Smoked mural pigment spectrum unmixing method and system

Abstract

The invention relates to a smoked mural pigment spectral unmixing method, and belongs to the field of hyperspectral unmixing. The method comprises the following steps: S1, establishing a pure pigment spectrum library and a smoking spectrum library as a data basis, S2, constructing a sparse unmixing model based on end member linear combination of the smoking spectrum library, S3, introducing a spatial self-adaptive mechanism based on spectrum similarity measurement, and dynamically adjusting regularization weight through abundance gradient analysis to optimize an objective function. And S4, implementing layered iterative optimization by adopting an alternating least square method in combination with spectral smoothing constraint, and finally realizing accurate unmixing of smoke pigment components. According to the method, smoke layer interference and a mixed pixel nonlinear effect are effectively overcome through dynamic weight adjustment, and spectrum similarity analysis and abundance space distribution characteristics are fused. The method is mainly applied to quantitative analysis of original pigment components under a smoked covering layer in ancient murals, and provides accurate material composition data support for cultural relic restoration.

Description

Technical Field

[0001] The present invention relates to the field of hyperspectral unmixing. More specifically, the present invention relates to a method and system for spectral unmixing of pigments in smoked murals. Background Art

[0002] Due to the non-contact and non-destructive detection characteristics of hyperspectral imaging technology, it has become a research hotspot for the identification of mural pigments. In recent years, the problem of smoke pollution on ancient murals has gradually attracted attention. Smoke is mainly a complex mixture composed of carbon black particles, saturated fatty acid glycerides or saturated fatty acids, which usually forms a thin film on the surface of the mural, thus changing the spectral reflection characteristics of the pigments, resulting in the measured spectrum being a mixed spectrum of smoke pollution and pigments. Therefore, it is necessary to analyze the specific pigment types through spectral unmixing means.

[0003] Traditional hyperspectral unmixing methods usually use the Linear Mixde Model (LMM), which can be roughly divided into three categories, namely geometric, statistical and sparse methods. Spectral unmixing based on geometric methods mainly utilizes the characteristic that all pixels in the spectral data are distributed in a high-dimensional simplex space or a positive convex cone region, and considers the vertices of the simplex surrounding the data set as endmembers. This type of method can be intuitively geometrically interpreted; spectral unmixing based on statistical methods aims to use parameter estimation techniques to determine the endmember set and abundance matrix, and this type of method does not require much prior knowledge; spectral unmixing based on sparse regression methods mainly utilizes the prior knowledge of using a spectral library as a dictionary, and transforms the spectral unmixing problem into a sparse regression problem through a semi-supervised method. When dealing with the unmixing problem of pigments in smoked murals, such classical models have certain limitations. First, the spectral coupling between smoke pollution and the pigment layer shows spatial heterogeneity, and traditional endmember extraction (determining the basic pigments that make up the mixed pixels) algorithms are not sensitive enough to sparsely distributed trace components; second, the spectral non-linear superposition effect between the smoke layer and the pigment layer leads to the accumulation of errors in abundance inversion (calculating the proportion of each basic pigment in the mixed pixel), especially in the low signal-to-noise ratio region, artifacts are easily generated. Therefore, there is an urgent need to conduct unmixing research on smoked murals to fill the academic gap in the field of hyperspectral unmixing of smoked murals. Summary of the Invention

[0004] An object of the present invention is to provide a method and system for spectral unmixing of pigments in smoked murals to at least solve the above problems.

[0005] To achieve the objectives and other advantages of the present invention, a method for spectral unmixing of smoked mural pigments is provided, including: S1. Data preparation and preprocessing: Establish a pure pigment spectral library and a smoked spectral library based on hyperspectral imaging data; S2. Sparse unmixing model construction: Represent the spectral signal of each pixel in the hyperspectral image of the smoked pigment as a linear combination of the endmember spectra in the smoked spectral library, and construct a sparse unmixing model; S3. Objective function design: Based on spectral similarity measurement and abundance gradient, dynamically adjust the regularization weight to construct the objective function of the sparse unmixing model; The dynamic adjustment of the regularization weight adopts a spatial adaptive mechanism based on spectral similarity, and the weight update is realized by calculating the abundance; S4. Hierarchical optimization and unmixing: Use the endmember matrix constructed from the pure pigment spectral library as the input, and adopt the alternating least squares method combined with spectral smoothing constraints to iteratively optimize the objective function to obtain the unmixing result of the smoked pigment.

[0006] Preferably, in S1, before using the hyperspectral imaging data, radiometric calibration is required, and the radiometric calibration formula is:

[0007]

[0008] where R is the hyperspectral data of the target object after calibration, R raw is the original hyperspectral data of the target object, R dark is the dark current data, and R white is the standard reflectance panel data.

[0009] Preferably, in S1, the pure pigment includes at least three mineral pigments selected from ochre, ultramarine, graphite, malachite green, and clam powder, and the pure pigment spectral library satisfies: spectral resolution ≤ 5 nm, signal-to-noise ratio ≥ 50 dB, and the spectral mean of more than 10 pollution-free samples of each pigment is collected; The smoked pigment is obtained by smoking a simulated mural sample in a closed smoked environment for a preset duration, and is divided into three categories: mild, moderate, and severe according to the smoking duration.

[0010] Preferably, in S2, the sparse unmixing model is specifically: y j = D1a j + n j

[0011] where y j is the spectral vector of the j-th pixel in the hyperspectral image of the smoked pigment, D1 is the endmember matrix constructed from the smoked spectral library, a j is the sparse coefficient vector of the j-th pixel, and n j is the noise term of the j-th pixel.

[0012] Preferably, in S3, the objective function is specifically:

[0013] Among them, X is the sparse coefficient matrix, D is the endmember matrix of pure pigments, y is the hyperspectral data matrix of smoked pigments, ‖‖ F represents the norm, ∑ i,j ω i,j |X i,j | is the adaptive L1 regularization term, |X i,j | is the absolute value of the coefficient value of the corresponding i-th band and j-th pixel point in the sparse coefficient matrix. The proportion of non-zero elements in the sparse coefficient vector does not exceed 5%, and the absolute value of non-zero elements ≥ 0.1, ω i,j is the adaptive regularization weight, and the calculation formula is:

[0014]

[0015] Among them, S i,j is the spectral similarity metric value, S i,j ∈[0,1], β is the smoothness control parameter, is the abundance gradient.

[0016] Preferably, in S3, the spectral similarity metric value S i,j is calculated by the following formula:

[0017]

[0018] In the formula, P i is the spectral vector of the i-th band in the pure pigment spectral library, y j is the spectral vector of the j-th pixel point in the smoked pigment hyperspectral image, and the calculation result is normalized.

[0019] Preferably, in S4, the hierarchical optimization specifically includes:

[0020] (a) Fix the endmember matrix D (k) , and update the sparse coefficient matrix X (k+1) by sparse regression:

[0021]

[0022] Among them, X (k+1) is the updated sparse coefficient matrix, D (k) is the endmember matrix, the initial endmember matrix is constructed from the pure pigment spectral library, X (k) is the sparse coefficient matrix, and the initial sparse coefficient matrix is initially estimated by least squares or sparse coding;

[0023] (b) Fix the sparse coefficient matrix X (k+1) , and update the endmember matrix D (k +1) by the least squares method combined with spectral smoothness constraints:

[0024]

[0025] Among them, D (k+1) is the updated endmember matrix, λ is the regularization parameter, D T is the transpose of the endmember matrix, is the spectral smoothing constraint matrix;

[0026] (c) Repeat steps (a) and (b) until the objective function converges or reaches the preset number of iterations. The convergence criterion is that the relative change rate of the objective function value for 5 consecutive iterations is <0.01% or the change amount of the F-norm is 1e -4 .

[0027] Preferably, the spectral unmixing method for the smoked mural pigment further includes: comparing the unmixing result with the spectral data in the pure pigment spectral library, and evaluating the accuracy by using at least one of the root mean square error (RMSE) and the spectral information divergence (SID). Among them, RMSE ≤ 0.1 and / or SID ≤ 0.05, meeting the accuracy requirements.

[0028] The present invention also provides a spectral unmixing system for the smoked mural pigment, including: a data preparation and preprocessing module, which is used to establish a pure pigment spectral library and a smoked spectral library based on hyperspectral imaging data; a sparse unmixing model construction module, which is used to represent the spectral signal of each pixel point in the hyperspectral image of the smoked pigment as a linear combination of the endmember spectra in the smoked spectral library and construct a sparse unmixing model; an objective function design module, which is used to dynamically adjust the regularization weight based on spectral similarity measurement and abundance gradient, construct the objective function of the sparse unmixing model, and dynamically adjust the regularization weight by using a spatial adaptive mechanism based on spectral similarity, and update the weight by calculating the abundance; a hierarchical optimization and unmixing module, which is used to take the endmember matrix constructed from the pure pigment spectral library as the input, and iteratively optimize the objective function by using the alternating least squares method combined with spectral smoothing constraints to obtain the unmixing result of the smoked pigment.

[0029] The present invention has at least the following beneficial effects:

[0030] First, by constructing a dual-spectrum library system and a hierarchical optimization mechanism, the adaptability of disentangling pigments in smoked murals is effectively improved. The pure pigment spectrum library provides the benchmark endmember features, while the smoked spectrum library quantifies the spectral distortion patterns of the smoked layer. The collaborative use of the two can cover the mixing characteristics of pigments under different pollution levels. The dynamic weight mechanism based on spectral similarity can adjust the regularization intensity according to the local mixing degree, reducing the sparse constraint in areas with thinner smoked layers to avoid over-suppressing real endmembers, and enhancing the constraint in areas with dense smoked deposits to suppress noise interference. In hierarchical optimization, the endmember matrix and the sparse coefficient matrix are alternately updated, combined with spectral smoothing constraints, which not only maintains the computational efficiency of the linear model but also alleviates the non-linear effects caused by smoking through iterative approximation, ultimately achieving a balance between computational complexity and accuracy. This method has strong robustness to the overlap of endmember spectra and noise interference in mixed pixels, and the disentangling error is reduced by about 30% compared with traditional methods.

[0031] Second, by defining the types of pure pigments and the parameters of the spectrum library (resolution ≤ 5nm, signal-to-noise ratio ≥ 50dB), it is ensured that the spectrum library covers the spectral characteristics of common mineral pigments in murals. At the same time, the acquisition error of a single sample is reduced by the mean value of multiple samples. The smoked samples are classified according to the smoking duration (mild / moderate / severe), and spectral variation models with different pollution levels can be constructed. When combined with the pure spectrum library, it can more accurately characterize the optical properties of the smoked layer. The dual constraints of spectral resolution and signal-to-noise ratio can effectively distinguish the subtle differences between smoked substances and pigments in the near-infrared band. For example, the characteristic absorption peak of malachite green at 750nm and the scattering effect of smoked carbon black in this band, thus improving the distinguishability of endmember spectra.

[0032] Third, through a linear combination model, the smoked spectrum library is used as the endmember matrix D1 to explicitly model the covering effect of the smoked layer on the original pigments. The introduction of the noise term can separate the random scattering noise and systematic noise in the smoked layer, avoiding misjudging them as endmember components. While maintaining the simplicity of the linear mixing framework, this model regards the smoked layer as an independent endmember to participate in disentangling through the endmember expansion of the smoked spectrum library, thus bypassing the modeling problem of non-linear mixing of smoked pigments in traditional methods. Experiments show that the adaptability of this model to the thickness change of the smoked layer is increased by 40%. Especially in the moderately smoked area, the estimation error of endmember abundance can be controlled within 8%.

[0033] Fourth, the adaptive L1 regularization term dynamically adjusts the weight through spectral similarity and abundance gradient to achieve spatially adaptive sparse constraints. In areas with low spectral similarity (such as the smoked-pigment mixing boundary), the weight is increased to suppress redundant endmembers; in areas with gentle gradients (such as uniformly smoked coverage areas), the weight is reduced to retain weak-signal endmembers. The exponential term in the formula It can smooth the abundance mutation and avoid weight oscillation caused by local gradient anomalies. While maintaining the overall sparsity of the model, this mechanism preserves the spatial distribution characteristics of fine pigment particles. After testing, it can reduce the misjudgment of false endmembers by more than 30%, and at the same time reduce the missed detection rate of effective endmembers to less than 5%.

[0034] Fifth, the spectral similarity is calculated using the inverse cosine function, and the similarity between the pure endmember and the mixed spectrum is measured by the vector included angle, which has stronger band correlation characterization ability compared with the traditional Euclidean distance. Normalization eliminates the influence of energy differences in different bands on the similarity measurement. For example, cross-band comparability is achieved between the visible light band with strong absorption of smoke (400 - 600 nm) and the relatively stable near-infrared band (800 - 1000 nm). This measurement method is sensitive to the spectral band shift caused by the smoke layer (such as the right shift of the reflection peak of cinnabar at 550 nm), and can accurately identify contaminated endmembers. Experiments show that its mismatching rate is reduced by about 25% compared with the Spectral Angle Matcher (SAM).

[0035] Sixth, hierarchical optimization gradually approaches the optimal solution in the iteration by alternately updating the endmember matrix D and the sparse coefficient matrix X, combined with spectral smoothing constraints. When fixing D and updating X, sparse regression retains the main endmember components; when fixing X and updating D, spectral smoothing constraints suppress the high-frequency noise of the endmember spectrum and maintain its physical rationality (such as the smooth shape of the absorption valley of azurite at 680 nm). This strategy avoids the local minimum problem caused by optimizing all parameters at once, and the convergence speed is increased by about 50% compared with traditional global optimization. The double judgment criteria of the F-norm change threshold (1e -4 ) and the relative change rate of the objective function (<0.01%) ensure that the unmixing result reaches stability within a limited number of iterations, and the measured number of iterations usually does not exceed 20 times.

[0036] Seventh, the unmixing accuracy is evaluated by the double indicators of RMSE and SID, which quantify the reliability of the results from the perspectives of numerical error and distribution similarity respectively. The RMSE constraint ensures that the absolute error between the abundance estimation value and the true pigment ratio is controllable. For example, the abundance error of shell powder ≤ 10%; the SID constraint ensures the waveform consistency between the unmixed spectrum and the reference spectrum, avoiding misjudgment of the overall reflectance shift caused by the absorption of the smoke layer. This evaluation system provides a quantitative acceptance standard for cultural relic restoration. In actual measurements, the unmixing results that meet the double-indicator constraints have a coincidence rate of more than 98% in the expert visual inspection, which is significantly better than the single-indicator evaluation method.

[0037] Other advantages, objectives, and features of the present invention will be partially reflected by the following description, and partially will also be understood by those skilled in the art through the research and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1It is a schematic flowchart of the spectral unmixing method for smoked mural pigments according to an embodiment of the present invention. Detailed implementation manners

[0039] The present invention will be further described in detail below in conjunction with embodiments and drawings, so that those skilled in the art can implement it with reference to the text of the specification.

[0040] It should be understood that terms such as "having", "including", and "comprising" used herein do not exclude the presence or addition of one or more other elements or combinations thereof.

[0041] It should be noted that the experimental methods described in the following embodiments are all conventional methods unless otherwise specified, and the reagents and materials can be obtained from commercial channels unless otherwise specified.

[0042] As Figure 1 As shown, in an embodiment of the present invention, a spectral unmixing method for smoked mural pigments is provided, including: S1. Data preparation and preprocessing: Establish a pure pigment spectral library and a smoked spectral library based on hyperspectral imaging data; S2. Sparse unmixing model construction: Represent the spectral signal of each pixel point in the hyperspectral image of the smoked pigment as a linear combination of endmember spectra in the smoked spectral library, and construct a sparse unmixing model; S3. Objective function design: Based on spectral similarity measurement and abundance gradient, dynamically adjust the regularization weight to construct the objective function of the sparse unmixing model; The dynamic adjustment of the regularization weight adopts a spatial adaptive mechanism based on spectral similarity, and the weight update is realized by calculating the abundance; S4. Hierarchical optimization and unmixing: Use the endmember matrix constructed from the pure pigment spectral library as the input, and adopt the alternating least squares method combined with spectral smoothing constraints to iteratively optimize the objective function to obtain the unmixing result of the smoked pigment.

[0043] In the above technical solution, the spectral unmixing method for smoked mural pigments includes four core steps. Among them, the "pure pigment spectral library" refers to a set of spectral data of uncontaminated mineral pigments collected by hyperspectral imaging technology; the "smoked spectral library" is a set of spectral data obtained by simulating the smoked environment and smoking the mural samples to different degrees; the "sparse unmixing model" refers to representing the spectral signal of the smoked pigment as a linear combination of endmember spectra in the smoked spectral library; the "alternating least squares method" is an iterative algorithm for optimizing the objective function by alternately fixing variables; the "spectral smoothing constraint" is a mathematical constraint condition imposed on the smoothness of the endmember spectra.

[0044] Specifically, in stage S1, first, hyperspectral data of pure mineral pigments (such as ochre, ultramarine, etc.) are collected. Device noise and environmental interference are eliminated through radiometric calibration to construct a standardized pure pigment spectral library. Meanwhile, the simulated mural samples are placed in a closed smoking device and smoked for a preset duration (such as 20 minutes for mild, 40 minutes for moderate, and 60 minutes for severe) to obtain spectral data of different pollution levels, forming a smoking spectral library. In stage S2, each pixel of the smoked hyperspectral image is modeled as a linear combination of the endmembers in the smoking spectral library, and a sparsity assumption is introduced, that is, each pixel is only composed of a small number of endmembers mixed together. In stage S3, when designing the objective function, the regularization weight is dynamically adjusted according to spectral similarity (calculated through the inverse cosine function) and abundance gradient (characterizing the change in spatial distribution). Specifically, the weight is reduced in the areas with a thinner smoking layer to retain weak signals, and the weight is increased in the areas with dense smoking to suppress noise. In stage S4, an alternating optimization strategy is adopted: first, the endmember matrix is fixed, and the sparse coefficients are updated through sparse regression; then, the sparse coefficient matrix is fixed, and the endmember matrix is updated in combination with spectral smoothing constraints, and the loop iteration is carried out until convergence.

[0045] Through the dynamic weight mechanism and the hierarchical optimization strategy, the unmixing accuracy of the smoked murals is significantly improved. Experiments show that compared with traditional methods, the endmember abundance estimation error is reduced by about 30%. Especially in the areas where the thickness of the smoking layer changes, the spatial continuity of the unmixing results is improved. In addition, while maintaining the computational efficiency, the alternating optimization strategy effectively alleviates the influence of the non-linear mixing effect, and the number of iterations usually does not exceed 20 times to converge, meeting the real-time requirements of cultural relic restoration.

[0046] In another embodiment of the present invention, in S1, radiometric calibration is required before using the hyperspectral imaging data, and the radiometric calibration formula is:

[0047]

[0048] where R is the hyperspectral data of the target object after calibration, R raw is the original hyperspectral data of the target object, R dark is the dark current data, and R white is the standard reflectance panel data.

[0049] In the above technical solution, "radiometric calibration" refers to the process of eliminating the inherent noise of the hyperspectral imaging device and environmental interference through mathematical processing; "dark current data" is the noise signal recorded by the sensor under the condition of no light; "standard reflectance panel data" is the reference data obtained through a standard white panel with a known reflectance, which is used to calibrate the reflectance of the target object.

[0050] Specifically, in the data preprocessing stage, the original hyperspectral data, dark current data, and standard whiteboard data of the target object (mural surface) are collected first. The dark current data is obtained by turning off the light source and recording the sensor output, which characterizes the base noise of the device. The standard whiteboard data is used to calibrate the reflectance benchmark. During radiometric calibration, the original data is subtracted by the dark current noise, then divided by the difference between the whiteboard and the dark current, and finally multiplied by 99% to retain the dynamic range of the effective signal. This step can eliminate the influence of sensor dark current noise and ambient light fluctuations, ensuring the accurate physical meaning of the spectral data.

[0051] After radiometric calibration, the signal-to-noise ratio of the spectral data is increased to over 50 dB, effectively eliminating the baseline drift caused by device noise. For example, in the visible light band (400 - 700 nm), the reflectance curve of the calibrated data is closer to the true pigment characteristics, and the separation degree between the absorption characteristics of the smoke layer and the pigment reflection peak is increased by about 20%, providing reliable input for subsequent unmixing.

[0052] In another embodiment of the present invention, in S1, the pure pigments include at least three mineral pigments selected from ochre, ultramarine, graphite, malachite, and shell powder, and the pure pigment spectral library satisfies: spectral resolution ≤ 5 nm, signal-to-noise ratio ≥ 50 dB, and the spectral mean of more than 10 pollution-free samples are collected for each pigment; the smoked pigments are obtained by smoking the simulated mural samples in a closed smoking environment for a preset duration and are classified into three categories: light, medium, and heavy according to the smoking duration.

[0053] In the above technical solution, "spectral resolution ≤ 5 nm" means that the width of each band in the spectral library does not exceed 5 nanometers, ensuring the capture of fine spectral features; "signal-to-noise ratio ≥ 50 dB" means that the effective signal intensity is more than 10 5 times that of the noise intensity; "pollution-free sample" means that the surface of the pigment sample has no physical damage or chemical contamination, and the spectral data reflects the characteristics of pure substances.

[0054] Specifically, the pure pigment spectral library needs to include at least three mineral pigments (such as ochre, ultramarine, graphite), and more than 10 pollution-free samples are selected for each pigment. Hyperspectral imaging equipment (such as the VNIR / 400H hyperspectral imager of Themis Vision System company) is used to collect sample data, with the spectral range covering 400 - 1000 nm, and a halogen lamp is used as the light source. During collection, it is necessary to ensure uniform illumination and avoid interference from shadows or reflections. When preparing smoked samples, the simulated mural is placed in a closed combustion chamber, and spectral data of different pollution levels are generated by controlling the combustion time (such as 20 minutes for light, 40 minutes for medium, and 60 minutes for heavy) and stored in the smoked spectral library after classification.

[0055] Furthermore, the simulated mural samples are samples made according to the materials and techniques of ancient murals. The samples (size 24cm x 20cm x 1cm) are composed of a 2 / 3 thick clay layer, a 1 / 3 fine clay layer, and a background color layer about 0.5mm thick. The thick clay layer uses a clay-to-sand mass ratio of 2:1 and adds wheat straw with a length of about 1cm and a mass fraction of 3%. The fine clay layer uses a clay-to-sand mass ratio of 2:1 and adds hemp fiber with a mass ratio of 3%. After the test blocks are dried, calcite powder and 5% gelatin are mixed and applied on the surface of the fine clay layer as the color layer. A variety of mineral pigments (such as ochre, ultramarine, graphite, malachite green, and clam powder) that are not prone to chemical reactions with air at high temperatures are applied on the color layer. The mineral pigments are all produced by Jiang Sixutang. Then, the hyperspectral data of the simulated mural samples are collected to obtain the original mural spectral data P1. A self-made smoking device is used to smoke the samples. The self-made device is 73 cm high and 34 cm wide. Combustible materials are placed at the bottom of the device, water is added on both sides of the device as a coolant, an iron wire mesh plate is placed in the upper-middle part of the device, and the samples are placed on the iron wire mesh plate. The smoking is generated by burning sawdust, charcoal, candle particles, and incense. The temperature of the smoking device is controlled below 200°C. First, the sample without a pigment layer (24cm x 20cm x 1cm) is continuously exposed to the smoke. It is found that the smoke particles can be completely covered when the smoking duration reaches 60 minutes. Therefore, according to the different smoking durations, the smoking degree of the mural is divided into 3 categories: light smoking (20 minutes), medium smoking (40 minutes), and heavy smoking (60 minutes). Data of the smoked murals are collected according to the above time periods, and 3 groups of simulated smoked mural data (S1, S2, S3) are obtained. After the original mural spectral data P1 and the simulated smoked mural data (S1, S2, S3) are radiometrically corrected, the spectral characteristics of different pigments in each region of P1 are analyzed and compared with the existing spectral library in the laboratory to ensure the accuracy of the measurement. The obtained pure pigment spectral data (ochre, ultramarine, graphite, malachite green, clam powder) constitute the pure pigment spectral library of this experiment, and the obtained S1, S2, S3 are used to establish a smoked spectral library D1 according to the smoking degree.

[0056] The spectral library can clearly distinguish the characteristic absorption peaks of pigments. For example, the absorption peak of malachite green at 750nm is significantly different from the scattering spectrum of smoked carbon black. The mean processing of multiple samples improves the stability of the spectral library, and the acquisition error of a single sample is reduced to less than 3%. The spectral data classified by smoking duration can accurately model the effects of different pollution degrees, and the matching error during unmixing is reduced by 15%.

[0057] In another embodiment of the present invention, in S2, the sparse unmixing model is specifically: y j = D1a j + n j

[0058] where y jis the spectral vector of the j-th pixel in the hyperspectral image of the smoked pigment, D1 is the endmember matrix constructed from the smoked spectral library, and a j is the sparse coefficient vector of the j-th pixel, and n j is the noise term of the j-th pixel.

[0059] In the above technical solution, the "endmember matrix" is composed of spectral vectors in the smoked spectral library arranged by columns, representing possible mixing components; the "sparse coefficient vector" represents the mixing ratio of each endmember in each pixel; the "noise term" includes random errors such as sensor noise and environmental interference.

[0060] Specifically, the sparse unmixing model represents the spectrum y of each pixel in the smoked hyperspectral image j as a linear combination of the endmember matrix D1 and the sparse coefficient vector a j , and adds the noise term n j . The column vectors of the endmember matrix are the spectral curves of each endmember in the smoked spectral library. The sparsity constraint requires that the proportion of non-zero elements in each coefficient vector does not exceed 5%, and the absolute value ≥ 0.1, ensuring that only the main components are retained in the mixing model.

[0061] This model explicitly introduces smoked endmembers, regards the smoked layer as an independent component to participate in unmixing, and avoids the modeling problem of the non-linear mixing of smoke-pigment in traditional methods. Experiments show that in the moderately smoked area, the endmember abundance estimation error is controlled within 8%, and the accuracy is improved by 40% compared with the model without introducing smoked endmembers.

[0062] In another embodiment of the present invention, in S3, the objective function is specifically:

[0063]

[0064] where X is the sparse coefficient matrix, D is the endmember matrix of the pure pigment, y is the hyperspectral data matrix of the smoked pigment, ‖‖ F represents the norm, ∑ i,j ω i,j |X i,j | is the adaptive L1 regularization term, |X i,j | is the absolute value of the coefficient value of the corresponding i-th band and j-th pixel in the sparse coefficient matrix. The proportion of non-zero elements in the sparse coefficient vector does not exceed 5%, and the absolute value of non-zero elements ≥ 0.1, ω i,j is the adaptive regularization weight, and the calculation formula is:

[0065]

[0066] where S i,j is the spectral similarity metric value, S i,j ∈[0,1], and β is the smoothness control parameter. is the abundance gradient.

[0067] In the above technical solution, the "adaptive L1 regularization term" is a regularization method that dynamically adjusts the sparse constraint intensity according to local mixing characteristics; the "spectral similarity metric value" quantifies the similarity between the pure endmember and the mixed spectrum; the "abundance gradient" reflects the spatial change rate of the endmember proportion and is calculated using the spatial difference method.

[0068] Specifically, the objective function includes a data fitting term and an adaptive regularization term. The regularization weight ω is jointly determined by the spectral similarity S and the abundance gradient : the lower the similarity (such as the soot-pigment mixing boundary), the greater the weight to suppress redundant endmembers; the greater the gradient (such as the pigment distribution mutation region), the smaller the weight to avoid over-smoothing. The exponential term is used to smooth spatial mutations, and the β parameter controls the smoothing intensity.

[0069] The dynamic weight mechanism enables the model to retain weak signal endmembers in the thin soot layer (high similarity, small gradient), suppress noise in the thick layer (low similarity, large gradient), and reduce false endmember misjudgments by 30%. The smoothing term avoids weight oscillations caused by local gradient anomalies, and improves spatial continuity by 25%.

[0070] In another embodiment of the present invention, in S3, the spectral similarity metric value S i,j is calculated by the following formula:

[0071]

[0072] where P i is the spectral vector of the i-th band in the pure pigment spectral library, and y j is the spectral vector of the j-th pixel in the soot pigment hyperspectral image, and the calculation result is normalized.

[0073] In the above technical solution, the "arccosine function" measures spectral similarity by calculating the vector included angle, and the smaller the included angle, the higher the similarity; the "normalization process" scales the similarity value to the range of 0-1 to eliminate the influence of energy differences between bands.

[0074] Specifically, the calculation of the spectral similarity S is divided into three steps: 1) Calculate the cosine similarity between the pure endmember spectral vector X i and the mixed spectrum y j ; 2) Convert it to the included angle radian value through the arccosine function; 3) Normalize the process to make the S value fall between 0 (completely similar) and 1 (completely dissimilar). This measurement method is sensitive to spectral band shifts caused by soot. For example, when the reflection peak of cinnabar shifts to the right at 550 nm, the S value increases significantly.

[0075] Compared with the traditional Euclidean distance, the sensitivity of the inverse cosine metric to spectral waveform changes is improved, and the false matching rate is reduced by 25%. Normalization ensures cross-band comparability. For example, between the visible light band with strong absorption of smoke and the stable near-infrared band, the consistency of similarity evaluation is improved.

[0076] In another embodiment of the present invention, in S4, the hierarchical optimization specifically includes:

[0077] (a) Fix the endmember matrix D (k) , and update the sparse coefficient matrix X through sparse regression (k+1) :

[0078]

[0079] Among them, X (k+1) is the updated sparse coefficient matrix, D (k) is the endmember matrix, the initial endmember matrix is constructed from the pure pigment spectral library, X (k) is the sparse coefficient matrix, and the initial sparse coefficient matrix is initially estimated by least squares or sparse coding;

[0080] (b) Fix the sparse coefficient matrix X (k+1) , and update the endmember matrix D by combining the least squares method with spectral smoothing constraints (k +1) :

[0081]

[0082] Among them, D (k+1) is the updated endmember matrix, λ is the regularization parameter, D T is the transpose of the endmember matrix, is the spectral smoothing constraint matrix;

[0083] (c) Repeat steps (a) and (b) until the objective function converges or reaches the preset number of iterations. The convergence determination criterion is that the relative change rate of the objective function value for 5 consecutive iterations is <0.01% or the change amount of the F norm is 1e -4 .

[0084] In the above technical solution, "sparse regression" is an optimization process for solving sparse coefficients under the condition of a fixed endmember matrix; the "spectral smoothing constraint matrix" is constructed by the Laplace operator and is used to suppress the high-frequency noise of the endmember spectrum.

[0085] Specifically, the hierarchical optimization is divided into two-step iteration: 1) Fix the endmember matrix D, update the sparse coefficient X through L1-regularized regression, and retain the main endmember components; 2) Fix X, and combine the least squares method with Update the constraint D to ensure the smoothness of the endmember spectral curves. The convergence criterion adopts a dual standard: the change rate of the objective function is <0.01% for 5 consecutive iterations or the change in the F norm is <1e -4 .

[0086] The alternating optimization strategy improves the computational efficiency by 50% and can converge within 20 iterations. The spectral smoothing constraint effectively removes the high-frequency noise of the endmember spectra. For example, the absorption valley morphology of azurite at 680 nm is closer to the true physical characteristics, and the endmember reconstruction error is reduced to less than 5%.

[0087] In another embodiment of the present invention, the method for spectral unmixing of smoked mural pigments further includes: comparing the unmixing result with the spectral data in the pure pigment spectral library, and evaluating the accuracy using at least one of the root mean square error (RMSE) and the spectral information divergence (SID), where RMSE ≤ 0.1 and / or SID ≤ 0.05, meeting the accuracy requirements.

[0088] In the above technical solution, the "root mean square error (RMSE)" measures the absolute deviation between the abundance estimate value and the true value; the "spectral information divergence (SID)" evaluates the spectral waveform consistency through the probability distribution difference.

[0089] Specifically, after the unmixing is completed, the result is compared with the pure spectral library, and the RMSE and SID are calculated. The requirement for RMSE is ≤ 0.1 to ensure that the abundance error is less than 10%; the requirement for SID is ≤ 0.05 to ensure that the unmixed spectral waveform is highly consistent with the reference spectrum. For example, the abundance RMSE of shell powder needs to be ≤ 0.08 and the SID needs to be ≤ 0.03. Among them,

[0090] The formula for calculating the root mean square error (RMSE) is:

[0091]

[0092] M is the total number of pixel points in the hyperspectral image of the smoked pigment, j is the jth pixel point, N is the total number of bands in the hyperspectral image of the smoked pigment, P i is the spectral vector of the ith band in the pure pigment spectral library, is the spectral vector of the ith band after unmixing.

[0093] The formula for calculating the spectral information divergence (SID) is:

[0094]

[0095] where R i and P i are the values of the ith band in the two spectral signals respectively, R i is the spectral signal value of the ith band of the pigment after unmixing, P iThe spectral vector of the i-th band in the pure pigment spectral library.

[0096] The dual-index evaluation system comprehensively quantifies the unmixing accuracy. In actual measurements, more than 95% of the area meets the constraint conditions, and the passing rate of expert visual inspection exceeds 98%, which is significantly better than the single-index evaluation method.

[0097] In another embodiment of the present invention, a spectral unmixing system for smoked mural pigments is further provided, including: a data preparation and preprocessing module for establishing a pure pigment spectral library and a smoked spectral library based on hyperspectral imaging data; a sparse unmixing model construction module for expressing the spectral signal of each pixel point in the hyperspectral image of the smoked pigment as a linear combination of the endmember spectra in the smoked spectral library and constructing a sparse unmixing model; an objective function design module for dynamically adjusting the regularization weight based on spectral similarity measurement and abundance gradient to construct the objective function of the sparse unmixing model, and the dynamic adjustment of the regularization weight adopts a spatial adaptive mechanism based on spectral similarity, and the weight update is realized by calculating the abundance; a hierarchical optimization and unmixing module for taking the endmember matrix constructed by the pure pigment spectral library as the input, and using the alternating least squares method combined with spectral smoothing constraints to iteratively optimize the objective function to obtain the unmixing result of the smoked pigment.

[0098] In the above technical solution, the "data preparation and preprocessing module" is responsible for spectral library construction and data correction; the "sparse unmixing model construction module" realizes linear mixing modeling; the "hierarchical optimization module" performs alternating iterative optimization.

[0099] Specifically, the system is composed of four modules in series: 1) The preprocessing module performs radiometric correction on the original hyperspectral data and constructs a dual spectral library; 2) The model construction module models each pixel spectrum as a linear combination of smoked endmembers; 3) The objective function module dynamically calculates the regularization weight; 4) The optimization module iteratively solves by the alternating least squares method and outputs the unmixing result. Each module transfers parameters through the data interface to ensure the automation of the process.

[0100] After system integration, the processing efficiency is increased by 40%, and the unmixing time of a single hyperspectral image (1000×1000 pixels) is shortened to within 10 minutes. The modular design supports flexible expansion. For example, when adding a new type of smoked endmember, only the spectral library needs to be updated without modifying the core algorithm.

[0101] The number of devices and the processing scale described here are used to simplify the description of the present invention. The application, modification, and variation of the method and system for spectral unmixing of smoked mural pigments of the present invention will be obvious to those skilled in the art.

[0102] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and embodiments. It can be fully applied to various fields suitable for the present invention. For those skilled in the art, additional modifications can be easily made. Therefore, without departing from the general concept defined by the claims and the equivalent scope, the present invention is not limited to specific details.

Claims

1. A spectral unmixing method for smoked mural pigments, characterized in that, Including: S1. Data preparation and preprocessing: Establish a pure pigment spectral library and a smoked spectral library based on hyperspectral imaging data; S2. Sparse unmixing model construction: Represent the spectral signal of each pixel in the hyperspectral image of smoked pigments as a linear combination of endmember spectra in the smoked spectral library, and construct a sparse unmixing model; S3. Objective function design: Based on spectral similarity measurement and abundance gradient, dynamically adjust the regularization weight to construct the objective function of the sparse unmixing model; The dynamic adjustment of the regularization weight adopts a spatial adaptive mechanism based on spectral similarity, and the weight update is realized by calculating the abundance; S4. Hierarchical optimization and unmixing: Using the endmember matrix constructed from the pure pigment spectral library as the input, adopt the alternating least squares method combined with spectral smoothing constraints to iteratively optimize the objective function to obtain the unmixing result of the smoked pigments.

2. The spectral unmixing method of the smoked mural pigment according to claim 1, characterized in that, In S1, before using the hyperspectral imaging data, radiometric correction is required, and the radiometric correction formula is: Among them, R is the calibrated hyperspectral data of the target object, and R raw is the original hyperspectral data of the target object, and R dark is the dark current data, and R white is the standard reflectance panel data.

3. The spectral unmixing method of the smoked mural pigment according to claim 1, characterized in that, In S1, the pure pigments include at least three mineral pigments selected from ochre, ultramarine, graphite, malachite green, and clam powder. The pure pigment spectral library satisfies: spectral resolution ≤ 5nm, signal-to-noise ratio ≥ 50dB, and the spectral mean of more than 10 pollution-free samples is collected for each pigment; The smoked pigments are obtained by smoking the simulated mural samples in a closed smoking environment for a preset duration, and are divided into three categories: mild, moderate, and severe according to the smoking duration.

4. The spectral unmixing method of the smoked mural pigment according to claim 1, characterized in that, In S2, the sparse unmixing model is specifically: y j = D1a j + n j where y j is the spectral vector of the j-th pixel in the hyperspectral image of the smoked pigment, D1 is the endmember matrix constructed from the smoked spectral library, a j is the sparse coefficient vector of the j-th pixel, and n j is the noise term of the j-th pixel.

5. The spectral unmixing method of the smoked mural pigment according to claim 4, characterized in that, In S3, the objective function is specifically: Among them, X is the sparse coefficient matrix, D is the endmember matrix of pure pigments, y is the hyperspectral data matrix of smoked pigments, ‖‖ F represents the norm, ∑ i,j ω i,j |X i,j | is the adaptive L1 regularization term, |X i,j | is the absolute value of the coefficient value of the corresponding i-th band and j-th pixel point in the sparse coefficient matrix. The proportion of non-zero elements in the sparse coefficient vector does not exceed 5%, and the absolute value of non-zero elements ≥ 0.1, ω i,j is the adaptive regularization weight, and the calculation formula is: Among them, S i,j is the spectral similarity metric value, S i,j ∈[0,1], β is the smoothness control parameter, is the abundance gradient.

6. The spectral unmixing method of the smoked mural pigment according to claim 5, characterized in that, In S3, the spectral similarity metric value S i,j is calculated by the following formula: where P i is the spectral vector of the i-th band in the pure pigment spectral library, and y j is the spectral vector of the j-th pixel in the hyperspectral image of the smoked pigment, and the calculation results are normalized.

7. The spectral unmixing method of the smoked mural pigment according to claim 6, characterized in that, In S4, the hierarchical optimization specifically includes: (a) Fixed-end element matrix D (k) and update the sparse coefficient matrix X through sparse regression (k+1) : Among them, X (k+1) is the updated sparse coefficient matrix, D (k) is the endmember matrix, and the initial endmember matrix is constructed from the pure pigment spectral library. X (k) is the sparse coefficient matrix, and the initial sparse coefficient matrix is initially estimated by least squares or sparse coding; (b) Fixed sparse coefficient matrix X (k+1) , update the endmember matrix D by combining the least squares method with spectral smoothing constraints (k+1) : Among them, D (k+1) is the updated endmember matrix, λ is the regularization parameter, D T is the transpose of the endmember matrix, is the spectral smoothing constraint matrix; (c) Repeat steps (a) and (b) until the objective function converges or reaches a preset number of iterations. The convergence criterion is that the relative change rate of the objective function value for 5 consecutive iterations is < 0.01% or the change in the F-norm is 1e -4 .

8. The spectral unmixing method of the smoked mural pigment according to claim 1, characterized in that, Also including: Compare the unmixing result with the spectral data in the pure pigment spectral library, and use at least one of the root mean square error (RMSE) and spectral information divergence (SID) as the accuracy evaluation index. Among them, RMSE ≤ 0.1 and / or SID ≤ 0.05, meeting the accuracy requirements.

9. A spectral unmixing system for smoked mural pigments, characterized in that, Including: A data preparation and preprocessing module, which is used to establish a pure pigment spectral library and a smoked spectral library based on hyperspectral imaging data; A sparse unmixing model construction module, which is used to represent the spectral signal of each pixel in the hyperspectral image of smoked pigments as a linear combination of endmember spectra in the smoked spectral library, and construct a sparse unmixing model; An objective function design module, which is used to dynamically adjust the regularization weight based on spectral similarity measurement and abundance gradient to construct the objective function of the sparse unmixing model. The dynamic adjustment of the regularization weight adopts a spatial adaptive mechanism based on spectral similarity, and the weight update is realized by calculating the abundance; A hierarchical optimization and unmixing module, which is used to use the endmember matrix constructed from the pure pigment spectral library as the input, adopt the alternating least squares method combined with spectral smoothing constraints to iteratively optimize the objective function to obtain the unmixing result of the smoked pigments.

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