A SERDS spectral reconstruction method with universal adaptability

Abstract

The application discloses a SERDS spectrum reconstruction method with universal adaptability, comprising the following steps: collecting original spectrum data under N different excitation wavelengths; calculating the intensity ratio of each original spectrum data and reference spectrum data, constructing the intensity ratio curve corresponding to each original spectrum data, extracting the smooth light intensity ratio curve, and constructing the spectrum intensity distortion matrix corresponding to each original spectrum data based on the smooth light intensity ratio curve; the method constructs the spectrum structured model of each original spectrum data, constructs the adaptive statistical weight of the signal-to-noise ratio, introduces the mixed regularization constraint, constructs the mixed regularization operator, constructs the convex optimization objective function based on the adaptive statistical weight, the mixed regularization operator and the global linear matrix, automatically obtains the optimal regularization parameter based on the L-Curve parameter scanning, solves the convex optimization objective function by using the augmented matrix non-negative least square, and obtains the corrected pure Raman spectrum.

Description

Technical Field

[0001] This invention belongs to the field of Raman spectroscopy technology, specifically relating to a universally adaptable SERDS spectral reconstruction method. Background Technology

[0002] Raman spectroscopy is widely used in chemical analysis and substance identification, but it is often limited by strong fluorescence background interference from some samples. Frequency-shifted excitation Raman differential spectroscopy (SERDS) is an effective means to solve this problem. Its basic principle is to utilize the physical property that the spectral position of Raman scattered light shifts with the excitation wavelength, while the fluorescence background remains relatively stationary. By performing differential summation algorithms on the spectra acquired at two adjacent excitation wavelengths, fluorescence suppression and Raman signal extraction can be achieved. However, mainstream SERDS reconstruction methods (such as integral methods, iterative deconvolution methods, NNLS, etc.) are mainly based on idealized rigid translation models. This model assumes that the spectral envelope shape of the light source remains unchanged before and after the excitation wavelength changes, and that the light intensity only undergoes a linear scalar-level decay.

[0003] This mathematical assumption reveals significant limitations when considering two practical light source implementation paths: Firstly, for precision detection paths based on single-mode lasers (such as DFB), this path typically uses two lasers with fixed output wavelengths, switching between them to achieve adjacent wavelength excitation. Despite high-quality light sources, minor power fluctuations and waveform drift are unavoidable during prolonged operation or precise switching. Conventional rigid models ignore these perturbations, preventing the system from exceeding the shot noise limit and hindering the achievement of optimal signal-to-noise ratio detection for trace substances. Secondly, for general detection paths based on multimode lasers (such as FP), this path utilizes a temperature control module to adjust the laser chip temperature, driving continuous shifts in the excitation wavelength to obtain adjacent wavelength spectra. Due to the inherent mode competition of FP lasers, the spectral envelope undergoes significant non-rigid deformation and random jumps during temperature changes, resulting in noticeable intensity distortion in the generated spectrum. Conventional models, unable to describe this complex dynamic evolution, lead to severe algorithm distortion, resulting in residual fluorescence, spectral line distortion, and structural artifacts.

[0004] Furthermore, existing data processing strategies are often limited to low-dimensional two-point logic, that is, differential reconstruction using only the spectra of two adjacent excitation wavelengths. This approach fails to fully exploit the rich physical information contained in multi-wavelength continuous excitation sequences and ignores the potential for signal-to-noise ratio gain and error correction that can be brought about by expanding the measurement dimension. Summary of the Invention

[0005] The purpose of this invention is to address the problems raised in the background art by proposing a universally adaptable SERDS spectral reconstruction method.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] This invention proposes a universally adaptable SERDS spectral reconstruction method, comprising:

[0008] Collect raw spectral data at N different excitation wavelengths;

[0009] The intensity ratios at each point are calculated using the original spectral data and the reference spectral data, and the intensity ratio curves corresponding to each original spectral data are constructed. Smooth light intensity ratio curves are extracted, and the spectral intensity distortion matrix corresponding to each original spectral data is constructed based on each smooth light intensity ratio curve.

[0010] Construct the shift matrix of each original spectral data relative to the excitation wavelength of the reference spectral data;

[0011] By coupling each displacement matrix and the spectral intensity distortion matrix, a spectral structured model of each original spectral data is constructed, and the spectral structured models of N original spectral data are stacked in dimensions to construct a global linear matrix.

[0012] A signal-to-noise ratio (SNR)-aware adaptive statistical weight is constructed, a hybrid regularization constraint is introduced, and a hybrid regularization operator is built. Based on the adaptive statistical weight, the hybrid regularization operator, and the global linear matrix, a convex optimization objective function is constructed, and the optimal value is automatically obtained based on L-Curve parameter scanning. The regularization parameter is used, and the convex optimization objective function is solved by non-negative least squares of the augmented matrix to obtain the corrected pure Raman spectrum.

[0013] Preferably, the step of calculating the intensity ratio point-by-point using each original spectral data and reference spectral data, constructing the intensity ratio curve corresponding to each original spectral data, extracting a smooth light intensity ratio curve, and constructing the spectral intensity distortion matrix corresponding to each original spectral data based on each smooth light intensity ratio curve includes:

[0014] Select one original spectral data at one excitation wavelength from N original spectral data at different excitation wavelengths as the reference spectral data;

[0015] Calculate the intensity ratio between N original spectral data and reference spectral data point by point, and construct a curve for each original spectral data with the x-axis representing the pixel point and the y-axis representing the intensity ratio;

[0016] The intensity ratio curves were processed using a smoothing fitting algorithm to filter out local ratio abrupt changes caused by peak shift and random noise, and to extract smooth light intensity ratio curves corresponding to each original spectral data.

[0017] Construct a diagonal spectral intensity distortion matrix based on each smooth light intensity ratio curve.

[0018] Preferably, constructing the shift matrix of the excitation wavelength of each original spectral data relative to the reference spectral data includes:

[0019] Calculate the wavelength difference between the excitation wavelength of N raw spectral data and the excitation wavelength of the reference spectral data, and convert each wavelength difference into a sub-pixel displacement using the pixel-wavelength calibration function of the spectrometer.

[0020] Decompose each subpixel-level displacement into integer parts. and decimal part And using the corresponding integer and fractional parts, each sub-pixel level displacement is used to construct a displacement matrix, and the displacement matrix... The values ​​of the elements in each row and column of the displacement matrix are as follows:

[0021] ;

[0022] in, Indicates the first The displacement matrix corresponding to the original spectral data at the excitation wavelength is... Line 1 The values ​​that the elements of the column can take, where This represents the total number of pixels in each original spectral data set.

[0023] Preferably, the formula for the spectral structured model of each original spectral data is as follows:

[0024] ;

[0025] in, For the first Raw spectral data at each excitation wavelength For the first The spectral intensity distortion matrix corresponding to each excitation wavelength For the first The displacement matrix corresponding to each original spectral data The corrected pure Raman spectrum is the one to be solved. The static fluorescence background to be solved is... In order to be with the first Measurement noise and unmodeled residuals corresponding to the original spectral data.

[0026] Preferably, when stacking the spectral structured models of N original spectral data in terms of dimensions, the stacked models are... and The coefficients form a global linear matrix, and the global linear matrix The formula is as follows:

[0027] .

[0028] Preferably, the construction of the signal-to-noise ratio-aware adaptive statistical weights includes:

[0029] The integral intensity of each raw spectral data point is calculated as a signal quantity index, and the second-order difference norm of each raw spectral data point is calculated as a noise quantity index. Based on the signal quantity index and the noise quantity index, a confidence score function for each raw spectral data point is constructed. This confidence score function is then multiplied by the identity matrix to construct a confidence level. The diagonal weight matrix is ​​used as the adaptive statistical weight for signal-to-noise ratio sensing.

[0030] Preferably, the step of introducing hybrid regularization constraints and constructing a hybrid regularization operator includes:

[0031] Based on the sparse constraint of pure Raman spectroscopy and the smooth constraint of static fluorescence background, constraint sub-matrices are constructed respectively, and the two constraint sub-matrices are diagonally spliced ​​to form a hybrid regularization operator.

[0032] Preferably, the formula for the convex optimization objective function is as follows:

[0033] ;

[0034] in, For signal-to-noise ratio-aware adaptive statistical weights, A matrix consisting of raw spectral data from N different excitation wavelengths. Let be the matrix consisting of the corrected pure Raman spectrum to be solved and the static fluorescence background to be solved. To balance the regularization parameter between residuals and smoothness, For hybrid regularization operators, The square of the L2 norm. This is the optimal solution.

[0035] Preferably, the optimal value is automatically obtained through the L-Curve parameter scanning. Regularization parameters are applied, and the convex optimization objective function is solved using augmented matrix nonnegative least squares to obtain the corrected pure Raman spectrum, which in turn yields the reconstructed pure Raman spectrum, including:

[0036] Extract the unconstrained objective function from the convex optimization objective function, solve the first gradient of the unconstrained objective function and set the first gradient to zero to obtain the analytical solution equation of the unconstrained objective function;

[0037] In the convex optimization objective function Within a preset sequence range of regularization parameters, matrix inversion is used to quickly solve analytical equations to obtain different... Unconstrained test solution sequence under different regularization parameter values;

[0038] For each unconstrained test solution, calculate the weighted measurement residual norm and regularized solution norm of the current unconstrained test solution. Construct an L-Curve curve using all weighted measurement residual norms and regularized solution norms. Select the unconstrained test solution corresponding to the maximum curvature in the L-Curve curve, and assign the selected unconstrained test solution to the corresponding L-Curve curve. Regularization parameter as optimal Regularization parameters ;

[0039] Using augmented matrix stitching technology to achieve the best Regularization parameters An augmented matrix and augmented vector are constructed from the global linear matrix. Using these augmented matrices and vectors, the convex optimization objective function is transformed into a non-negative least squares problem. The optimal solution is then obtained using non-negative least squares. And the optimal solution The former Each component is the corrected pure Raman spectrum, and thus the reconstructed pure Raman spectrum is obtained.

[0040] Among them, augmented matrix The formula is as follows:

[0041] .

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] 1. This universally adaptable SERDS spectral reconstruction method constructs a spectral structured model of each original spectral data, builds signal-to-noise ratio-aware adaptive statistical weights, introduces hybrid regularization constraints, and constructs a hybrid regularization operator. Based on the adaptive statistical weights, hybrid regularization operator, and global linear matrix, a convex optimization objective function is constructed, and the optimal value is automatically obtained based on L-Curve parameter scanning. The regularization parameter is used, and the convex optimization objective function is solved by non-negative least squares of the augmented matrix to obtain the corrected pure Raman spectrum;

[0044] 2. This method eliminates structural artifacts and false peaks caused by envelope distortion and alignment quantization errors. Without the need for expensive frequency stabilization devices and external calibration optical paths, it can compensate for the severe distortion of multimode lasers and the nonlinear power attenuation of single-mode lasers. This allows the same algorithm architecture to be applied to detection systems with different costs and accuracies, making it highly applicable.

[0045] 3. This method further decomposes subpixel-level displacements into integer and fractional parts, forming a displacement matrix to strictly guarantee accurate spectral translation under discrete grids. A global linear matrix is ​​constructed using raw spectral data from N different excitation wavelengths to accumulate weak signals, improving the signal-to-noise ratio. Based on adaptive statistical weights, modal jumps or random noise in single spectral data are automatically identified and suppressed, giving the algorithm high noise robustness. A hybrid regularization operator is used to effectively suppress high-frequency noise, ensuring both absolute smoothness of the static fluorescence background and perfect preservation of the sharpness of pure Raman spectral peaks, solving the peak collapse or baseline spike problems easily caused by single regularization. In the solution stage, an optimal solution is obtained quickly and automatically using L-Curve parameter scanning. The regularization parameter, through the augmented matrix, transforms the complex weighted objective function into a standard non-negative least squares problem, ensuring the stable and rapid acquisition of the global optimal solution and meeting the high-precision, real-time detection requirements in complex environments. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the process of the universally adaptable SERDS spectral reconstruction method of the present invention;

[0047] Figure 2 This is a schematic diagram illustrating the first and second curves of the present invention;

[0048] Figure 3 This is a schematic diagram of the displacement matrix of the present invention;

[0049] Figure 4 This is a schematic diagram of the spectral structured model of N original spectral data of the present invention stacked in dimensions;

[0050] Figure 5 This is a schematic diagram of the L-Curve curve of the present invention;

[0051] Figure 6 This is a schematic diagram comparing the original spectral data of the method of the present invention at the first to fifth excitation wavelengths;

[0052] Figure 7 This is a schematic diagram comparing the corrected pure Raman spectra obtained by the method of the present invention with those obtained by two existing methods. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.

[0055] In one embodiment, such as Figures 1-7 As shown, a universally adaptable SERDS spectral reconstruction method is provided, including:

[0056] Step 1: Collect raw spectral data at N different excitation wavelengths;

[0057] Wherein, N different excitation wavelengths are represented as , Indicates the first The original spectral data at N different excitation wavelengths are represented as follows: , Indicates the first The original spectral data at each excitation wavelength, N≥2, preferably N≥5;

[0058] The specific data collection process is as follows:

[0059] Construct a SERDS synchronous detection system, which includes a host computer, a laser, a temperature control module, and a spectral acquisition module (CCD). For the first... The acquisition process of the raw spectral data for each excitation wavelength is as follows:

[0060] The host computer will the first The temperature setpoint corresponding to each excitation wavelength is written into the temperature control module, and at the same time, a signal from the host computer to start acquisition is sent to the temperature control module. At this time, the spectrum acquisition module is in a suspended waiting state and does not perform exposure.

[0061] The temperature control module drives the laser to change its temperature. The laser is divided into two types. For single-mode lasers, this stage achieves precise locking of a tiny wavelength. For multi-mode lasers, this stage "freezes" the intense mode competition to a certain stable state.

[0062] When the temperature control module determines that the current laser state has reached the set value and the fluctuation is less than the threshold, it sends out a brief "laser temperature stabilization signal" (such as a TTL high-level pulse).

[0063] After the spectral acquisition module detects the pulse signal, it immediately initiates "Signal Acquisition and Transmission Begins". Since the light source is in an absolutely physical steady state at this time, the spectral acquisition module captures a single frame of spectrum (i.e., raw spectral data) with no ghosting and high fidelity.

[0064] Step 2: Calculate the intensity ratio point-by-point using each original spectral data and the reference spectral data, construct the intensity ratio curve corresponding to each original spectral data, and extract the smoothed intensity ratio curve. Based on each smoothed intensity ratio curve, construct the spectral intensity distortion matrix corresponding to each original spectral data, including:

[0065] Step 2.1: Select the original spectral data of one excitation wavelength from the original spectral data of N different excitation wavelengths as the reference spectral data; in this embodiment, the original spectral data corresponding to the middle wavelength is selected as the reference spectral data;

[0066] Step 2.2: Calculate the intensity ratio between the N original spectral data and the reference spectral data point by point (i.e., calculate the intensity ratio of each pixel), and construct a curve for each original spectral data with the pixel as the x-axis and the intensity ratio as the y-axis;

[0067] The formula for calculating the point-by-point strength ratio is as follows:

[0068] ;

[0069] in, For the x-coordinate with the total number of pixels M, the th x-coordinate is... Raw spectral data at each excitation wavelength Compared with reference spectral data The point-by-point intensity ratio, This is a preset value used to prevent division errors with zero values, and ,when When using reference spectral data, the point-by-point intensity ratio is 1;

[0070] like Figure 2 As shown, a curve is constructed with the horizontal axis representing pixels and the vertical axis representing the intensity ratio. Figure 2 The curve representing the point-by-point intensity ratio between the original spectral data and the reference spectral data at an excitation wavelength of 785.5 nm is called the first curve. Figure 2 Medium green curve;

[0071] Step 2.3: Process the intensity ratio curves using a smoothing fitting algorithm to filter out local ratio abrupt changes caused by peak displacement and random noise. Figure 2 The red circle in the image indicates one of the mutations), and the smooth intensity ratio curves corresponding to each original spectral data are extracted (e.g., Figure 2 The black curve in the image, also known as the second curve); from Figure 2As can be seen, the fitted smooth light intensity ratio curve exhibits a significant negative slope trend (decreasing from 1.03 to 0.97), indicating that the original light source in this frame underwent non-uniform tilt deformation, accompanied by power attenuation. This non-rigid change is the main reason for artifacts generated by conventional reconstruction algorithms.

[0072] Step 2.4: Construct the corresponding diagonal spectral intensity distortion matrix based on each smooth light intensity ratio curve; that is, construct the diagonal spectral intensity distortion matrix from the ordinate values ​​of the smooth light intensity ratio curves, and the spectral intensity distortion matrix is ​​expressed as follows: ,in, Indicates the first The smooth intensity ratio curves corresponding to the original spectral data at each excitation wavelength correspond to the ordinate value of the Mth wavenumber. The spectral intensity distortion matrix not only corrects the scalar differences in intensity but also corrects the wavelength-dependent vector distortion, providing an accurate intensity distortion matrix for the subsequent construction of a high-precision unified forward model.

[0073] Step 3: Construct the shift matrix of the excitation wavelength of each original spectral data relative to the reference spectral data, including:

[0074] Step 3.1: Calculate the wavelength difference between the excitation wavelength of the N original spectral data and the excitation wavelength of the reference spectral data, and convert each wavelength difference into a sub-pixel displacement using the pixel-wavelength calibration function of the spectrometer (since the change of physical wavelength is continuous, the calculated sub-pixel displacement is usually a floating-point number with a decimal part).

[0075] Step 3.2: Given that the physical pixels of a spectrometer are discretely distributed, it is difficult to directly and accurately characterize non-integer multiple pixel shifts of wavenumber (i.e., sub-pixel level displacements often contain fractional pixels). Directly rounding to the nearest integer would introduce a quantization error as high as 0.5 pixels, severely compromising the reconstruction accuracy of the differential spectrum. Therefore, each sub-pixel level displacement is decomposed into its integer part. and decimal part And using the corresponding integer and fractional parts, each sub-pixel level displacement is used to construct a displacement matrix, and the displacement matrix... The values ​​of the elements in each row and column of the displacement matrix are as follows:

[0076] ;

[0077] in, Indicates the first The displacement matrix corresponding to the original spectral data at the excitation wavelength is... Line 1 The values ​​that the elements of the column can take, where Let be the wavenumber of each original spectral data. The displacement matrix is ​​as follows: Figure 3 As shown. Through this construction, matrix operations... It can mathematically simulate standard spectra accurately on discrete spectral grids. The continuous physical translations that occur eliminate the position quantization errors caused by discrete sampling, providing an accurate displacement matrix for the subsequent construction of a high-precision unified forward model.

[0078] Step 4: Couple the displacement matrices and spectral intensity distortion matrices to construct spectral structured models for each original spectral data. Stack the spectral structured models of the N original spectral data in dimensionality to construct a global linear matrix, including:

[0079] Step 4.1: The formulas for the spectral structured models of each raw spectral data are as follows:

[0080] ;

[0081] in, For the first Raw spectral data at each excitation wavelength For the first The spectral intensity distortion matrix corresponding to each excitation wavelength (characterizing the modulation effect of the envelope deformation or power attenuation of the excitation source on the final spectrum, and the spectral intensity distortion matrix not only acts on the excitation wavelength) It also acts on ), For the first The displacement matrix corresponding to each original spectral data (representing the translational motion of the Raman peak on the spectrometer pixel due to the change in excitation wavelength). The corrected pure Raman spectrum to be solved (does not change with the excitation wavelength, only shifts). The static fluorescence background to be solved is... In order to be with the first Measurement noise and unmodeled residuals corresponding to the original spectral data;

[0082] Step 4.2: Stack the spectral structured models of N original spectral data in terms of dimensions (e.g., ...). Figure 4 As shown in the figure, the global model formed after stacking is expressed by the following formula:

[0083] ;

[0084] in, A matrix consisting of raw spectral data from N different excitation wavelengths, i.e. , For transpose, Let be the matrix consisting of the corrected pure Raman spectrum to be solved and the static fluorescence background to be solved, i.e. , ;

[0085] Step 4.3: When stacking the spectral structured models of N original spectral data in terms of dimensions, the stacked... and The coefficients form a global linear matrix, and the global linear matrix The formula is as follows:

[0086] ;

[0087] in, Acting on , Acting on .

[0088] Step 5: Construct signal-to-noise ratio-aware adaptive statistical weights, introduce hybrid regularization constraints, and construct a hybrid regularization operator. Based on the adaptive statistical weights, hybrid regularization operator, and global linear matrix, construct a convex optimization objective function, and automatically obtain the optimal value based on L-Curve parameter scanning. Regularization parameters are used, and the convex optimization objective function is solved using augmented matrix nonnegative least squares to obtain the corrected pure Raman spectrum, including:

[0089] Step 5.1: Construct signal-to-noise ratio-aware adaptive statistical weights, including:

[0090] The integral intensity (i.e., the area of ​​the entire spectrum) of each raw spectral data is calculated as a signal quantity index, and the second-order difference norm of each raw spectral data is calculated as a noise quantity index (the noise quantity index will increase significantly when the laser experiences severe mode hopping and generates random glitches). Based on the signal quantity index and the noise quantity index, a confidence score function for each raw spectral data is constructed, and the calculation formula for the confidence score function is as follows:

[0091] ;

[0092] in,

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] in, For the first Confidence scoring function for raw spectral data at each excitation wavelength For the first Signal quantity index of raw spectral data at each excitation wavelength This is a set of signal quantity indices for the raw spectral data at all excitation wavelengths. For the first The noise level of the raw spectral data at each excitation wavelength This is a set of noise indices for the raw spectral data at all excitation wavelengths. To adjust the parameters, For the first The raw spectral data at the excitation wavelength at the ... The intensity value at each pixel.

[0098] The confidence score function of each original spectral data is constructed by multiplying it with the identity matrix. The diagonal weight matrix is ​​used as the adaptive statistical weight for signal-to-noise ratio sensing, and the adaptive statistical weight is... ,in for The identity matrix.

[0099] Step 5.2: Introduce hybrid regularization constraints and construct hybrid regularization operators, including:

[0100] Based on the sparsity constraint of pure Raman spectroscopy and the smoothing constraint of static fluorescence background, constraint sub-matrices are constructed respectively (i.e., hybrid regularization constraints are introduced). The two constraint sub-matrices are then diagonally concatenated to form a hybrid regularization operator. The representation is as follows:

[0101] ;

[0102] in,

[0103] ;

[0104] ;

[0105] in, The constraint submatrix representing the sparse constraint of pure Raman spectroscopy. The constraint submatrix represents the static fluorescence background smoothing constraint. It is a second-order difference matrix. and These are the weighting coefficients. Much larger , Used to smooth out minor burrs and noise in localized areas. I is equivalent to the baseline zeroing term, which can both prevent the solution process from diverging and maintain the sharp sparsity of the Raman peak. Hybrid regularization operator Balancing the sharpness of pure Raman spectra with the smoothness of static fluorescence background provides a reliable mathematical basis for the subsequent accurate separation of the two signals.

[0106] Step 5.3: Construct a convex optimization objective function based on adaptive statistical weights, a hybrid regularization operator, and a global linear matrix. The formula for the convex optimization objective function is as follows:

[0107] ;

[0108] in, For signal-to-noise ratio-aware adaptive statistical weights, A matrix consisting of raw spectral data from N different excitation wavelengths. Let be the matrix consisting of the corrected pure Raman spectrum to be solved and the static fluorescence background to be solved. To balance the regularization parameter between residuals and smoothness, The square of the L2 norm. This is the optimal solution.

[0109] Step 5.4: Automatically obtain the optimal value based on L-Curve parameter scanning. Regularization parameters are used, and the convex optimization objective function is solved using augmented matrix nonnegative least squares to obtain the corrected pure Raman spectrum, including:

[0110] Step 5.3.1: Extract the unconstrained optimization objective function from the convex optimization objective function, and the unconstrained optimization objective function... The expression is as follows:

[0111] ;

[0112] Solving for the first gradient of the unconstrained objective function and setting it to zero yields the analytical solution equation for the unconstrained objective function (setting the first gradient of the unconstrained objective function with respect to x to zero...). By finding the local minimum point, the normal equation for the global minimum can be derived through rigorous matrix differentiation, as follows:

[0113] .

[0114] Step 5.3.2, in the convex optimization objective function Within the preset sequence range of the regularization parameter ( The preset sequence range for the regularization parameter is Using matrix inversion operations, analytical equations can be solved quickly to obtain different... The sequence of unconstrained test solutions under different regularization parameter values, and the calculation formulas for each unconstrained test solution are as follows:

[0115] ;

[0116] in, Indicates the regularization parameter The unconstrained test solution is given.

[0117] Step 5.3.3: For each unconstrained test solution, calculate the weighted measurement residual norm (characterizing data fitting error) and the regularized solution norm (characterizing spectral smoothness and sparsity) of the current unconstrained test solution, as shown in the following formulas:

[0118] ;

[0119] ;

[0120] in, Indicates the regularization parameter The weighted measurement residual norm of the unconstrained test solution under the given conditions is expressed as the regularization parameter. The regularization of the unconstrained test solution under the given conditions;

[0121] And L-Curve curves are constructed using all weighted measurement residual norms and regularization norms (e.g.) Figure 5 As shown, the horizontal left side is The vertical axis is Select the maximum curvature in the L-Curve curve (i.e., the inflection point of the L-Curve curve, i.e.) Figure 5 The unconstrained test solution corresponding to the red pentagram in the diagram is selected, and the corresponding value of the selected unconstrained test solution is... Regularization parameter as optimal Regularization parameters This step achieves an automatic balance between "underfitting (excessive residuals)" and "overfitting (unsmoothed noise)".

[0122] Step 5.3.4: Use augmented matrix stitching technology to select the best... Regularization parameters , An augmented matrix and augmented vector are constructed from the global linear matrix. Using these augmented matrices and vectors, the convex optimization objective function is transformed into a non-negative least squares problem. The optimal solution is then obtained using non-negative least squares. And the optimal solution The former Each component is the corrected pure Raman spectrum;

[0123] It should be noted that, in order to ensure the physical non-negativity of spectral intensity, the weighted data fidelity term and the regularization penalty term are vertically concatenated along the tensor dimension to construct an augmented matrix. With augmented vector The formula is as follows:

[0124] ;

[0125] ;

[0126] The convex optimization objective function is then transformed into a nonnegative least squares problem:

[0127] (1);

[0128] Formula (1) is a standard single NNLS (non-negative least squares) optimization problem. Solving Formula (1) using non-negative least squares yields the optimal solution. (Include and And the optimal solution The former Each component represents the corrected pure Raman spectrum. Thus, the reconstructed pure Raman spectrum is obtained.

[0129] In another embodiment, to verify the effectiveness of this method under complex and non-ideal light source conditions, a set of spectral test data that highly replicates the real detection environment was constructed and compared with existing methods (including integral methods and least squares methods). The core physical and environmental parameters of the test data are set as follows:

[0130] Environmental background interference: The broadband fluorescence background is set to be strong, and the intensity ratio of the pure Raman spectrum to the static fluorescence background is 1:20, so the weak Raman signal is masked by the strong fluorescence.

[0131] Signal-to-noise ratio: The SNR after the superposition of shot noise and detector dark noise is set to 20, and there is obvious high-frequency random white noise interference;

[0132] Light source instability: During simulated excitation temperature tuning, the output power of the light source decreases by about 5% per frame, and this decrease is non-uniform in wavenumber.

[0133] like Figure 6 The diagram shows a comparison of the original spectral data at the first to fifth excitation wavelengths under the core physical and environmental parameters of the test data set above (wherein...). Figure 6 In the image, the raw spectral data at the 1st to 5th excitation wavelengths are represented as frames 1 to 5, respectively.

[0134] like Figure 7 The diagram shows a comparison of the corrected pure Raman spectra obtained by this method and two existing methods under the core physical and environmental parameters of the above-mentioned test data.

[0135] The reconstruction results are shown in the attached image. Figure 7 As shown, when facing complex environmental conditions, this method can reconstruct weak Raman signals with high signal-to-noise ratio and high robustness, unlike conventional reconstruction methods which may produce residual fluorescence, spectral distortion, and structural artifacts.

[0136] This universally adaptable SERDS spectral reconstruction method constructs a spectral structured model of each original spectral data point, builds signal-to-noise ratio-aware adaptive statistical weights, introduces hybrid regularization constraints, and constructs a hybrid regularization operator. Based on the adaptive statistical weights, the hybrid regularization operator, and the global linear matrix, a convex optimization objective function is constructed, and the optimal value is automatically obtained based on L-Curve parameter scanning. Regularization parameters are applied, and the convex optimization objective function is solved using non-negative least squares of the augmented matrix to obtain the corrected pure Raman spectrum. This method eliminates structural artifacts and spurious peaks caused by envelope distortion and alignment quantization errors. Without requiring expensive frequency stabilization devices or external calibration optical paths, it can compensate for the severe distortion of multimode lasers and the nonlinear power attenuation of single-mode lasers, making the same algorithm architecture applicable to detection systems with different costs and accuracies, demonstrating strong applicability. Furthermore, this method decomposes subpixel-level displacements into integer and fractional parts, forming a displacement matrix, strictly guaranteeing the spectral accuracy under discrete grid conditions. The algorithm achieves precise translation; it constructs a global linear matrix using raw spectral data from N different excitation wavelengths to accumulate weak signals, thus improving the signal-to-noise ratio; based on adaptive statistical weights, it automatically identifies and suppresses mode jumps or random noise in single spectral data, giving the algorithm high noise robustness; it employs a hybrid regularization operator to effectively suppress high-frequency noise, ensuring both absolute smoothness of the static fluorescence background and perfect preservation of the sharpness of pure Raman spectral peaks, solving the peak collapse or baseline spike problems that are easily caused by single regularization; in the solution stage, it uses L-Curve parameter scanning to quickly and automatically obtain the optimal solution. The regularization parameter, through the augmented matrix, transforms the complex weighted objective function into a standard non-negative least squares problem, ensuring the stable and rapid acquisition of the global optimal solution and meeting the high-precision, real-time detection requirements in complex environments.

[0137] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0138] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0139] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A universally adaptable SERDS spectral reconstruction method, characterized in that: The universally adaptable SERDS spectral reconstruction method includes: Collect raw spectral data at N different excitation wavelengths, where N≥2; The intensity ratios at each point are calculated using the original spectral data and the reference spectral data, and the intensity ratio curves corresponding to each original spectral data are constructed. Smooth light intensity ratio curves are extracted, and the spectral intensity distortion matrix corresponding to each original spectral data is constructed based on each smooth light intensity ratio curve. Construct the shift matrix of each original spectral data relative to the excitation wavelength of the reference spectral data; By coupling each displacement matrix and the spectral intensity distortion matrix, a spectral structured model of each original spectral data is constructed, and the spectral structured models of N original spectral data are stacked in dimensions to construct a global linear matrix. A signal-to-noise ratio (SNR)-aware adaptive statistical weight is constructed, a hybrid regularization constraint is introduced, and a hybrid regularization operator is built. Based on the adaptive statistical weight, the hybrid regularization operator, and the global linear matrix, a convex optimization objective function is constructed, and the optimal value is automatically obtained based on L-Curve parameter scanning. The regularization parameter is used, and the convex optimization objective function is solved by non-negative least squares of the augmented matrix to obtain the corrected pure Raman spectrum.

2. The universally adaptable SERDS spectral reconstruction method as described in claim 1, characterized in that: The process involves calculating the intensity ratio point-by-point using each original spectral data and reference spectral data, constructing the intensity ratio curve corresponding to each original spectral data, extracting a smooth intensity ratio curve, and constructing a spectral intensity distortion matrix corresponding to each original spectral data based on each smooth intensity ratio curve, including: Select one original spectral data at one excitation wavelength from N original spectral data at different excitation wavelengths as the reference spectral data; Calculate the intensity ratio between N original spectral data and reference spectral data point by point, and construct a curve for each original spectral data with the x-axis representing the pixel point and the y-axis representing the intensity ratio; The intensity ratio curves were processed using a smoothing fitting algorithm to filter out local ratio abrupt changes caused by peak shift and random noise, and to extract smooth light intensity ratio curves corresponding to each original spectral data. Construct a diagonal spectral intensity distortion matrix based on each smooth light intensity ratio curve.

3. The universally adaptable SERDS spectral reconstruction method as described in claim 1, characterized in that: The construction of the shift matrix of the excitation wavelength of each original spectral data relative to the reference spectral data includes: Calculate the wavelength difference between the excitation wavelength of N raw spectral data and the excitation wavelength of the reference spectral data, and convert each wavelength difference into a sub-pixel displacement using the pixel-wavelength calibration function of the spectrometer. Decompose each subpixel-level displacement into integer parts. and decimal part And using the corresponding integer and fractional parts, each sub-pixel level displacement is used to construct a displacement matrix, and the displacement matrix... The values ​​of the elements in each row and column of the displacement matrix are as follows: ； in, Indicates the first The displacement matrix corresponding to the original spectral data at the excitation wavelength is... Line 1 The values ​​that the elements of the column can take, where This represents the total number of pixels in each original spectral data set.

4. The universally adaptable SERDS spectral reconstruction method as described in claim 3, characterized in that: The formulas for the spectral structured models of the original spectral data are as follows: ； in, For the first Raw spectral data at each excitation wavelength For the first The spectral intensity distortion matrix corresponding to each excitation wavelength For the first The displacement matrix corresponding to each original spectral data The corrected pure Raman spectrum is the one to be solved. The static fluorescence background to be solved is... In order to be with the first Measurement noise and unmodeled residuals corresponding to the original spectral data.

5. The universally adaptable SERDS spectral reconstruction method as described in claim 4, characterized in that: When stacking spectral structured models of N original spectral data in a dimensional manner, the stacked model will... and The coefficients form a global linear matrix, and the global linear matrix The formula is as follows: 。 6. The universally adaptable SERDS spectral reconstruction method as described in claim 3, characterized in that: The construction of the signal-to-noise ratio-aware adaptive statistical weights includes: The integral intensity of each raw spectral data point is calculated as a signal quantity index, and the second-order difference norm of each raw spectral data point is calculated as a noise quantity index. Based on the signal quantity index and the noise quantity index, a confidence score function for each raw spectral data point is constructed. This confidence score function is then multiplied by the identity matrix to construct a confidence level. The diagonal weight matrix is ​​used as the adaptive statistical weight for signal-to-noise ratio sensing.

7. The universally adaptable SERDS spectral reconstruction method as described in claim 1, characterized in that: The introduction of hybrid regularization constraints and the construction of hybrid regularization operators include: Based on the sparse constraint of pure Raman spectroscopy and the smooth constraint of static fluorescence background, constraint sub-matrices are constructed respectively, and the two constraint sub-matrices are diagonally spliced ​​to form a hybrid regularization operator.

8. The universally adaptable SERDS spectral reconstruction method as described in claim 1, characterized in that: The formula for the convex optimization objective function is as follows: ； in, For signal-to-noise ratio-aware adaptive statistical weights, A matrix consisting of raw spectral data from N different excitation wavelengths. Let be the matrix consisting of the corrected pure Raman spectrum to be solved and the static fluorescence background to be solved. To balance the regularization parameter between residuals and smoothness, For hybrid regularization operators, The square of the L2 norm. This is the optimal solution.

9. The universally adaptable SERDS spectral reconstruction method as described in claim 8, characterized in that: The optimal scanning method based on L-Curve parameters is automatically obtained. Regularization parameters are applied, and the convex optimization objective function is solved using augmented matrix nonnegative least squares to obtain the corrected pure Raman spectrum, which in turn yields the reconstructed pure Raman spectrum, including: Extract the unconstrained objective function from the convex optimization objective function, solve the first gradient of the unconstrained objective function and set the first gradient to zero to obtain the analytical solution equation of the unconstrained objective function; In the convex optimization objective function Within a preset sequence range of regularization parameters, matrix inversion is used to quickly solve analytical equations to obtain different... Unconstrained test solution sequence under different regularization parameter values; For each unconstrained test solution, calculate the weighted measurement residual norm and regularized solution norm of the current unconstrained test solution. Construct an L-Curve curve using all weighted measurement residual norms and regularized solution norms. Select the unconstrained test solution corresponding to the maximum curvature in the L-Curve curve, and assign the selected unconstrained test solution to the corresponding L-Curve curve. Regularization parameter as optimal Regularization parameters ; Using augmented matrix stitching technology to achieve the best Regularization parameters An augmented matrix and augmented vector are constructed from the global linear matrix. Using these augmented matrices and vectors, the convex optimization objective function is transformed into a non-negative least squares problem. The optimal solution is then obtained using non-negative least squares. And the optimal solution The former Each component is the corrected pure Raman spectrum, and thus the reconstructed pure Raman spectrum is obtained. Among them, augmented matrix The formula is as follows: 。

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