A PolSAR image classification method and related apparatus based on complex convolutional Kolmogorov-Arnold networks

Abstract

This invention discloses a PolSAR image classification method and related apparatus based on a complex convolutional Kolmogorov-Arnold network, belonging to the field of land cover classification technology. The method includes: acquiring a PolSAR image to be processed and performing preprocessing; inputting the preprocessed PolSAR image into a preset complex convolutional Kolmogorov-Arnold network to obtain a classification result; wherein the preset complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks, and CV-PolyLoss. This invention has promising prospects for practical remote sensing application deployment.

Description

Technical Field

[0001] This invention belongs to the field of land cover classification technology, specifically relating to a PolSAR image classification method and related apparatus based on complex convolutional Kolmogorov-Arnold networks. Background Technology

[0002] Land cover classification is a key task in remote sensing image analysis. It aims to assign specific land cover categories to each pixel in an image and is widely used in fields such as environmental monitoring, urban planning, and resource surveys.

[0003] Early classification methods were mostly model-driven, relying on manually designed features. Feature extraction encompasses two main directions: remote sensing polarization features and image features. Polarimetric target decomposition, which obtains physical parameters by analyzing observational data, can be divided into coherent decomposition (e.g., Pauli and Krogager decomposition) and incoherent decomposition. Incoherent decomposition includes eigenvalue analysis-based methods (e.g., Cloude-Pottier and Touzi decomposition) and physical model-based methods (e.g., Freeman-Durden and Yamaguchi decomposition). Based on the statistical properties of PolSAR data, such as the Wishart and K-distributions, researchers have also combined statistical models of remote sensing data with target decomposition theory. Furthermore, image characteristics such as texture and spatial features are also widely used in classification tasks.

[0004] With breakthroughs in computer technology, machine learning-based methods for classifying remote sensing images of ground features have become mainstream in the last decade. Algorithms such as Support Vector Machines, k-Nearest Neighbors, and Random Forests have achieved significant results. However, the performance of these methods still heavily relies on manual feature design, a process requiring deep domain knowledge and exhibiting limited generalization ability. Deep neural networks, with their data-driven modeling advantages, have been extensively studied in this field. Convolutional Neural Networks (CNNs) play a crucial role in this task through parameter-sharing, translationally equivariant inductive biases. Subsequently, the Visual Transformer model has shown development potential, achieving good performance in several studies. However, the fixed computational patterns of CNNs and ViTs limit their ability to adapt to dynamic data and complex polarization relationships.

[0005] In recent years, integrating mathematical theory with deep learning to enhance the modeling capabilities of complex data structures has become a new trend. A typical example is the KAN network, based on the Kolmogorov-Arnold theorem, which replaces the traditional weight matrix with a learnable nonlinear function, becoming an effective alternative to MLP. This architecture shifts the learning focus from weight adjustment to nonlinear mapping learning, exhibiting excellent performance in parameter efficiency and generalization ability. Building on this, researchers have further proposed KAN convolutional layers to improve traditional convolutions. Studies have shown that converting linear convolutions into nonlinear mappings can further enhance the network's adaptability, thus leading to the proposal of KAN convolutional layers as a replacement for standard convolutional layers.

[0006] Although existing studies have confirmed that KAN-based networks have outstanding capabilities in modeling complex data relationships, the potential of KAN convolution in the field of remote sensing has not yet been fully explored. Furthermore, existing real-valued versions of KAN convolutional networks are unable to fully utilize the complex characteristics of some remote sensing data (especially polarimetric synthetic aperture radar data, i.e., PolSAR data), and ignore the hidden information carried by its phase components.

[0007] Therefore, the defects and shortcomings of the existing technology are as follows: (1) Insufficient utilization of phase information: Existing real-valued KAN and KAN convolutional layers cannot directly process complex remote sensing data, which leads to the neglect of the hidden information contained in its phase components, thus limiting the feature expression ability. (2) Limited nonlinear modeling capability: Traditional CNN convolution kernels use linear transformations with fixed weights, which makes it difficult to adaptively fit complex nonlinear feature relationships in remote sensing data; (3) Insufficient multi-scale feature extraction: Single-scale convolution operations cannot capture polarization features in different spatial ranges at the same time, and are not good at expressing the details and overall structure of ground features. (4) Poor adaptability of loss function: The existing complex classification loss function fails to take into account the class imbalance characteristics of remote sensing data, resulting in insufficient robustness of the model; (5) Imbalance between computational efficiency and performance: Although advanced models such as ViT have high accuracy, they have a large number of parameters and computational overhead, while lightweight models often have to sacrifice classification performance. Summary of the Invention

[0008] This invention provides a PolSAR image classification method and related apparatus based on complex convolutional Kolmogorov-Arnold networks, aiming to overcome the defects and shortcomings of existing technologies.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: PolSAR image classification methods based on complex convolutional Kolmogorov-Arnold networks include: Acquire the PolSAR image to be processed and perform preprocessing; The preprocessed PolSAR image is input into a pre-defined complex convolutional Kolmogorov-Arnold network to obtain the classification result; the pre-defined complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks, and CV-PolyLoss. Complex KAN convolutional layers are used to directly process the complex input of PolSAR data. They perform nonlinear mapping on the real and imaginary parts through learnable spline functions to preserve and make full use of phase information for feature extraction. Multi-branch complex KAN convolutional blocks are used to integrate multiple complex KAN convolutional layers with different kernel sizes to extract multi-scale spatial features in parallel, and enhance the network's ability to express ground structure and details through channel splicing and fusion. CV-PolyLoss is used to calculate polynomial-weighted losses for the real and imaginary parts of the output of the complex convolutional Kolmogorov-Arnold network, in order to alleviate the class imbalance problem in remote sensing image classification and improve the model's generalization ability.

[0010] A further improvement of this invention lies in acquiring the PolSAR image to be processed and performing preprocessing, including: For a pixel in a PolSAR image, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score, and then a sliding window is used to extract a portion of the standardized image. Small image patches are input as samples into a pre-defined complex convolutional Kolmogorov-Arnold network, where the label of each sample is the land cover category corresponding to the center pixel.

[0011] A further improvement of this invention lies in the following method for implementing complex KAN convolutional layers: Given complex input Complex weights , superscript Indicates the real part, superscript Indicates the imaginary part. Represent the imaginary unit, define complex number transformation functions. :

[0012] in , For B-spline basis functions, For the corresponding linear weights, the grid dimension Activation function The complex KAN convolutional layer substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output :

[0013]

[0014] The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, loop unrolling and vectorization are used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Zero padding (padding=1) and dilation (dilation=1) are used for boundary processing to maintain spatial resolution.

[0015] A further improvement of this invention is that the multi-branch complex KAN convolutional block contains four parallel branches, each branch containing a residual complex batch normalization path; the input tensor is simultaneously input into four parallel complex KAN convolutional layers, and the kernel sizes of these four convolutional layers are respectively... , , and Subsequently, the output of each convolutional layer is fed in parallel into a complex batch normalization layer. A complex covariance matrix is ​​constructed to perform joint batch normalization on the real and imaginary parts to stabilize the training process. Finally, the outputs of the four convolutional layers and the four complex batch normalization layers are concatenated along the channel dimension. The concatenated high-dimensional features are then fed into a... The complex KAN convolutional layers are used for feature fusion and dimensionality reduction, and the final output channel number of the block is adjusted to a preset scale.

[0016] A further improvement of the present invention is that, for those having For a classification task involving multiple categories, CV-PolyLoss is defined as follows:

[0017] in, and The model is for the first The real and imaginary parts of the class prediction vector values; and It is the real and imaginary parts of the one-hot encoding of the real label, where the correct category position value is The rest are 0; These are the polynomial coefficients.

[0018] A PolSAR image classification device based on a complex convolutional Kolmogorov-Arnold network includes: The image acquisition and preprocessing unit is used to acquire the PolSAR image to be processed and perform preprocessing. The image classification unit is used to input the preprocessed PolSAR image into a preset complex convolutional Kolmogorov-Arnold network to obtain the classification result; wherein the preset complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks and CV-PolyLoss; Complex KAN convolutional layers are used to directly process the complex input of PolSAR data. They perform nonlinear mapping on the real and imaginary parts through learnable spline functions to preserve and make full use of phase information for feature extraction. Multi-branch complex KAN convolutional blocks are used to integrate multiple complex KAN convolutional layers with different kernel sizes to extract multi-scale spatial features in parallel, and enhance the network's ability to express ground structure and details through channel splicing and fusion. CV-PolyLoss is used to calculate polynomial-weighted losses for the real and imaginary parts of the output of the complex convolutional Kolmogorov-Arnold network, in order to alleviate the class imbalance problem in remote sensing image classification and improve the model's generalization ability.

[0019] A further improvement of the present invention is that, in the image acquisition and preprocessing unit, the PolSAR image to be processed is acquired and preprocessed, including: For a pixel in a PolSAR image, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score, and then a sliding window is used to extract a portion of the standardized image. Small image patches are input as samples into a pre-defined complex convolutional Kolmogorov-Arnold network, where the label of each sample is the land cover category corresponding to the center pixel.

[0020] A further improvement of this invention lies in the following method for implementing the complex KAN convolutional layer in the image classification unit: Given complex input Complex weights , superscript Indicates the real part, superscript Indicates the imaginary part. Represent the imaginary unit, define complex number transformation functions. :

[0021] in , For B-spline basis functions, For the corresponding linear weights, the grid dimension Activation function The complex KAN convolutional layer substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output :

[0022]

[0023] The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, loop unrolling and vectorization are used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Zero padding (padding=1) and dilation (dilation=1) are used for boundary processing to maintain spatial resolution.

[0024] An electronic device includes: a processor and a memory coupled to the processor, the memory storing a computer program that, when executed by the processor, implements the steps of the PolSAR image classification method based on a complex convolutional Kolmogorov-Arnold network.

[0025] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the PolSAR image classification method based on a complex convolutional Kolmogorov-Arnold network.

[0026] Compared with the prior art, the present invention has at least the following beneficial technical effects: (1) Complete preservation of polarization information: The real and imaginary parts of the input data are recombined after nonlinear transformation by the complex KAN convolutional layer, so that the network weights and feature expressions contain amplitude and phase information, which improves the ability to analyze the polarization scattering mechanism. Compared with the real KAN convolutional layer, the classification performance is improved. (2) Enhanced adaptive nonlinear fitting capability: Learnable spline functions are used to optimize fixed convolutional kernel weights, allowing each connection to learn nonlinear mappings independently, resulting in higher parameter efficiency. The fitting capability for complex polarization features is significantly better than that of traditional CNNs, achieving higher classification accuracy with the same number of parameters; (3) Deep fusion of multi-scale features: A multi-branch complex KAN convolutional block is designed to integrate four types of convolutional kernels: 3×3, 1×1, 3×1 and 1×3. Nonlinear features of different spatial scales are extracted in parallel and fused by channel splicing. Combined with complex batch normalization layer, the consistency of feature distribution is enhanced, the hierarchy and discriminativeness of polarization representation are enriched, and the average classification accuracy and Kappa coefficient are greatly improved. (4) Improve the robustness and generalization of the model: The complex PolyLoss loss function is proposed. Based on the characteristics of complex network output, the real part and the imaginary part are calculated by polynomial weighted cross-entropy to alleviate the problems of class imbalance and overfitting. Experiments show that this design helps to improve the stability of the model. (5) Computational efficiency and performance balance: Through the parameter sharing mechanism of KAN convolution and the lightweight network architecture, the network can achieve excellent performance while maintaining low parameters and low complexity. Moreover, it has lower theoretical computational overhead than existing models. This algorithm has the prospect of practical remote sensing application deployment. Attached Figure Description

[0027] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0028] Figure 1 This is a diagram of the CV-CPKAN network architecture.

[0029] Figure 2 This is a flowchart of a complex KAN convolutional layer.

[0030] Figure 3 Classification graphs for different methods on the Dutch Flevoland dataset: (a) pseudo-RGB image; (b) ground truth label; (c) support vector machine; (d) Haar-convolutional neural network; (e) complex-valued convolutional neural network; (f) SDF2Net; (g) visual Transformer; (h) hybrid complex-valued network; (i) complex-valued multi-scale attention visual Transformer; (j) VMamba; (k) CFAT; (l) scheme.

[0031] Figure 4 This is a block diagram of a PolSAR image classification device based on a complex convolutional Kolmogorov-Arnold network. Detailed Implementation

[0032] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0033] In the description of this invention, it should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0034] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0035] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0036] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0037] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0038] Example 1 The PolSAR image classification method based on complex convolutional Kolmogorov-Arnold networks provided by this invention includes: Acquire the PolSAR image to be processed and perform preprocessing; The preprocessed PolSAR image is input into a pre-defined complex convolutional Kolmogorov-Arnold network to obtain the classification result; the pre-defined complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks, and CV-PolyLoss. Complex KAN convolutional layers are used to directly process the complex input of PolSAR data. They perform nonlinear mapping on the real and imaginary parts through learnable spline functions to preserve and make full use of phase information for feature extraction. Multi-branch complex KAN convolutional blocks are used to integrate multiple complex KAN convolutional layers with different kernel sizes to extract multi-scale spatial features in parallel, and enhance the network's ability to express ground structure and details through channel splicing and fusion. CV-PolyLoss is used to calculate polynomial-weighted losses for the real and imaginary parts of the output of the complex convolutional Kolmogorov-Arnold network, in order to alleviate the class imbalance problem in remote sensing image classification and improve the model's generalization ability.

[0039] In this embodiment, the PolSAR image to be processed is acquired and preprocessed, including: For a pixel in a PolSAR image, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score, and then a sliding window is used to extract a portion of the standardized image. Small image patches are input as samples into a pre-defined complex convolutional Kolmogorov-Arnold network, where the label of each sample is the land cover category corresponding to the center pixel.

[0040] In this embodiment, the implementation method of the complex KAN convolutional layer is as follows: Given complex input Complex weights , superscript Indicates the real part, superscript Indicates the imaginary part. Represent the imaginary unit, define complex number transformation functions. :

[0041] in , For B-spline basis functions, For the corresponding linear weights, the grid dimension Activation function The complex KAN convolutional layer substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output :

[0042]

[0043] The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, loop unrolling and vectorization are used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Zero padding (padding=1) and dilation (dilation=1) are used for boundary processing to maintain spatial resolution.

[0044] In this embodiment, the multi-branch complex KAN convolutional block contains four parallel branches, each containing a residual complex batch normalization path; the input tensor is simultaneously input into four parallel complex KAN convolutional layers, and the kernel sizes of these four convolutional layers are respectively... , , and Subsequently, the output of each convolutional layer is fed in parallel into a complex batch normalization layer. A complex covariance matrix is ​​constructed to perform joint batch normalization on the real and imaginary parts to stabilize the training process. Finally, the outputs of the four convolutional layers and the four complex batch normalization layers are concatenated along the channel dimension. The concatenated high-dimensional features are then fed into a... The complex KAN convolutional layers are used for feature fusion and dimensionality reduction, and the final output channel number of the block is adjusted to a preset scale.

[0045] In this embodiment, for having For a classification task involving multiple categories, CV-PolyLoss is defined as follows:

[0046] in, and The model is for the first The real and imaginary parts of the class prediction vector values; and It is the real and imaginary parts of the one-hot encoding of the real label, where the correct category position value is The rest are 0; These are the polynomial coefficients.

[0047] Example 2 1. Overview of the overall technical solution This invention provides a PolSAR image classification method (CV-CPKAN) based on a complex convolutional Kolmogorov-Arnold network. The core of this method lies in constructing an end-to-end deep neural network that can directly process complex PolSAR data. Through multi-branch complex KAN convolutional blocks composed of complex KAN convolutional layers, it automatically and fully learns the complete scattering characteristics of ground targets from amplitude to phase, ultimately achieving high-precision and high-efficiency pixel-level classification.

[0048] The overall network architecture of this invention is as follows: Figure 1 As shown in the diagram, the following section will explain in detail the data flow processing and the functions and connections of each module, using this architecture diagram as a reference. The overall process of the CV-CPKAN technical solution is divided into three stages: data preprocessing, feature extraction, and classification decision. Its core innovation lies in the mathematical derivation and implementation of the complex KAN convolutional layer, and the multi-scale feature fusion mechanism based on this layer.

[0049] 2. Data Preprocessing For a raw remote sensing image, the size is ,in This represents the number of channels in the remote sensing data. For a single pixel in the PolSAR data, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score to ensure the stability of the model input. Then, a sliding window is used to extract a portion of the standardized image. Small image patches are input into the network as samples, where the label of each sample is the land cover category corresponding to the center pixel.

[0050] 3. Overall Network Architecture The data processing flow of the network in this invention is as follows: The input layer receives samples and passes them into a multi-branch complex KAN convolutional block for feature extraction. After activation and dimensionality reduction through complex activation functions and complex average pooling, the samples are input into the next multi-branch complex KAN convolutional block. The network contains two multi-branch complex KAN convolutional blocks, each followed by a complex activation function and complex average pooling. Finally, the corresponding values ​​for each land cover category are obtained through a flattening layer and a fully connected complex layer. The category corresponding to the component with the largest value is the predicted category output by the network. The network is updated under the guidance of the CV-PolyLoss loss function, using the AdamW optimizer, and employing the CosineAnnealingLR learning rate scheduler to dynamically reduce the parameter learning rate as the training period increases.

[0051] 4. Complex Kaan convolutional layer This is the core innovative module of the invention, and its mathematical principles and operating procedures are as follows: Figure 2 As shown, its mathematical derivation is as follows.

[0052] Given complex input Complex weights , Define complex transformation functions:

[0053] The linear combination of B-spline basis functions Grid dimension Activation function Unlike ordinary KAN convolutional layers that calculate the real and imaginary parts separately and combine them at the output stage, the complex KAN convolutional layer proposed in this invention substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output :

[0054]

[0055] The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, a loop unrolling and vectorization approach is used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Boundary handling employs zero padding (padding=1) and dilation (dilation=1) to maintain spatial resolution.

[0056] 5. Multi-branch complex KAN convolutional blocks like Figure 1 As shown, the multi-branch complex KAN convolutional block contains four parallel branches, each containing a residual complex batch normalization path. The input tensor is simultaneously fed into four parallel complex KAN convolutional layers, with kernel sizes of the four layers being [missing information]. , , and This design aims to capture spatial nonlinear features at different scales and in both horizontal and vertical directions. The output of each convolutional layer is then fed in parallel into a complex batch normalization layer. This layer performs joint batch normalization on the real and imaginary parts by constructing a complex covariance matrix to stabilize the training process. Finally, the outputs of the four convolutional layers and the four complex batch normalization layers are concatenated along the channel dimension. The concatenated high-dimensional features are then fed into a... The complex KAN convolutional layers are used for feature fusion and dimensionality reduction, and the final output channel number of the block is adjusted to a preset scale.

[0057] 6. CV-PolyLoss To address the class imbalance problem and improve generalization ability, this invention extends the existing classification loss function PolyLoss to the complex domain. Specifically, for classes with... For a classification task involving multiple categories, CV-PolyLoss is defined as follows:

[0058] in, and The model is for the first The real and imaginary parts of the class prediction vector values. and It is the real and imaginary parts of the one-hot encoding of the real label, where the correct category position value is The rest are 0. These are the polynomial coefficients, which are set to 1 by default.

[0059] This loss function forces the model to focus not only on the probability of the correct class during the optimization process, but also to smoothly handle the prediction distribution of other classes, thereby obtaining a more robust decision boundary.

[0060] Example 3 In a practical application case of agricultural monitoring, the CV-CPKAN framework proposed in this invention was used to validate ground cover classification on a PolSAR remote sensing image dataset of the Flevoland region in the Netherlands. This dataset has 750×1024 pixels and 15 categories. Supervised training of the model was performed using 10% of the labeled pixels, and the remaining 10% of the labeled pixels were used for testing. Five independent experiments were conducted, and the average performance and corresponding standard deviation (STD) are reported. The comparative methods used in the comparative experiments include: Support Vector Machine: A polarimetric SAR image classification method based on support vector machine, which optimizes polarimetric feature indices to surpass the standard Wishart classifier.

[0061] Haar-Convolutional Neural Network: A polarimetric SAR image classification method based on convolutional neural networks, which utilizes Haar wavelet transform to extract features, thereby improving classification accuracy and suppressing speckle noise.

[0062] Complex-valued convolutional neural network: A polarimetric SAR image classification method that combines attention-based multi-scale complex-valued convolutional neural networks with SE attention modules to enhance inter-channel interaction.

[0063] SDF2Net: A three-branch feature fusion framework based on complex-valued convolutional neural networks with squeeze excitation modules. It employs a 3D complex-valued convolutional neural network with SE attention and ultimately fuses multi-level features from all branches.

[0064] Visual Transformer: A supervised polarimetric SAR image classification method based on visual Transformer, which captures global features through a self-attention mechanism to improve classification performance.

[0065] Hybrid Complex Value Network: A polarimetric SAR image classification method that integrates complex value convolutional neural networks and complex value visual Transformers, improving accuracy through complementary feature fusion and global dependency modeling.

[0066] Complex-scale attention visual Transformer: A complex-scale attention visual Transformer designed specifically for polarimetric SAR image classification, capable of jointly modeling spatial structure and polarimetric features to achieve superior classification accuracy.

[0067] VMamba: An advanced visual backbone network for natural image analysis that introduces state-space sequence modeling to achieve efficient global dependency learning and enhanced visual representation capabilities.

[0068] CFAT: A polarimetric SAR image classification method based on a CNN-Transformer hybrid architecture, which employs the Fieldy attention mechanism to capture local and global dependencies to enhance the model's generalization ability.

[0069] The experimental accuracy results of the comparative experiments are shown in Table 1. Under the same experimental conditions, CV CPKAN achieved an overall accuracy (OA) of 99.86%, an average accuracy (AA) of 99.72%, and a Kappa coefficient of 99.70 on the test set. Furthermore, it has the lowest standard deviation among all the comparative models, indicating that it has better stability. Table 1. Classification performance of different comparison methods on the Flevoland dataset.

[0070] The number of model parameters and computational complexity of each method are shown in Table 2. CV The CPKAN model has only 0.134M parameters and only 0.080G FLOPs of computation, which is significantly lower than existing models such as ViT (Visual Transformer). Table 2. Model parameter count and computational complexity of different comparison methods

[0071] The prediction and classification results of each method on the Flevoland dataset in the Netherlands are shown in the figure below. Figure 3 As shown, from Figure 3 It is evident that CV CPKAN's classification results are highly consistent with the true annotations, especially in farmland boundaries and the easily confused rapeseed category, showing better contextual consistency and continuity, and significantly reducing misclassified blocks; Ablation experiment such as Figure 3 As shown in the figure. Ablation experiments further demonstrate that introducing complex KAN convolutional layers brings a 0.16% improvement in accuracy compared to the real-valued version, while adding a multi-branch structure contributes a 2.54% performance gain. This intuitively verifies that the present invention, through the synergistic effect of complex modeling, multi-scale fusion, and a dedicated loss function, can significantly improve the feature representation and classification robustness of complex PolSAR data while maintaining efficient computation. To evaluate the effectiveness of each part of CV-CPKAN, ablation experiments were conducted. Since the classification results on the Flevoland dataset in the Netherlands are close to saturation, for a clearer comparison, this ablation experiment was conducted on the San Francisco dataset in the United States. The experimental results are shown in Table 3.

[0072] Table 3 leads to the conclusion that, compared to traditional convolutional neural networks, using KAN convolutional layers can improve overall accuracy (OA) by 2.90% and average accuracy (AA) by 8.36%. The performance improved by 10.45%, with a lower standard deviation. This demonstrates the core advantage of the KAN convolutional layer compared to traditional convolutional layers: stronger and more robust nonlinear fitting and adaptive capabilities. Furthermore, introducing complex numerical design resulted in a slight improvement: OA increased by 0.16%, and AA increased by 0.45%. The 0.57% improvement indicates that complex numerical representation can capture phase features often neglected by real-valued networks. In summary, by combining the newly designed MBComplexKConv module, CV-CPKAN achieves optimal classification performance, with its OA, AA, and... They reached 99.80%, 99.24%, and 99.05%, respectively.

[0073] Table 3 Ablation experimental results of CV-CPKAN on the San Francisco dataset

[0074] The inventive points protected by this invention are: (1) Complex KAN convolutional layer structure: Based on the Kolmogorov-Arnold theorem, the complex KAN convolutional operation performs nonlinear transformations on the real and imaginary parts of the input complex features, and achieves amplitude-phase joint feature extraction through complex weighted recombination; (2) Multi-branch complex KAN convolution block: It includes parallel multi-scale complex KAN convolution layers (with different kernel parameters) and complex batch normalization layers, and finally fuses the multi-scale amplitude and phase features of each branch, and performs channel recalibration of complex features at the end of the module. (3) Complex PolyLoss loss function: For the real and imaginary parts of the output of the complex classification network, calculate the polynomial weighted PolyLoss loss and perform joint optimization; (4) The overall network architecture of the algorithm consists of two multi-branch complex KAN convolutional blocks, complex activation functions, complex average pooling layers and complex fully connected layers connected in series, which are dedicated to end-to-end classification of remote sensing images.

[0075] Example 4 like Figure 4 As shown, the PolSAR image classification device based on complex convolutional Kolmogorov-Arnold network provided by the present invention includes: The image acquisition and preprocessing unit is used to acquire the PolSAR image to be processed and perform preprocessing. The image classification unit is used to input the preprocessed PolSAR image into a preset complex convolutional Kolmogorov-Arnold network to obtain the classification result; wherein the preset complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks and CV-PolyLoss; Complex KAN convolutional layers are used to directly process the complex input of PolSAR data. They perform nonlinear mapping on the real and imaginary parts through learnable spline functions to preserve and make full use of phase information for feature extraction. Multi-branch complex KAN convolutional blocks are used to integrate multiple complex KAN convolutional layers with different kernel sizes to extract multi-scale spatial features in parallel, and enhance the network's ability to express ground structure and details through channel splicing and fusion. CV-PolyLoss is used to calculate polynomial-weighted losses for the real and imaginary parts of the output of the complex convolutional Kolmogorov-Arnold network, in order to alleviate the class imbalance problem in remote sensing image classification and improve the model's generalization ability.

[0076] In the image acquisition and preprocessing unit of this embodiment, the PolSAR image to be processed is acquired and preprocessed, including: For a pixel in a PolSAR image, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score, and then a sliding window is used to extract a portion of the standardized image. Small image patches are input as samples into a pre-defined complex convolutional Kolmogorov-Arnold network, where the label of each sample is the land cover category corresponding to the center pixel.

[0077] In the image classification unit of this embodiment, the implementation method of the complex KAN convolutional layer is as follows: Given complex input Complex weights , superscript Indicates the real part, superscript Indicates the imaginary part. Represent the imaginary unit, define complex number transformation functions. :

[0078] in , For B-spline basis functions, For the corresponding linear weights, the grid dimension Activation function The complex KAN convolutional layer substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output :

[0079]

[0080] The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, loop unrolling and vectorization are used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Zero padding (padding=1) and dilation (dilation=1) are used for boundary processing to maintain spatial resolution.

[0081] Example 5 The present invention provides an electronic device comprising: a processor and a memory coupled to the processor, the memory storing a computer program, wherein the computer program, when executed by the processor, implements the steps of the PolSAR image classification method based on complex convolutional Kolmogorov-Arnold network.

[0082] The electronic device may also include one or more of a multimedia component, an input / output (I / O) interface, and a communication component.

[0083] The processor controls the overall operation of the electronic device to complete all or part of the steps in the storage medium sharing method. The memory stores various types of data to support the operation of the electronic device. This data may include, for example, instructions for any application or method operating on the electronic device, and application-related data such as contact data, sent and received messages, pictures, audio, video, etc. The memory can be implemented using any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. Multimedia components may include a screen and audio components. The screen may be, for example, a touchscreen, and the audio components are used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in memory or transmitted via a communication component. The audio component also includes at least one speaker for outputting audio signals. The I / O interface provides an interface between the processor and other interface modules, such as a keyboard, mouse, buttons, etc. These buttons may be virtual or physical. The communication component is used for wired or wireless communication between the electronic device and other devices. Wireless communication includes Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination thereof; therefore, the corresponding communication component may include a Wi-Fi module, a Bluetooth module, or an NFC module.

[0084] In an exemplary embodiment, the electronic device may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components for performing a storage medium sharing method.

[0085] Example 6 The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the PolSAR image classification method based on a complex convolutional Kolmogorov-Arnold network.

[0086] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This application is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A system that specifies functions in one or more boxes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the scope of the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0091] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A PolSAR image classification method based on complex convolutional Kolmogorov-Arnold networks, characterized in that, include: Acquire the PolSAR image to be processed and perform preprocessing; The preprocessed PolSAR image is input into a pre-defined complex convolutional Kolmogorov-Arnold network to obtain the classification result; The pre-defined complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks, and CV-PolyLoss; Complex KAN convolutional layers are used to directly process the complex input of PolSAR data. They perform nonlinear mapping on the real and imaginary parts through learnable spline functions to preserve and make full use of phase information for feature extraction. Multi-branch complex KAN convolutional blocks are used to integrate multiple complex KAN convolutional layers with different kernel sizes to extract multi-scale spatial features in parallel. Channel stitching and fusion are used to enhance the network's ability to represent ground feature structure and details. Each multi-branch complex KAN convolutional block contains four parallel branches, each containing a residual complex batch normalization path. The input tensor is simultaneously fed into four parallel complex KAN convolutional layers, with kernel sizes of [missing data]. , , and After that, the output of each convolutional layer is fed in parallel into a complex batch normalization layer, which performs joint batch normalization on the real and imaginary parts by constructing a complex covariance matrix to stabilize the training process. Finally, the outputs of the four convolutional layers and the outputs of the four complex batch normalization layers are concatenated along the channel dimension; the concatenated high-dimensional features are then fed into a... The complex KAN convolutional layer is used for feature fusion and dimensionality reduction, and the final output channel number of the block is adjusted to a preset scale. CV-PolyLoss is used to calculate polynomial-weighted losses for the real and imaginary parts of the output of the complex convolutional Kolmogorov-Arnold network, in order to alleviate the class imbalance problem in remote sensing image classification and improve the model's generalization ability.

2. The PolSAR image classification method based on complex convolutional Kolmogorov-Arnold network according to claim 1, characterized in that, Acquire the PolSAR image to be processed and perform preprocessing, including: For a pixel in a PolSAR image, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score, and then a sliding window is used to extract a portion of the standardized image. Small image patches are input as samples into a pre-defined complex convolutional Kolmogorov-Arnold network, where the label of each sample is the land cover category corresponding to the center pixel.

3. The PolSAR image classification method based on complex convolutional Kolmogorov-Arnold network according to claim 1, characterized in that, The implementation method of complex KAN convolutional layers is as follows: Given complex input Complex weights , superscript Indicates the real part, superscript Indicates the imaginary part. Represent the imaginary unit, define complex number transformation functions. : in , For B-spline basis functions, For the corresponding linear weights, the grid dimension Activation function The complex KAN convolutional layer substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output : The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, loop unrolling and vectorization are used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Zero padding (padding=1) and dilation (dilation=1) are used for boundary processing to maintain spatial resolution.

4. The PolSAR image classification method based on complex convolutional Kolmogorov-Arnold network according to claim 1, characterized in that, For those with For a classification task with 10 categories, CV-PolyLoss is defined as follows: in, and The model is for the first The real and imaginary parts of the class prediction vector values; and It is the real and imaginary parts of the one-hot encoding of the real label, where the correct category position value is The rest are 0; These are the polynomial coefficients.

5. A PolSAR image classification device based on a complex convolutional Kolmogorov-Arnold network, characterized in that, include: The image acquisition and preprocessing unit is used to acquire the PolSAR image to be processed and perform preprocessing. The image classification unit is used to input the preprocessed PolSAR image into a pre-defined complex convolutional Kolmogorov-Arnold network to obtain the classification result; The pre-defined complex convolutional Kolmogorov-Arnold network includes complex KAN convolutional layers, multi-branch complex KAN convolutional blocks, and CV-PolyLoss; Complex KAN convolutional layers are used to directly process the complex input of PolSAR data. They perform nonlinear mapping on the real and imaginary parts through learnable spline functions to preserve and make full use of phase information for feature extraction. Multi-branch complex KAN convolutional blocks are used to integrate multiple complex KAN convolutional layers with different kernel sizes to extract multi-scale spatial features in parallel. Channel stitching and fusion are used to enhance the network's ability to represent ground feature structure and details. Each multi-branch complex KAN convolutional block contains four parallel branches, each containing a residual complex batch normalization path. The input tensor is simultaneously fed into four parallel complex KAN convolutional layers, with kernel sizes of [missing data]. , , and After that, the output of each convolutional layer is fed in parallel into a complex batch normalization layer, which performs joint batch normalization on the real and imaginary parts by constructing a complex covariance matrix to stabilize the training process. Finally, the outputs of the four convolutional layers and the outputs of the four complex batch normalization layers are concatenated along the channel dimension; the concatenated high-dimensional features are then fed into a... The complex KAN convolutional layer is used for feature fusion and dimensionality reduction, and the final output channel number of the block is adjusted to a preset scale. CV-PolyLoss is used to calculate polynomial-weighted losses for the real and imaginary parts of the output of the complex convolutional Kolmogorov-Arnold network, in order to alleviate the class imbalance problem in remote sensing image classification and improve the model's generalization ability.

6. The PolSAR image classification device based on complex convolutional Kolmogorov-Arnold network according to claim 5, characterized in that, The image acquisition and preprocessing unit acquires the PolSAR image to be processed and performs preprocessing, including: For a pixel in a PolSAR image, extract the upper triangular elements of its coherence matrix. This forms a 6-dimensional complex vector. The entire image is first standardized using the complex Z-score, and then a sliding window is used to extract a portion of the standardized image. Small image patches are input as samples into a pre-defined complex convolutional Kolmogorov-Arnold network, where the label of each sample is the land cover category corresponding to the center pixel.

7. The PolSAR image classification device based on complex convolutional Kolmogorov-Arnold network according to claim 5, characterized in that, In the image classification unit, the implementation method of the complex KAN convolutional layer is as follows: Given complex input Complex weights , superscript Indicates the real part, superscript Indicates the imaginary part. Represent the imaginary unit, define complex number transformation functions. : in , For B-spline basis functions, For the corresponding linear weights, the grid dimension Activation function The complex KAN convolutional layer substitutes the above rule into the complex multiplication formula, calculates by combining the real and imaginary parts, and obtains the real part output. With imaginary part output : The final complex KAN convolutional layer output Each complex KAN convolutional layer contains There are trainable parameters, among which The convolution kernel spatial size is defined. For computational optimization, loop unrolling and vectorization are used. Spline basis function values ​​are pre-calculated for each convolution position and stored in a lookup table to accelerate computation and avoid redundant calculations. Zero padding (padding=1) and dilation (dilation=1) are used for boundary processing to maintain spatial resolution.

8. An electronic device, characterized in that, include: A processor and a memory coupled to the processor, the memory storing a computer program that, when executed by the processor, implements the steps of the PolSAR image classification method based on the complex convolutional Kolmogorov-Arnold network as described in any one of claims 1-4.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the PolSAR image classification method based on the complex convolutional Kolmogorov-Arnold network as described in any one of claims 1-4.

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