Remote sensing image fusion method and system based on momentum integral enhanced neurodynamics model

Abstract

The invention belongs to the field of computer vision, image processing, neurodynamics algorithms and control, and discloses a remote sensing image fusion method and system based on a momentum integral enhanced neurodynamics model, and the method comprises the steps: constructing a recognized spectrum degradation form and a space degradation form of a full-resolution image; estimating an actual multispectral image and a panchromatic image and a model estimation error by using a maximum likelihood estimation method, and converting into an optimization problem; the equation is simplified into a Silverster equation; converting into a series of linear equations; for each linear equation, an error function is defined as an error for measuring the current moment and the actual situation; establishing a gradient descent neurodynamics model enhanced by momentum integral to solve a remote sensing image fusion equation; and finally, an optimal image fusion vector is obtained according to a solved result, so that the efficiency and accuracy of image fusion are greatly improved.

Description

Technical Field

[0001] The present invention belongs to the fields of computer vision, image processing, neural dynamics algorithms and control, and specifically relates to a remote sensing image fusion method and system based on a momentum integral enhanced neural dynamics model. Background Art

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

[0003] Image fusion technology aims to effectively integrate and complement image data from different sensors capturing the same scene, or from different modes within the same sensor, through specific algorithmic models. This technology generates 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 object recognition, 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 a variety of remote sensing image fusion methods, which can be categorized into two main categories: traditional methods and deep learning methods. Traditional fusion methods can be divided into component replacement and multiresolution analysis. Component replacement involves converting a low-resolution multispectral image to a specific space (such as the luminance-chrominance-saturation space), replacing its luminance component with the details of a high-resolution panchromatic image, and then converting it back to the original space. Its advantages are computational simplicity, high efficiency, and significant infusion of spatial detail. However, its disadvantages include the tendency to cause severe spectral distortion, particularly in hyperspectral fusion. The replacement process is crude, potentially leading to distorted spectral features or unnatural spatial information. Multiresolution analysis utilizes multi-scale and multi-directional transformation tools to decompose the image into different frequency and directional subbands. Fusion rules are designed in the transform domain (such as coefficient maximization, weighted averaging, and regional energy-based fusion) to fuse the detail information. Finally, an inverse transform 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 effect of improving spatial details is limited by the number of decomposition layers and the choice of directional basis. It is sensitive to the registration error between source images and has a relatively high computational complexity.

[0005] In recent years, deep learning methods, such as convolutional neural networks, generative adversarial networks, and Transformers, have made significant progress in image fusion. These methods can automatically learn complex nonlinear mappings from massive amounts of data, possessing powerful feature extraction and representation capabilities. Their fusion results outperform traditional methods across multiple metrics, particularly in balancing spatial detail enhancement and spectral preservation. However, remote sensing data acquisition is expensive, and precisely registered, high-quality training samples from multiple sources are particularly scarce, limiting the training and application of these models. Furthermore, deep models often contain millions or even billions of parameters, requiring extensive computing resources for training and inference, making them difficult to implement on resource-constrained platforms such as satellites and drones, or for real-time or near-real-time processing scenarios. Furthermore, trained models may not be adaptable to new sensor types, imaging conditions, or ground object scenarios outside the training data distribution, necessitating retraining or fine-tuning.

[0006] Neural dynamics models are a class of dynamical systems described by differential equations, inspired by biological neural systems. They demonstrate unique advantages in optimization, associative memory, pattern recognition, and image processing. Model 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. Furthermore, the core of this model is typically a system of ordinary differential equations (ODEs), which offers a compact structure. Unlike deep learning, which requires time-consuming offline pre-training, solutions can typically be obtained with a single iterative evolution, making them particularly suitable for embedded or real-time systems with limited computing resources. Furthermore, model parameters are typically set based on physical meaning or empirical evidence, rather than relying on training with specific datasets. Summary of the Invention

[0007] In order to solve the problems existing in the prior art, the present invention provides a remote sensing image fusion method and system based on a momentum integral enhanced neural dynamics model, aiming to improve the computer's fusion efficiency and accuracy of panchromatic images and multispectral images.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] A remote sensing image fusion method based on a momentum integral enhanced neural dynamics model, the method comprising:

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

[0011] S2. Based on the spectral degradation form and spatial degradation form of the full-resolution image, the multispectral image and the panchromatic image are obtained to have the matrix Gaussian distribution property. The maximum likelihood estimation method is used to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and the error is converted into an optimization problem.

[0012] S3, transform the optimization problem in S2 into the Sylvester equation and derive it;

[0013] S4, transforming 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 enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under the current state, and pass it to the next moment;

[0016] S7. Update the state variables of the constructed linear equation and return to S5 until the current number of iterations 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 S1, based on the principle of multispectral and panchromatic image fusion, the method for constructing the spectral degradation form and spatial degradation form of the full-resolution image includes:

[0018] The matrix form of the preset full-resolution image is ,in Indicates the number of bands of remote sensing images, Represents the full-resolution image pixels; Represents the number of pixels in the image, where is the number of rows, is the number of columns;

[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 full-color image, is the spectral degradation matrix, is the spatial degradation matrix, 、 Represent the noise of multispectral image and panchromatic image respectively.

[0022] Preferably, in S2, based on the spectral degradation form and spatial degradation form of the full-resolution image, the multispectral image and the panchromatic image are obtained to have a matrix Gaussian distribution property, and the maximum likelihood estimation method is used to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and the method of converting it into an optimization problem includes:

[0023] noise 、 Is 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 match between the actual observation data and the linear model prediction, by maximizing To estimate ,in Indicates that the full-resolution image is known Based on the multispectral image or panchromatic image or The probability distribution of ; by maximizing the log-likelihood, the image fusion is transformed into an optimization problem, namely

[0024] ;

[0025] in Represents the matrix norm.

[0026] Preferably, in S3, the method of converting the optimization problem in S2 into the Sylvester equation and deriving it includes:

[0027] Assume that the objective function of the optimization problem is , since any two norms in a finite-dimensional space must be equivalent, we set it as F norm, then Derivative Then take the derivative of the two terms separately, namely:

[0028] ;

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

[0030] ;

[0031] After simplification, we get:

[0032] ;

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

[0034] ;

[0035] in , , .

[0036] Preferably, in S4, the method of converting the optimality condition obtained in S3 into a series of linear equations includes:

[0037] right Perform feature decomposition, and we have ,in is an orthogonal matrix, , represents the identity matrix, so substitute it into the Sylvester equation and multiply it by the matrix on the right ,have to:

[0038] ;

[0039] And simplify, let and have:

[0040] ;

[0041] because is a diagonal matrix, Perform column decomposition to obtain independent equations for each column, namely:

[0042] ;

[0043] in Indicates the List, express No. List, express No. List, express No. List.

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

[0045] .

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

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

[0048] ;

[0049] in, Indicates the extraction time. is the integration variable, Express The differential of is the corresponding error function;

[0050] Based on the momentum integral enhancement term, a momentum integral enhanced neural dynamics model is established, and its discrete form is expressed as:

[0051] ;

[0052] in, Indicates the iterations, Indicates the The secondary momentum term, Indicates the The secondary error term, Indicates the The image vector in the iteration, , is the sampling interval, is the momentum weight vector, is the coefficient term.

[0053] Preferably, in S7, each state variable of the constructed linear equation is updated, and the process returns to S5 until the current number of iterations exceeds a preset value or the algorithm error is lower than a preset value, and the information matrix of the full-resolution image is obtained, and the method for completing the fusion of the multispectral image and the panchromatic image includes:

[0054] S701: Preset multispectral image , full-color 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 moment If the number of iterations is greater than the maximum number of iterations, the calculation is stopped and the optimal solution is output; otherwise, the process goes to step S703;

[0056] S703: Establish an integral enhanced gradient descent neural dynamics algorithm to calculate , get the optimal solution at the current moment;

[0057] S704: Go to step S702;

[0058] S705: Obtain the information matrix of the full-resolution image and complete the fusion of the multispectral image and the panchromatic image.

[0059] The present invention also provides a remote sensing image fusion system based on a momentum integral enhanced neural dynamics model, the system is used to implement the above method, the system includes: a construction module, a conversion module, a calculation module, a transformation module, an error module, an optimal solution module and a fusion module;

[0060] The construction module is used to construct the spectrally degraded form and the spatially degraded form of the full-resolution image based on the multispectral and panchromatic image fusion principle;

[0061] The conversion module is used to obtain the matrix Gaussian distribution properties of the multispectral image and the panchromatic image based on the spectral degradation form and the spatial degradation form of the full-resolution image, and use the maximum likelihood estimation method to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and convert it into an optimization problem;

[0062] The calculation module is used to convert the optimization problem in the conversion module into a Sylvester equation and to obtain its derivative;

[0063] The conversion module is used to convert 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 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 enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under 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 to the error module until the current number of iterations 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 present invention has the following beneficial effects:

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

[0069] (2) This invention is inspired by control theory and is based on calculating the error of the corresponding linear equation Reasonable construction of momentum integral enhancement term makes the momentum integral enhanced neural dynamics model have strong noise tolerance;

[0070] (3) At the same time, the method of the present invention solves the Sylvester equation for image fusion based on the momentum integral enhanced neural dynamics model, avoiding the pseudo-inverse of the coefficient matrix and the information matrix of the full-resolution image, and can improve the computer's solution efficiency for target extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0072] Figure 1 Flowchart of a remote sensing image fusion method based on a momentum integral enhanced neural dynamics model in an embodiment of the present invention;

[0073] Figure 2 is a multispectral image in an embodiment of the present invention;

[0074] Figure 3 is a full-color image in an embodiment of the present invention;

[0075] Figure 4 This is a schematic diagram of the result of fusing a multispectral image and a panchromatic image using the momentum integral enhanced gradient neural dynamics model algorithm proposed in the present invention. DETAILED DESCRIPTION

[0076] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0077] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0078] Example 1

[0079] like Figure 1 As shown, an embodiment of the present invention discloses a remote sensing image fusion method based on a momentum integral enhanced neural dynamics model, the method comprising:

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

[0081] S2. Based on the spectral degradation form and spatial degradation form of the full-resolution image, the multispectral image and the panchromatic image are obtained to have the matrix Gaussian distribution property. The maximum likelihood estimation method is used to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and the error is converted into an optimization problem.

[0082] S3, transform the optimization problem in S2 into the Sylvester equation and derive it;

[0083] S4, transforming 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 enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under the current state, and pass it to the next moment;

[0086] S7. Update the state variables of the constructed linear equation and return to S5 until the current number of iterations 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, the recognized spectral degradation form and spatial degradation form of full-resolution image are constructed;

[0089] Specifically, assuming that the matrix form of the full-resolution image is ,in Indicates the number of bands of remote sensing images, Represents the full-resolution image pixels, Represents the number of pixels in the image, where is the number of rows, is the number of columns. Based on this, the spectral degradation form and spatial degradation form of the constructed image are:

[0090] ;

[0091] in Represents a multispectral image; Represents a full-color image. is the spectral degradation matrix, is the spatial degradation matrix, 、 represents the noise of these two images.

[0092] S2. Based on S1, we know that the multispectral image and the panchromatic image have the matrix Gaussian distribution property. We use the maximum likelihood estimation method to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and convert it into an optimization problem.

[0093] Specifically, noise 、 Is 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 match between the actual observation data and the linear model prediction, by maximizing To estimate ,in Indicates that the full-resolution image is known Based on the multispectral image or panchromatic image or (use By maximizing the log-likelihood, image fusion is transformed into an optimization problem, namely:

[0094] ;

[0095] in Represents the matrix norm.

[0096] S3, to obtain the minimum value of the optimization problem in S2, the optimization problem in S2 is transformed into the Sylvester equation and differentiated;

[0097] Specifically, let the objective function of the optimization problem be , since any two norms in a finite-dimensional space must be equivalent, let us assume that they are both F norms. Then, Derivative Then take the derivative of the two terms separately, namely:

[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 the 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 converted into a series of linear equations. First, it is simplified and converted into a series of linear equations.

[0107] Specifically, Perform feature decomposition, and we have ,in is an orthogonal matrix, , represents the identity matrix. So substitute it into the Sylvester equation and multiply it by the matrix on the right , we can get:

[0108] ;

[0109] Simplify it, let and have:

[0110] ;

[0111] because is a diagonal matrix, By decomposing the columns, we can get an independent set of equations for each column, namely:

[0112] ;

[0113] in Indicates the List, express No. List, express No. List, express No. 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 enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under the current state, and pass it to the next moment;

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

[0118] ;

[0119] in, Indicates the extraction time. is the integration variable, Express The differential of is the corresponding error function;

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

[0121] ;

[0122] in, Indicates the iterations, Indicates the The secondary momentum term, Indicates the The secondary error term, Indicates the The image vector in the iteration, , is the sampling interval, is the momentum weight vector, is the coefficient term.

[0123] S7. Update the state variables of the constructed linear equation and return to S5 until the current number of iterations 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 ; Full color 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 moment If the number of iterations is greater than the maximum number of iterations, the calculation is stopped and the optimal solution is output; otherwise, the process goes to step S703;

[0127] S703: Establish momentum integral enhanced neural dynamics model, calculate , get the optimal solution at the current moment;

[0128] S704: Go to step S702;

[0129] S705: Obtain the information matrix of the full-resolution image and complete the fusion of the multispectral image and the panchromatic image.

[0130] Specifically, for each column vector, the optimal solution calculated in step S702 is obtained. , put them together in order to obtain the information matrix of the full-resolution image Then, by calculating , the full-resolution image can be calculated, that is, the fusion of multispectral image and panchromatic image is completed.

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

[0132] Specifically, the method of the present invention is experimentally simulated by taking the fusion of a multispectral image and a panchromatic image as an example using MATLAB software and ENVI software.

[0133] Figure 2 is the multispectral image in this embodiment.

[0134] Figure 3 This is a full-color image in this embodiment.

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

[0136] from Figure 4 Judging from the fusion results, the proposed momentum integral enhanced gradient neural dynamics model algorithm can better fuse panchromatic images and multispectral images.

[0137] Example 2

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

[0139] A construction module for constructing spectrally degraded and spatially degraded forms of full-resolution images based on the principle of multispectral and panchromatic image fusion;

[0140] A conversion module is used to obtain the matrix Gaussian distribution properties of the multispectral image and the panchromatic image based on the spectral degradation form and spatial degradation form of the full-resolution image, and to estimate the error between the actual multispectral image and the panchromatic image and the model estimation using the maximum likelihood estimation method, and convert it into an optimization problem;

[0141] A calculation module, used to convert the optimization problem in the conversion module into a Sylvester equation and to obtain its derivative;

[0142] A conversion module, used to convert 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 is used to measure the error between the current moment and the actual situation;

[0144] The optimal solution module is used to introduce the momentum integral enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under the current state, and pass 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 number of iterations exceeds the preset value or the algorithm error is lower than the preset value, thereby obtaining the information matrix of the full-resolution image and completing the fusion of the multispectral image and the panchromatic image.

[0146] Example 3

[0147] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the image fusion method in the above embodiment when executing the program.

[0148] Example 4

[0149] The present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program. When the computer program is executed, the image fusion method in the above embodiment is implemented.

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

Claims

1. A remote sensing image fusion method based on momentum integral enhanced neural dynamics model, characterized by: The method comprises: S1. Based on the principle of multispectral and panchromatic image fusion, the spectral degradation form and spatial degradation form of the full-resolution image are constructed; S2. Based on the spectral degradation form and spatial degradation form of the full-resolution image, the multispectral image and the panchromatic image are obtained to have the matrix Gaussian distribution property. The maximum likelihood estimation method is used to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and the error is converted into an optimization problem. S3, transform the optimization problem in S2 into the Sylvester equation and derive it; S4, transforming the optimality conditions obtained in S3 into a series of linear equations; S5. For each linear equation, define an error function to measure the error between the current moment and the actual situation; S6. Introduce the momentum integral enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under the current state, and pass it to the next moment; S7. Update the state variables of the constructed linear equation and return to S5 until the current number of iterations 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 S1, based on the principle of multispectral and panchromatic image fusion, the method for constructing the spectral degradation form and spatial degradation form of the full-resolution image includes: The matrix form of the preset full-resolution image is ,in Indicates the number of bands of remote sensing images, Represents the full-resolution image pixels; Represents the number of pixels in the image, where is the number of rows, is the number of columns; 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 full-color image, is the spectral degradation matrix, is the spatial degradation matrix, 、 Represent the noise of multispectral image and panchromatic image respectively.

3. The method according to claim 2, characterized in that In S2, based on the spectral degradation form and spatial degradation form of the full-resolution image, the multispectral image and the panchromatic image are obtained to have a matrix Gaussian distribution property, and the maximum likelihood estimation method is used to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and the method of converting it into an optimization problem includes: noise 、 Is 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 match between the actual observation data and the linear model prediction, by maximizing To estimate ,in Indicates that the full-resolution image is known Based on the multispectral image or panchromatic image or The probability distribution of ; by maximizing the log-likelihood, the image fusion is transformed into an optimization problem, namely ； in Represents the matrix norm.

4. The method according to claim 3, characterized in that In S3, the method of converting the optimization problem in S2 into the Sylvester equation and deriving it includes: Assume that the objective function of the optimization problem is , since any two norms in a finite-dimensional space must be equivalent, we set it as F norm, then Derivative Then take the derivative of the two terms separately, namely: ； Then add the two gradients together and set the total gradient to zero: ； After simplification, we get: ； This is the standard form of a Sylvester equation: ； in , , .

5. The method according to claim 4, characterized in that In S4, the method of converting the optimality condition obtained in S3 into a series of linear equations includes: right Perform feature decomposition, and we have ,in is an orthogonal matrix, , represents the identity matrix, so substitute it into the Sylvester equation and multiply it by the matrix on the right ,have to: ； And simplify, let and have: ； because is a diagonal matrix, Perform column decomposition to obtain independent equations for each column, namely: ； in Indicates the List, express No. List, express No. List, express No. List.

6. The method according to claim 5, characterized in that In S5, for each linear equation, an error function is defined as a method for measuring the error between the current moment and the actual situation, including: 。 7. The method according to claim 6, characterized in that In S6, the method of introducing momentum integral to enhance the neural dynamics model includes: Based on the constructed error function, construct the integral enhancement term: ； in, Indicates the extraction time. is the integration variable, Express The differential of is the corresponding error function; Based on the momentum integral enhancement term, a momentum integral enhanced neural dynamics model is established, and its discrete form is expressed as: ； in, Indicates the iterations, Indicates the The secondary momentum term, Indicates the The secondary error term, Indicates the The image vector in the iteration, , is the sampling interval, is the momentum weight vector, is the coefficient term.

8. The method according to claim 7, characterized in that In S7, each state variable of the constructed linear equation is updated, and the process returns to S5 until the current number of iterations exceeds a preset value or the algorithm error is lower than a preset value, thereby obtaining an information matrix of a full-resolution image and completing the fusion of a multispectral image and a panchromatic image. The method includes: S701: Preset multispectral image , full-color 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 moment If the number of iterations is greater than the maximum number of iterations, the calculation is stopped and the optimal solution is output; otherwise, the process goes to step S703; S703: Establish an integral enhanced gradient descent neural dynamics algorithm to calculate , get the optimal solution at the current moment; S704: Go to step S702; S705: Obtain the information matrix of the full-resolution image and complete the fusion of the multispectral image and the panchromatic image.

9. A remote sensing image fusion system based on a momentum integral enhanced neural dynamics model, the system being used to implement the method according to any one of claims 1 to 8, characterized in that: The system includes: a construction module, a conversion module, a calculation module, a transformation module, an error module, an optimal solution module and a fusion module; The construction module is used to construct the spectrally degraded form and the spatially degraded form of the full-resolution image based on the multispectral and panchromatic image fusion principle; The conversion module is used to obtain the matrix Gaussian distribution properties of the multispectral image and the panchromatic image based on the spectral degradation form and the spatial degradation form of the full-resolution image, and use the maximum likelihood estimation method to estimate the error between the actual multispectral image and the panchromatic image and the model estimation, and convert it into an optimization problem; The calculation module is used to convert the optimization problem in the conversion module into a Sylvester equation and to obtain its derivative; The conversion module is used to convert 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 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 enhanced neural dynamics model, input the state variables of the linear equation at the current moment into the momentum integral enhanced neural dynamics model, construct the momentum integral enhancement term based on the calculated error function, calculate the optimal solution under 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 to the error module until the current number of iterations 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.

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