparse optimization operation;

[0053] Using the following logic, the nonlinear compression function f(x) Acting on high frequency coefficients x superior:

[0054] (11)

[0055] In the formula, It is a small positive number to prevent mathematical singularity. represents the absolute value of the high-frequency coefficient, is a symbolic function;

[0056] The variable decomposition level dual-tree complex wavelet transform VDL-DTCWT provided by the present invention introduces sparse optimization operation and dual-tree complex wavelet transform DTCWT, especially optimizes the high-frequency region of infrared spectral data, can significantly reduce the influence of noise on spectral data, and improves the accuracy of spectral analysis.

[0057] The present invention performs infrared spectral remote sensing monitoring based on variable decomposition layer dual-tree complex wavelet transform VDL-DTCWT, focusing on solving the problem of real-time background spectrum acquisition in open light path scenarios. By combining dual-tree complex wavelet transform with sparse optimization operation, multi-layer decomposition and high-frequency coefficient optimization of spectral data are performed, thus improving the roadside infrared spectral remote sensing monitoring effect.

[0058] use L 1 Regularization strategy, according to the following logic, sparse optimization operation is performed on the model parameters to find the applicable coefficient vector as the model parameters , to complete the minimization operation of the optimization problem:

[0059] (12)

[0060] in, Represents dependence on compressed data y , model parameters The loss function L ; is the model parameter of L 1 norm, that is is the regularization parameter.

[0061] The present invention realizes adaptive estimation of background spectrum based on variable decomposition layer dual tree complex wavelet transform VDL-DTCWT. In the process of background spectrum estimation, the present invention processes spectral bands with different characteristics by varying the number of decomposition layers, and utilizes nonlinear compression and L 1 Regularization strategy is combined with processing high-frequency coefficients to ensure the reliability of background spectrum estimation by iteratively comparing the estimated background spectrum with the original spectrum until convergence to a stable solution or a predefined maximum number of iterations is reached.

[0062] The present invention can effectively improve the processing accuracy of spectral data under complex environmental conditions through sparse optimization technology. The present invention uses sparse optimization technology to selectively strengthen important features and suppress non-important variables to improve the prediction accuracy and interpretability of the model. The present invention has a significant effect on distinguishing background spectra from signal spectra in complex spectral data.

[0063] In a more specific technical solution, in S6, the signal recovery operation is performed using the following logic to obtain the recovered background spectrum: :

[0064]

[0065] in, represents the spectral estimator, bg Indicates the background, represents the frequency domain, IDTCWT represents the inverse dual-tree complex wavelet transform, represents the low-frequency component, l Indicates low frequency, represents the sparsely optimized high-frequency component, Indicates the inverse dual-tree complex wavelet transform of low-frequency components and sparse optimized high-frequency components.

[0066] In a more specific technical solution, in S7, the background correction operation is performed using the following formula to obtain a corrected reconstructed background spectrum signal: :

[0067]

[0068] in, Indicates the current wave number The corresponding background measurement spectrum, represents the spectral estimator, bg indicates background, (new) indicates correction operation, represents the corrected reconstructed background spectrum signal, It represents the operation of taking the maximum value of the reconstructed background spectrum signal and the corrected reconstructed background spectrum signal point by point.

[0069] The present invention uses dual-tree complex wavelet transform DTCWT and sparse optimization, and the technology has more advantages in high-frequency data processing, can more effectively eliminate noise, and ensure the accurate recovery of background spectrum. The VDL-DTCWT method ensures the acquisition of applicable background spectrum through iterative background correction, which is more accurate than the voiceprint recognition method that relies solely on model optimization.

[0070] The variable decomposition layer dual tree complex wavelet transform VDL-DTCWT provided by the present invention introduces sparse optimization processing, focuses on optimizing the high-frequency coefficients of the spectral signal, and solves the problem of real-time acquisition and correction of the background spectrum in a complex environment. Compared with the existing technology, it not only improves the accuracy of the spectral signal, but also ensures that the estimation of the background spectrum is more stable through iterative convergence operations.

[0071] In a more specific technical solution, in S8, the following logical constraints are used to determine whether to end the iteration operation:

[0072] OR n≤N

[0073] in, Indicates wave number The corresponding corrected reconstructed background spectrum signal, Indicates wave number The corresponding measured spectrum, represents the preset error convergence value, n Indicates the current iteration number, N Indicates the maximum number of iterations.

[0074] In a more specific technical solution, in S10, the following logic is used to perform an iterative update operation to update the measured spectrum: :

[0075]

[0076] In the formula, represents the corrected reconstructed background spectrum signal, Indicates the current wave number The corresponding corrected reconstructed background spectrum signal.

[0077] In a more specific technical solution, the roadside infrared spectrum remote sensing monitoring system based on VDL-DTCWT includes:

[0078] Spectrum reading module, used to read the measured spectrum of the incident spectrum ;

[0079] The layer number and iteration number preset module is used to preset the decomposition layer number and the maximum iteration number of different wave number bands. The layer number and iteration number preset module is connected with the spectrum reading module;

[0080] A DTCWT application module is used to apply a dual-tree complex wavelet transform DTCWT to the measured spectrum, and obtains a real component and an imaginary component by using a first independent wavelet filter tree and a second independent wavelet filter tree, and performs a basic wavelet transform enhancement operation on the real component and the imaginary component to obtain a dual-tree complex wavelet transform signal. The DTCWT application module is connected to a layer number and iteration number preset module;

[0081] Decomposition module, used to decompose the dual-tree complex wavelet transform signal into n Layer, get the double tree complex wavelet decomposition spectral signal I(W) , observe the double-tree complex wavelet decomposition spectral signal I(W) The coefficients of different frequency bands, the decomposition module is connected with the DTCWT application module;

[0082] A sparse optimization module is used to perform sparse optimization operations on high-frequency components in coefficients of different frequency bands to obtain sparse optimized high-frequency components. The sparse optimization module is connected to the decomposition module.

[0083] The signal restoration module decomposes the spectral signal by double-tree complex wavelet based on sparse optimization of high-frequency components I(W) Perform signal restoration operation to obtain restored background spectrum, and connect the signal restoration module with the sparse optimization module;

[0084] A background correction module is used to perform background correction operation on the restored background spectrum to obtain a corrected reconstructed background spectrum signal, and the background correction module is connected to the signal restoration module;

[0085] An iterative judgment module is used to obtain a calculated spectrum according to the corrected reconstructed background spectrum signal, to judge whether the residual between the calculated spectrum and the measured spectrum has reached the convergence of a stable solution, or whether the iterative update operation has reached the maximum number of iterations. The iterative judgment module is connected to the background correction module and the layer number and iteration number preset module;

[0086] Iterative output module is used to output the corrected reconstructed background spectrum signal when the residual between the calculated spectrum and the measured spectrum converges to a stable solution or the iterative update operation reaches the maximum number of iterations , the iteration output module is connected with the iteration judgment module;

[0087] A continuous iteration module is used to perform iterative update operations until an applicable background spectrum is estimated, and the continuous iteration module is connected to the iterative judgment module;

[0088] The inversion module is used to perform a nonlinear least square concentration inversion operation according to an applicable background spectrum, and the inversion module is connected to the continuous iteration module.

[0089] Compared with the prior art, the present invention has the following advantages:

[0090] The present invention can collect and correct the background spectrum in real time in an open optical path environment through the variable decomposition level dual-tree complex wavelet transform (VDL-DTCWT). The dual-tree complex wavelet transform adopted by the present invention provides an efficient signal processing framework, which captures the details and smooth parts in the data through two orthogonal wavelet tree structures. This structure can effectively separate and represent the multi-scale features in the spectral data, and dynamically adjust the number of DTCWT decomposition levels according to the absorption characteristics, signal-to-noise ratio differences and spectral complexity in different wavenumber ranges, so as to capture different scale features. The present invention improves the ability to identify the characteristics of polluted gases by improving the acquisition accuracy of the background spectrum, can better cope with rapidly changing environmental conditions, and provides strong adaptability.

[0091] The variable decomposition level dual-tree complex wavelet transform VDL-DTCWT provided by the present invention introduces sparse optimization operation and dual-tree complex wavelet transform DTCWT, especially optimizes the high-frequency region of infrared spectral data, can significantly reduce the influence of noise on spectral data, and improves the accuracy of spectral analysis.

[0092] The present invention realizes adaptive estimation of background spectrum based on variable decomposition layer dual tree complex wavelet transform VDL-DTCWT. In the process of background spectrum estimation, the present invention processes spectral bands with different characteristics by varying the number of decomposition layers, and utilizes nonlinear compression and L 1 Regularization strategy is combined with processing high-frequency coefficients to ensure the reliability of background spectrum estimation by iteratively comparing the estimated background spectrum with the original spectrum until convergence to a stable solution or a predefined maximum number of iterations is reached.

[0093] The present invention can effectively improve the processing accuracy of spectral data under complex environmental conditions through sparse optimization technology. The present invention uses sparse optimization technology to selectively strengthen important features and suppress non-important variables to improve the prediction accuracy and interpretability of the model. The present invention has a significant effect on distinguishing background spectra from signal spectra in complex spectral data.

[0094] The present invention uses dual-tree complex wavelet transform DTCWT and sparse optimization, and the technology has more advantages in high-frequency data processing, can more effectively eliminate noise, and ensure the accurate recovery of background spectrum. The VDL-DTCWT method ensures the acquisition of applicable background spectrum through iterative background correction, which is more accurate than the voiceprint recognition method that relies solely on model optimization.

[0095] The present invention solves the technical problem that the prior art is difficult to collect background spectral data in real time in a scenario with an open optical path, which restricts the adaptability and accuracy of OP-FTIR technology under complex environmental conditions and leads to low characterization accuracy of gaseous pollutants. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 Schematic diagram of basic steps of the roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to Example 1 of the present invention;

[0097] Figure 2 This is a schematic diagram of the basic principle of remote sensing OP-FTIR according to Example 1 of the present invention;

[0098] Figure 3 This is a schematic diagram of data flow processing for decomposition operation in dual-tree complex wavelet transform DTCWT according to embodiment 1 of the present invention;

[0099] Figure 4 This is a schematic diagram of signal restoration data flow processing in a dual-tree complex wavelet transform DTCWT according to Embodiment 1 of the present invention;

[0100] Figure 5 This is a reconstructed background spectrum based on VDL-DTCWT and measured spectrum according to Example 2 of the present invention;

[0101] Figure 6 This is the OP-FTIR full-band transmittance spectrum of Example 2 of the present invention;

[0102] Figure 7a The fitted transmittance spectrum and the measured transmittance spectrum of CH4 in Example 2 of the present invention;

[0103] Figure 7b The fitted transmittance spectrum and the measured transmittance spectrum of CO in Example 2 of the present invention;

[0104] Figure 7c The fitted transmittance spectrum and the measured transmittance spectrum of CO2 in Example 2 of the present invention;

[0105] Figure 7d Schematic diagram of the fitted transmittance spectrum and the measured transmittance spectrum of NO in Example 2 of the present invention;

[0106] Figure 7e Schematic diagram of the fitted transmittance spectrum and the measured transmittance spectrum of NO2 in Example 2 of the present invention;

[0107] Figure 8a This is a residual spectrum diagram of CH4 of CH4 in Example 2 of the present invention;

[0108] Figure 8b This is the residual spectrum of CO of CO in Example 2 of the present invention;

[0109] Figure 8c This is the residual spectrum of CO2 of CO2 in Example 2 of the present invention;

[0110] Figure 8d This is the residual spectrum of NO of NO in Example 2 of the present invention;

[0111] Figure 8e This is the residual spectrum of NO2 of NO2 in Example 2 of the present invention. DETAILED DESCRIPTION

[0112] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0113] Example 1

[0114] like Figure 1 As shown, the roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT provided by the present invention includes the following basic steps:

[0115] S1. Read the measured spectrum of the incident spectrum ;

[0116] In this embodiment, the infrared light source 1 emits a wide spectrum infrared light, as shown in the following formula (1):

[0117] (1)

[0118] in, is the light source intensity, R Represents the light source, is the spectral shape function, Indicates frequency.

[0119] like Figure 2 As shown, in this embodiment, a wide spectrum infrared light is emitted from an infrared light source 1 to pass through the target gas on the road side, and the infrared light emitted from the road side gas is received by a Fourier transform infrared spectrometer 2, and the measured spectrum of the incident spectrum of the Fourier transform infrared spectrometer 2 is read. ;

[0120] In this embodiment, when the wide-spectrum infrared light passes through the target gas in the atmosphere, part of the light of a specific wavelength is absorbed. According to the Lambert-Beer law, the transmittance of light It can be expressed as the following formula:

[0121] (2)

[0122] in, It is j Gas at frequency The absorption coefficient at is the absorption coefficient, It is j The concentration of the gas, L is the optical path length.

[0123] In this embodiment, the Fourier transform infrared spectrometer 2 at the receiving end receives the measured spectrum after being absorbed by the target gas. :

[0124] (3)

[0125] in, Represents the background spectrum without absorption by the target gas.

[0126] After the wide spectrum infrared light reaches the Fourier transform infrared spectrometer 2, it is split by the interferometer to generate an interference pattern. In this embodiment, the interference pattern in the time domain The measured spectrum can be expressed as The inverse Fourier transform of is:

[0127] (4)

[0128] in, t Indicates time, e Represents a natural constant.

[0129] In this embodiment, the Fourier transform infrared spectrometer 2 transforms the interference pattern in the time domain into Converted into measured spectrum , and obtain the light intensity distribution of each wavelength:

[0130] (5)

[0131] in, d represents the maximum optical path difference of the interferometer, represents the standing wave parameter;

[0132] In this embodiment, by measuring the spectrum and background spectrum , the absorbance spectrum can be calculated A(ν) , and by standard absorbance spectrum As(ν) , identify the gas components in the light path, as shown in formula (6).

[0133] (6)

[0134] Although the Lambert-Beer law only describes the corresponding relationship between the true absorbance and the concentration, in practical applications, it is usually assumed that there is also a proportional relationship between the measured absorbance and the concentration as shown in the above formula (6), and the standard model is established using the above formula (6). This default assumes that there is a linear relationship between the true absorbance and the apparent absorbance. Since the apparent spectrum is the convolution of the true spectrum and the instrument line type, in actual measurements, in order to ensure that the true absorbance and the apparent absorbance satisfy the linear relationship, the instrument line type must be narrower than the spectral line type. This means that the resolution value must be smaller than the spectral line type. However, at one atmosphere, the line width of a typical single spectral line of a small molecule with a rotatable structure is 0.05~0.15cm-1, while that of most FTIR spectrometers is 0.5~4cm-1, which causes a deviation from the linear relationship between the apparent spectrum and the true spectrum.

[0135] In addition, in the open-path Fourier-transform Infrared (OP-FTIR) system, the background gas is difficult to completely remove due to the presence of common atmospheric gas components in the optical path. These background gases make the background spectrum Real-time measurement is difficult.

[0136] S2, preset the number of decomposition layers and the maximum number of iterations for different wave number bands;

[0137] In this embodiment, the absorption intensity of gas components at different spectral wavenumber positions is different. Therefore, when processing in different wavenumber ranges, the required number of decomposition levels (Leve1s) and the maximum number of iterations (Iterations) are also different. and the maximum number of iterations The settings are shown in the following formulas (13) and (14):

[0138] (13)

[0139] Use the following logic to set the maximum number of iterations:

[0140] (14)

[0141] In the formula, the function Indicated in wave number The absorption peak characteristics at For the wave number The signal-to-noise ratio at Indicated in wave number Spectral complexity at wave number The wide band is ,v1 represents the minimum wave number in a wide band, v2 Broadband maximum wave number, is the proportionality constant.

[0142] S3. Measure the spectrum Applying the dual-tree complex wavelet transform DTCWT, by using the first independent wavelet filter tree and the second independent wavelet filter tree, processing to obtain real components and imaginary components, performing basic wavelet transform enhancement operations on the real components and the imaginary components, and obtaining a dual-tree complex wavelet transform signal;

[0143] In the background spectrum estimation process of this embodiment, spectral bands with different characteristics are processed by varying the number of decomposition layers;

[0144] Wavelet transform has been effectively used for background spectrum reconstruction. For details, see the following references: A background elimination method based on wavelet transform for Raman spectra. Chemometrics and Intelligent Laboratory Systems, 85, 94-101; An improved background-correction algorithm for Raman spectroscopy based on the wavelet transform[J]. Applied Spectroscopy, 2019, 73(1): 78-87; An improved spectral background subtraction method based on wavelet energy[J]. Applied Spectroscopy, 2016, 70(12): 1994-2004); An opensource, iterative dual-tree wavelet background subtraction method extendedfrom automated diffraction pattern analysis to optical spectroscopy[J].Applied spectroscopy, 2019, 73(12): 1370-1379. Due to its significant advantages in processing non-stationary signals and multi-scale features, wavelet transform can provide information about the signal in both the time domain and the frequency domain, enabling the wavelet transform to capture signal details and changes. In addition, wavelet transform has good denoising performance and resolution, and can effectively reduce noise interference when extracting background spectra, thereby improving signal clarity and accuracy. The above advantages make the application of wavelet transform in background spectrum reconstruction more and more extensive and in-depth.

[0145] In this embodiment, the following formula is used to measure the spectrum Apply the aforementioned dual-tree complex wavelet transform DTCWT:

[0146]

[0147] in, Represents the low-frequency part of the signal after decomposition, represents the high-frequency part of the signal after decomposition, l Indicates low frequency, h Indicates high frequency.

[0148] Due to the limitations of traditional methods in acquiring target background, the background spectrum Real-time acquisition is not possible. In FTIR spectroscopy, the spectrum is measured As the current wave number The function of the absorption peak reflects the vibration mode of the molecule. In the measured spectrum, the sharp absorption peak is the manifestation of the specific vibration mode of the molecule, including the high-frequency components of the signal. In contrast, the background spectrum comes from the instrument response, and the background spectrum shows a smooth change, which belongs to the low-frequency component. By analyzing and extracting the low-frequency part of the measured spectrum, the background spectrum can be effectively obtained and separated in real time, further improving the accuracy and reliability of the analysis.

[0149] like Figure 3 As shown, the dual-tree complex wavelet transform DTCWT adopted in this embodiment enhances the basic wavelet transform by using two independent wavelet filter trees to process the real component and the imaginary component. Compared with the traditional discrete wavelet transform, this modification introduces improved shift invariance and directional selectivity, and can effectively extract the low-frequency information of the signal. Figure 3 In represents the first independent wavelet filter tree A at level 0. n Layer filter processing measurement data m , represents the first level of the first independent wavelet filter tree A. n Layer filter processing measurement data m , represents the use of the 0th level of the second independent wavelet filter tree A n Layer filter processing measurement data m , represents the first level of the second independent wavelet filter tree A. n Layer filter processing measurement data m .

[0150] The dual-tree complex wavelet transform DTCWT uses two parallel wavelet filter trees to generate the real and imaginary parts of the wavelet coefficients respectively. For each level of wavelet decomposition, the filters of the first independent wavelet filter tree A and the second independent wavelet filter tree B are downsampled respectively.

[0151] In this embodiment, the first independent wavelet filter tree A uses the first group k Wavelet filter Transform to obtain the real component, as shown in the following formula (7):

[0152] (7)

[0153] in, represents matrix multiplication, are the wavelet coefficients obtained by the first independent wavelet filter tree A, Represents the original signal.

[0154] The second independent wavelet filter tree B uses the second set k Wavelet filter , used to generate the imaginary component, as shown in the following formula (8):

[0155] (8)

[0156] Among them, * represents the convolution operation, is the wavelet coefficient obtained by the second independent wavelet filter tree B, the second group k Wavelet filter The first group k Wavelet filter By Hilbert transform, we can ensure that the second group k Wavelet filter The first group k Wavelet filter are mutually orthogonal in the frequency domain.

[0157] In this embodiment, the first group of the first independent wavelet filter tree A k Wavelet filter and the second group of the second independent wavelet filter tree B k Wavelet filter Designed to be Hilbert pairs:

[0158] (9)

[0159] in, For the first group k Wavelet filter Perform a Hilbert transform operation. In the frequency domain, the effect of the Hilbert transform is to shift the signal phase of the positive frequency part by +90∘ and the signal phase of the negative frequency part by −90∘.

[0160] The complex wavelet coefficients can be formed by combining the outputs of the first independent wavelet filter tree A and the second independent wavelet filter tree B, so that the phase and amplitude information of the complex wavelet coefficients can be used for further signal analysis and processing. The complex wavelet coefficients can be expressed as:

[0161] (10)

[0162] in, represents the dual-tree complex wavelet transform signal obtained by performing a dual-tree complex wavelet transform operation on the real component and the imaginary component, represents the real part, represents the imaginary part, R represents the real part, I represents the imaginary part, i Represents the imaginary unit.

[0163] S4. Decompose the dual-tree complex wavelet transform signal into n Layer, get the double tree complex wavelet decomposition spectral signal I(W) , observe the double-tree complex wavelet decomposition spectral signal I(W) Different frequency band coefficients;

[0164] In this embodiment, the double-tree complex wavelet decomposition spectrum signal is obtained by decomposition. I(W) The mathematical logic is as follows:

[0165]

[0166] in, represents the frequency domain, Represents the low frequency part, Represents the high frequency part, k Indicates the decomposition level, n Indicates the current iteration number.

[0167] S5, performing sparse optimization operation on high-frequency components in coefficients of different frequency bands to obtain sparse optimized high-frequency components;

[0168] In this embodiment, the above-mentioned sparse optimization operation is performed using the following formula:

[0169]

[0170] in, represents the high frequency component, Indicates Gas, hIndicates high frequency, represents the sparsely optimized high-frequency component, Represents a sparse optimization operation.

[0171] The present invention uses DTCWT and sparse optimization technology, which has more advantages in high-frequency data processing, can more effectively eliminate noise and ensure accurate signal recovery.

[0172] In the dual-tree complex wavelet transform process of this embodiment, the high-frequency signal parameter selection operation is performed. The traditional hard threshold or soft threshold method has limitations. The present invention reduces the dynamic range of the data and enhances the weak components in the signal by applying logarithmic nonlinear compression to the signal. The nonlinear compression function f Acting on high frequency coefficients x As shown in the following formula (11):

[0173] (11)

[0174] in, is a small positive number to prevent mathematical singularity, ensuring that x Near 0 o'clock f ( x ) remains stable.

[0175] In this embodiment, nonlinear compression is performed through nonlinear least squares analysis; L1 regularization is combined to process high frequency coefficients; L 1 Regularization strategy is used to achieve sparse model parameters, thereby improving the interpretability and computational efficiency of the model. y = f ( x ) will be used for sparse optimization. The goal of sparse optimization is to find a coefficient vector as the model parameters , so that the following optimization problem is minimized, as shown in equation (12):

[0176] (12)

[0177] in, Represents dependence on compressed data y , model parameters The loss function L ; is the model parameter of L 1 norm, that is , using the model parameters of L The 1-norm provides a measure of sparsity; is a regularization parameter that controls the strength of sparsity in the optimization problem.

[0178] In this embodiment, nonlinear compression and L 1 Regularization combined with the use of can handle a lot of noise or a wide dynamic range of data, nonlinear compression by changing the distribution of signal amplitude, can enhance the algorithm's sensitivity to low-amplitude signal components, which may be ignored in the uncompressed data. At the same time, L 1 Regularization promotes the sparsity of the solution, which not only helps to improve computational efficiency but also enhances the interpretability of the model because L 1 Regularization tends to select a small number of important features.

[0179] S6. Decompose the spectral signal by double-tree complex wavelet according to the sparse optimization of high-frequency components I(W) Perform signal restoration operation to obtain a restored background spectrum;

[0180] like Figure 4 As shown, in this embodiment, after high-frequency coefficient processing, the signal is restored using the following formula to obtain the restored background spectrum:

[0181]

[0182] Wherein, IDTCWT represents the inverse dual-tree complex wavelet transform. Figure 4 In represents the first independent wavelet filter tree A at level 0. n Layer filter processing measurement data m The equivalent substitution of the result is, represents the first level of the first independent wavelet filter tree A. n Layer filter processing measurement data m The equivalent substitution of the result is, represents the use of the 0th level of the second independent wavelet filter tree A n Layer filter processing measurement data m The equivalent substitution of the result is, represents the first level of the second independent wavelet filter tree A. n Layer filter processing measurement data m Equivalence substitution of results.

[0183] S7, performing background correction operation on the restored background spectrum to obtain a corrected reconstructed background spectrum signal;

[0184] In this embodiment, the background correction operation is performed using the following formula:

[0185]

[0186] in, Indicates the current wave number The corresponding background measurement spectrum, represents the spectral estimator, bg indicates background, (new) indicates correction operation, represents the corrected reconstructed background spectrum signal, It represents the operation of taking the maximum value of the reconstructed background spectrum signal and the corrected reconstructed background spectrum signal point by point;

[0187] S8, obtaining a calculated spectrum according to the corrected reconstructed background spectrum signal, and judging whether the residual between the calculated spectrum and the measured spectrum has reached the convergence of a stable solution, or whether the iterative update operation has reached the maximum number of iterations;

[0188] In this embodiment, the following formula is used to determine whether to end the iteration operation:

[0189] OR n≤N

[0190] in, Indicates wave number The corresponding corrected reconstructed background spectrum signal, Indicates wave number The corresponding measured spectrum, represents the preset error convergence value, n Indicates the current iteration number, N Indicates the maximum number of iterations;

[0191] S9, if yes, then output the corrected reconstructed background spectrum signal ;

[0192] S10, if not, performing an iterative update operation until an applicable background spectrum is estimated;

[0193] In this embodiment, the above-mentioned iterative update operation is performed using the following formula:

[0194]

[0195] in, represents the corrected reconstructed background spectrum signal, Indicates the current wave number The corresponding corrected reconstructed background spectrum signal.

[0196] In this embodiment, the VDL-DTCWT method ensures that the most suitable background spectrum is obtained through iterative background correction, which is more accurate than the voiceprint recognition method that relies solely on model optimization.

[0197] The present invention proposes a variable decomposition layer dual tree complex wavelet transform (VDL-DTCWT) method to reconstruct background spectrum. The dual-tree complex wavelet transform provides an efficient signal processing framework that captures details and smooth parts in the data through two orthogonal wavelet tree structures. This structure can effectively separate and represent multi-scale features in spectral data. Specific references: Discussion on dual–tree complexwavelet transform and generalized regression neural network based concentration-resolved fluorescence spectroscopy for oil identification[J].Analytical Methods, 2019, 11(36): 4566-4574) Multiscale representation learning for image classification: A survey[J]. IEEE Transactions on Artificial Intelligence, 2021, 4(1): 23-43. The number of DTCWT decomposition layers is dynamically adjusted according to the absorption characteristics, signal-to-noise ratio differences and spectral complexity in different wavenumber ranges to capture different scale features.In addition, sparse optimization techniques improve the prediction accuracy and interpretability of the model by selectively strengthening important features and suppressing unimportant variables, which is particularly critical for distinguishing background from signal in complex spectral data. Joint bilateral filtering and spectral similarity-based sparse representation: A generic framework for effective feature extraction and data classification in hyperspectral imaging[J]. Pattern Recognition, 2018, 77: 316-328; Demixing sines and spikes: Robust spectral super-resolution in the presence of outliers[J]. Information and Inference: A Journal of the IMA, 2018, 7(1): 105-168. By improving the accuracy of background spectrum acquisition, not only the ability to identify the characteristics of pollutant gases is enhanced, but also it can better cope with rapidly changing environmental conditions and provide strong adaptability.

[0198] The present invention uses the VDL-DTCWT method to monitor infrared spectroscopy remote sensing under open optical path conditions, and performs multi-level decomposition and sparse optimization of spectral data through dual-tree complex wavelet transform (DTCWT), thereby achieving real-time correction of the background spectrum. This method focuses on improving the accuracy of gaseous pollutant detection in complex environments.

[0199] S11, performing a nonlinear least squares concentration inversion operation according to an applicable background spectrum;

[0200] In this embodiment, nonlinear least squares (NLS) analysis fits the measured spectrum to the calculated spectrum through iteration, and compares the estimated calculated spectrum with the original background spectrum until the residual between the calculated spectrum and the measured spectrum approaches an acceptable minimum.

[0201] In this embodiment, nonlinear least squares (NLS) analysis is another quantitative analysis method that does not rely on the implicit linear Lambert-Beer law. For details, see the literature: Completely automated open-path Fourier transform infrared spectroscopy (Griffiths PR, Shao L, Leytem A B. Completely automated open-path FT-IR spectrometry [J]. Analytical and bioanalytical chemistry, 2009, 393: 45-50). Analytical and bioanalytical chemistry (Completely automated open-path FT-IRspectrometry) Challenges associated with the atmospheric monitoring of areal emission sources and the need for optical remote sensing techniques—an open-path Fourier transforminfrared (OP-FTIR) spectroscopy experience report. Environ Earth Sci 75, 919(2016). https: / / doi.org / 10.1007 / s12665-016-5482-z). NLS fits the measured spectrum by iteratively calculating the spectrum until the residual between the calculated and measured spectra is close to an acceptable minimum.

[0202] In the Lambert-Beer law, the relationship between the absorbance and concentration of a sample is as shown in the following equation (15):

[0203] (15)

[0204] in, I m (v) is the current wave number ν The corresponding sample measurement spectrum, m Represents measurement data, I 0 (v) is the current wave number ν The corresponding initial background spectrum is Lis the optical path length, It is j The absorption coefficient of the gas, is the absorption coefficient, Ci It is j The concentration of the gas, ν is the current wave number, e is a natural constant.

[0205] In this embodiment, the transmittance spectrum The calculation method of is shown in the following formula (16):

[0206] (16)

[0207] in, meas Indicates actual measurement.

[0208] In this embodiment, the transmittance τ obtained by the preset gas composition and environmental parameters is convoluted with the instrument linear function ILS Generate calibrated transmittance , as shown in the following formula (17):

[0209] (17)

[0210] in, cal It represents the calculation, and the convolution result of the field angle and the apodization function is f ( v ), represents matrix multiplication, e is a natural constant.

[0211] NLS fits the measured spectrum by iterative calculation until the residual between the calculated spectrum and the measured spectrum converges to an acceptable minimum, and finally obtains the best fitting spectrum and the gas concentration information, as shown in the following equation (18):

[0212] (18)

[0213] in, is the number of spectral points in the fitting area, Indicates j The theoretical synthetic transmittance spectra of the gases, Indicates j The measured transmittance spectra of the gases, cal Indicates calculation, meas Indicates actual measurement.

[0214] In this embodiment, the matching degree in the best fit search algorithm is Calculate according to formula (19):

[0215] (19)

[0216] in, n Indicates the current iteration number, f is the total number of variables for all peak and baseline functions, n - f represents the degrees of freedom; mi For the j The measurement data of the gas, and ci For the j Calculation data for the gases; NRMS Represents an estimate of the RMS noise of the measured data in the fitted region.

[0217] Example 2

[0218] In this embodiment, in order to verify the applicability of the background spectrum reconstruction method based on VDL-DTCWT, real-time monitoring of exhaust emissions was carried out on the roadside.

[0219] The OP-FTIR instrument parameters used in this example are shown in Table 1 below:

[0220] Table 1. Experimental instrument parameters

[0221]

[0222] In the data processing process of this embodiment, the real-time absorption spectrum of the roadside atmosphere is continuously measured by OP-FTIR, and the background spectrum is reconstructed using the real-time absorption spectrum to achieve the inversion of gas component concentration. The background spectrum reconstruction parameters based on VDL-DTCWT are shown in Table 2 below:

[0223] Table 2. Variable bands and corresponding decomposition levels and maximum number of iterations

[0224]

[0225] Based on the parameters in Table 2 above, the background spectrum is reconstructed using the real-time absorption spectrum and the VDL-DTCWT algorithm. The background spectrum of the absorption band can be found in Figure 5 , and better realize the function of real-time acquisition of background spectrum.

[0226] Based on the reconstructed background spectrum and the measured spectrum, the transmittance spectrum can be calculated. For the full-band transmittance spectrum, see Figure 6 . The present invention combines the dual-tree complex wavelet transform with sparse optimization through the VDL-DTCWT method, which enhances the signal recovery capability and can adjust and correct the background spectrum data in real time. The concentration inversion is performed through the nonlinear least squares method, which effectively overcomes the background spectrum acquisition problem of OP-FTIR technology in complex environments and improves the accuracy of pollutant characterization.

[0227] After obtaining the transmittance spectrum, the above nonlinear least squares method is used to perform real-time quantitative analysis of roadside emission gas components. The mainstream pollutant gases include: CH4, CO, CO2, NO, NO2. The nonlinear least squares fitting parameters are shown in Table 3 below, including but not limited to: window function, temperature, pressure and optical path:

[0228] Table 3. Nonlinear least squares fitting parameters

[0229]

[0230] The inversion bands of the mainstream pollutant gas component concentrations of CH4, CO, CO2, NO, and NO2 are shown in Table 4.

[0231] Table 4. Summary of inversion intervals for each gas component

[0232]

[0233] The nonlinear fitting results are shown in Figures 7a to 7e , it can be seen that the fitting results of CO, CO2, and NO are better.

[0234] In this embodiment, the transmittance spectrum fitting residuals of different gas components can be calculated based on the fitted transmittance spectra and the measured transmittance spectra of different gas components, see Figures 8a to 8e As shown in Figure 2, it can be seen that the fitting residuals of CO, CO2, NO, and NO2 are all small.

[0235] based on Figures 8a to 8e The residual spectrum in can be used to calculate the RMS (Root Mean Square) value to characterize the degree of spectral fitting. In practical applications, the accuracy of the fitting model can be quantitatively evaluated by calculating the RMS value of the residual spectrum. The size of the RMS value directly reflects the quality of spectral fitting. The smaller the value, the better the fitting, and vice versa. The calculation method of the RMS value is shown in equation (20).

[0236] (20)

[0237] in, M represents the number of measurement points in the fitting band, represents the value of the residual spectrum, Indicates j The value of the residual spectrum of the gas.

[0238] In the process of nonlinear least squares iterative inversion, the covariance matrix of multiple parameters is further calculated through the iterative value matrix. The aforementioned parameters include: calculated concentration value, number of fitting items and spectral offset value, and effective radian value. The covariance matrix provides an uncertainty assessment of the concentration value. The standard error (SE, Standard Error) is calculated through the covariance matrix. The calculation method is shown in the following equation (21). The size of the standard error reflects the accuracy and reliability of the concentration value. A smaller standard error indicates that the concentration value has a higher precision. In addition to the standard error of the concentration value, the standard errors of other fitting parameters, such as the spectral offset value and the effective radian value, are calculated by a similar method:

[0239] (twenty one)

[0240] in, SE is the covariance matrix x The square root of the diagonal elements, x represents the fitted gas order and cov represents the covariance.

[0241] The spectrum was measured 10 times in succession, and the background spectrum was reconstructed by median moving filter and VDL-DTCWT respectively, and the quantitative analysis effect of nonlinear least squares under different background spectra was compared, as shown in Table 5. The window size of the median moving filter can be set to, for example, 401, and the number of filtering times can be set to, for example, 100.

[0242] In Table 5 below, Conc represents the quantitative concentration value, RMS (Root Mean Square) represents the root mean square representing the degree of spectral fitting, and SE (Standard Deviation) represents the standard error of the concentration value. By comparing the nonlinear least squares quantitative analysis effects under different background reconstruction methods, the performance difference of the two methods in spectral analysis can be evaluated.

[0243] Table 5. Summary of the values ​​and errors of the inversion of various gas components

[0244]

[0245] For the concentration inversion of all measured gas components, the RMS value of the VDL-DTCWT method is less than or equal to the RMS value of the median shift filter. In particular, in the concentration inversion of CO, the background spectrum reconstructed by the median filter fails under this parameter, resulting in negative concentration values, while the background spectrum reconstructed by the VDL-DTCWT is successful when the RMS value is very small. This shows that the VDL-DTCWT method has better robustness and accuracy when dealing with complex or noisy spectral data.

[0246] For gas components such as CO2, NO, NO2, and CH4, the RMS difference between the two methods is small, but the VDL-DTCWT method still shows a slightly better fitting effect. In order to further quantitatively compare the performance of the median moving filter and VDL-DTCWT in the inversion of different gas component concentrations, the ratio of the standard error to the concentration value (SE / Conc) can be used. This ratio can more intuitively show the differences in error distribution between different methods, thereby providing a more comprehensive performance evaluation, as shown in Table 6 below:

[0247] Table 6. Summary of inversion errors of various gas components

[0248]

[0249] From the data in Table 6, it can be seen that the VDL-DTCWT method is superior to the median moving filter in the SE / Conc ratio of most gas components. This result further proves the stability and reliability of VDL-DTCWT in the inversion of different gas concentrations. Especially in the concentration inversion of CO, CO2, NO and NO2, the standard error of the VDL-DTCWT method is significantly smaller and the effect is excellent. The VDL-DTCWT method performs better in the synthesis of complex multi-component background spectra and can achieve real-time and high-precision measurement of OP-FTIR. Especially for the inversion of CO2 and NO, the fitting error is less than 1.5% and the standard error is less than 0.1, providing more reliable real-time environmental monitoring data.

[0250] The estimated background spectrum is applied to nonlinear least squares concentration inversion. The experimental results show that the fitting errors of CO2 and NO inversion are less than 1.5%, and the standard error is less than 0.1, which can achieve high-precision real-time measurement of roadside pollutants. The present invention significantly improves the adaptability and accuracy of OP-FTIR technology under complex environmental conditions, and provides a more reliable technical means for real-time monitoring of atmospheric pollutants.

[0251] By comparing the RMS value, standard deviation SE, and quantitative concentration values ​​of Conc, it can be concluded that the performance of the VDL-DTCWT method in the inversion of concentrations of various gas components is better than that of the median shift filter. This provides an important reference for selecting appropriate background spectrum reconstruction methods in practical applications. In particular, the VDL-DTCWT method shows higher accuracy and reliability in high-precision spectral analysis and gas concentration measurement.

[0252] The present invention proposes a dual-tree complex wavelet transform (VDL-DTCWT) method with a variable number of decomposition layers to address the challenge of difficult adaptive estimation of background spectra in OP-FTIR active remote sensing technology. By dynamically adjusting the number of decomposition layers and combining nonlinear compression with L1 regularization technology, accurate characterization of the background spectra of gaseous pollutants is achieved in an open optical path environment. Experimental results show that the fitting errors of the VDL-DTCWT method in CO2 and NO inversion are both less than 1.5%, and the standard error is less than 0.1, indicating that it has excellent automatic recognition and accurate detection capabilities in complex road environments. The present invention not only improves the accuracy of background spectrum acquisition and enhances the ability to identify polluted gases, but also can better adapt to rapidly changing environmental conditions and ensure the reliability of remote sensing monitoring of atmospheric pollution.

[0253] The VDL-DTCWT method adopted in the present invention is mainly used for infrared spectral remote sensing monitoring under open optical paths. It uses dual-tree complex wavelet transform (DTCWT) and sparse optimization technology to perform layered processing on spectral data, correct the background spectrum in real time and improve the characterization accuracy of gaseous pollutants in complex environments.

[0254] In terms of specific application scenarios, the VDL-DTCWT method provided by the present invention is used for spectral analysis, focusing on gas pollutant monitoring, and improving the accuracy of spectral data processing through real-time correction of background spectra. The processing object of the VDL-DTCWT method mainly processes infrared spectral signals and optimizes background spectral data. The VDL-DTCWT method uses multi-layer wavelet decomposition combined with sparse optimization to ensure accurate real-time correction of the background spectrum. The VDL-DTCWT method of the present invention: In view of the defect that traditional spectral monitoring methods are difficult to correct the background spectrum in real time, the dual-tree complex wavelet transform and sparse optimization technology are used to achieve accurate correction of the background spectrum in a complex environment, ensuring the stability and accuracy of data acquisition under open optical path conditions. The advantages of the VDL-DTCWT method are:

[0255] Strong real-time performance: Able to correct the spectral background in real time under dynamic environment.

[0256] Adapt to complex environments: Through sparse optimization and dual-tree complex wavelet technology, it can maintain high-precision data processing in complex environments.

[0257] In summary, the present invention can collect and correct the background spectrum in real time in an open optical path environment through the variable decomposition level-dual-tree complex wavelet transform (VDL-DTCWT). The dual-tree complex wavelet transform adopted by the present invention provides an efficient signal processing framework, which captures the details and smooth parts in the data through two orthogonal wavelet tree structures. This structure can effectively separate and represent the multi-scale features in the spectral data, and dynamically adjust the number of DTCWT decomposition levels according to the absorption characteristics, signal-to-noise ratio differences and spectral complexity in different wavenumber ranges, so as to capture different scale features. The present invention improves the ability to identify the characteristics of polluted gases by improving the acquisition accuracy of the background spectrum, can better cope with rapidly changing environmental conditions, and provides strong adaptability.

[0258] The variable decomposition level dual-tree complex wavelet transform VDL-DTCWT provided by the present invention introduces sparse optimization operation and dual-tree complex wavelet transform DTCWT, especially optimizes the high-frequency region of infrared spectral data, can significantly reduce the influence of noise on spectral data, and improves the accuracy of spectral analysis.

[0259] The present invention realizes adaptive estimation of background spectrum based on variable decomposition layer dual tree complex wavelet transform VDL-DTCWT. In the process of background spectrum estimation, the present invention processes spectral bands with different characteristics by varying the number of decomposition layers, and utilizes nonlinear compression and L 1 Regularization strategy is combined with processing high-frequency coefficients to ensure the reliability of background spectrum estimation by iteratively comparing the estimated background spectrum with the original spectrum until convergence to a stable solution or a predefined maximum number of iterations is reached.

[0260] The present invention can effectively improve the processing accuracy of spectral data under complex environmental conditions through sparse optimization technology. The present invention uses sparse optimization technology to selectively strengthen important features and suppress non-important variables to improve the prediction accuracy and interpretability of the model. The present invention has a significant effect on distinguishing background spectra from signal spectra in complex spectral data.

[0261] The present invention uses dual-tree complex wavelet transform DTCWT and sparse optimization, and the technology has more advantages in high-frequency data processing, can more effectively eliminate noise, and ensure the accurate recovery of background spectrum. The VDL-DTCWT method ensures the acquisition of applicable background spectrum through iterative background correction, which is more accurate than the voiceprint recognition method that relies solely on model optimization.

[0262] The present invention solves the technical problem that the prior art is difficult to collect background spectral data in real time in a scenario with an open optical path, which restricts the adaptability and accuracy of OP-FTIR technology under complex environmental conditions and leads to low characterization accuracy of gaseous pollutants.

[0263] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A roadside infrared spectroscopy remote sensing monitoring method based on VDL-DTCWT is characterized by: The method comprises: S1. Read the measured spectrum of the incident spectrum ; S2, preset the number of decomposition layers and the maximum number of iterations for different wave number bands; S3, measuring the spectrum Applying a dual-tree complex wavelet transform DTCWT, by using a first independent wavelet filter tree and a second independent wavelet filter tree to obtain a real component and an imaginary component, performing a basic wavelet transform enhancement operation on the real component and the imaginary component, and obtaining a dual-tree complex wavelet transform signal; S4, decomposing the dual-tree complex wavelet transform signal into n layer, and obtain the double-tree complex wavelet decomposition spectral signal I(W) , observe the dual-tree complex wavelet decomposition spectral signal I(W) Different frequency band coefficients; S5, performing a sparse optimization operation on the high-frequency components in the coefficients of different frequency bands to obtain sparse optimized high-frequency components; S6, according to the sparse optimization of high-frequency components, decomposing the spectral signal of the dual-tree complex wavelet I(W) Perform signal restoration operation to obtain a restored background spectrum; S7, performing a background correction operation on the restored background spectrum to obtain a corrected reconstructed background spectrum signal; S8, obtaining a calculated spectrum according to the corrected reconstructed background spectrum signal, and determining whether the residual between the calculated spectrum and the measured spectrum has reached a convergence to a stable solution, or whether the iterative update operation has reached the maximum number of iterations; S9, if yes, then output the corrected reconstructed background spectrum signal ; S10, if not, performing the iterative update operation until an applicable background spectrum is estimated; S11. Perform a nonlinear least squares concentration inversion operation according to the applicable background spectrum.

2. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S2, the number of decomposition layers is preset using the following logic: : （13） The maximum number of iterations is preset using the following logic: N : （14） In the formula, the function Indicated in wave number The absorption peak characteristics at P Indicates the absorption peak characteristics, At the wave number The signal-to-noise ratio at Indicated in the wave number The spectral complexity at C Indicates the spectral complexity, the wave number The wide band is , v1 represents the minimum wave number in a wide band, v2 Broadband maximum wave number, is the proportionality constant.

3. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S3, the measured spectrum is processed by the dual-tree complex wavelet transform DTCWT using the following logic: : In the formula, Represents the low-frequency part of the signal after decomposition, Represents the high-frequency part of the signal after decomposition, l Indicates low frequency, h Indicates high frequency; According to the following logic, with the first independent wavelet filter tree, using the first group k Wavelet filter Transform to get the real part: (7) In the formula, represents matrix multiplication, are the wavelet coefficients obtained by the first independent wavelet filter tree A, represents the original signal, t Indicates time, g represents the filters of the first independent wavelet filter tree; According to the following logic, with the second independent wavelet filter tree, using the second group k Wavelet filter Continue the transformation to generate the imaginary component: (8) In the formula, * represents the convolution operation, is the wavelet coefficient obtained by the second independent wavelet filter tree B, h a filter representing a second independent wavelet filter tree; Using the following logic, the first group k Wavelet filter The second group k Wavelet filter Designed to be Hilbert pairs: (9) In the formula, Indicates that the first group k Wavelet filter Perform the Hilbert transform operation, H represents the Hilbert transform; The real component and the imaginary component are combined to obtain complex wavelet coefficients, and an analytical operation is performed according to the dual-tree complex wavelet transform to obtain phase and amplitude information of the complex wavelet coefficients. Signal analysis processing is performed according to the phase and amplitude information to obtain the dual-tree complex wavelet transform signal, wherein the complex wavelet coefficients are expressed using the following logic: (10) In the formula, represents the dual-tree complex wavelet transform signal obtained by performing a dual-tree complex wavelet transform operation on the real component and the imaginary component, represents the real component, represents the imaginary component, W represents the frequency domain, R represents the real part, I represents the imaginary part, i Represents the imaginary part.

4. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S4, the following logic is used to decompose the dual-tree complex wavelet decomposition spectrum signal: I(W) : In the formula, represents the frequency domain, Represents the low frequency part, Represents the high frequency part, k Indicates the decomposition level, n Indicates the current iteration number, represents the summation of the low-frequency parts, represents the summation of the high frequency parts.

5. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S5, the sparse optimization operation is performed using the following formula: In the formula, represents the high frequency component, Indicates Gas, h Indicates high frequency, represents the sparse optimized high frequency component, represents the sparse optimization operation; Using the following logic, the nonlinear compression function f(x) Acting on high frequency coefficients x superior: （11） In the formula, It is a small positive number to prevent mathematical singularity. represents the absolute value of the high-frequency coefficient, is a symbolic function; use L 1 Regularization strategy, according to the following logic, the sparse optimization operation is performed on the model parameters to find the applicable coefficient vector as the model parameters , to complete the minimization operation of the optimization problem: （12） In the formula, Represents dependence on compressed data y , the model parameters The loss function L ; is the model parameter of L 1 norm, that is is the regularization parameter.

6. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S6, the signal restoration operation is performed using the following logic to obtain the restored background spectrum : In the formula, represents the spectral estimator, bg Indicates the background, represents the frequency domain, IDTCWT represents the inverse dual-tree complex wavelet transform, represents the low-frequency component, l Indicates low frequency, represents the sparsely optimized high-frequency component, It indicates that an inverse dual-tree complex wavelet transform is performed on the low-frequency component and the sparse optimized high-frequency component.

7. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S7, the background correction operation is performed using the following formula to obtain the corrected reconstructed background spectrum signal: : In the formula, Indicates the current wave number The corresponding background measurement spectrum, represents the spectral estimator, bg indicates background, (new) indicates correction operation, represents the corrected reconstructed background spectrum signal, It represents an operation of taking the maximum value of the reconstructed background spectrum signal and the corrected reconstructed background spectrum signal point by point.

8. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S8, the following logical constraints are used to determine whether to end the iteration operation: OR n≤N In the formula, Indicates wave number The corresponding corrected reconstructed background spectrum signal, Indicates the wave number The corresponding measured spectrum, represents the preset error convergence value, n Indicates the current iteration number, N Indicates the maximum number of iterations.

9. The roadside infrared spectrum remote sensing monitoring method based on VDL-DTCWT according to claim 1 is characterized in that: In S10, the iterative update operation is performed using the following logic to update the measured spectrum : In the formula, represents the corrected reconstructed background spectrum signal, Indicates the current wave number The corresponding corrected reconstructed background spectrum signal.

10. The roadside infrared spectrum remote sensing monitoring system based on VDL-DTCWT is characterized by: The system comprises: Spectrum reading module, used to read the measured spectrum of the incident spectrum ; A layer number and iteration number preset module is used to preset the number of decomposition layers and the maximum number of iterations for different wave number bands, and the layer number and iteration number preset module is connected to the spectrum reading module; A DTCWT application module is used to apply a dual-tree complex wavelet transform DTCWT to the measured spectrum, obtain a real component and an imaginary component by using a first independent wavelet filter tree and a second independent wavelet filter tree, perform a basic wavelet transform enhancement operation on the real component and the imaginary component, and obtain a dual-tree complex wavelet transform signal, wherein the DTCWT application module is connected to the layer number and iteration number preset module; A decomposition module is used to decompose the dual-tree complex wavelet transform signal into n layer, and obtain the double-tree complex wavelet decomposition spectral signal I(W) , observe the dual-tree complex wavelet decomposition spectral signal I(W) The decomposition module is connected with the DTCWT application module; A sparse optimization module, used for performing a sparse optimization operation on the high-frequency components in the coefficients of different frequency bands to obtain sparse optimized high-frequency components, wherein the sparse optimization module is connected to the decomposition module; The signal restoration module decomposes the spectral signal of the dual-tree complex wavelet according to the sparse optimized high-frequency component. I(W) Performing a signal restoration operation to obtain a restored background spectrum, wherein the signal restoration module is connected to the sparse optimization module; A background correction module, used for performing background correction operation on the restored background spectrum to obtain a corrected reconstructed background spectrum signal, wherein the background correction module is connected to the signal restoration module; An iterative judgment module, used for obtaining a calculated spectrum according to the corrected reconstructed background spectrum signal, judging whether the residual between the calculated spectrum and the measured spectrum has reached the convergence of a stable solution, or whether the iterative update operation has reached the maximum number of iterations, the iterative judgment module being connected to the background correction module and the layer number and iteration number preset module; An iterative output module is used to output the corrected reconstructed background spectrum signal when the residual between the calculated spectrum and the measured spectrum reaches the convergence of the stable solution or the iterative update operation reaches the maximum number of iterations. , the iteration output module is connected to the iteration judgment module; A continuous iteration module, used for performing the iterative update operation until an applicable background spectrum is estimated, the continuous iteration module being connected to the iterative judgment module; An inversion module is used to perform a nonlinear least squares concentration inversion operation according to the applicable background spectrum, and the inversion module is connected to the continuous iteration module.

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