A remote sensing image fusion method based on KAN using implicit guided sampling in space-frequency dual domains

Abstract

The present invention belongs to the field of image processing technology, and relates to a KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method, including training sample construction, creating a KAN-based space-frequency dual-domain implicit guided sampling network, network training and inputting the image to be fused into the trained network, and generating a fused image with high spatial resolution and high spectral resolution after mapping. The network includes a coding unit, a spatial implicit guiding unit, a frequency implicit guiding unit and a decoding unit. The coding unit is composed of parallel KANs to map the hyperspectral and multispectral remote sensing images to a deep latent space. The spatial implicit guiding unit and the frequency implicit guiding unit respectively perform guided implicit sampling on HSI in the space and frequency domains, and the decoding unit fuses the space-frequency domain sampling features and generates the final fused image. The present invention is a pure KAN-driven architecture, which replaces the previous reliance on multi-layer perceptrons and has a good degree of lightweight.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and in particular relates to a hyperspectral and multispectral remote sensing image fusion method based on a KAN space-frequency dual-domain implicit guided sampling network. Background Art

[0002] Hyperspectral remote sensing images (HSI) can capture the two-dimensional spatial reflectance information of the target through continuous and dense one-dimensional spectral channels, where the one-dimensional spectral channel reflects the detailed properties of the target pixels, while the two-dimensional space depicts the distribution and fine structure of the target. However, due to the physical limitations of sensor photon detection, hyperspectral imaging usually retains rich spectral information while weakening the ability to capture spatial information to a certain extent, resulting in HSI often lacking sufficient spatial information expression, limiting its application potential. Although multispectral remote sensing images (MSI) lack the ability to perceive spectral information, they have wider bandwidth imaging and higher spatial resolution. Based on this, the fusion of HSI and MSI (HMIF) can achieve spatial and spectral information complementarity and generate high spatial resolution hyperspectral images (HR-HSI), which can effectively improve the application scope of remote sensing data.

[0003] In the field of HMIF research, traditional methods such as Pansharpening and decomposition-based methods rely on hand-designed physical models. These methods are based on specific physical processes and prior knowledge and can accurately simulate the interaction between spectral and spatial features to a certain extent. However, these prior knowledge often have limitations and it is difficult to fully capture the complex nonlinear relationships in the image fusion process. In recent years, deep learning has significantly surpassed the performance of traditional methods due to its powerful nonlinear modeling capabilities. By constructing neural networks, deep learning can automatically mine complex associations between data and has become the core direction for promoting the advancement of HMIF technology. Although deep learning methods have made significant progress in image fusion quality, many existing algorithms rely on explicit discrete domain information fitting, which deviates from the actual continuous space and limits the model's ability to fit details. In addition, most algorithms only perform fusion in the spatial domain, ignoring the effective use of frequency domain features, which weakens the potential for further improving fusion accuracy. In order to improve fusion accuracy, existing methods usually achieve this by deepening or widening the network structure, or introducing attention mechanisms such as Transformer. However, the overly complex network structure and the high computational complexity brought by Transformer greatly increase the computational and memory requirements of the model, limiting the realization of lightweight design.

[0004] Recently, based on the Kolmogorov-Arnold representation theorem, researchers proposed the Kolmogorov-Arnold Network (KAN), which achieves a more refined feature representation by decomposing a multivariable function into several univariate functions based on B-splines, while greatly reducing the number of parameters. KAN can not only learn complex features like a multi-layer perceptron (MLP), but also optimize feature representation through its unique structure. It is expected to become a potential second-generation cornerstone model in the field of deep learning. In terms of continuous domain modeling, implicit neural representation (INR) has shown significant advantages. INR maps discrete data to continuous space and captures image details in detail, breaking through the limitations of traditional discrete methods and becoming a new choice for high-fidelity image reconstruction and fine feature capture.

[0005] Based on this, in view of the problems existing in HMIF at this stage and based on the advantages of KAN and INR, it is very necessary to construct a KAN-based space-frequency dual-domain implicit guided sampling network for HMIF, which has wide application value. Summary of the invention

[0006] The purpose of the present invention is to provide a hyperspectral and multispectral remote sensing image fusion method based on a KAN-based space-frequency dual-domain implicit guided sampling network, so as to solve the problem that the architecture is driven by KAN, avoids dependence on multi-layer perceptrons, and maintains a good degree of lightweight.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] A KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method includes the following steps:

[0009] S1. Construction of training samples: First, Gaussian filtering is used to blur HSI; then, it is spatially downsampled based on bilinear interpolation to generate hyperspectral data for training; the same method is used for MSI to generate multispectral images for training; the original hyperspectral image that has not been downsampled is used as a reference image and as a training label;

[0010] S2. Create a KAN-based space-frequency dual-domain implicitly guided sampling network, which includes an encoding unit, a spatial implicitly guided sampling unit, a frequency implicitly guided sampling unit and a decoding unit; wherein the encoding unit is composed of parallel KAN modules; the spatial implicitly guided sampling unit and the frequency implicitly guided sampling unit sample HSI in space and frequency respectively to generate spatial and frequency guided features, and the decoding unit fuses the spatial and frequency guided features and decodes to generate a fused image;

[0011] S3, conduct network training. During the training process, the Adam optimizer is used to optimize the network, and a network with accurate mapping parameters is generated after multiple rounds of iterations;

[0012] S4. The hyperspectral and multispectral remote sensing images to be fused are input into the trained network, and a fused image with high spatial resolution and high spectral resolution is generated after mapping.

[0013] Further, step S1 is specifically as follows: according to the requirements of the Wald protocol, the HSI and MSI are spatially downsampled to generate low spatial resolution HSI and high spatial resolution MSI used for training the network. In this process, a 5*5 Gaussian kernel is used to perform spatial filtering on the original HSI and MSI to simulate the sensor point spread function, and then they are spatially sampled based on bilinear interpolation to generate training samples, which are combined with the original HSI as a reference image as a label image.

[0014] Furthermore, in step S2, KAN uses a learnable activation function and places it at the edge of the network. A KAN with N layers can be expressed as:

[0015] ,

[0016] in, is the input feature, For the layer KAN network; for each KAN layer, Contains the input dimensions and output dimensions Product of learnable activation functions :

[0017] ,

[0018] in, The parameters involved in training and the connections between layers are realized through these parameterized spline functions.

[0019] Furthermore, in step S2, guided implicit sampling is a module for sampling in feature space. KAN is used for nonlinear fitting in the fitting process to guide implicit sampling through high spatial resolution features. Bootstrapping low spatial resolution features Spatial interpolation on a continuous domain includes the following steps:

[0020] First, based on the Bilinear Perform spatial interpolation, and Perform spatial alignment, for any query coordinates The spectral value of Coordinate grid of ,turn up The set of 4 adjacent spectral vectors adjacent to the query point in and the corresponding exist Spectral vector; each for The interpolation calculation is expressed as:

[0021] ,

[0022] in, For the Spectral vector The interpolation result of the query spectrum vector; in this process, the spectrum dimension is expanded; the last channel is used to store the contribution of the calculated spectrum vector to the final result; through parallel calculation, the interpolation spectrum vectors of the four grid points will be combined to generate , then the channels are separated to form and Two parts, finally in Guided implicit sampling results of points is through and The weighted summation of the estimated weights of the third dimension of is:

[0023] ,

[0024] in, It represents element-by-element multiplication. Through the above method, all query points are traversed to generate the result of GIS output.

[0025] Furthermore, in step S2, the encoding unit is used to perform preliminary feature extraction of HSI and MSI, and map the features to a deeper space, and KAN is used to encode HSI and MSI, wherein the order of the KAN spline function is set to 3, the grid size parameter is set to 5, and the dimension of the encoded features is unified. The process formula of the encoding unit is expressed as follows:

[0026] ,

[0027] ,

[0028] in, and They are HSI and MSI, and is the coded HSI and HSI, and satisfies , output feature dimension Set to 64.

[0029] Furthermore, in step S2, the spatial implicit guided sampling unit uses the high spatial resolution of the encoded MSI to guide the spatial interpolation of the encoded HSI, and enhances the feature expression of the spatial dimension with the help of implicit functions; the spatial implicit guided sampling unit uses the MSI features to establish a high-resolution coordinate grid, determine the sampling direction and position, and upsample the HSI features through its GIS module, which is expressed as follows:

[0030] ,

[0031] in, The spatial guidance features generated by GIS, is a relative coordinate set.

[0032] Further, in step S2, the frequency implicit guided sampling unit is used to enhance the spatial and spectral information expression of the fused image through the guidance of frequency domain information. The frequency implicit guided sampling unit first performs Fourier transform on the encoded HSI and MSI data to convert them into frequency domain representation. In this process, the real part and the imaginary part obtained by Fourier transform are separated, corresponding to the cosine component and the sine component of the image respectively; then, GIS is applied to the cosine and sine components respectively to generate cosine guided features and sine guided features; finally, these guided features are combined and restored to frequency domain guided features through inverse Fourier transform. The mathematical expression of the frequency implicit guided sampling unit is:

[0033] ,

[0034] ,

[0035] ,

[0036] ,

[0037] ,

[0038] in, are the cosine and sine components of the encoded HSI, The cosine and sine components of the encoded MSI, and They are respectively the frequency domain cosine and sine guided features, The frequency domain guided features output by the frequency implicit guided sampling unit.

[0039] Furthermore, in step S2, the decoding unit is used to fuse the guiding features in the spatial domain and the frequency domain, and generate a high-resolution fused image through spectral mapping. Specifically, an additive fusion strategy is first adopted to combine the spatial guiding features and the frequency domain guiding features; then KAN is used to perform spectral mapping on the fused features to restore them to the target spectral dimension. The mathematical representation of the decoding unit is:

[0040] ,

[0041] in, is the fused image output by the network.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention provides a space-frequency dual-domain implicit guided sampling network based on KAN (Kolmogorov-Arnold Network) for the fusion of hyperspectral and multispectral images. The network comprises an encoding unit, a space implicit guided unit, a frequency implicit guided unit and a decoding unit, wherein the encoding unit is composed of parallel KANs to map the hyperspectral and multispectral remote sensing images to a deep latent space, the space implicit guided unit and the frequency implicit guided unit perform guided implicit sampling on HSI in the space and frequency domains respectively, and the decoding unit fuses the space-frequency domain sampling features and generates a final fused image; the present invention is a pure KAN-driven architecture, which replaces the previous dependence on a multi-layer perceptron and has a good degree of lightweight. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0045] Figure 1 This is a flow chart of the KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method of the present invention.

[0046] Figure 2 This is a network structure diagram of the space-frequency dual-domain implicit guided sampling remote sensing image fusion method based on KAN in the present invention.

[0047] Figure 3 This is a comparison chart of the fusion results of the present invention with different HMIF algorithms. DETAILED DESCRIPTION

[0048] When the Wald protocol is used to objectively evaluate the performance of hyperspectral image fusion, it often faces the problem of missing actual reference images. The quality assessment of fused images is usually carried out using a paradigm originally proposed by Wald et al., which is widely accepted in the research community. This paradigm is based on two key properties: consistency and compositionality. The consistency property requires that the fused hyperspectral image (HSI) is reversible, ensuring that the original low-resolution HSI and high-resolution multispectral image (MSI) can be accurately derived from the fused high-resolution HSI. The compositionality property strives to make the fused high-resolution HSI very similar to the image of the same scene captured by the same sensor at high spatial-spectral resolution. A simulated observation image is synthesized from an ideal high-resolution HSI so that the final fused image that can be obtained by the HSI-MSI fusion method can be compared and evaluated with this ideal reference image. The protocol includes the following steps:

[0049] (1) An ideal high resolution is used as a reference image, and spatial downsampling is applied to it to obtain the low-resolution HSI of the simulated observation. , spectral downsampling was applied to obtain high-resolution MSI of simulated observations.

[0050] (2) Apply the HSI-MSI fusion method to be evaluated to the simulated low-resolution HSI and high-resolution MSI to obtain a fused high-resolution HS.

[0051] (3) Finally, the fused high-resolution HSI is compared with the ideal reference image to obtain a quantitative quality measure.

[0052] The present invention provides a remote sensing image fusion method based on KAN space-frequency dual-domain implicit guided sampling, comprising the following steps:

[0053] S1. Construction of training samples. Limited by the fact that there are no well-fused images in the real world as reference, the present invention constructs training samples based on the Wald protocol. The process is: first, the HSI is blurred by Gaussian filtering; then, it is spatially downsampled based on bilinear interpolation to generate hyperspectral data for training, and then the MSI is processed in the same way to generate multispectral images for training. The original hyperspectral image that has not been downsampled is used as a reference image and as a training label.

[0054] S2. Create a KAN-based space-frequency dual-domain implicitly guided sampling network. The network includes an encoding unit, a spatial implicitly guided sampling unit, a frequency implicitly guided sampling unit, and a decoding unit. The encoding unit is composed of parallel KAN modules; the spatial implicitly guided sampling unit and the frequency implicitly guided sampling unit sample HSI in space and frequency respectively to generate spatial and frequency guided features, and the decoding unit fuses the spatial and frequency guided features and decodes to generate a fused image.

[0055] S3. Perform network training. During the training process, the Adam optimizer is used to optimize the network, and a network with accurate mapping parameters is generated after multiple rounds of iterations.

[0056] S4. The hyperspectral and multispectral remote sensing images to be fused are input into the trained network, and a fused image with high spatial resolution and high spectral resolution is generated after mapping.

[0057] Step S1, specifically, is as follows: According to the Wald protocol requirements, HSI and MSI need to be spatially downsampled to generate low spatial resolution HSI and high spatial resolution MSI used for training the network. In this process, a 5*5 Gaussian kernel is used to perform spatial filtering on the original HSI and MSI to simulate the sensor point spread function, and then they are spatially downsampled based on bilinear interpolation to generate training samples, which are combined with the original HSI as a reference image as a label image.

[0058] In step S2, the modules used in forming the network are as follows:

[0059] The architecture of KAN is similar to traditional MLP, but with a significant difference: KAN adopts a learnable activation function and places it at the edge of the network. This design abandons the use of linear weights and replaces each weight parameter with a parameterized spline function. Specifically, a KAN with N layers can be expressed as:

[0060] ,

[0061] in, is the input feature, For the For each KAN layer, Contains the input dimensions and output dimensions Product of learnable activation functions :

[0062] ,

[0063] in, The parameters involved in training and the connections between layers are realized through these parameterized spline functions.

[0064] Guided Implicit Sampling (GIS) is a module that samples in feature space. Different from the traditional implicit neural representation (INR), the present invention no longer uses the original MLP driver in the fitting process, but uses KAN for nonlinear fitting. GIS uses high spatial resolution features to Bootstrapping low spatial resolution features The process of spatial interpolation on a continuous domain is as follows:

[0065] First, based on the Bilinear Perform spatial interpolation, and Perform spatial alignment, for any query coordinates The spectral value of Coordinate grid of ,turn up The set of 4 adjacent spectral vectors adjacent to the query point in and the corresponding exist Spectral vector; each for The interpolation calculation can be expressed as:

[0066] ,

[0067] in, For the Spectral vector The interpolation result of the query spectrum vector; in this process, the spectrum dimension is expanded; the last channel is used to store the contribution of the calculated spectrum vector to the final result; through parallel calculation, the interpolation spectrum vectors of the four grid points will be combined to generate , then the channels are separated to form and Two parts, finally in Guided implicit sampling results of points is through and The weighted summation of the estimated weights of the third dimension of is:

[0068] ,

[0069] in, It represents element-by-element multiplication. Through the above method, all query points are traversed to generate the result of GIS output.

[0070] The core function of the encoding unit is to perform preliminary feature extraction of HSI and MSI, and map these features to a deeper space to provide support for subsequent implicit guidance. Different from the convolutional layer encoders that rely on MLP commonly used in previous studies, the present invention uses KAN to encode HSI and MSI, where the order of the KAN spline function is set to 3 to provide sufficient flexibility to capture complex patterns in the data while maintaining computational feasibility. In addition, the grid size parameter is set to 5, which means that the spline function will be defined on 5 segments, which helps to capture key features in the image data while maintaining computational efficiency. In order to achieve spectral alignment between different image types and provide a unified feature space for subsequent implicit guidance, the present invention unifies the encoded feature dimensions. The process formula of the encoding unit is expressed as follows:

[0071] ,

[0072] ,

[0073] in, and They are HSI and MSI, and is the coded HSI and HSI, and satisfies , output feature dimension Set to 64.

[0074] The spatial implicit guided sampling unit uses the high spatial resolution of the encoded MSI to guide the spatial interpolation of the encoded HSI, and uses implicit functions to enhance the feature expression of the spatial dimension. First, the spatial implicit guided sampling unit uses the MSI features to establish a high-resolution coordinate grid, determine the sampling direction and position, and upsample the HSI features through its GIS module. Since this process uses implicit guidance, the sampling weights can be dynamically adjusted to avoid feature blurring or mosaic phenomena that are common in traditional interpolation methods. This not only supplements high-frequency detail information while maintaining spectral accuracy, but also effectively avoids information loss and distortion. The spatial implicit guided sampling unit ensures accurate interpolation, maintains clear spatial details, enhances the spectral and spatial consistency of HSI, and achieves high-quality image fusion. The formula is as follows:

[0075] ,

[0076] in, The spatial guidance features generated by GIS, is a relative coordinate set.

[0077] The function of the frequency implicit guided sampling unit is to enhance the spatial and spectral information expression of the fused image through the guidance of frequency domain information. The frequency implicit guided sampling unit first performs Fourier transform on the encoded HSI and MSI data to convert it into frequency domain representation. In this process, the present invention separates the real part and the imaginary part obtained by Fourier transform, which correspond to the cosine component and the sine component of the image respectively. Subsequently, GIS is applied to the cosine and sine components respectively to generate cosine guided features and sine guided features. Finally, these guided features are combined and restored to frequency domain guided features through inverse Fourier transform. The key to this process is that by guiding the cosine and sine components respectively, the high-frequency details of HSI can be more effectively captured in the frequency domain. At the same time, by combining with the high-resolution spatial information of MSI, the spatial and spectral information of the fused image are ensured to be coordinated and consistent, achieving higher global consistency and detail fidelity. The mathematical expression of the frequency implicit guided sampling unit is:

[0078] ,

[0079] ,

[0080] ,

[0081] ,

[0082] ,

[0083] in, are the cosine and sine components of the encoded HSI, The cosine and sine components of the encoded MSI, and They are respectively the frequency domain cosine and sine guided features, The frequency domain guided features output by the frequency implicit guided sampling unit.

[0084] The role of the decoding unit is to fuse the guiding features in the spatial domain and the frequency domain, and generate a high-resolution fused image through spectral mapping. Specifically, the additive fusion strategy is first adopted to combine the spatial guiding features and the frequency domain guiding features to ensure that the two complement and coordinate each other at the feature level, thereby optimizing the global information expression of the fused image. Subsequently, KAN is used to perform spectral mapping on the fused features and restore them to the target spectral dimension to ensure the integrity and accuracy of the spectral information and achieve accurate fusion of spatial and spectral information. The mathematical representation of the decoding unit is:

[0085] ,

[0086] in, is the fused image output by the network.

[0087] Example 1: Figure 1 As shown, a spatial-frequency dual-domain implicit guided sampling remote sensing image fusion method based on KAN includes the following steps:

[0088] S1. Construction of training samples. Limited by the fact that there are no well-fused images in the real world as reference, the present invention constructs training samples based on the Wald protocol. First, the hyperspectral image (HSI) is blurred by Gaussian filtering, and then it is spatially downsampled based on bilinear interpolation to generate hyperspectral data for training. The multispectral image (MSI) is then processed in the same way to generate a multispectral image for training. The original hyperspectral image that has not been downsampled is used as a reference image as a training label.

[0089] S2. Create a KAN-based space-frequency dual-domain implicitly guided sampling network. The network includes an encoding unit, a spatial implicitly guided sampling unit, a frequency implicitly guided sampling unit, and a decoding unit. The encoding unit is composed of parallel KAN modules; the spatial implicitly guided sampling unit and the frequency implicitly guided sampling unit sample HSI in space and frequency respectively to generate spatial and frequency guided features, and the decoding unit fuses the spatial and frequency guided features and decodes to generate a fused image.

[0090] S3. Perform network training. During the training process, the Adam optimizer is used to optimize the network. After multiple rounds of iterations, a network with accurate mapping parameters is generated.

[0091] S4. The hyperspectral and multispectral remote sensing images to be fused are input into the trained network, and a fused image with high spatial resolution and high spectral resolution is generated after mapping.

[0092] In order to demonstrate the effect of the present invention, the images taken by the ITRES CASI 1500 sensor were subjected to fusion experiments with 4, 8 and 16 times the spatial resolution difference, and compared with the new fusion method at this stage. The results are shown in Figure 3 . Figure 3 The first row is the fusion image, the second row represents the SAM error heat map, the third row is the MRAE error heat map, and the fourth row is the difference map. The SAM error heat map reflects the spectral fidelity of the fused image, the MRAE error heat map reflects the degree of global consistency of the fused image, and the difference map measures the residual of individual bands. The darker the color, the better the fusion result. It can be clearly seen that the present invention has the best effect. The quantitative evaluation of 4x, 8x and 16x fusion is shown in Table 1, and a complexity comparison analysis is carried out with the current deep algorithm (Table 2), which once again shows that the present invention has certain advantages and lightweight.

[0093] Table 1 Quantitative evaluation of fusion experiments of the present invention and the comparison algorithm

[0094]

[0095] In addition, the complexity analysis of the present invention and the commonly used deep learning algorithms under equal conditions is statistically performed to evaluate their lightweight degree. By calculating the model size (Modelsize), the number of parameters (Params) and the number of floating-point operations (Flops), the differences in resource consumption and computational efficiency of different algorithms can be quantified. As shown in Table 2, the present invention shows the lowest values ​​in both model size and number of parameters, which are 1.24M and 0.15M, respectively, indicating that the model has significant advantages in storage requirements and complexity. In terms of Flops, PSRT performs best, reaching 9.17G, and although the present invention fails to achieve the best, its FLOPs of 15.54G is not much different from PSRT. Comprehensively considering the indicators of model size, number of parameters and number of floating-point operations, the present invention shows higher computational efficiency while maintaining lower resource consumption, and its fusion accuracy is also better than the comparison method. Therefore, it can be considered that the present invention has good performance in lightweight design.

[0096] Table 2 Comparison of complexity between the present invention and the comparative algorithm

[0097] Methods Model size (M) Params (M) Flops (G) HyperKite 1.81 0.47 217.73 ITF-GAN 2.01 0.52 55.55 PSRT 2.19 0.55 9.17 3DT-Net 15.52 3.95 277.81 The present invention 1.24 0.15 15.54

[0098] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method, characterized in that: The following steps are involved: S1, training sample construction, first use Gaussian filtering to blur HSI; then, it is spatially downsampled based on bilinear interpolation to generate hyperspectral data used for training; then the same method is used for MSI to generate multispectral images used for training; The original hyperspectral image without downsampling is used as the reference image and the training label; S2. Create a KAN-based space-frequency dual-domain implicit guided sampling network, which includes an encoding unit, a spatial implicit guided sampling unit, a frequency implicit guided sampling unit and a decoding unit; wherein the encoding unit is composed of parallel KAN modules; the spatial implicit guided sampling unit and the frequency implicit guided sampling unit sample HSI in space and frequency respectively to generate spatial and frequency guided features, and the decoding unit fuses the spatial and frequency guided features and decodes to generate a fused image; Guided implicit sampling is a module that samples in feature space. KAN is used for nonlinear fitting in the fitting process to guide implicit sampling through high spatial resolution features. Bootstrapping low spatial resolution features Perform spatial interpolation on a continuous domain; generate implicit guided sampling output results; The coding unit is used to extract the initial features of HSI and MSI and map the features to a deeper space. KAN is used to encode HSI and MSI. The order of the KAN spline function is set to 3, the grid size parameter is set to 5, and the dimension of the encoded features is unified. The process formula of the coding unit is expressed as follows: , ， in, and They are HSI and MSI, and is the coded HSI and HSI, and satisfies , the output feature dimension D is set to 64; The spatial implicit guided sampling unit uses the high spatial resolution of the encoded MSI to guide the spatial interpolation of the encoded HSI, and uses implicit functions to enhance the feature expression of the spatial dimension; the spatial implicit guided sampling unit uses the MSI features to establish a high-resolution coordinate grid, determine the sampling direction and position, and upsample the HSI features through its GIS module. The formula is as follows: ， in, is the spatial guidance feature generated by GIS. is a relative coordinate set; The frequency implicit guided sampling unit is used to enhance the spatial and spectral information expression of the fused image through the guidance of frequency domain information. The frequency implicit guided sampling unit first performs Fourier transform on the encoded HSI and MSI data to convert them into frequency domain representation. In this process, the real part and imaginary part obtained by Fourier transform are separated, corresponding to the cosine component and sine component of the image respectively; then, GIS is applied to the cosine and sine components respectively to generate cosine guided features and sine guided features; finally, these guided features are combined and restored to frequency domain guided features through inverse Fourier transform; S3, conduct network training. During the training process, the Adam optimizer is used to optimize the network, and a network with accurate mapping parameters is generated after multiple rounds of iterations; S4. The hyperspectral and multispectral remote sensing images to be fused are input into the trained network, and a fused image with high spatial resolution and high spectral resolution is generated after mapping.

2. According to claim 1, a KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method is characterized in that: Step S1, specifically, is as follows: according to the Wald protocol requirements, HSI and MSI are spatially downsampled to generate low spatial resolution HSI and high spatial resolution MSI used for training the network. In this process, a 5×5 Gaussian kernel is used to perform spatial filtering on the original HSI and MSI to simulate the sensor point spread function, and then they are spatially downsampled based on bilinear interpolation to generate training samples, which are combined with the original HSI as a reference image as a label image.

3. The KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method according to claim 1, characterized in that: In step S2, KAN uses a learnable activation function and places it at the edge of the network. A KAN with N layers can be expressed as: ， in, is the input feature, For the layer KAN network; for each KAN layer, Contains the input dimensions and output dimensions Product of learnable activation functions : ， in, are the parameters involved in training, and the connections between layers are realized through these parameterized spline functions.

4. The KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method according to claim 1, characterized in that: In step S2, implicit sampling is guided through high spatial resolution features Bootstrapping low spatial resolution features Spatial interpolation on a continuous domain includes the following steps: First, based on the Bilinear Perform spatial interpolation, and Perform spatial alignment, for any query coordinates The spectral value of The coordinate grid C, find The set of 4 adjacent spectral vectors adjacent to the query point in and the corresponding exist Spectral vector; each for The interpolation calculation is expressed as: ， in, For the Spectral vector The interpolation result of the query spectrum vector; in this process, the spectrum dimension is expanded; the last channel is used to store the contribution of the calculated spectrum vector to the final result; through parallel calculation, the interpolation spectrum vectors of the four grid points will be combined to generate , then the channels are separated to form and Two parts, finally in Guided implicit sampling results of points is through and The weighted summation of the estimated weights of the third dimension of is obtained: , in, It represents element-by-element multiplication. Through the above method, all query points are traversed to generate the result of GIS output.

5. The KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method according to claim 1, characterized in that: In step S2, the mathematical expression of the frequency implicit guided sampling unit is: ， in, are the cosine and sine components of the encoded HSI, are the cosine and sine components of the encoded MSI, and are the frequency domain cosine and sine guided features, respectively. The frequency domain guided features output by the frequency implicit guided sampling unit.

6. The KAN-based space-frequency dual-domain implicit guided sampling remote sensing image fusion method according to claim 5 is characterized by: In step S2, the decoding unit is used to fuse the guiding features in the spatial domain and the frequency domain, and generate a high-resolution fused image through spectral mapping. Specifically, an additive fusion strategy is first used to combine the spatial guiding features and the frequency domain guiding features; then KAN is used to perform spectral mapping on the fused features to restore them to the target spectral dimension. The mathematical representation of the decoding unit is: ， in, is the fused image output by the network.

Images