A SIF spectral inversion method based on singular value decomposition and machine learning regression

Abstract

The application discloses a SIF spectrum inversion method based on singular value decomposition and machine learning regression. The method comprises the following steps: step 1, acquiring sample radiance spectrum data, solar-induced chlorophyll fluorescence spectrum data corresponding to the radiance spectrum data and the like; step 2, performing singular value decomposition on a feature matrix, selecting a plurality of main singular vectors to construct a reconstruction base matrix, and calculating low-dimensional expansion coefficients of the fluorescence spectrum; step 3, performing singular value decomposition on the feature matrix; step 4, taking the low-dimensional feature coefficients of the radiance spectrum, preset key band radiance features, band ratio features and observation geometry features as input variables of a machine learning regression model; and step 5, inputting a sample to be inverted into the trained machine learning regression model. The application converts the high-dimensional solar-induced chlorophyll fluorescence spectrum inversion problem into a low-dimensional expansion coefficient prediction problem, and has the advantages of high inversion efficiency, strong model stability and suitability for popularization and application.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing quantitative inversion technology, specifically relating to a solar-induced chlorophyll fluorescence (SIF) spectral inversion method based on singular value decomposition and machine learning regression. Background Technology

[0002] Solar-induced chlorophyll fluorescence (SIF) is an important remote sensing parameter characterizing the photosynthetic state of vegetation, and it has significant application value in crop growth monitoring, vegetation physiological state inversion, ecosystem productivity assessment, and carbon cycle research. Existing SIF retrieval methods mostly model single bands, local windows, or local features, typically requiring direct processing of high-dimensional spectral information. This leads to problems such as high model input dimensionality, severe feature redundancy, high computational complexity, and insufficient model stability.

[0003] For solar-induced chlorophyll fluorescence spectral inversion, directly building an inversion model band-by-band using high-dimensional spectra as output not only requires handling a large number of output variables but is also susceptible to noise, variable correlation, and imbalanced sample distribution, thus reducing model training efficiency and inversion stability. Therefore, a technical method is needed to transform the high-dimensional solar-induced chlorophyll fluorescence spectral inversion problem into a low-dimensional parameter prediction problem. This would reduce modeling complexity and improve inversion efficiency, stability, and accuracy while preserving key spectral variation information. Summary of the Invention

[0004] To address the problems of high output dimensionality, complex modeling process, low computational efficiency, and insufficient model stability in existing solar-induced chlorophyll fluorescence spectral inversion technologies, this invention provides a solar-induced chlorophyll fluorescence spectral inversion method based on singular value decomposition and machine learning regression.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A SIF spectral inversion method based on singular value decomposition and machine learning regression includes the following steps:

[0007] Step 1: Obtain the sample radiance spectral data, the solar-induced chlorophyll fluorescence spectral data corresponding to the radiance spectral data, wavelength information, and observation geometry information;

[0008] Step 2: Arrange the solar-induced chlorophyll fluorescence spectra in the training sample set into a feature matrix in a uniform manner, perform singular value decomposition on the feature matrix, select the first few main singular vectors to construct the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix, and calculate the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum.

[0009] Step 3: Arrange the radiance spectra in the training sample set in the same way as in Step 2 to form a radiance spectral feature matrix; then perform singular value decomposition on the radiance spectral feature matrix, select the first few main singular vectors to construct the radiance feature basis matrix, and calculate the low-dimensional feature coefficients of the radiance spectrum.

[0010] Step 4: Use the low-dimensional feature coefficients of the radiance spectrum, the preset key band radiance features, band ratio features, and observation geometric features as input variables for the machine learning regression model, and use the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum as output variables to train the model and establish the mapping relationship between the input variables and the output variables.

[0011] Step 5: Input the sample to be inverted into the trained machine learning regression model to obtain the predicted value of the low-dimensional expansion coefficient of the corresponding solar-induced chlorophyll fluorescence spectrum. Then, combine the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix to reconstruct the solar-induced chlorophyll fluorescence spectrum of the sample to be inverted.

[0012] In the SIF spectral inversion method based on singular value decomposition and machine learning regression, in step 1, the sample radiance spectral data and solar-induced chlorophyll fluorescence spectral data correspond one-to-one on a sample basis, and the observation geometric information includes at least solar zenith angle information.

[0013] The SIF spectral inversion method based on singular value decomposition and machine learning regression, in step 2, involves performing singular value decomposition on the solar-induced chlorophyll fluorescence spectral feature matrix to obtain several singular vectors. The first few principal singular vectors are selected to construct the solar-induced chlorophyll fluorescence spectral reconstruction basis matrix, thus characterizing the main variation features of the solar-induced chlorophyll fluorescence spectrum. The specific formula for singular value decomposition is as follows:

[0014] (1)

[0015] In the formula, M is the solar-induced chlorophyll fluorescence spectral characteristic matrix, U is the left singular vector matrix, Σ is the diagonal matrix composed of singular values, and V is the right singular vector matrix. T The transpose of this matrix is ​​used; the first few principal singular vectors in the right singular vector matrix are selected to form the basis matrix A for reconstructing the solar-induced chlorophyll fluorescence spectrum.

[0016] In the SIF spectral inversion method based on singular value decomposition and machine learning regression, step 2 involves projecting the real solar-induced chlorophyll fluorescence spectrum onto the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix A to obtain low-dimensional expansion coefficients. The calculation formula for the low-dimensional expansion coefficients is as follows:

[0017] (2)

[0018] In the formula, A is the basis matrix for reconstructing solar-induced chlorophyll fluorescence spectra, S is the actual solar-induced chlorophyll fluorescence spectrum data, and C is the low-dimensional expansion coefficient of the actual solar-induced chlorophyll fluorescence spectrum on the basis matrix.

[0019] The SIF spectral inversion method based on singular value decomposition and machine learning regression, in step 3, arranges the radiance spectra in the training sample set in the same way as in step 2 to form a radiance spectral feature matrix; then, singular value decomposition is performed on this radiance spectral feature matrix to obtain several singular vectors, and the first few main singular vectors are selected to form a radiance feature basis matrix to characterize the main variation features of the radiance spectrum; the specific formula for singular value decomposition is as follows:

[0020] (3)

[0021] In the formula, Let U be the radiance spectral characteristic matrix, Σ be the left singular vector matrix, Σ be the diagonal matrix composed of singular values, and V be the right singular vector matrix. Its transpose matrix; select the first few principal singular vectors from the right singular vector matrix to form the radiance feature basis matrix. .

[0022] In the SIF spectral inversion method based on singular value decomposition and machine learning regression, step 3 involves projecting the radiance spectrum onto the radiance feature basis matrix to obtain low-dimensional feature coefficients of the radiance spectrum. The calculation formula for the low-dimensional feature coefficients is as follows:

[0023] (4)

[0024] In the formula, The radiance characteristic basis matrix, For radiance spectral data, The radiance spectrum is represented by the low-dimensional characteristic coefficients on the radiance characteristic basis matrix.

[0025] The SIF spectral inversion method based on singular value decomposition and machine learning regression, in step 4, includes the preset key band radiance features as follows: the radiance features of the 675 nm band and the radiance features of the 775 nm band; the band ratio features as follows: the ratio of the radiance of the 675 nm band to that of the 775 nm band; and the observation geometric features as follows: the cosine of the solar zenith angle. .

[0026] In the SIF spectral inversion method based on singular value decomposition and machine learning regression, step 4, the machine learning regression model is an XGBoost regression model.

[0027] In the SIF spectral inversion method based on singular value decomposition and machine learning regression, step 5 uses the following formula to reconstruct the solar-induced chlorophyll fluorescence spectrum:

[0028] (5)

[0029] In the formula, To reconstruct the obtained solar-induced chlorophyll fluorescence spectrum, The predicted low-dimensional expansion coefficients of solar-induced chlorophyll fluorescence spectra are obtained from machine learning regression models.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] Firstly, this invention transforms the high-dimensional solar-induced chlorophyll fluorescence spectrum inversion problem into a low-dimensional expansion coefficient prediction problem, which helps to reduce model complexity and improve training efficiency.

[0032] Secondly, by comprehensively utilizing the low-dimensional characteristic coefficients, key band information, and observational geometric information of the radiance spectrum, this invention can more comprehensively characterize the feature information related to the changes in solar-induced chlorophyll fluorescence spectrum, thereby improving the model's ability to express the laws of solar-induced chlorophyll fluorescence spectrum changes and its predictive stability.

[0033] Thirdly, this invention recovers the solar-induced chlorophyll fluorescence spectrum by reconstructing the basis matrix of the solar-induced chlorophyll fluorescence spectrum, which takes into account both the ability to retain spectral information and the inversion efficiency, and avoids the problems of excessively high output dimensionality and complex modeling caused by direct band-by-band inversion. Attached Figure Description

[0034] Figure 1 Comparison of prediction results for low-dimensional expansion coefficients of solar-induced chlorophyll fluorescence spectra;

[0035] Figure 2 Comparison of solar-induced chlorophyll fluorescence spectrum reconstruction results;

[0036] Figure 3 Comparison of solar-induced chlorophyll fluorescence inversion results at 685 nm and 740 nm wavelengths. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited to the following embodiments.

[0038] Step 1: Sample data acquisition and organization.

[0039] Sample data was generated using SCOPE and MODTRAN coupled simulations to obtain radiance spectral data, corresponding solar-induced chlorophyll fluorescence spectral data, wavelength information, and observational geometric information under different atmospheric conditions, canopy parameter conditions, and observational geometric conditions. These data were then organized into a sample dataset based on a one-to-one correspondence between samples. Each sample in the dataset includes one radiance spectrum, one solar-induced chlorophyll fluorescence spectrum, and corresponding observational geometric parameters. The sample dataset was then divided into a training sample set and a validation sample set. The training sample set was used to construct the feature basis matrix, calculate low-dimensional coefficients, and train a machine learning regression model. The validation sample set was used to evaluate the accuracy of the inversion results.

[0040] Step 2: Construct the basis matrix for reconstructing the solar-induced chlorophyll fluorescence spectrum and calculate the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum.

[0041] The solar-induced chlorophyll fluorescence spectra in the training sample set are arranged in a uniform manner (each spectrum is a column vector, and the column vectors of all samples are arranged side by side in sample order to form a matrix), forming the solar-induced chlorophyll fluorescence spectral feature matrix 𝑀. Then, singular value decomposition is performed on the solar-induced chlorophyll fluorescence spectral feature matrix 𝑀 to obtain the corresponding singular vectors. The singular value decomposition formula is as follows:

[0042] (1)

[0043] In the formula, M is the solar-induced chlorophyll fluorescence spectral characteristic matrix, U is the left singular vector matrix, Σ is the diagonal matrix composed of singular values, and V is the right singular vector matrix. This is its transpose matrix. In this example, the first three principal singular vectors in the right singular vector matrix are selected to form the basis matrix A for reconstructing the solar-induced chlorophyll fluorescence spectrum, in order to characterize the main variation features of the solar-induced chlorophyll fluorescence spectrum.

[0044] After constructing the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix A, the real solar-induced chlorophyll fluorescence spectrum corresponding to each training sample is projected onto the reconstruction basis matrix to obtain the low-dimensional expansion coefficients corresponding to that sample. The calculation formula for the low-dimensional expansion coefficients is as follows:

[0045] (2)

[0046] In the formula, A is the basis matrix for reconstructing solar-induced chlorophyll fluorescence spectra, S is the actual solar-induced chlorophyll fluorescence spectrum data, and C is the expansion coefficient of the actual solar-induced chlorophyll fluorescence spectrum on the reconstructed basis matrix. The low-dimensional expansion coefficients are used to characterize the main information of the solar-induced chlorophyll fluorescence spectrum in low-dimensional space and serve as the output variables of the subsequent machine learning regression model.

[0047] Step 3: Construct the radiance characteristic basis matrix and calculate the low-dimensional characteristic coefficients of the radiance spectrum.

[0048] Arrange the radiance spectra in the training sample set in the same manner as in step 2 to form a radiance spectral feature matrix. Then, singular value decomposition is performed on the radiance spectral feature matrix to obtain the corresponding singular vectors. The specific formula for singular value decomposition is as follows:

[0049] (3)

[0050] In the formula, Let U be the radiance spectral characteristic matrix, Σ be the left singular vector matrix, Σ be the diagonal matrix composed of singular values, and V be the right singular vector matrix. Its transpose is then used. The first six principal singular vectors from the right singular vector matrix are selected to form the radiance characteristic basis matrix. To characterize the main variation features of the radiance spectrum.

[0051] Subsequently, the radiance spectrum corresponding to each training sample is projected onto the radiance feature basis matrix to obtain the low-dimensional feature coefficients of the radiance spectrum of each sample. The calculation formula is as follows:

[0052] (4)

[0053] In the formula, The radiance characteristic basis matrix, For radiance spectral data, These are the low-dimensional characteristic coefficients of the radiance spectrum on the radiance characteristic basis matrix. These low-dimensional characteristic coefficients characterize the main variations of the radiance spectrum in the low-dimensional space and serve as part of the input variables for subsequent machine learning regression models.

[0054] Step 4: Construct the input and output variables of the machine learning regression model and train the model.

[0055] The low-dimensional feature coefficients of the radiance spectrum obtained in step 3 are used as the basic input features. At the same time, the radiance features, band ratio features and observation geometric features of the preset key bands are extracted to form the input variables of the machine learning regression model. The low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum obtained in step 2 are used as the output variables of the machine learning regression model to train the model, thereby establishing the mapping relationship between the input variables and the output variables.

[0056] The preset key band radiance features include 675 nm band radiance features and 775 nm band radiance features; the band ratio features include the ratio of 675 nm to 775 nm band radiance features; and the observation geometry features include the cosine of the solar zenith angle. .

[0057] In this embodiment, the machine learning regression model employs the XGBoost regression model to achieve a nonlinear mapping between the input variables and the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum. By learning from the training sample set, a machine learning regression model is obtained for predicting the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum.

[0058] Step 5: Predict the low-dimensional expansion coefficient of the solar-induced chlorophyll fluorescence spectrum and reconstruct the solar-induced chlorophyll fluorescence spectrum.

[0059] For the validation sample set or the sample to be inverted, first extract the low-dimensional feature coefficients of the radiance spectrum, the preset key band radiance features, band ratio features, and observation geometric features in the same way as in steps 3 and 4, as in the training phase. Then, input these into the trained machine learning regression model to obtain the predicted value of the low-dimensional expansion coefficient of the solar-induced chlorophyll fluorescence spectrum corresponding to the sample. Then, the predicted values ​​of the low-dimensional expansion coefficients are... Combined with the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix A constructed in step 2, the solar-induced chlorophyll fluorescence spectrum of the sample to be inverted is reconstructed. The reconstruction formula is as follows:

[0060] (5)

[0061] In the formula, To reconstruct the obtained solar-induced chlorophyll fluorescence spectrum, The values ​​are the predicted low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum obtained from the machine learning regression model. The reconstruction capability and inversion accuracy of the method can be evaluated by comparing the reconstructed solar-induced chlorophyll fluorescence spectrum with the reference solar-induced chlorophyll fluorescence spectrum in the validation sample set.

[0062] Figure 1The image shows a comparison of the predicted low-dimensional expansion coefficients of solar-induced chlorophyll fluorescence spectra. It illustrates the scatter distribution between the low-dimensional expansion coefficients predicted by the method of this invention and the reference expansion coefficients obtained by projecting the actual fluorescence spectra onto the validation sample set. Taking the first expansion coefficient as an example, the coefficient of determination (R²) between the predicted and reference values ​​reaches over 0.999, with a relative root mean square error (RRMSE) of only 1.12%. The scatter points are closely distributed near the 1:1 diagonal. This indicates that, using the low-dimensional characteristic coefficients of the radiance spectrum, the radiance characteristics of key bands, the band ratio characteristics, and the observational geometric characteristics as inputs, the XGBoost regression model can accurately establish the nonlinear mapping relationship between the input features and the low-dimensional expansion coefficients of the fluorescence spectra, resulting in high accuracy and low error in the low-dimensional expansion coefficient prediction.

[0063] Figure 2 The image shows a comparison of the solar-induced chlorophyll fluorescence spectrum reconstruction results, displaying the curves of fluorescence spectra reconstructed using the method of this invention for several randomly selected samples from the validation sample set, and comparing them with the reference real fluorescence spectra. It can be seen that the reconstructed spectra (dashed line) and the real spectra (solid line) are highly consistent in overall shape, peak position, and trend in the 650-800 nm band. Especially at the main fluorescence emission peaks (around 685 nm and 740 nm), the reconstructed spectra accurately capture the characteristic information of the real spectrum. Minor deviations in a few bands mainly originate from higher-order detail information discarded when selecting principal components in singular value decomposition; these deviations are within acceptable limits. This demonstrates that the "dimensionality reduction-reconstruction" strategy adopted in this invention can effectively reduce the dimensionality of the model output while retaining the main variation information of the fluorescence spectrum.

[0064] Figure 3 The accompanying graphs show a comparison of the solar-induced chlorophyll fluorescence inversion results at 685 nm and 740 nm bands. They display scatter plots comparing the fluorescence values ​​(i.e., the values ​​of the corresponding bands in the reconstructed spectra) obtained by the method of this invention in the validation sample set with the reference true fluorescence values. The scatter plots for both bands are closely distributed near the 1:1 diagonal, with coefficients of determination (R²) exceeding 0.99. Furthermore, no systematic overestimation or underestimation was observed across different fluorescence intensity ranges. This indicates that the method of this invention not only performs excellently in overall spectral reconstruction but also possesses extremely high accuracy in the quantitative inversion of individual key bands, meeting the requirements for quantitative chlorophyll fluorescence inversion in applications such as vegetation physiological status monitoring and ecosystem productivity assessment.

[0065] It should be understood that those skilled in the art can make several improvements and substitutions to this invention without departing from the principles of this invention, such as adjusting the number of singular vectors, adjusting the preset key band position, or replacing the type of machine learning regression model. All equivalent transformations made using the concept of this invention should fall within the protection scope of this invention.

Claims

1. A SIF spectral inversion method based on singular value decomposition and machine learning regression, characterized in that, Includes the following steps: Step 1: Obtain sample radiance spectral data, solar-induced chlorophyll fluorescence spectral data corresponding to the radiance spectral data, wavelength information, and observation geometric information, wherein the observation geometric information includes at least solar zenith angle information; Step 2: Arrange the solar-induced chlorophyll fluorescence spectra in the training sample set into a feature matrix in a uniform manner, perform singular value decomposition on the feature matrix, select the first few main singular vectors to construct the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix, and calculate the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum. The real solar-induced chlorophyll fluorescence spectrum is projected onto the reconstructed basis matrix A of the solar-induced chlorophyll fluorescence spectrum to obtain the low-dimensional expansion coefficients; the calculation formula for the low-dimensional expansion coefficients is as follows: (2)； In the formula, A is the basis matrix for reconstructing solar-induced chlorophyll fluorescence spectrum, S is the actual solar-induced chlorophyll fluorescence spectrum data, and C is the low-dimensional expansion coefficient of the actual solar-induced chlorophyll fluorescence spectrum on the basis matrix. Step 3: Arrange the radiance spectra in the training sample set in the same manner as in Step 2 to form a radiance spectral feature matrix; then perform singular value decomposition on the radiance spectral feature matrix, select the first few principal singular vectors to construct a radiance feature basis matrix, and calculate the low-dimensional feature coefficients of the radiance spectrum; project the radiance spectrum onto the radiance feature basis matrix to obtain the low-dimensional feature coefficients of the radiance spectrum; the calculation formula for the low-dimensional feature coefficients is as follows: (4)； In the formula, The radiance characteristic basis matrix, For radiance spectral data, The radiance spectrum represents the low-dimensional characteristic coefficients of the radiance characteristic basis matrix. Step 4: Use the low-dimensional feature coefficients of the radiance spectrum, the preset key band radiance features, band ratio features, and observation geometric features as input variables for the machine learning regression model, and use the low-dimensional expansion coefficients of the solar-induced chlorophyll fluorescence spectrum as output variables to train the model and establish the mapping relationship between the input variables and the output variables. Step 5: Input the sample to be inverted into the trained machine learning regression model to obtain the predicted low-dimensional expansion coefficients of its corresponding solar-induced chlorophyll fluorescence spectrum. Then, combine this with the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix to reconstruct the solar-induced chlorophyll fluorescence spectrum of the sample to be inverted. The reconstruction formula for the solar-induced chlorophyll fluorescence spectrum is as follows: (5)； In the formula, To reconstruct the obtained solar-induced chlorophyll fluorescence spectrum, The predicted low-dimensional expansion coefficients of solar-induced chlorophyll fluorescence spectra are obtained from machine learning regression models.

2. The SIF spectral inversion method based on singular value decomposition and machine learning regression as described in claim 1, characterized in that, In step 1, the sample radiance spectrum data and the solar-induced chlorophyll fluorescence spectrum data are matched one-to-one with each sample.

3. The SIF spectral inversion method based on singular value decomposition and machine learning regression as described in claim 1, characterized in that, In step 2, singular value decomposition is performed on the solar-induced chlorophyll fluorescence spectrum feature matrix to obtain several singular vectors. The first few main singular vectors are selected to form the solar-induced chlorophyll fluorescence spectrum reconstruction basis matrix to characterize the main variation features of the solar-induced chlorophyll fluorescence spectrum. The specific formula for singular value decomposition is as follows: (1)； In the formula, M is the solar-induced chlorophyll fluorescence spectral characteristic matrix, U is the left singular vector matrix, Σ is the diagonal matrix composed of singular values, and V is the right singular vector matrix. T The transpose of this matrix is ​​used; the first few principal singular vectors in the right singular vector matrix are selected to form the basis matrix A for reconstructing the solar-induced chlorophyll fluorescence spectrum.

4. The SIF spectral inversion method based on singular value decomposition and machine learning regression as described in claim 1, characterized in that, In step 3, the radiance spectra in the training sample set are arranged in the same manner as in step 2 to form a radiance spectral feature matrix. Then, singular value decomposition is performed on this radiance spectral feature matrix to obtain several singular vectors. The first few main singular vectors are selected to form a radiance feature basis matrix to characterize the main variation features of the radiance spectrum. The specific formula for singular value decomposition is as follows: (3)； In the formula, Let U be the radiance spectral characteristic matrix, Σ be the left singular vector matrix, Σ be the diagonal matrix composed of singular values, and V be the right singular vector matrix. Its transpose matrix; select the first few principal singular vectors from the right singular vector matrix to form the radiance feature basis matrix. .

5. The SIF spectral inversion method based on singular value decomposition and machine learning regression as described in claim 1, characterized in that, In step 4, the preset key band radiance features include 675 nm band radiance features and 775 nm band radiance features; the band ratio features include the ratio of 675 nm to 775 nm band radiance features; and the observation geometric features include the cosine of the solar zenith angle. .

6. The SIF spectral inversion method based on singular value decomposition and machine learning regression as described in claim 1, characterized in that, In step 4, the machine learning regression model is the XGBoost regression model.

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