A lake COD inversion method

Abstract

The present invention discloses a lake COD inversion method. The method comprises the following steps: obtaining hyperspectral images and true COD values of water sampling points, generating an original training set and an original test set; constructing a COD parameter inversion model; adjusting spectral data of selected bands of samples in the original training set, generating a reconstructed training set corresponding to the selected bands, training the COD parameter inversion model using the original training set and the reconstructed training sets corresponding to the selected bands, selecting important bands, and training the COD parameter inversion model based on the spectral data of the important bands of samples in the original training set, so as to obtain a COD parameter inversion model that has finally completed the training. The method can automatically select the most important bands, obtain the most important spectral information, automatically learn and filter out important spatial information, reduce the influence of flares near sampling points and impurities such as aquatic plants on spatial information, and improve the COD inversion accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of lake water environment remote sensing technology. Based on the hyperspectral image of a lake taken by a hyperspectral camera onboard an unmanned aerial vehicle (UAV), the present invention provides a lake COD inversion method suitable for inverting the chemical oxygen demand (COD) in a lake. Background Art

[0002] Chemical oxygen demand (COD) is an important indicator for measuring the degree of organic pollution in water bodies. It uses chemical methods to measure the amount of reducing substances that need to be oxidized in water samples. It is widely used in water treatment, environmental protection, industrial wastewater monitoring and other fields. By regularly testing COD values, pollution sources can be discovered in a timely manner and corresponding control measures can be taken to ensure the sustainable use of water resources.

[0003] Compared with field sampling and indoor testing, satellite remote sensing images have a wide coverage area and are easy to obtain, and are widely used in the field of water quality monitoring. However, due to the influence of cloudy weather, satellite revisit period, and image spatial and spectral resolution, it is impossible to continuously obtain high-quality, high-spatial, and high-spectral resolution lake satellite remote sensing images. The emergence of drone remote sensing technology provides a better solution. The drone-mounted hyperspectral camera can obtain high-spatial, high-spectral resolution lake water imagery containing more texture and band information, but too many bands in hyperspectral images will produce spectral information redundancy, reducing the inversion accuracy of COD parameters. Currently, many scholars use Pearson coefficients or principal component analysis (PCA) to calculate the correlation between each band and the COD parameter value, and sort the correlations to screen the important spectral band information in the hyperspectral image. Then, machine learning and other methods are used to establish an inversion model. However, these screening methods usually calculate the linear importance features between the band values and the COD values, and cannot mine nonlinear importance features. Secondly, in terms of spatial information, high spatial resolution brings about feature refinement while also causing information redundancy or noise. The current method of obtaining the image corresponding to the sampling point is mostly centered on the sampling point and cropping the surrounding 5 5 (or 3 3) Pixel grids. However, sometimes surrounding pixels may experience flare or interference from impurities such as aquatic plants, reducing the usability of the image. Meanwhile, deep learning has demonstrated promising performance in water quality parameter inversion, enabling the learning of deeper nonlinear features and exhibiting strong generalizability. In summary, existing research has not fully leveraged the advantages of deep learning models for automated, precise screening and learning of important spatial and spectral features. Summary of the Invention

[0004] In response to the problems in the existing technology of using hyperspectral imagery to invert lake COD parameters, the model does not adaptively screen important spatial and spectral features of the image, ignores the relationship between important spatial and spectral features and COD values, and the problem of poor COD inversion accuracy using simple machine learning models, the present invention proposes a lake COD inversion method (ISBLNet Important Spatial and Band Learning Network) and equipment, which can improve the inversion accuracy of COD in lakes and have better performance than basic neural network models and random forest models.

[0005] The above technical problems of the present invention are mainly solved by the following technical solutions:

[0006] A lake COD inversion method comprises the following steps:

[0007] Step 1: Obtain hyperspectral images and true COD values of water sampling points, construct samples based on hyperspectral images, use true COD values as sample labels, and generate original training sets and original test sets;

[0008] Step 2: Construct COD parameter inversion model;

[0009] Step 3: Train the COD parameter inversion model based on the original training set, and calculate the determination coefficient R² value corresponding to the COD parameter inversion model, adjust the spectral data of the selected bands of the samples in the original training set, generate a reconstructed training set corresponding to the selected bands, use the reconstructed training sets corresponding to each selected band to train the COD parameter inversion model, and calculate the determination coefficient R² value corresponding to the COD parameter inversion model trained with each reconstructed training set, select several important bands that have the most important influence on the determination coefficient R² value of the COD parameter inversion model, and train the COD parameter inversion model based on the spectral data of the important bands of the samples in the original training set to obtain the COD parameter inversion model that has finally completed the training;

[0010] Step 4: Input the hyperspectral image to be predicted into the COD parameter inversion model to obtain the final predicted COD value.

[0011] As described above, constructing a sample based on a hyperspectral image includes: performing radiation correction on the hyperspectral image data, locating a water body sampling point in the hyperspectral image after radiation correction, and cropping the image according to a set window range to obtain a cropped hyperspectral image, and using the cropped hyperspectral image as a sample.

[0012] As mentioned above, the COD parameter inversion model includes a spatial feature self-learning module, a convolution module, and a fully connected module.

[0013] The sample is input into the spatial feature self-learning module to obtain the feature map of important spatial features after dimensionality reduction;

[0014] The feature map of the important spatial features after dimensionality reduction is input to the convolution module, and the convolution module outputs the flattened feature vector;

[0015] The flattened feature vector is input to the fully connected module, and the fully connected module outputs the predicted COD value.

[0016] The dimension of the sample input to the spatial feature self-learning module is batch aisle high Width, in the spatial feature self-learning module:

[0017] The pixel points of the sample are randomly extracted in a window manner to generate window samples, and each window sample is merged in the channel dimension in the extraction order to obtain the window feature map.

[0018] Perform global maximum pooling operation on the window feature map to generate a pooled feature map.

[0019] Perform a two-dimensional convolution operation on the pooled feature map to generate a spatial information weight factor with linear features.

[0020] Multiply the window feature map with the spatial information weight factor to generate an important spatial information feature map.

[0021] A two-dimensional convolution operation is performed on the important spatial information feature map to restore the number of channels of the important spatial information feature map to the same number of channels as the sample input to the spatial feature self-learning module, and obtain the feature map of the important spatial features after dimensionality reduction.

[0022] The convolution module of the COD parameter inversion model as described above includes a first convolution layer, a first ReLU activation function, a second convolution layer, and a second ReLU activation function.

[0023] The feature map of important spatial features after dimensionality reduction is input to the first convolutional layer.

[0024] The output features of the first convolutional layer are operated by the first ReLU activation function to further obtain the first nonlinear features.

[0025] The first nonlinear feature is input to the second convolutional layer,

[0026] The output features of the second convolutional layer are operated by the second ReLU activation function to further obtain the second nonlinear features.

[0027] The height and width of the second nonlinear feature are flattened to obtain a flattened feature vector.

[0028] As described above, the fully connected module of the COD parameter inversion model includes a first fully connected layer, a third activation function, a second fully connected layer, a fourth activation function, and a third fully connected layer.

[0029] The flattened feature vector is input to the first fully connected layer,

[0030] The output features of the first fully connected layer are operated by the third activation function to introduce nonlinear features and obtain the third nonlinear features.

[0031] The third nonlinear feature is input to the second fully connected layer,

[0032] The output features of the second fully connected layer are operated by the fourth activation function to introduce nonlinear features and obtain the fourth nonlinear features.

[0033] The fourth nonlinear feature is input to the third fully connected layer, and the third fully connected layer outputs the predicted COD value.

[0034] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above-mentioned inversion method when executing the computer program.

[0035] A computer-readable storage medium stores a computer program, which implements the steps of the above-mentioned inversion method when executed by a processor.

[0036] A computer program product comprises a computer program, which implements the steps of the above-mentioned inversion method when executed by a processor.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. Compared with using the Pearson coefficient to calculate the correlation between the reflectance value of each band in the hyperspectral image (each band is a spectral information) and the COD value, and using the PCA method to screen the important spectral features of the hyperspectral image, the COD parameter inversion model constructed by the neural network model in the present invention is combined with the band value replacement method. It can automatically select the most important bands and obtain the most important spectral information, avoiding the limitations of manual selection. It not only considers the linear relationship between spectral information and COD value, but also the nonlinear relationship, making the screening of important spectral features more effective and reducing the problem of spectral information redundancy in hyperspectral image data.

[0039] 2. Compared with direct sampling near 5 5 pixel range of hyperspectral image cropping, the present invention crops 7 near the sampling point 7 range of images, and the 7 7 windows perform multiple random sampling of the spatial range to generate multiple 5 5-size window samples are combined in the channel dimension according to the extraction order to create a spatial attention mechanism, which automatically learns to filter out important spatial information, reduces the impact of flares and impurities such as aquatic plants near the sampling point on spatial information, and improves the COD inversion accuracy.

[0040] 3. Compared with the basic network and random forest methods, the present invention achieves higher accuracy. Figure 1 Table 1 shows the fitting effect of the present invention on the original test set (compared with the basic network, the spatial feature self-learning module and the spectral feature self-learning module are removed). It can be seen that after adding the spatial feature self-learning module and the spectral feature self-learning module, the present invention has a better determination coefficient R than the basic network. 2 The R 2 It increased by 0.0854 and the RMSE decreased by 0.8228 mg / L. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The fitting results of the present invention, the basic network, and the random forest on the original test data set are shown in Figure 2 (R 2 is the coefficient of determination, and RMSE is the root mean square error), where (a) is a diagram showing the fitting results of the coefficient of determination and the root mean square error of the present invention on the original test data set; (b) is a diagram showing the fitting results of the coefficient of determination and the root mean square error of the basic network on the original test data set; (c) is a diagram showing the fitting results of the coefficient of determination and the root mean square error of the random forest on the original test data set;

[0042] Figure 2 is a flow chart of the present invention;

[0043] Figure 3 Schematic diagram of noise at water sampling points; (a) is a schematic diagram of noise with aquatic plants and other organisms on the water surface at the water sampling point; (b) is a schematic diagram of noise with flares on the water surface at the water sampling point;

[0044] Figure 4 This is a structural diagram of the spatial feature self-learning module;

[0045] Figure 5 It is a structural diagram of the convolution module;

[0046] Figure 6 This is a structural diagram of the fully connected module. DETAILED DESCRIPTION

[0047] In order to facilitate ordinary technicians in this field to understand and implement the present invention, the present invention is further described in detail below in conjunction with implementation examples. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0048] Example 1

[0049] A lake COD inversion method (ISBLNet) includes the following steps.

[0050] Step 1: Obtain hyperspectral images and true COD values of water sampling points, construct samples based on hyperspectral images, use true COD values as sample labels, and generate original training sets and original test sets.

[0051] This step mainly includes the acquisition of water samples and hyperspectral images, the acquisition of the actual COD value of laboratory COD measurement, water image processing and data set division. Specifically, it includes the following steps:

[0052] The collection of hyperspectral image data is carried out through the following steps: using a water sampler to obtain water samples at various water sampling points in the target water area, and using a drone equipped with a hyperspectral camera to image the target water area to obtain hyperspectral image data, performing radiation correction on the hyperspectral image data, locating the water sampling points in the radiation-corrected hyperspectral image, and cropping it according to the set window range to obtain the cropped hyperspectral image.

[0053] The collection of the true COD value is carried out through the following steps: the water samples obtained from each water sampling point are sent to the laboratory to determine their chemical oxygen demand (COD) values as the corresponding true COD values.

[0054] The cropped hyperspectral image is used as a sample, the corresponding true COD value is used as a label, and the sample is randomly divided to construct an original training set and an original test set. In this embodiment, the number of original training sets and original test sets is 76 and 32, respectively.

[0055] Step 2: Construct the COD parameter inversion model. The COD parameter inversion model includes a spatial feature self-learning module, a convolution module, and a fully connected module, such as Figures 4 to 6 .

[0056] Step 2.1: The sample is input into the spatial feature self-learning module to obtain the feature map of important spatial features after dimensionality reduction.

[0057] Step 2.1.1: Input the samples into the spatial feature self-learning module in batches. The dimension of the samples is the batch banch_size Channel bands height Width width, dimension size is 8 125 7 7. The batch size refers to the number of samples input into the spatial feature self-learning module during each training. The initial number of channels is the number of sample bands.

[0058] Step 2.1.2: Randomly extract the pixels of each sample in a batch (8 in this invention) in a window manner to generate n channels high Width is 125 5 5 window samples (each window dimension size is 125 5 5, n in the present invention is 441), each window sample is merged in the channel dimension according to the extraction order, and finally a batch will generate a dimension size of 8 125n 5 Window feature map of 5.

[0059] Step 2.1.3: Perform global maximum pooling on the window feature map to generate a dimension of 8 125n 1 1’s pooled feature map.

[0060] Step 2.1.4: Convolution kernel size is 1 on the pooled feature map 1 two-dimensional convolution operation, generating a dimension size of 8 125n 1 1 is the spatial information weight factor with linear features.

[0061] Step 2.1.5: Multiply the window feature map with the spatial information weight factor to generate a dimension of 8 125n 5 5. Important spatial information feature map.

[0062] Step 2.1.6: Convolution kernel size is 1 for important spatial information feature map 1, performs dimensionality reduction processing on the important spatial information feature map, and restores the number of channels of the important spatial information feature map to the number of channels of the sample input to the spatial feature self-learning module (that is, restores its number of bands to the original 125), generating a dimension size of 8 125 5 Feature map of important spatial features after dimensionality reduction of 5.

[0063] like Figure 3As shown in (a), there are some organisms such as water plants on the water surface, and due to the angle of incidence of sunlight, there will also be some flare phenomena, such as Figure 3 As shown in (b), these phenomena cause the reflectivity of the pixel to change, and it is no longer the reflectivity of the water body, which leads to a decrease in the accuracy of COD parameter inversion. Usually, these areas are actively avoided when cropping images near the sampling point, but sometimes the pixels of these phenomena are discontinuous and cannot be completely avoided, which will cause the cropped hyperspectral image to be mixed with some irrelevant spatial information. Using a window to randomly extract images near the sampling point can randomly generate window samples of multiple spatial position combinations, and then use the spatial self-learning feature module to learn important spatial information. This can enable the neural network to ignore some irrelevant information and improve the accuracy of COD parameter inversion.

[0064] Step 2.2: The feature map of the important spatial features after dimensionality reduction is input to the convolution module, and the convolution module outputs the flattened feature vector. The convolution module includes a first convolution layer, a first ReLU activation function, a second convolution layer, and a second ReLU activation function.

[0065] Step 2.2.1: The feature map of the important spatial features after dimensionality reduction is input to the first convolutional layer, and after the first convolutional layer operation (the number of input channels is 125, the number of output channels is 64, and the convolution kernel size is 3 3, filled with 0), the dimension of the output feature of the first convolutional layer is 8 64 3 3.

[0066] Step 2.2.2: The output features of the first convolutional layer are processed by the first ReLU activation function to further obtain the first nonlinear feature. The dimension of the first nonlinear feature is 8. 64 3 3.

[0067] Step 2.2.3: The first nonlinear feature is input to the second convolutional layer, and after the second convolutional layer operation (the number of input channels is 64, the number of output channels is 32, and the convolution kernel size is 3 3, filled with 0), the dimension of the output feature of the second convolutional layer is 8 32 1 1.

[0068] Step 2.2.4: The output features of the second convolutional layer are operated by the second ReLU activation function to further obtain the second nonlinear feature. The dimension of the second nonlinear feature is 8. 32 1 1.

[0069] Step 2.2.5: The height and width of the second nonlinear feature are flattened to a one-dimensional vector, and the flattened feature vector size is 8. 32 (8 is the batch size) to facilitate connection to the fully connected layer.

[0070] Step 2.3: Input the flattened feature vector into the fully connected module, which outputs the predicted COD value. The fully connected module includes a first fully connected layer, a third activation function, a second fully connected layer, a fourth activation function, and a third fully connected layer.

[0071] Step 2.3.1: Flatten the feature vector and input it into the first fully connected layer. After the first fully connected layer operation, the dimension size is increased from 8 to 32 becomes 8 64, learning high-level features.

[0072] Step 2.3.2: The output features of the first fully connected layer are operated by the third activation function to introduce nonlinear features and further obtain the third nonlinear feature. The dimension of the third nonlinear feature is 8. 64.

[0073] Step 2.3.3: The third nonlinear feature is input to the second fully connected layer. After the second fully connected layer operation, the feature size is reduced from 8 64 becomes 8 128, further learning high-level features.

[0074] Step 2.3.4: The output features of the second fully connected layer are operated by the fourth activation function to introduce nonlinear features and further obtain the fourth nonlinear feature. The dimension of the fourth nonlinear feature is 8. 128.

[0075] Step 2.3.5: The fourth nonlinear feature is input to the third fully connected layer. After the third fully connected layer operation, the feature size is reduced from 8 128 becomes 8 1. Map the features to an output predicted COD value.

[0076] Step 3: In the spectral feature self-learning module, the COD parameter inversion model is trained based on the original training set, and the determination coefficient R² value corresponding to the COD parameter inversion model is calculated. The spectral data of the selected bands of the samples in the original training set are adjusted to generate a reconstructed training set corresponding to the selected bands. The COD parameter inversion model is trained using the reconstructed training sets corresponding to each selected band, and the determination coefficient R² value corresponding to the COD parameter inversion model trained with each reconstructed training set is calculated. Several important bands that have the most important influence on the determination coefficient R² value of the COD parameter inversion model are selected. The COD parameter inversion model is trained based on the spectral data of the important bands of the samples in the original training set to obtain the COD parameter inversion model that has finally completed the training.

[0077] The COD parameter inversion model is trained based on minimizing the loss function: the loss of the predicted COD value and the true COD value is calculated using the mean square error (MSE) loss function, and the loss is back-propagated for optimizing and updating the parameters of the COD parameter inversion model. During training, the loss will gradually decrease until convergence (the loss value is stable). The network training generations of the present invention are 50, and finally an accurate predicted COD value is output.

[0078] Step 3.1: Use the original training set to train the COD parameter inversion model, use the original test set to test the trained COD parameter inversion model, and calculate the determination coefficient R² value of the COD parameter inversion model.

[0079] Step 3.2: Randomly shuffle the spectral information of the selected bands of the samples in the original training set to regenerate the reconstructed training set, further obtain the reconstructed training set corresponding to each selected band, use the reconstructed training set corresponding to each selected band to train the COD parameter inversion model respectively, use the original test set to test the COD parameter inversion model trained by each reconstructed training set respectively, and calculate the determination coefficient R² value of the COD parameter inversion model trained by each reconstructed training set.

[0080] Step 3.3: Select a predetermined number of bands that have a greater impact on the determination coefficient R² value (in this embodiment, the first 20 bands that have a greater impact on the determination coefficient R² value) as important bands, and train the COD parameter inversion model based on the spectral data of the important bands of the samples in the original training set to obtain a finally trained COD parameter inversion model.

[0081] Step 4: Input the hyperspectral image to be predicted into the COD parameter inversion model to obtain the final predicted COD value.

[0082] The original test set was used to test the COD parameter inversion model, basic network, random forest and other models that were finally trained. The predicted COD value was output and the accuracy evaluation and comparative analysis were performed. The results of the comparative analysis are shown in Table 1. It can be seen from the table that the proposed method is superior to the basic network and random forest models in terms of the determination coefficient R² value and root mean square error RMSE.

[0083] Table 1 Test results of various models based on the original test set

[0084]

[0085] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0086] Example 2

[0087] In this embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0088] Example 3

[0089] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0090] Example 4

[0091] In this embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0092] It should be noted that the embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A lake COD inversion method, characterized in that: The following steps are involved: Step 1: Obtain hyperspectral images and true COD values of water sampling points, construct samples based on hyperspectral images, use true COD values as sample labels, and generate original training sets and original test sets; Step 2: Construct COD parameter inversion model; Step 3: Train the COD parameter inversion model based on the original training set, and calculate the determination coefficient R² value corresponding to the COD parameter inversion model, adjust the spectral data of the selected bands of the samples in the original training set, generate a reconstructed training set corresponding to the selected bands, use the reconstructed training sets corresponding to each selected band to train the COD parameter inversion model, and calculate the determination coefficient R² value corresponding to the COD parameter inversion model trained with each reconstructed training set, select several important bands that have the most important influence on the determination coefficient R² value of the COD parameter inversion model, and train the COD parameter inversion model based on the spectral data of the important bands of the samples in the original training set to obtain the COD parameter inversion model that has finally completed the training; Step 4: Input the hyperspectral image to be predicted into the COD parameter inversion model to obtain the final predicted COD value.

2. A lake COD inversion method according to claim 1, characterized in that: The method of constructing a sample based on a hyperspectral image includes performing radiation correction on the hyperspectral image data, locating a water body sampling point in the hyperspectral image after radiation correction, and cropping the image according to a set window range to obtain a cropped hyperspectral image, and using the cropped hyperspectral image as a sample.

3. The method for inverting COD of a lake according to claim 1, characterized in that: The COD parameter inversion model includes a spatial feature self-learning module, a convolution module, and a fully connected module. The sample is input into the spatial feature self-learning module to obtain the feature map of important spatial features after dimensionality reduction; The feature map of the important spatial features after dimensionality reduction is input to the convolution module, and the convolution module outputs the flattened feature vector; The flattened feature vector is input to the fully connected module, and the fully connected module outputs the predicted COD value.

4. A lake COD inversion method according to claim 3, characterized in that: The dimension of the sample input to the spatial feature self-learning module is batch aisle high Width, in the spatial feature self-learning module: The pixel points of the sample are randomly extracted in a window manner to generate window samples, and each window sample is merged in the channel dimension in the extraction order to obtain the window feature map. Perform global maximum pooling operation on the window feature map to generate a pooled feature map. Perform a two-dimensional convolution operation on the pooled feature map to generate a spatial information weight factor with linear features. Multiply the window feature map with the spatial information weight factor to generate an important spatial information feature map. A two-dimensional convolution operation is performed on the important spatial information feature map to restore the number of channels of the important spatial information feature map to the same number of channels as the sample input to the spatial feature self-learning module, and obtain the feature map of the important spatial features after dimensionality reduction.

5. A lake COD inversion method according to claim 3, characterized in that: The convolution module of the COD parameter inversion model includes a first convolution layer, a first ReLU activation function, a second convolution layer, and a second ReLU activation function. The feature map of important spatial features after dimensionality reduction is input to the first convolutional layer. The output features of the first convolutional layer are operated by the first ReLU activation function to further obtain the first nonlinear features. The first nonlinear feature is input to the second convolutional layer, The output features of the second convolutional layer are operated by the second ReLU activation function to further obtain the second nonlinear features. The height and width of the second nonlinear feature are flattened to obtain a flattened feature vector.

6. A lake COD inversion method according to claim 3, characterized in that: The fully connected module of the COD parameter inversion model includes a first fully connected layer, a third activation function, a second fully connected layer, a fourth activation function, and a third fully connected layer. The flattened feature vector is input to the first fully connected layer, The output features of the first fully connected layer are operated by the third activation function to introduce nonlinear features and obtain the third nonlinear features. The third nonlinear feature is input to the second fully connected layer, The output features of the second fully connected layer are operated by the fourth activation function to introduce nonlinear features and obtain the fourth nonlinear features. The fourth nonlinear feature is input to the third fully connected layer, and the third fully connected layer outputs the predicted COD value.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the inversion method according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the inversion method according to any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the inversion method according to any one of claims 1 to 6 are implemented.

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