Remote Sensing Image Fusion Method and System Based on Momentum Integral Enhanced Neurodynamic Model

Abstract

This invention belongs to the fields of computer vision, image processing, neurodynamics algorithms and control. It discloses a remote sensing image fusion method and system based on a momentum integral-enhanced neurodynamic model, including: constructing a recognized spectral degradation form and spatial degradation form for full-resolution images; using the maximum likelihood estimation method to estimate the error between the actual multispectral image and panchromatic image and the model estimation, transforming it into an optimization problem; simplifying it into the Sylvester equation; transforming it into a series of linear equations; defining an error function for each linear equation as a measure of the error between the current moment and the actual situation; establishing a momentum integral-enhanced gradient descent neurodynamic model to solve the remote sensing image fusion equation; and finally, obtaining the optimal image fusion vector based on the solution results, which significantly improves the efficiency and accuracy of image fusion.

Description

Technical Field

[0001] This invention belongs to the fields of computer vision, image processing, neurodynamics algorithms and control, and specifically relates to a remote sensing image fusion method and system based on momentum integral enhancement neurodynamics model. Background Technology

[0002] Remote sensing technology, as a crucial means of acquiring information about the Earth's surface, plays an irreplaceable role in fields such as resource exploration, environmental monitoring, precision agriculture, urban planning, disaster emergency response, and national defense. Different types of remote sensing sensors (such as optical, infrared, radar, hyperspectral, and panchromatic sensors) are limited by their physical mechanisms, resulting in image data with varying advantages and limitations in spatial resolution, spectral resolution, temporal resolution, and information dimensions. For example, panchromatic images typically have high spatial resolution but lack spectral information; multispectral or hyperspectral images have rich spectral information but lower spatial resolution; radar images have all-weather capabilities but limited ability to identify specific ground features.

[0003] Image fusion technology aims to effectively integrate and complement image data from different sensors or different modes of the same sensor on the same scene through specific algorithm models, generating a comprehensive image with high spatial resolution, high spectral fidelity, and rich information content. High-quality fused images can significantly improve the accuracy and reliability of ground feature identification, classification, change detection, and target interpretation, and are a key preprocessing step for remote sensing information extraction and application.

[0004] To meet these needs, researchers have proposed various remote sensing image fusion methods, which can be broadly categorized into traditional methods and deep learning methods. Traditional fusion methods can be further divided into component substitution methods and multi-resolution analysis methods. Component substitution methods convert low-resolution multispectral images to a specific space (such as luminance-chrominance-saturation space), replace the luminance component with details from a high-resolution panchromatic image, and then convert it back to the original space. Its advantages include computational simplicity, high efficiency, and significant injection of spatial details. However, its disadvantages include the potential for severe spectral distortion, especially in hyperspectral fusion; and a coarse substitution process that may lead to distorted spectral features or unnatural spatial information. Multi-resolution analysis methods utilize multi-scale, multi-directional transformation tools to decompose the image into different frequency bands and directional sub-bands. Fusion rules are designed in the transform domain (such as maximizing coefficients, weighted averaging, and region-energy-based fusion) to fuse detailed information, and finally, an inverse transformation is performed to reconstruct the fused image. However, its disadvantages are that the design of fusion rules is complex and has a huge impact on the final result; improper selection can easily introduce artifacts, blurring or ringing effects; the improvement of spatial details is limited by the number of decomposition layers and the choice of orientation basis; it is sensitive to the registration error between source images; and the computational complexity is relatively high.

[0005] In recent years, deep learning methods, represented by convolutional neural networks, generative adversarial networks, and Transformers, have made significant progress in the field of image fusion. They can automatically learn complex nonlinear mapping relationships from massive amounts of data, possess powerful feature extraction and representation capabilities, and outperform traditional methods in many metrics, particularly excelling in balancing spatial detail enhancement and spectral preservation. However, the high cost of acquiring remote sensing data and the scarcity of accurately registered, high-quality multi-source training samples limit the training and application scope of these models. Furthermore, deep models typically contain millions or even billions of parameters, requiring substantial computational resources for training and inference, which is insufficient for resource-constrained platforms such as spaceborne and unmanned aerial vehicles, or for real-time / near-real-time processing scenarios. In addition, well-trained models may lack adaptability to new sensor types, imaging conditions, and terrain features outside the training data distribution, necessitating retraining or fine-tuning.

[0006] Neurodynamic models are a class of dynamic systems inspired by biological neural systems and described by differential equations. They exhibit unique advantages in fields such as optimization, associative memory, pattern recognition, and image processing. The model's behavior is defined by clear differential equations, and the optimization process can be viewed as the dynamic evolution of a physical system, making it easy to understand and analyze. Moreover, the core of this model is typically a system of ordinary differential equations (ODEs), resulting in a compact structure. Unlike deep learning, it does not require time-consuming offline pre-training; it can usually be solved in a single iterative evolution, making it particularly suitable for embedded or real-time systems with limited computational resources. Furthermore, the model parameters are usually set based on physical meaning or experience, independent of training on specific datasets. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a remote sensing image fusion method and system based on a momentum integral enhanced neurodynamic model, aiming to improve the efficiency and accuracy of computer fusion of panchromatic images and multispectral images.

[0008] To achieve the above objectives, the present invention provides the following solution:

[0009] A remote sensing image fusion method based on momentum integral-enhanced neurodynamics model, the method comprising:

[0010] S1. Based on the principle of multispectral and panchromatic image fusion, construct the spectral degradation form and spatial degradation form of full-resolution image;

[0011] S2. Based on the spectral and spatial degradation forms of the full-resolution image, it is found that the multispectral and panchromatic images have a matrix Gaussian distribution property. Using the maximum likelihood estimation method, the estimation error between the actual multispectral and panchromatic images and the model is estimated, which is transformed into an optimization problem.

[0012] S3. Transform the optimization problem in S2 into the Sylvester equation and find its derivative;

[0013] S4. Transform the optimality conditions obtained in S3 into a series of linear equations;

[0014] S5. For each linear equation, define an error function to measure the error between the current moment and the actual situation.

[0015] S6. Introduce the momentum integral enhancement neurodynamic model, input the state variables of the linear equation at the current moment into the momentum integral enhancement neurodynamic model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution in the current state, and pass it to the next moment.

[0016] S7. Update the state variables of the constructed linear equation, return to S5, until the current iteration number exceeds the preset value, or the algorithm error is lower than the preset value, obtain the information matrix of the full-resolution image, and complete the fusion of the multispectral image and the panchromatic image.

[0017] Preferably, in step S1, the method for constructing the spectral degradation form and spatial degradation form of a full-resolution image based on the principle of multispectral and panchromatic image fusion includes:

[0018] The default full-resolution image is in matrix form. ,in Indicates the number of bands in a remote sensing image. Represents the full-resolution image. One pixel; This represents the number of pixels in the image, where For the number of rows, For column numbers;

[0019] Based on the matrix form of the full-resolution image, the spectral degradation form and spatial degradation form of the full-resolution image are constructed as follows:

[0020] ;

[0021] in Represents a multispectral image. Represents a panchromatic image. It is the spectral degradation matrix. It is a spatial degeneracy matrix. , These represent the noise in the multispectral image and the panchromatic image, respectively.

[0022] Preferably, in step S2, based on the spectral and spatial degradation forms of the full-resolution image, the method for obtaining multispectral and panchromatic images with matrix Gaussian distribution properties, and using the maximum likelihood estimation method to estimate the error between the actual multispectral and panchromatic images and the model estimation, transforming it into an optimization problem, includes:

[0023] noise , It follows a matrix normal distribution. Since the observed data is the result of noise superimposed on the degraded signal, according to the properties of linear transformation, and It is also a matrix normal distribution; considering the degree of matching between actual observed data and linear model predictions, by maximizing To estimate ,in Indicates a known full-resolution image Based on this, multispectral images or panchromatic images or The probability distribution; by maximizing the log-likelihood, image fusion is transformed into an optimization problem, namely...

[0024] ;

[0025] in Represents the matrix norm.

[0026] Preferably, in step S3, the method for transforming the optimization problem in S2 into the Sylvester equation and then differentiating it includes:

[0027] Let the objective function of the optimization problem be... Since any two norms in a finite-dimensional space are necessarily equivalent, let's call them the F-norm. Then, for... Differentiation Then, taking the derivative with respect to each term, we get:

[0028] ;

[0029] Then, add the two gradients together and set the total gradient to zero:

[0030] ;

[0031] After simplification, we get:

[0032] ;

[0033] That is, the standard form of a Sylvester equation:

[0034] ;

[0035] in , , .

[0036] Preferably, in step S4, the method for transforming the optimality conditions obtained in S3 into a series of linear equations includes:

[0037] right Perform eigenvalue decomposition, and we have ,in It is an orthogonal matrix, and has , Let represent the identity matrix, then substitute it into the Sylvester equation and multiply by the matrix on the right. ,have to:

[0038] ;

[0039] And simplify, let and have:

[0040] ;

[0041] because It is a diagonal matrix, for Perform column decomposition to obtain a system of independent equations for each column, i.e.:

[0042] ;

[0043] in Indicates the first List, express The List, express The List, express The List.

[0044] Preferably, in step S5, for each linear equation, an error function is defined as a method to measure the error between the current moment and the actual situation, including:

[0045] .

[0046] Preferably, in step S6, the method of introducing momentum integral to enhance the neurodynamic model includes:

[0047] Based on the constructed error function, an integral enhancement term is constructed:

[0048] ;

[0049] in, Indicates the extraction time. For integration variables, Indicates to The differential, This is the corresponding error function;

[0050] Based on the momentum integral enhancement term, a momentum integral enhancement neurodynamic model is established, which is expressed in discrete form as follows:

[0051] ;

[0052] in, Indicates the first iteration Indicates the first Secondary momentum term, Indicates the first Secondary error term Indicates the first Image vectors in the next iteration , The sampling interval is... This is the momentum weight vector. This is the coefficient term.

[0053] Preferably, in step S7, updating the state variables of the constructed linear equation and returning to step S5, until the current iteration count exceeds a preset value or the algorithm error is lower than a preset value, to obtain the information matrix of the full-resolution image, the method for completing the fusion of multispectral and panchromatic images includes:

[0054] S701: Preset multispectral image panchromatic image Preset maximum number of iterations Preset initial filter vector Preset spectral degradation matrix Preset spatial degradation matrix ;

[0055] S702: Calculate the error at the current time. If the number of iterations is greater than the maximum number of iterations, stop the calculation and output the optimal solution; otherwise, proceed to step S703.

[0056] S703: Establish an integral-enhanced gradient descent neural dynamics algorithm and calculate... To obtain the optimal solution at the current moment;

[0057] S704: Proceed to step S702;

[0058] S705: Obtains the information matrix of the full-resolution image and completes the fusion of multispectral and panchromatic images.

[0059] This invention also provides a remote sensing image fusion system based on a momentum integral enhanced neurodynamic model. The system is used to implement the aforementioned method and includes: a construction module, a conversion module, a calculation module, an error module, an optimal solution module, and a fusion module.

[0060] The construction module is used to construct the spectral degradation form and spatial degradation form of a full-resolution image based on the principle of multispectral and panchromatic image fusion.

[0061] The conversion module is used to obtain the multispectral and panchromatic images with matrix Gaussian distribution properties based on the spectral and spatial degradation forms of the full-resolution image. It then uses the maximum likelihood estimation method to estimate the error between the actual multispectral and panchromatic images and the model estimation, thus converting it into an optimization problem.

[0062] The calculation module is used to transform the optimization problem in the transformation module into the Sylvester equation and then differentiate it.

[0063] The transformation module is used to transform the optimality conditions obtained in the calculation module into a series of linear equations;

[0064] The error module is used to define an error function for each linear equation, which serves as a measure of the error between the current moment and the actual situation.

[0065] The optimal solution module is used to introduce the momentum integral enhancement neurodynamic model, input the state variables of the linear equation at the current moment into the momentum integral enhancement neurodynamic model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution in the current state, and pass it to the next moment.

[0066] The fusion module is used to update the state variables of the constructed linear equation and return them to the error module until the current iteration number exceeds a preset value or the algorithm error is lower than a preset value, thereby obtaining the information matrix of the full-resolution image and completing the fusion of the multispectral image and the panchromatic image.

[0067] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0068] (1) This invention combines multispectral images, panchromatic images and full-resolution images through estimation methods to simplify the Sylvester equation, which helps to solve it efficiently;

[0069] (2) This invention is inspired by control theory and is based on the calculation of the error of the corresponding linear equation. By constructing momentum integral enhancement terms, the momentum integral enhancement neurodynamic model exhibits strong noise tolerance.

[0070] (3) Meanwhile, the method of the present invention solves the Sylvester equation for image fusion based on the momentum integral enhanced neural dynamics model, avoiding the need to find the pseudo-inverse of the coefficient matrix and the information matrix of the full-resolution image, which can improve the computer's solution efficiency for target extraction. Attached Figure Description

[0071] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 This is a flowchart of the remote sensing image fusion method based on the momentum integral enhanced neurodynamic model in an embodiment of the present invention;

[0073] Figure 2 The image shown is a multispectral image from an embodiment of the present invention.

[0074] Figure 3 This refers to a panchromatic image in an embodiment of the present invention;

[0075] Figure 4 This is a schematic diagram illustrating the result of fusing multispectral and panchromatic images using the momentum integral enhanced gradient neurodynamics model algorithm proposed in this invention, as an embodiment of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] Example 1

[0079] like Figure 1 As shown, this invention discloses a remote sensing image fusion method based on a momentum integral-enhanced neurodynamic model, the method comprising:

[0080] S1. Based on the principle of multispectral and panchromatic image fusion, construct the spectral degradation form and spatial degradation form of full-resolution image;

[0081] S2. Based on the spectral and spatial degradation forms of the full-resolution image, it is found that the multispectral and panchromatic images have a matrix Gaussian distribution property. Using the maximum likelihood estimation method, the estimation error between the actual multispectral and panchromatic images and the model is estimated, which is transformed into an optimization problem.

[0082] S3. Transform the optimization problem in S2 into the Sylvester equation and find its derivative;

[0083] S4. Transform the optimality conditions obtained in S3 into a series of linear equations;

[0084] S5. For each linear equation, define an error function to measure the error between the current moment and the actual situation.

[0085] S6. Introduce the momentum integral enhancement neurodynamic model, input the state variables of the linear equation at the current moment into the momentum integral enhancement neurodynamic model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution in the current state, and pass it to the next moment.

[0086] S7. Update the state variables of the constructed linear equation, return to S5, until the current iteration number exceeds the preset value, or the algorithm error is lower than the preset value, obtain the information matrix of the full-resolution image, and complete the fusion of the multispectral image and the panchromatic image.

[0087] The specific implementation process includes:

[0088] S1. Based on the principle of multispectral and panchromatic image fusion, a recognized form of spectral degradation and spatial degradation of full-resolution images is constructed.

[0089] Specifically, assuming the full-resolution image is in matrix form as follows: ,in Indicates the number of bands in a remote sensing image. Represents the full-resolution image. One pixel, This represents the number of pixels in the image, where For the number of rows, Let be the column number. Based on this, the spectral degradation form and spatial degradation form of the constructed image are:

[0090] ;

[0091] in Represents multispectral images; This represents a panchromatic image. It is the spectral degradation matrix. It is a spatial degeneracy matrix. , This represents the noise in these two images.

[0092] S2. Based on S1, it can be seen that multispectral images and panchromatic images have the property of matrix Gaussian distribution. Using the maximum likelihood estimation method, the estimation error between the actual multispectral image and panchromatic image and the model estimation is estimated, which is transformed into an optimization problem.

[0093] Specifically, noise , It follows a matrix normal distribution. Since the observed data is the result of noise superimposed on the degraded signal, according to the properties of linear transformation, and It is also a matrix normal distribution. Considering the degree of matching between actual observed data and linear model predictions, by maximizing... To estimate ,in Indicates a known full-resolution image Based on this, multispectral images or panchromatic images or (use The probability distribution (generally represented). By maximizing the log-likelihood, image fusion is transformed into an optimization problem, namely:

[0094] ;

[0095] in Represents the matrix norm.

[0096] S3. To find the minimum value of the optimization problem in S2, the optimization problem in S2 is transformed into the Sylvester equation and its derivative is calculated.

[0097] Specifically, let the objective function of the optimization problem be... Since any two norms in a finite-dimensional space are necessarily equivalent, let's assume they are both F-norms. Then, for... Differentiation Then, taking the derivative with respect to each term, we get:

[0098] ;

[0099] Then, add the two gradients together and set the total gradient to zero:

[0100] ;

[0101] After simplification, we get:

[0102] ;

[0103] This is the standard form of a Sylvester equation:

[0104] ;

[0105] in , , .

[0106] S4. Since the space complexity required to directly solve the Sylvester equation is too high, the optimality condition obtained in S3 is transformed into a series of linear equations. First, it is simplified and transformed into a series of linear equations.

[0107] Specifically, for Perform eigenvalue decomposition, and we have ,in It is an orthogonal matrix, and has , Let represent the identity matrix. Therefore, substituting this into the Sylvester equation and multiplying by the matrix on the right... We can obtain:

[0108] ;

[0109] Simplify it, let and have:

[0110] ;

[0111] because It is a diagonal matrix, for By performing column decomposition, we can obtain a system of independent equations for each column, i.e.:

[0112] ;

[0113] in Indicates the first List, express The List, express The List, express The List.

[0114] S5. For each linear equation, define an error function to measure the error between the current moment and the actual situation.

[0115] Specifically .

[0116] S6. Introduce the momentum integral enhancement neurodynamic model, input the state variables of the linear equation at the current moment into the momentum integral enhancement neurodynamic model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution in the current state, and pass it to the next moment.

[0117] Specifically, based on the constructed error function, a momentum integral enhancement term is constructed:

[0118] ;

[0119] in, Indicates the extraction time. For integration variables, Indicates to The differential, This is the corresponding error function;

[0120] Based on the momentum integral enhancement term, a momentum integral enhancement neurodynamic model is established. Due to the characteristics of computers, its discrete form is expressed as:

[0121] ;

[0122] in, Indicates the first iteration Indicates the first Secondary momentum term, Indicates the first Secondary error term Indicates the first Image vectors in the next iteration , The sampling interval is... This is the momentum weight vector. This is the coefficient term.

[0123] S7. Update the state variables of the constructed linear equation, return to S5, until the current iteration number exceeds the preset value, or the algorithm error is lower than the preset value, obtain the information matrix of the full-resolution image, and complete the fusion of the multispectral image and the panchromatic image.

[0124] Specifically, including,

[0125] S701: Preset multispectral image panchromatic image Preset maximum number of iterations Preset initial filter vector Preset spectral degradation matrix Preset spatial degradation matrix ;

[0126] S702: Calculate the error at the current time. If the number of iterations is greater than the maximum number of iterations, stop the calculation and output the optimal solution; otherwise, proceed to step S703.

[0127] S703: Establish a momentum integral-enhanced neurodynamic model and calculate... To obtain the optimal solution at the current moment;

[0128] S704: Proceed to step S702;

[0129] S705: Obtains the information matrix of the full-resolution image and completes the fusion of multispectral and panchromatic images.

[0130] Specifically, for each column vector, the optimal solution calculated in step S702 is obtained. By piecing them together in order, we obtain the information matrix of the full-resolution image. Then, through calculation This allows the full-resolution image to be calculated, which means the fusion of multispectral and panchromatic images can be completed.

[0131] The image fusion method based on momentum integral enhanced gradient descent neural algorithm of the present invention will be further described below with specific embodiments.

[0132] Specifically, the method of the present invention is experimentally simulated using MATLAB and ENVI software to fuse a multispectral image and a panchromatic image.

[0133] Figure 2 This is a multispectral image from this embodiment.

[0134] Figure 3 This is the panchromatic image in this embodiment.

[0135] Figure 4 This is the result of fusing multispectral and panchromatic images using the momentum integral enhanced gradient neurodynamic model algorithm proposed in this invention.

[0136] from Figure 4 Based on the fusion results, the proposed momentum integral enhanced gradient neurodynamics model algorithm can effectively fuse panchromatic and multispectral images.

[0137] Example 2

[0138] The present invention also provides a remote sensing image fusion system based on a momentum integral enhanced neurodynamic model. The system is used to implement the method of Embodiment 1. The system includes: a construction module, a conversion module, a calculation module, an error module, an optimal solution module, and a fusion module.

[0139] The module is used to construct the spectral and spatial degradation forms of full-resolution images based on the principles of multispectral and panchromatic image fusion.

[0140] The conversion module is used to obtain multispectral and panchromatic images with matrix Gaussian distribution properties based on the spectral and spatial degradation forms of full-resolution images. Using the maximum likelihood estimation method, the error between the actual multispectral and panchromatic images and the model estimation is estimated, which is transformed into an optimization problem.

[0141] The computation module is used to transform the optimization problem in the transformation module into the Sylvester equation and then find its derivative.

[0142] The transformation module is used to transform the optimality conditions obtained in the calculation module into a series of linear equations.

[0143] The error module is used to define an error function for each linear equation, which measures the error between the current moment and the actual situation.

[0144] The optimal solution module is used to introduce the momentum integral enhancement neurodynamic model. It inputs the state variables of the linear equation at the current moment into the momentum integral enhancement neurodynamic model, constructs the momentum integral enhancement term based on the calculated error function, calculates the optimal solution in the current state, and passes it to the next moment.

[0145] The fusion module is used to update the state variables of the constructed linear equation and return to the error module until the current iteration number exceeds the preset value or the algorithm error is lower than the preset value, to obtain the information matrix of the full-resolution image and complete the fusion of the multispectral image and the panchromatic image.

[0146] Example 3

[0147] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the image fusion method described in the above embodiments.

[0148] Example 4

[0149] The present invention also provides a computer-readable storage medium storing a computer program that, when executed, implements the image fusion method described in the above embodiments.

[0150] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A remote sensing image fusion method based on a momentum integral-enhanced neurodynamic model, characterized in that, The method includes: S1. Based on the principles of multispectral and panchromatic image fusion, construct the spectral degradation form and spatial degradation form of full-resolution images, including: The default full-resolution image is in matrix form. ,in Indicates the number of bands in a remote sensing image. Represents the full-resolution image. One pixel; This represents the number of pixels in the image, where For the number of rows, For column numbers; Based on the matrix form of the full-resolution image, the spectral degradation form and spatial degradation form of the full-resolution image are constructed as follows: ； in Represents a multispectral image. Represents a panchromatic image. It is the spectral degradation matrix. It is a spatial degeneracy matrix. , These represent noise in multispectral and panchromatic images, respectively. S2. Based on the spectral and spatial degradation forms of the full-resolution image, the multispectral and panchromatic images are found to have a Gaussian matrix distribution. Using the maximum likelihood estimation method, the estimation error between the actual multispectral and panchromatic images and the model estimation is estimated, transforming it into an optimization problem, including: noise , It follows a matrix normal distribution. Since the observed data is the result of noise superimposed on the degraded signal, according to the properties of linear transformation, and It is also a matrix normal distribution; considering the degree of matching between actual observed data and linear model predictions, by maximizing To estimate ,in Indicates a known full-resolution image Based on this, multispectral images or panchromatic images or The probability distribution; by maximizing the log-likelihood, image fusion is transformed into an optimization problem, namely... ； in Represents the matrix norm; S3. Transform the optimization problem in S2 into the Sylvester equation and find its derivative, including: Let the objective function of the optimization problem be... Since any two norms in a finite-dimensional space are necessarily equivalent, let's call them the F-norm. Then, for... Differentiation Then, taking the derivative with respect to each term, we get: ； Then, add the two gradients together and set the total gradient to zero: ； After simplification, we get: ； That is, the standard form of a Sylvester equation: ； in , , ; S4. Transform the optimality conditions obtained in S3 into a series of linear equations, including: right Perform eigenvalue decomposition, and we have ,in It is an orthogonal matrix, and has , Let represent the identity matrix, then substitute it into the Sylvester equation and multiply by the matrix on the right. ,have to: ； And simplify, let and have: ； because It is a diagonal matrix, for Perform column decomposition to obtain a system of independent equations for each column, i.e.: ； in Indicates the first List, express The List, express The List, express The List; S5. For each linear equation, define an error function to measure the error between the current moment and the actual situation, including: ； S6. Introducing a momentum integral-enhanced neurodynamic model: The state variables of the current linear equation are input into the momentum integral-enhanced neurodynamic model. Based on the calculated error function, a momentum integral enhancement term is constructed, the optimal solution in the current state is calculated, and the solution is passed to the next time step. The methods for introducing the momentum integral-enhanced neurodynamic model in S6 include: Based on the constructed error function, an integral enhancement term is constructed: ； in, Indicates the extraction time. For integration variables, Indicates to The differential, This is the corresponding error function; Based on the momentum integral enhancement term, a momentum integral enhancement neurodynamic model is established, which is expressed in discrete form as follows: ； in, Indicates the first iteration Indicates the first Secondary momentum term, Indicates the first Secondary error term Indicates the first Image vectors in the next iteration , The sampling interval is... This is the momentum weight vector. For coefficient terms; S7. Update the state variables of the constructed linear equation, return to S5, until the current iteration number exceeds the preset value, or the algorithm error is lower than the preset value, obtain the information matrix of the full-resolution image, and complete the fusion of the multispectral image and the panchromatic image.

2. The method according to claim 1, characterized in that, In step S7, the state variables of the constructed linear equation are updated, and the process returns to S5 until the current iteration count exceeds a preset value or the algorithm error is lower than a preset value. This process yields the information matrix of the full-resolution image. The method for fusing multispectral and panchromatic images includes: S701: Preset multispectral image panchromatic image Preset maximum number of iterations Preset initial filter vector Preset spectral degradation matrix Preset spatial degradation matrix ; S702: Calculate the error at the current time. If the number of iterations is greater than the maximum number of iterations, stop the calculation and output the optimal solution; otherwise, proceed to step S703. S703: Establish an integral-enhanced gradient descent neural dynamics algorithm and calculate... To obtain the optimal solution at the current moment; S704: Proceed to step S702; S705: Obtains the information matrix of the full-resolution image and completes the fusion of multispectral and panchromatic images.

3. A remote sensing image fusion system based on a momentum integral-enhanced neurodynamic model, the system being used to implement the method described in any one of claims 1-2, characterized in that, The system includes: a construction module, a transformation module, a calculation module, an error module, an optimal solution module, and a fusion module; The construction module is used to construct the spectral degradation form and spatial degradation form of a full-resolution image based on the principle of multispectral and panchromatic image fusion. The conversion module is used to obtain the multispectral and panchromatic images with matrix Gaussian distribution properties based on the spectral and spatial degradation forms of the full-resolution image. It then uses the maximum likelihood estimation method to estimate the error between the actual multispectral and panchromatic images and the model estimation, thus converting it into an optimization problem. The calculation module is used to transform the optimization problem in the transformation module into the Sylvester equation and then differentiate it. The transformation module is used to transform the optimality conditions obtained in the calculation module into a series of linear equations; The error module is used to define an error function for each linear equation, which serves as a measure of the error between the current moment and the actual situation. The optimal solution module is used to introduce the momentum integral enhancement neurodynamic model, input the state variables of the linear equation at the current moment into the momentum integral enhancement neurodynamic model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution in the current state, and pass it to the next moment. The fusion module is used to update the state variables of the constructed linear equation and return them to the error module until the current iteration number exceeds a preset value or the algorithm error is lower than a preset value, thereby obtaining the information matrix of the full-resolution image and completing the fusion of the multispectral image and the panchromatic image.

Images