An image space super-resolution method with high generalization based on Kolmogorov-Arnold neural operator
By using a deep unfolded network based on the Kolmogorov-Arnold neural operator, the problem of poor generalization of existing super-resolution methods is solved, and effective modeling and image reconstruction of complex degradation processes are achieved, improving the spatial consistency and interpretability of image reconstruction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-04-29
- Publication Date
- 2026-07-21
AI Technical Summary
Existing super-resolution methods have poor generalization ability in image reconstruction, cannot effectively utilize the potential of deep learning to mine deep hidden features, and do not fully consider the complexity of multi-factor degradation processes, resulting in fragile reconstruction results.
A highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator is adopted. By constructing a deep unfolding network, which includes three parts: spatial degradation modeling, spectral information reconstruction, and residual information reconstruction, the complexity in the image space is approximated by multiple linear functions. The image reconstruction is performed by combining KAN theory and UNet network.
It achieves effective modeling of complex degradation processes, improves the spatial consistency and generalization ability of image reconstruction, and enhances the interpretability and robustness of the model.
Smart Images
Figure CN122434734A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of image processing technology, and more specifically, to a highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator. Background Technology
[0002] From a mathematical perspective, the definition of single-image super-resolution (SR) is:
[0003]
[0004] in, For low-resolution images (LR). For the corresponding high-resolution image (HR).
[0005] The degradation process is mediated by fuzzy kernels. and downsampling operation This is achieved through a combination of factors, where s represents the downsampling scale, typically set to a factor of 2, 4, or 8. (Noise) It is typically assumed to be additive white Gaussian noise (AWGN), with its standard deviation (or noise level)... .
[0006] The development of super-resolution technology has made reconstructing high-resolution (HR) images from low-resolution (LR) images inherently challenging, as it constitutes an ill-posed inverse problem. Current super-resolution (SR) methods aim to recover the mapping function of these lost high-frequency components, thereby facilitating the reconstruction of HR images from given observed LR images. Mainstream methods can be broadly categorized into two types: traditional models with handcrafted priors and deep learning (DL)-based techniques. Traditional SR methods typically employ manually designed priors to formulate and solve complex constrained optimization problems, such as utilizing principles like sparsity and low rank. However, these methods inherently rely on carefully designed prior constraints, which are often tailored to specific image features and may generalize poorly across diverse natural images.
[0007] Over the past decade, the continuous emergence of large-scale datasets has driven the development of deep learning (DL)-based methods, which leverage parameterized neural networks to autonomously capture complex image priors. While achieving state-of-the-art performance in spatial reasoning (SR) tasks, the black-box nature of deep networks limits interpretability. To mitigate this issue, researchers have recently worked to integrate DL with physical priors. By embedding domain-specific constraints into the neural architecture, these hybrid approaches enhance the interpretability, generalization, and robustness of SR applications.
[0008] However, despite the significant attention DL has received for embedding interpretable knowledge, its application in SR tasks remains challenging, with several key issues yet to be resolved:
[0009] Limitation 1: Most interpretable models are built on specific assumptions that the main factors (such as noise, downsampling, or blur) contribute to the degradation of HR images into their corresponding LR images. The actual degradation process is inherently complex, often involving the interaction of multiple factors. This oversimplified single-factor assumption inevitably makes super-resolution results very fragile.
[0010] Limitation 2: Existing interpretability models for SR tasks primarily focus on deep approximations of local variables and iterative processes for global optimization. The latter approach, represented by deep unrolling techniques, strictly adheres to expert-driven modeling principles. While the optimization process is highly interpretable, it fails to fully leverage the potential of deep learning in uncovering deep, latent features. Therefore, a novel approach is urgently needed to address this technical challenge. Summary of the Invention
[0011] This invention addresses the technical problems existing in the prior art by providing a highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator. This technical solution is practically feasible and scalable for real-world image super-resolution tasks.
[0012] To achieve the above objectives, the technical solution of this invention is as follows: This application designs a novel image spatial super-resolution method based on the Kolmogorov-Arnold neural operator with high generalization, the process of which is as follows: Figure 1 As shown. This method also proposes a coarse fitting module for spatial degradation modeling ( (Optimized from the network), the process is as follows: Figure 2 As shown, the spectral degradation modeling module comprehensively considers spatial spectral characteristics ( Optimize sub-networks), the process is as follows: Figure 3 As shown, the process includes a nonlinear feature fitting module (residual information reconstructed from the network), and the workflow is as follows: Figure 4 As shown below. The following section will provide a detailed explanation of the above content.
[0013] To effectively utilize the prior knowledge of the super-resolution reconstruction model, this invention constructs a deep unfolded network based on the model. This network mainly consists of three parts, as follows: Optimization of the subnetwork (spatial degradation modeling). The optimized subnetwork (spectral information reconstruction), and Optimize the subnetwork (reconstruct the remaining information).
[0014] The main process of this invention includes the following steps:
[0015] Step 1: Obtain low-resolution images with spatial scale degradation, corresponding degradation blur kernels, and corresponding high-resolution images to form training and testing sets.
[0016] Step 2: Process the low-resolution image using bicubic spline interpolation to obtain a primary super-resolution image.
[0017] Step 3: Process the primary super-resolution image using the Laplacian operator to obtain an auxiliary image. Copy the primary super-resolution image to obtain a coarse super-resolution image. Subtract the coarse super-resolution image from the primary super-resolution image to obtain the super-resolution residual image. Initialize the super-resolution blur kernel using a Gaussian kernel.
[0018] Furthermore, the parameters are initialized as follows:
[0019]
[0020]
[0021]
[0022]
[0023]
[0024] in, This represents bicubic spline interpolation with an upsampling scale of . , For supplementary information, used in and In the optimized subnetwork, spatial information is supplemented for relevant variables. This indicates the generation of a length of A one-dimensional Gaussian vector, This invention utilizes the Laplacian operator to process images. The Laplacian kernel used in this invention is:
[0025]
[0026] Step 4: Input the super-resolution blur kernel, the primary super-resolution image, and the low-resolution image into the blur kernel optimization sub-network to update the super-resolution blur kernel.
[0027] Step 5: Input the super-resolution blur kernel, primary super-resolution image, coarse super-resolution image, low-resolution image, and auxiliary image into the coarse super-resolution image update subnetwork, and update the coarse super-resolution image and auxiliary image.
[0028] Step 6: Input the super-resolution blur kernel, coarse super-resolution image, super-resolution residual image, low-resolution image, and auxiliary image into the super-resolution residual image update sub-network to update the super-resolution residual image and the auxiliary image. Add the coarse super-resolution image and the super-resolution residual image to obtain the updated primary super-resolution image.
[0029] Step 7: Repeat steps 4-6 twice to obtain the super-resolution blur kernel and the primary super-resolution image after the two updates.
[0030] Step 8: Input the super-resolution blur kernel and the primary super-resolution image obtained in Steps 4-7 into the loss function, obtain the training loss, and update the network parameters of the blur kernel optimization sub-network, the coarse super-resolution image update sub-network, and the super-resolution residual image update sub-network based on the loss.
[0031] Step 9: Repeat steps 4-8 for 400 rounds to obtain the updated fuzzy kernel optimization subnetwork, coarse super-resolution image update subnetwork, and super-resolution residual image update subnetwork.
[0032] Step 10: Input the low-resolution image and the corresponding degraded blur kernel from the test set into the blur kernel optimization subnetwork, the coarse super-resolution image update subnetwork, and the super-resolution residual image update subnetwork to obtain a high-resolution image.
[0033] Furthermore, the specific implementation process of step 4 is as follows:
[0034] Step 4-1: Calculate the fuzzy kernel The updated gradient, this process is represented as:
[0035]
[0036] in, To update the gradient for the fuzzy kernel, For the primary super-resolution image, The super-resolution fuzzy kernel, For the low-resolution image, and These represent vector transformation and inverse vector transformation, respectively. This represents the downsampling operator, with a downsampling scale of . , This indicates that the image dimensions are aggregated and transformed according to the blur kernel size and degradation scale, i.e. .
[0037] Step 4-2: Input the updated gradient of the fuzzy kernel and the super-fuzzy kernel into the following formula to obtain the updated super-fuzzy kernel:
[0038]
[0039] Among them, The gradient update step size can be automatically optimized as the network trains.
[0040] Step 4-3: The super-resolution fuzzy kernel... Input a KAN-based subnetwork, for The initial reconstruction results are then finely corrected. This process can be expressed as:
[0041]
[0042]
[0043]
[0044]
[0045]
[0046] in, and These are intermediate results for spatial KAN. Output for the spatial KAN module. This represents the activation function. This is a standard KAN network. Note that... This indicates that the image is processed in the spatial dimension. and It is a two-dimensional convolution, and its spline function is also two-dimensional. This is to ensure that KAN can effectively preserve the original information when processing it. The information will and The data is added together and then integrated dimensionally to facilitate KAN's processing of the data to obtain... Note that this operation ensures that the KAN network can effectively fit the global spatial information of the blur kernel, thus achieving an effective assessment of image degradation.
[0047] Step 4-4: Considering that the number of channels in the fuzzy kernel is 1 in a real scene, and that all values are non-negative and sum to one, the super-resolution fuzzy kernel is... Further processing, this process can be described as follows:
[0048]
[0049]
[0050]
[0051] in, Indicates the kernel size as A two-dimensional convolution with an output channel dimension of 1.
[0052] Furthermore, the implementation process of step 5 of the highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator is as follows:
[0053] Step 5-1: The super-resolution fuzzy kernel... The primary super-resolution image The low-resolution image The coarse super-resolution image is obtained by inputting the following formula. Optimization gradient :
[0054]
[0055] in, Indicates the use of As the kernel, perform deconvolution with a stride of [value missing]. .
[0056] Step 5-2, to make the above To facilitate model convergence, normalization is performed, which is expressed as:
[0057]
[0058] in, Represents the identity matrix.
[0059] Step 5-3: Process the coarse super-resolution image and the optimization gradient Input the following formula to obtain the initial optimization results of the coarse super-resolution image based on the optimization model:
[0060]
[0061] Step 5-4: Process the coarse super-resolution image and the auxiliary images Follow the steps below to update and rebuild further. Spectral information in:
[0062]
[0063]
[0064]
[0065]
[0066]
[0067]
[0068] in, and The result after splicing along the channel dimensions. and These are the reconstruction results and final output of the spatial KAN, respectively. Note This information is then input into KAN to achieve precise correction of the spectral information. This indicates that the image is segmented along the spectral dimension, and the first C channels are divided into... The last C channels were divided into .
[0069] Furthermore, the implementation process of step 6 of the highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator is as follows:
[0070] Step 6-1: Input the super-resolution blur kernel, the coarse super-resolution image, the super-resolution residual image, the low-resolution image, and the auxiliary image into the following formula to calculate the optimized gradient of S, and obtain... Primary reconstruction results This process can be represented as:
[0071]
[0072]
[0073]
[0074]
[0075] Step 6-2: Input the super-resolution residual image and the auxiliary image into the improved UNet. The process of performing fine corrections to reconstruct the remaining information can be represented as:
[0076]
[0077]
[0078]
[0079]
[0080]
[0081]
[0082] in, Indicates the depth of UNet. for and The result after splicing along the channel. Indicates the kernel size as A two-dimensional convolution with an output channel dimension of . , For encoder output, , Intermediate output results for the improved UNet.
[0083] Note that when the stated The input is When the output is obtained, it is obtained by the following formula:
[0084]
[0085]
[0086]
[0087]
[0088]
[0089] Note that in the Encoder's... Layer, input is At this time, the feature processing process of this layer can be represented as:
[0090]
[0091] in, , ,when hour, for .
[0092] Note that in Deconder's... Layer, input is and At this time, the feature processing process of this layer can be represented as:
[0093]
[0094] in, , ,when hour, for Indicates that the convolution kernel is A deconvolution with a stride of 2.
[0095] Furthermore, the loss calculation process in step 8 of the highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator is as follows:
[0096] The super-fuzzy kernel and the primary super-resolution image The corresponding degenerate fuzzy kernel and the corresponding high-resolution image Enter the following formula:
[0097]
[0098] in, , Describing the L1 norm, and These are the weights for the corresponding loss terms, used to balance the losses.
[0099] Compared with the prior art, the present invention has the following advantages:
[0100] 1) More complete model for modeling complex degradation: This application proposes a new framework that reconstructs the super-resolution degradation model by introducing residual components into the optimized model to improve the model’s perception of complex degradation.
[0101] 2) Constructing a restoration model using interpretable deep modules: a coarse-fitting module for spatial degradation modeling. Unlike existing methods, KANO is based on KAT theory and uses the summation of multiple linear functions to approximate arbitrary complexity in image space. This method is not constrained by prior assumptions, enabling it to achieve spatially consistent alignment for image degradation of any complexity. Attached Figure Description
[0102] Figure 1 This is the overall flowchart of the super-resolution method;
[0103] Figure 2 yes Figure 1 K-optimized subnetwork in;
[0104] Figure 3 yes Figure 1 The O-optimized subnetwork in the middle;
[0105] Figure 4 yes Figure 1 The S-optimized subnetwork in the process. Detailed Implementation
[0106] To enhance understanding of the present invention, the embodiments will be described in detail below with reference to the accompanying drawings.
[0107] Example 1: See Figure 1 , Figure 2 A highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator is described below:
[0108] Step 1: Acquire low-resolution images with spatial scale degradation, corresponding degradation blur kernels, and corresponding high-resolution images to form training and testing sets. This patent is a super-resolution method, and its training mainly requires low-resolution-high-resolution image pairs. Currently, many super-resolution datasets with paired images can be collected online, such as: Set5, Set14, BSD100, Urban100, DIV2K, and Flickr2K. This patent uses DIV2K and Flickr2K as training sets and Set5, Set14, BSD100, and Urban100 as testing sets. Note that this example uses images with red, green, and blue bands as experimental data. If users have images with other band numbers in actual applications, this patent can also achieve super-resolution tasks.
[0109] Step 2: Process the low-resolution image using bicubic spline interpolation to obtain a primary super-resolution image.
[0110] Step 3: Process the primary super-resolution image using the Laplacian operator to obtain an auxiliary image. Copy the primary super-resolution image to obtain a coarse super-resolution image. Subtract the coarse super-resolution image from the primary super-resolution image to obtain the super-resolution residual image. Initialize the super-resolution blur kernel using a Gaussian kernel.
[0111] Specifically, the parameters are initialized as follows:
[0112]
[0113]
[0114]
[0115]
[0116]
[0117] in, This represents bicubic spline interpolation with an upsampling scale of . , For supplementary information, used in and In the optimized subnetwork, spatial information is supplemented for relevant variables. This indicates the generation of a length of A one-dimensional Gaussian vector, This invention utilizes the Laplacian operator to process images. The Laplacian kernel used in this invention is:
[0118]
[0119] Step 4: Input the super-resolution blur kernel, the primary super-resolution image, and the low-resolution image into the blur kernel optimization sub-network to update the super-resolution blur kernel. The specific process is as follows:
[0120] Step 4-1: Calculate the fuzzy kernel The updated gradient, this process is represented as:
[0121]
[0122] in, To update the gradient for the fuzzy kernel, For the primary super-resolution image, The super-resolution fuzzy kernel, For the low-resolution image, and These represent vector transformation and inverse vector transformation, respectively. This represents the downsampling operator, with a downsampling scale of . , This indicates that the image dimensions are aggregated and transformed according to the blur kernel size and degradation scale, i.e. .
[0123] Step 4-2: Input the updated gradient of the fuzzy kernel and the super-fuzzy kernel into the following formula to obtain the updated super-fuzzy kernel:
[0124]
[0125] Among them, The gradient update step size can be automatically optimized as the network trains.
[0126] Step 4-3: The super-resolution fuzzy kernel... Input a KAN-based subnetwork, for The initial reconstruction results are then fine-calibrated, specifically, such as... Figure 2 As shown. This process can be represented as:
[0127]
[0128]
[0129]
[0130]
[0131]
[0132] in, and These are intermediate results for spatial KAN. Output for the spatial KAN module. This represents the activation function. This is a standard KAN network. Note that... This indicates that the image is processed in the spatial dimension. and It is a two-dimensional convolution, and its spline function is also two-dimensional. This is to ensure that KAN can effectively preserve the original information when processing it. The information will and The data is added together and then integrated dimensionally to facilitate KAN's processing of the data to obtain... Note that this operation ensures that the KAN network can effectively fit the global spatial information of the blur kernel, thus achieving an effective assessment of image degradation.
[0133] Step 4-4: Considering that the number of channels in the fuzzy kernel is 1 in a real scene, and that all values are non-negative and sum to one, the super-resolution fuzzy kernel is... Further processing, this process can be described as follows:
[0134]
[0135]
[0136]
[0137] in, Indicates the kernel size as A two-dimensional convolution with an output channel dimension of 1.
[0138] Step 5: Input the super-resolution blur kernel, the primary super-resolution image, the coarse super-resolution image, the low-resolution image, and the auxiliary image into the coarse super-resolution image update sub-network to update the coarse super-resolution image and the auxiliary image. The specific process is as follows:
[0139] Step 5-1: The super-resolution fuzzy kernel... The primary super-resolution image The low-resolution image The coarse super-resolution image is obtained by inputting the following formula. Optimization gradient :
[0140]
[0141] in, Indicates the use of As the kernel, perform deconvolution with a stride of [value missing]. .
[0142] Step 5-2, to make the above To facilitate model convergence, normalization is performed, which is expressed as:
[0143]
[0144] in, Represents the identity matrix.
[0145] Step 5-3: Process the coarse super-resolution image and the optimization gradient Input the following formula to obtain the initial optimization results of the coarse super-resolution image based on the optimization model:
[0146]
[0147] Step 5-4: Process the coarse super-resolution image and the auxiliary images Specifically, such as Figure 3 As shown. It can be represented as the following process:
[0148]
[0149]
[0150]
[0151]
[0152]
[0153]
[0154] in, and The result after splicing along the channel dimensions. and These are the reconstruction results and final output of the spatial KAN, respectively. Note This information is then input into KAN to achieve precise correction of the spectral information. This indicates that the image is segmented along the spectral dimension, and the first C channels are divided into... The last C channels were divided into .
[0155] Step 6: Input the super-resolution blur kernel, the coarse super-resolution image, the super-resolution residual image, the low-resolution image, and the auxiliary image into the super-resolution residual image update sub-network to update the super-resolution residual image and the auxiliary image. Add the coarse super-resolution image and the super-resolution residual image to obtain the updated primary super-resolution image. The specific process is as follows:
[0156] This process can be represented as:
[0157]
[0158]
[0159]
[0160]
[0161] Step 2: Input the super-resolution residual image and the auxiliary image into the improved UNet. Perform fine-tuning to reconstruct the remaining information, specifically such as Figure 4 As shown. This process can be represented as:
[0162]
[0163]
[0164]
[0165]
[0166]
[0167]
[0168] in, Indicates the depth of UNet. for and The result after splicing along the channel. Indicates the kernel size as A two-dimensional convolution with an output channel dimension of . , For encoder output, , Intermediate output results for the improved UNet.
[0169] Note that when the stated The input is When the output is obtained, it is obtained by the following formula:
[0170]
[0171]
[0172]
[0173]
[0174]
[0175] Note that in the Encoder's... Layer, input is At this time, the feature processing process of this layer can be represented as:
[0176]
[0177] in, , ,when hour, for .
[0178] Note that in Deconder's... Layer, input is and At this time, the feature processing process of this layer can be represented as:
[0179]
[0180] in, , ,when hour, for Indicates that the convolution kernel is A deconvolution with a stride of 2.
[0181] Step 7: Repeat steps 4-6 twice to obtain the super-resolution blur kernel and the primary super-resolution image after the two updates.
[0182] Step 8: Input the super-resolution blur kernel and the primary super-resolution image obtained in Steps 4-7 into the loss function, obtain the training loss, and update the network parameters of the blur kernel optimization sub-network, the coarse super-resolution image update sub-network, and the super-resolution residual image update sub-network based on the loss.
[0183] Specifically, the loss calculation function is as follows:
[0184]
[0185] in, , Describing the L1 norm, and These are the weights for the corresponding loss terms, used to balance the losses.
[0186] Step 9: Repeat steps 4-8 for 400 rounds to obtain the updated fuzzy kernel optimization subnetwork, coarse super-resolution image update subnetwork, and super-resolution residual image update subnetwork.
[0187] Step 10: Input the low-resolution image and the corresponding degraded blur kernel from the test set into the blur kernel optimization subnetwork, the coarse super-resolution image update subnetwork, and the super-resolution residual image update subnetwork to obtain a high-resolution image.
[0188] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.
Claims
1. A highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator, characterized in that, The method includes the following steps: Step 1: Obtain low-resolution images with spatial scale degradation, corresponding degradation blur kernels, and corresponding high-resolution images to form training and testing sets. Step 2: Process the low-resolution image using bicubic spline interpolation to obtain a primary super-resolution image. Step 3: Process the primary super-resolution image using the Laplacian operator to obtain an auxiliary image. Copy the primary super-resolution image to obtain a coarse super-resolution image. Subtract the coarse super-resolution image from the primary super-resolution image to obtain the super-resolution residual image. Initialize the super-resolution blur kernel using a Gaussian kernel. Step 4: Input the super-resolution blur kernel, the primary super-resolution image, and the low-resolution image into the blur kernel optimization sub-network to update the super-resolution blur kernel. Step 5: Input the super-resolution blur kernel, primary super-resolution image, coarse super-resolution image, low-resolution image, and auxiliary image into the coarse super-resolution image update subnetwork, and update the coarse super-resolution image and auxiliary image. Step 6: Input the super-resolution blur kernel, coarse super-resolution image, super-resolution residual image, low-resolution image, and auxiliary image into the super-resolution residual image update sub-network. Update the super-resolution residual image and the auxiliary image. Add the coarse super-resolution image and the super-resolution residual image to obtain the updated primary super-resolution image. Step 7: Repeat steps 4-6 twice to obtain the super-resolution blur kernel and the initial super-resolution image after the two updates. Step 8: Input the super-resolution blur kernel and primary super-resolution image obtained in Steps 4-7, along with the corresponding degraded blur kernel and the corresponding high-resolution image, into the loss function to obtain the training loss. Then, based on the loss, update the network parameters of the blur kernel optimization sub-network, the coarse super-resolution image update sub-network, and the super-resolution residual image update sub-network. Step 9: Repeat steps 4-8 for 400 rounds to obtain the updated fuzzy kernel optimization subnetwork, coarse super-resolution image update subnetwork, and super-resolution residual image update subnetwork. Step 10: Input the low-resolution images from the test set, the corresponding degenerate blur kernels into the blur kernel optimization subnetwork, the coarse super-resolution image update subnetwork, and the super-resolution residual image update subnetwork to obtain high-resolution images.
2. The image spatial super-resolution method based on the Kolmogorov-Arnold neural operator with high generalization as described in claim 1, characterized in that, The specific implementation process of step 4 is as follows: Step 4-1: Calculate the fuzzy kernel The updated gradient is as follows: in, To update the gradient for the fuzzy kernel, For primary super-resolution images, Super-resolution fuzzy kernel, For low-resolution images, and These represent vector transformation and inverse vector transformation, respectively. This represents the downsampling operator, with a downsampling scale of . , This indicates that the image dimensions are aggregated and transformed according to the blur kernel size and degradation scale, i.e. , Step 4-2: Input the updated gradient of the fuzzy kernel and the super-fuzzy kernel into the following formula to obtain the updated super-fuzzy kernel: Among them, The gradient update step size can be automatically optimized as the network trains. Step 4-3: Apply the super-fuzzy kernel Input a KAN-based subnetwork, and... The initial reconstruction results are then fine-corrected; this process is represented as follows: in, and These are intermediate results for spatial KAN. Output for the spatial KAN module. This represents the activation function. For standard KAN networks, This indicates that the image is processed in the spatial dimension. and As a two-dimensional convolution, its spline function is also two-dimensional. This is to ensure that KAN can effectively take into account the original data when processing information. The information will and The data is added together and then integrated dimensionally to facilitate KAN's processing of the data to obtain... , Step 4-4: Considering that the number of channels in the blur kernel is 1 in a real scene, and that all values are non-negative and sum to one, the super-resolution blur kernel... Further processing is required, and this process is as follows: in, Indicates the kernel size as A two-dimensional convolution with an output channel dimension of 1.
3. The image spatial super-resolution method based on the Kolmogorov-Arnold neural operator with high generalization as described in claim 1, characterized in that, The implementation process of step 5 is as follows: Step 5-1: Apply the super-fuzzy kernel Primary super-resolution image Low-resolution images Input the following formula to obtain coarse super-resolution image Optimization gradient : in, Indicates the use of As the kernel, perform deconvolution with a stride of [value missing]. , Step 5-2, to make To facilitate model convergence, we normalize the model as follows: in, Represents the identity matrix. Step 5-3: Convert the coarse super-resolution image and optimizing gradients Input the following formula to obtain the initial optimization results of the coarse super-resolution image based on the optimization model: Step 5-4: Convert the coarse super-resolution image and auxiliary images Follow the steps below to update and rebuild further. Spectral information in: in, and The result after splicing along the channel dimensions. and These are the reconstruction processing results and final output of spatial KAN, respectively. This information is then input into KAN to achieve precise spectral correction. This indicates that the image is segmented along the spectral dimension, and the first C channels are divided into... The last C channels were divided into .
4. The image spatial super-resolution method based on the Kolmogorov-Arnold neural operator with high generalization as described in claim 1, characterized in that, The implementation process of step 6 is as follows: Step 6-1: Input the super-resolution blur kernel, coarse super-resolution image, super-resolution residual image, low-resolution image, and auxiliary image into the following formula to calculate the optimization gradient of S, and obtain... Primary reconstruction results The details are as follows: Step 6-2: Input the super-resolution residual image and the auxiliary image into the improved UNet. Fine-tuning is performed to reconstruct the remaining information, as follows: in, Indicates the depth of UNet. for and The result after splicing along the channel dimensions. Indicates the kernel size as A two-dimensional convolution with an output channel dimension of , , For encoder output, , To improve the intermediate output of UNet, when The input is When the output is obtained, it is obtained by the following formula: In the Encoder's... Layer, input is At that time, the feature processing process of this layer is represented as follows: in, , ,when hour, for , In Deconder's Layer, input is and At that time, the feature processing process of this layer is represented as follows: in, , ,when hour, for Indicates that the convolution kernel is A deconvolution with a stride of 2.
5. The image spatial super-resolution method based on the Kolmogorov-Arnold neural operator with high generalization as described in claim 1, characterized in that, The loss calculation process in step 8 is as follows: super-fuzzy kernel and primary super-resolution images With corresponding degenerate fuzzy kernel and corresponding high-resolution images Enter the following formula: in, , Describing the L1 norm, and These are the weights for the corresponding loss terms, used to balance the losses.
6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator as described in any one of claims 1 to 5.
7. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by a processor, the computer instructions implement the highly generalizable image spatial super-resolution method based on the Kolmogorov-Arnold neural operator as described in any one of claims 1-5.