Water quality parameter remote sensing inversion method and system based on KAN network

Abstract

The invention discloses a KAN network-based water quality parameter remote sensing inversion method and system, and the method comprises the following steps: 1, obtaining field detection water quality parameters of a set region, and carrying out the classification according to time; 2, acquiring and preprocessing a multispectral remote sensing image; 3, constructing a KAN model architecture, inputting the waveband reflectivity of the remote sensing image at a certain point, outputting the water quality parameter at the point, taking the label as the real detection data of the water quality parameter, and taking the loss function as the mean square error of the output and the label; 4, taking the water quality parameters and the wave band reflectivity data set as a training set, and training the KAN network by using a loss function; and 5, inputting the wave band reflectivity of the water quality parameter value to be detected into the trained KAN network to obtain the water quality parameter value of the whole water area. According to the method, the calculation cost and the model complexity can be effectively reduced, and the model result can be subjected to interpretable operation so as to better adapt to actual application requirements.

Description

Technical Field

[0001] The invention belongs to the technical field of inversion of water quality parameters in remote sensing, and in particular relates to a water quality parameter remote sensing inversion method and system based on a KAN network. Background Art

[0002] Remote sensing inversion technology has important applications in environmental monitoring, resource management and climate research. Through remote sensing images, researchers can obtain the characteristic parameters of the ground objects from the electromagnetic wave reflection and emission information on the surface of the ground objects, and realize the quantitative estimation of environmental parameters such as total nitrogen, total phosphorus, and chlorophyll-a in water quality. However, remote sensing images have the characteristics of multidimensionality, multiscale and high noise, which makes it difficult for traditional inversion methods such as statistical regression models to achieve high accuracy in complex scenes. These models fit the water quality parameters and band combination data to obtain the fitting equation between the water quality parameters and the band data for inversion. This method is mainly based on the previous study of the correlation between water quality parameters and a certain band, and then the bands with high correlation are combined and fitted. Although the method is simple, the demand for high accuracy in complex scenes has led researchers to turn their attention to the field of machine learning. In recent years, deep learning methods have shown strong potential in the field of remote sensing inversion. Therefore, inversion methods combining deep learning models and physical constraints have become a hot topic to improve inversion accuracy and maintain physical rationality. Water color parameters with optically sensitive signals include suspended matter concentration, phytoplankton pigment concentration, and colored dissolved organic matter (CDOMn). The optical signal of CODMn shows weak sensitivity. Total nitrogen, total phosphorus, and ammonia nitrogen are non-photosensitive signal water quality parameters. Although they may covariate with water color parameters, conventional single and multivariate linear regression models are difficult to construct a quantitative relationship between satellite data and water quality parameter data. In comparison, machine learning or deep learning algorithms can better express the potential complex relationship between satellite data and water quality parameters, at the expense of interpretability, to build a more accurate inversion model with better predictability.

[0003] With the advancement of deep learning algorithms, researchers hope that deep learning will not only show high performance, but also have better representation and explanation capabilities. In the existing published paper "KAN: Kolmogorov–Arnold Networks", researchers proposed a KAN network based on the Kolmogorov–Arnold representation theorem. The KAN network can theoretically represent the neural network of any multidimensional function. It uses the Kolmogorov–Arnold representation theorem to show that any continuous multidimensional function can be approximated by a combination of several one-dimensional functions. In remote sensing inversion, the KAN network can effectively represent the nonlinear relationship between ground object parameters and remote sensing data, and has strong adaptability in high-dimensional data modeling. The KAN network structure uses this theorem to form a complex nonlinear mapping relationship by stacking one-dimensional functions and activation functions, which is suitable for high-dimensional and nonlinear remote sensing data inversion tasks. Unlike traditional MLP-based neural networks, it fits by updating activation functions instead of weights and biases. MLP-based neural networks require a large amount of training data for fitting, while KAN networks only need 2-3 layers to achieve the target accuracy. In addition, KAN networks can eliminate parameters with smaller weights during training for further network pruning, and finally obtain visualization results and derive fitting functions. Therefore, based on these characteristics, this network is well adapted to the needs of remote sensing inversion tasks.

[0004] In summary, the main challenges faced in existing remote sensing inversion tasks are how to reduce resource consumption and how to ensure the interpretability of inversion while improving inversion accuracy. Based on this, the present invention uses the KAN network to construct a remote sensing inversion framework, and interprets the inversion results through the characteristics of the KAN network to provide a water quality parameter remote sensing inversion method and system based on the KAN network. Summary of the invention

[0005] In view of the problem that remote sensing inversion under the current deep learning algorithm uses a large amount of data sets and more complex hardware deployment through neural networks to build a more accurate model, the present invention proposes a water quality parameter remote sensing inversion method and system based on the KAN network.

[0006] To achieve the above object, the present invention adopts the following technical solutions: The remote sensing inversion method of water quality parameters based on KAN network is as follows: Step 1: Obtain water quality parameters detected on site in a specific area and classify them by time; Step 2: Obtain multispectral remote sensing images and perform data preprocessing, mainly for cloud removal, data reconstruction, and extraction of band reflectance at the location of water quality parameters; Step 3: Construct a KAN network model architecture, where the input is the band reflectance of the remote sensing image at a certain point, the output is the water quality parameter at that point, the label is the real detection data of the water quality parameter, and the loss function is the mean square error between the output and the label; Step 4, using the water quality parameter dataset generated in step 1 and the band reflectance dataset generated in step 2 as training sets, and training the KAN network using the loss function described in step 3; Step 5: Input the reflectance of other bands without field water quality parameter values ​​into the KAN network trained in step 4 to obtain the water quality parameter values ​​of the entire water area and complete the inversion.

[0007] Furthermore, in step 2, the multispectral remote sensing image is declouded after obtaining the cloud mask of the image through cloud detection. The pixel reflectance of the relevant area after declouding is 0. The band reflectance of the declouded image is reconstructed through a reconstruction algorithm, and then the band reflectance of the reconstructed remote sensing image at the location of the water quality parameters is extracted.

[0008] Furthermore, in step 3, the KAN network structure is set according to the training set, and the KAN network structure is preferably [x, 5, 1]. By constructing a simple three-layer network structure (input layer, hidden layer, output layer) with a small number of parameters, features are gradually extracted and the objective function is approximated, where x is the number of input layers, which is determined according to different numbers of band images of different remote sensing image types, 5 is the number of hidden layers, and 1 is the number of output layers; the objective function is the final required inversion function, which is specifically expressed as: ; ; ; in, f is a multivariable continuous function that needs to be approximated by the network, indicating that the input The mapping between the output results; is the characteristic transformation function of the hidden layer, which is used to transform the input variables Perform a univariate nonlinear transformation and generate the hidden layer output by summing all input variables p=1,2,…,n ; It is the nonlinear activation function of the output layer, responsible for outputting the hidden layer Mapped to output contribution value; output of hidden layer for q=0,1,…,2n Perform linear combination or nonlinear mapping to obtain the final function value .

[0009] Furthermore, in step 4, the loss function is calculated by the mean square error. The final model obtained after the update iterative training is used for the inversion operation. The loss function is the mean square error MSE, which is specifically expressed as: ; in, L is the function loss, n is the sample size, is the true value of the i-th sample, is the predicted value of the ith sample.

[0010] Furthermore, in step 4, when the training is completed, a function fitting is performed on the network output. The fitting process is a method of building a network based on the KAN idea. Each neuron in the network learns an activation function, but before fitting, there is only one function image at the neuron, which needs to be verified and compared with the existing known functions, such as After comparison, the existing known function is used to fit the function image at that location. By fitting the function of all neurons, the final water quality parameter inversion function is obtained. , x and y are both network inputs. This function can be used for the inversion in step 5, or the reflectivity of the band to be inverted can be input to the network for inversion. Due to the particularity of the network, the entire training process and results can be visualized.

[0011] Furthermore, the model obtained in step 5 is more lightweight and has higher inversion efficiency, and can be deployed more effectively and used in engineering practice.

[0012] Furthermore, the loss function It is used to measure network output With the objective function The objective function is the ideal result that the KAN network finally approximates, and the loss function is a tool to optimize the approximation process of the objective function.

[0013] The present invention also discloses a water quality parameter remote sensing inversion system based on a KAN network, which is used to execute the above method and includes the following modules: Water quality parameter acquisition module: obtains water quality parameters detected on site in a specific area and classifies them by time; Image acquisition and preprocessing module: acquire multispectral remote sensing images and implement data preprocessing, including cloud removal, data reconstruction, and extraction of band reflectance where water quality parameters are located; KAN network construction module: Construct the KAN network model architecture, where the input is the band reflectance of the remote sensing image at a certain point, and the output is the water quality parameter at that point. The label is the real detection data of the water quality parameter, and the loss function is the mean square error between the output and the label. Network training module: Use water quality parameter dataset and band reflectance dataset as training sets, and use loss function to train KAN network; Inversion module: Input the band reflectivity of the water quality parameter value to be detected into the trained KAN network to obtain the water quality parameter value of the entire water area.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention combines the declouding operation with the reconstruction operation, which can restore the missing data to a greater extent, thereby ensuring the accuracy of the inversion.

[0015] 2. The present invention introduces the KAN network for inversion, inputs all the band information into the network, and allows the network to derive a specific relationship between the band information and the water quality parameters, and this specific relationship can be expressed by a function.

[0016] 3. The inversion technology based on the KAN network proposed in the present invention not only improves the training speed, but also achieves a better inversion effect with extremely low parameter quantity and training amount, making it more suitable for deployment in embedded devices with limited resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic diagram of the network design-training-deployment process involved in the water quality parameter remote sensing inversion method based on the KAN network in Example 1 of the present invention; Figure 2 This is a data preprocessing flow chart of a water quality parameter remote sensing inversion method based on a KAN network in Example 1 of the present invention; Figure 3 A network training flow chart of a water quality parameter remote sensing inversion method based on a KAN network in Example 1 of the present invention; Figure 4 This is a block diagram of a water quality parameter remote sensing inversion system based on a KAN network in Example 2 of the present invention. DETAILED DESCRIPTION

[0018] In order to more clearly illustrate the embodiments of the present invention, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other accompanying drawings and other implementation methods can be obtained based on these accompanying drawings without creative work.

[0019] Embodiment 1:

[0020] This embodiment proposes a water quality parameter remote sensing inversion method based on KAN network. Figure 1The flow of a water quality parameter remote sensing inversion method based on a KAN network in this embodiment is shown. The KAN network is trained by using existing water quality parameters and band data, and the band data without water quality parameters is input into the KAN network to obtain all water quality parameters. Figure 2 This is a block diagram of the DINEOF data reconstruction method. By resampling the image data and extracting the cloud mask, the image is de-clouded and the data of the de-clouded part is reconstructed. Figure 3 This is a schematic diagram of KAN network training inversion. n bands of data are input to obtain predicted water quality parameters, and the network is updated by loss back propagation with the measured water quality parameters. This embodiment takes the L2A level (the level after atmospheric correction of Sentinel-2) image of Sentinel-2 / MSI and the water quality parameters of the sea area near a city as an example. The specific steps are as follows: Step 1: Obtain field survey water quality parameters with monthly time resolution from 2016 to 2023 in the sea area near a city, and classify them by time (month).

[0021] Step 2: Acquire Sentinel-2 images of the sea area near a certain city from 2016 to 2023 and perform data preprocessing. Extract the cloud mask through the QA60 band (quality assurance band: mask information used to identify clouds and shadows, a band unique to Sentinel-2 images after atmospheric correction) of Sentinel-2 and decloud the image. Reconstruct the processed cloud area in the image through the DINEOF algorithm (interpolation algorithm based on empirical orthogonal function (EOF) analysis) to obtain the actual reflectivity of the point.

[0022] Step 3: Construct the KAN network model architecture. Since Sentinel-2 has twelve bands, the input is the band reflectance of the 12 bands with field survey water quality values ​​in the sea area near a city in the remote sensing image, and the output is the measured water quality parameters at that point, where the label is the real detection data of the water quality parameters. The loss function is the MSE of the output and the label.

[0023] Step 4: Use the water quality parameters and band reflectance data sets generated in the above steps as training sets, and use the loss mentioned in step 3 as the loss function to train the KAN network.

[0024] Step 5: Input the band reflectance of the sea area near a city where there is no measured water quality parameter value into the KAN network trained in step 4 to obtain the water quality parameter value of the entire water area and complete the inversion.

[0025] The above steps are described in more detail as follows.

[0026] In step 1 of this embodiment, water quality parameters of a sea area near a certain city measured in the field from 2016 to 2023 are obtained with a time resolution of months and classified by month.

[0027] In step 2 of this embodiment, L2A-level images of Sentinel-2 / MSI of the sea area near a city from 2016 to 2023 are obtained, with three spatial resolutions of 10m, 20m, and 60m. The images are super-reconstructed to a spatial resolution of 10m, and then the images are de-clouded using a cloud mask of the QA60 band, and the removed points in the images are reconstructed.

[0028] In step 3 of this embodiment, the Sentinel-2 / MSI image has 12 bands, so the input of the network layer is set to 12, the middle layer is set to 5, and the output layer is set to 1. The relationship between the band reflectance and the water quality parameters is further fitted through the KAN network. The network parameters are more lightweight and the required training amount is also lighter. The loss function is calculated by the mean square error. The final model obtained after the update iterative training is used for the inversion operation. The loss function is the mean square error MSE, which is specifically expressed as: ; in, L is the function loss, n is the sample size, is the true value of the i-th sample, is the predicted value of the ith sample.

[0029] In step 4 of this embodiment, the water parameters generated in step 1 and the band reflectance data set generated in step 2 are used as training sets, and the loss mentioned in step 3 is used as a loss function to train the KAN network, and back propagation, update iteration, and network training are performed.

[0030] The specific implementation steps of this embodiment include the following steps based on logging in to the European Space Agency to download Sentinel-2 image data and performing preprocessing: 1. Constructing a training set: Since the band images of Sentinel-2 have three spatial resolutions of 10m, 20m, and 60m, and the QA60 cloud band image it has has a spatial resolution of 10m. Therefore, the band image is first reconstructed to 10m by super-resolution, and then the band image is declouded by the QA60 cloud mask. The pixel reflectivity of the original cloud layer of the processed image is NAN, so as to achieve the declouding operation. Secondly, the pixel points after declouding are reconstructed by the DINEOF algorithm to restore the ground or water quality band reflectivity of the image after declouding. The measured water quality parameters collected in the sea area near a certain city are chlorophyll-a, total nitrogen, total phosphorus and salinity, with a time resolution of months from 2016 to 2023. And the longitude and latitude of the location of the measured water quality parameters are obtained, and the twelve band reflectivities of the corresponding points on the band image are obtained by the longitude and latitude. The time and location planning dataset, band reflectance are used as input, measured water quality parameters are used as labels, and 70% is used as the training set and 30% as the test set.

[0031] 2. Design KAN network: Unlike the traditional MLP (multi-layer perceptron) network (MLP puts fixed activation functions on nodes ("neurons")), KAN puts learnable activation functions on edges ("weights"). Therefore, the KAN network has more powerful representation capabilities and lighter network parameters.

[0032] 3. Construct loss function: Set the input of KAN network by the number of bands, set different numbers of inputs for different remote sensing images, output is the predicted water quality parameters, and the label is the measured water quality parameters. Calculate the mean square error between the label and the output to get the function loss L.

[0033] 4. Training model: The loss is used as the training error of the KAN network. The final network model is obtained after updating the iterative training, and the results are further interpreted according to the characteristics of the KAN network.

[0034] 5. After the measured water quality parameters chlorophyll-a, total nitrogen, total phosphorus and salinity and band data are input into the network training, the following results are obtained: Figure 3 The network parameters shown in the figure, each node has obtained a function image, and the image is fitted with a function to obtain the function of the final band reflectance and water quality parameters. The band reflectance at the point without chlorophyll-a, total nitrogen, total phosphorus and salinity water quality parameters is input into the network or into the fitted function to calculate the water quality parameters of all the sea areas in a certain city. The following table lists the water quality parameter results of some areas in a certain city at some time, as follows: Table 1 Water quality parameter results of some areas in a city at some time

[0035] Embodiment 2: like Figure 4 As shown, this embodiment discloses a water quality parameter remote sensing inversion system based on a KAN network, which is used to execute the method described in Example 1, and includes the following modules: Water quality parameter acquisition module: obtains water quality parameters detected on site in a specific area and classifies them by time; Data acquisition and preprocessing module: obtain remote sensing images and water quality parameters from field surveys and implement data preprocessing, including cloud removal, data reconstruction, and extraction of band reflectance at the location of water quality parameters; KAN network construction module: Construct the KAN network model architecture, that is, construct a network input and output structure suitable for the acquired data, where the input is the band reflectance of the remote sensing image at a certain point, and the output is the water quality parameter at that point, the label is the real detection data of the water quality parameter, and the loss function is the mean square error between the output and the label; input the training set of the data acquisition and preprocessing module into the network of the KAN network construction module, and output the predicted water quality parameters; calculate the mean square error between the predicted water quality parameters and the measured water quality parameters as the loss; Network training module: The water quality parameter dataset and band reflectance dataset are used as training sets, and the loss in the loss calculation is introduced as the loss function for back propagation to train the KAN network; Inversion module: The band reflectance at the point without measured water quality parameters is taken as input, and the predicted water quality parameters at each point without measured water quality parameters are obtained through the trained KAN network to complete the inversion.

[0036] For other contents of this embodiment, please refer to Embodiment 1.

[0037] In summary, the present invention designs a water quality parameter remote sensing inversion method and system based on the KAN construction concept, which is used to achieve high-efficiency and high-quality water quality parameter inversion tasks and can be applied to various engineering application scenarios with limited resources.

[0038] It should be noted that the above description is only a detailed description of the preferred embodiments and principles of the present invention. For ordinary technicians in this field, there will be changes in the specific implementation methods based on the ideas provided by the present invention, and these changes should also be regarded as the scope of protection of the present invention.

Claims

1. The water quality parameter remote sensing inversion method based on KAN network is characterized by: The steps include: Step 1: Obtain water quality parameters detected on site in a set area and classify them by time; Step 2: Obtain multispectral remote sensing images and perform data preprocessing, including cloud removal, data reconstruction, and extracting the band reflectance of the location of water quality parameters; Step 3: Construct a KAN network model architecture, where the input is the band reflectance of the remote sensing image at a certain point, the output is the water quality parameter at the corresponding point, the label is the real detection data of the water quality parameter, and the loss function is the mean square error between the output and the label; Step 4, using the water quality parameter dataset generated in step 1 and the band reflectance dataset generated in step 2 as training sets, and training the KAN network using the loss function described in step 3; Step 5: Input the band reflectance of the water quality parameter value to be detected into the KAN network trained in step 4 to obtain the water quality parameter value of the entire water area.

2. The water quality parameter remote sensing inversion method based on KAN network as claimed in claim 1, characterized in that: In step 2, the multispectral remote sensing image is declouded after obtaining the cloud mask of the image through cloud detection. The pixel reflectance of the relevant area after declouding is 0. The band reflectance of the declouded image is reconstructed through the reconstruction algorithm, and then the band reflectance of the reconstructed remote sensing image at the location of the water quality parameters is extracted.

3. The water quality parameter remote sensing inversion method based on KAN network as claimed in claim 1, characterized in that: In step 3, the KAN network gradually extracts features and approximates the objective function by constructing a three-layer network structure, namely, an input layer, a hidden layer, and an output layer; the objective function is the final required inversion function, which is specifically expressed as: ； ； ； in, f is a multivariable continuous function that needs to be approximated by the network, indicating that the input The mapping between the output results; is the characteristic transformation function of the hidden layer, which is used to transform the input variables Perform a univariate nonlinear transformation and generate the hidden layer output by summing all input variables p=1,2,…,n ; It is the nonlinear activation function of the output layer, responsible for outputting the hidden layer Mapped to output contribution value; output of hidden layer for q=0,1,…,2n Perform linear combination or nonlinear mapping to obtain the final function value .

4. The water quality parameter remote sensing inversion method based on KAN network as claimed in claim 3, characterized in that: In step 4, the loss function is calculated by the mean square error, which is specifically expressed as: ； in, L is the function loss, n is the sample size, is the true value of the i-th sample, is the predicted value of the ith sample.

5. The water quality parameter remote sensing inversion method based on KAN network as claimed in claim 4, characterized in that: In step 4, when the training is completed, the output of the network is fitted with a function. The fitting process is a method of constructing a network based on KAN. Each neuron in the network learns an activation function. Before fitting, there is only one function image at the neuron, which needs to be verified and compared with the existing function, and then the existing function is used to fit the function image there. By fitting the function of all neurons, the final inversion function is obtained. The inversion function is used for the inversion of step 5 or the reflectivity of the band to be inverted is input into the KAN network for inversion.

6. The water quality parameter remote sensing inversion method based on KAN network as claimed in claim 4, characterized in that: Loss Function It is used to measure network output With the objective function The objective function is the ideal result that the KAN network finally approximates, and the loss function is a tool to optimize the approximation process of the objective function.

7. A water quality parameter remote sensing inversion system based on a KAN network, used to execute the method according to any one of claims 1 to 6, characterized in that: Includes the following modules: Water quality parameter acquisition module: obtains water quality parameters detected on site in a specific area and classifies them by time; Image acquisition and preprocessing module: acquire multispectral remote sensing images and implement data preprocessing, including cloud removal, data reconstruction, and extraction of band reflectance where water quality parameters are located; KAN network construction module: Construct the KAN network model architecture, where the input is the band reflectance of the remote sensing image at a certain point, and the output is the water quality parameter at that point. The label is the real detection data of the water quality parameter, and the loss function is the mean square error between the output and the label. Network training module: Use water quality parameter dataset and band reflectance dataset as training sets, and use loss function to train KAN network; Inversion module: Input the band reflectivity of the water quality parameter value to be detected into the trained KAN network to obtain the water quality parameter value of the entire water area.

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