A remote sensing image fusion method based on adaptive tensor decomposition

Abstract

This invention belongs to the field of remote sensing image fusion technology, specifically involving a remote sensing image fusion method based on adaptive tensor decomposition. It aims to solve the problems of difficult rank determination, low computational efficiency, and insufficient utilization of prior information in traditional tensor decomposition fusion methods. The method first acquires low spatial resolution hyperspectral and high spatial resolution multispectral images and constructs a nonlocal similarity cube tensor. A spatial-spectral observation model is built based on probability distribution, and the scale transformation is advanced to the input stage to reduce computational costs. An adaptive tensor decomposition model is constructed by combining t-tensor product and mixture norm constraints. A hyper-Laplace prior is introduced to form a complete fusion model. The solution is optimized through a proximal alternating minimization framework, dynamically preserving non-zero slices of the coefficient tensor to adaptively approximate the true rank. Finally, a high spatial resolution hyperspectral fused image is reconstructed. This invention achieves adaptive estimation of the tensor rank, improving fusion accuracy while significantly reducing computational overhead. It also jointly utilizes nonlocal and global prior information to effectively alleviate spectral distortion and spatial detail loss problems, and can be widely applied in environmental monitoring, resource exploration, and other fields.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing image fusion technology, specifically relating to a remote sensing image fusion method based on adaptive tensor decomposition. Background Technology

[0002] Remote sensing image fusion technology is a key means to integrate the advantages of multi-source remote sensing data and overcome the limitations of single sensor resolution. By fusing the fine spectral information of low spatial resolution hyperspectral images with the clear spatial details of high spatial resolution multispectral images, a fused image with both high spatial and high spectral resolution is generated. This can provide refined ground feature information support for fields such as environmental monitoring, resource exploration, and national defense security, and has important practical significance for the practical application and development of remote sensing technology.

[0003] In existing technologies, tensor decomposition-based methods have become one of the mainstream techniques for remote sensing image fusion. These methods construct remote sensing images into tensor form and mine low-dimensional structural features of the data through tensor decomposition to achieve fusion. Some methods combine strategies such as nonlocal similarity and various prior constraints to optimize the fusion effect. In the iterative optimization process, spatial or spectral scale transformation operations are repeatedly performed at the fused image level, and the rank or subspace dimension of the tensor decomposition needs to be manually preset. At the same time, block-based representation models are often used to characterize the spatial-spectral structure of the image.

[0004] However, current remote sensing image fusion methods based on tensor decomposition still have many technical shortcomings: the manually preset decomposition rank is difficult to accurately match the real low-dimensional structure of complex and heterogeneous remote sensing data, which can easily lead to insufficient utilization of prior information or model overfitting, reducing fusion accuracy; the repeated scale transformation operations in the iteration lack a redundancy removal mechanism, which greatly increases the computational cost and leads to low fusion efficiency; and there are shortcomings in characterizing the spatial-spectral structure of the image, making it difficult to simultaneously and effectively capture non-local similarity and global spatial-spectral correlation features, which can easily lead to problems such as spectral distortion, loss of spatial details, and distortion of ground feature structure in the fusion results. There is an urgent need to propose better fusion methods to solve these problems. Summary of the Invention

[0005] To address the problems existing in the background art, one aspect of the present invention provides a remote sensing image fusion method based on adaptive tensor decomposition, comprising:

[0006] S1: Acquire low spatial resolution hyperspectral images and high spatial resolution multispectral images, and represent them as three-dimensional tensors;

[0007] S2: Construct a nonlocal similarity cube tensor expression for the target high spatial resolution hyperspectral image based on the spatial consistency between the high spatial resolution multispectral image and the target high spatial resolution hyperspectral image;

[0008] S3: Based on the probability distribution model, construct a spatial observation model from a high spatial resolution multispectral image to a target high spatial resolution hyperspectral image, and a spectral observation model from a low spatial resolution hyperspectral image to a target high spatial resolution hyperspectral image using the maximum a posteriori probability criterion;

[0009] S4: The nonlocal similarity cube tensor expression of the target high spatial resolution hyperspectral image is transformed into a circular convolution form of subspace tensor and coefficient tensor using t-tensor product, and an adaptive tensor decomposition model is constructed by combining the mixture norm constraint.

[0010] S5: Based on the spatial observation model from high spatial resolution multispectral image to target high spatial resolution hyperspectral image, the spectral observation model from low spatial resolution hyperspectral image to target high spatial resolution hyperspectral image, and the adaptive tensor decomposition model, a remote sensing image fusion model is constructed using hyper-Laplace prior constraints.

[0011] S6: The remote sensing image fusion model is optimized by using proximal alternating minimization to estimate the optimal subspace tensor and coefficient tensor;

[0012] S7: Obtain the target high spatial resolution hyperspectral image based on the optimal subspace tensor and coefficient tensor.

[0013] Another aspect of the present invention provides a remote sensing image fusion system based on adaptive tensor decomposition, the system comprising a memory and a processor; the memory is used to store an application program; the processor is used to run the application program and execute the aforementioned remote sensing image fusion method based on adaptive tensor decomposition.

[0014] Another aspect of the present invention provides a computer storage medium storing a computer program, which, when executed by a processor, implements the aforementioned remote sensing image fusion method based on adaptive tensor decomposition.

[0015] The present invention has at least the following beneficial effects

[0016] This invention achieves adaptive estimation of tensor rank by combining hybrid norm constraints and dynamic preservation of non-zero coefficient tensor slices, accurately matching the true low-dimensional structure of remote sensing data, fully mining data information, and improving fusion accuracy. It advances scale transformation to the input stage and, combined with a dynamic reduction strategy for coefficient tensor dimensions, significantly reduces redundant computation, thereby lowering computational overhead and improving fusion efficiency. Furthermore, it utilizes nonlocal similarity and global hyperLaplace prior information to improve the spatial-spectral structure characterization, effectively mitigating spectral distortion and spatial detail loss in the fused image. The resulting high spatial resolution hyperspectral fused image can provide more accurate ground feature information support for environmental monitoring, resource exploration, and other fields, demonstrating significant practical application value. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0018] 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.

[0019] Please see Figure 1 One aspect of the present invention provides a remote sensing image fusion method based on adaptive tensor decomposition, comprising:

[0020] S1: Acquire low spatial resolution hyperspectral images and high spatial resolution multispectral images, and represent them as three-dimensional tensors;

[0021] In this embodiment, low spatial resolution hyperspectral images (LR-HSI) and high spatial resolution multispectral images (HR-MSI) of the same observation area and time period are first acquired from a professional remote sensing data platform to ensure accurate geospatial registration of the two types of images without significant positional shifts or distortions. Subsequently, the acquired low spatial resolution hyperspectral images are represented as three-dimensional tensors. ,in, and The width and height of this hyperspectral image, It determines the number of its spectral bands; simultaneously, it represents the high spatial resolution multispectral image as a three-dimensional tensor. ,in, and The width and height of this multispectral image, The number of its spectral bands, and satisfying , , ; It scales the spatial resolution and converts the two types of original remote sensing images into tensor form, providing standardized input data for subsequent fusion processing.

[0022] S2: Construct a nonlocal similarity cube tensor expression for the target high spatial resolution hyperspectral image based on the spatial consistency between the high spatial resolution multispectral image and the target high spatial resolution hyperspectral image;

[0023] Preferably, the nonlocal similarity cube tensor expression for constructing the target high spatial resolution hyperspectral image includes:

[0024] S21: High spatial resolution multispectral images The image is divided into multiple overlapping cubic blocks of the same size; wherein, adjacent cubic blocks overlap by a fixed voxel; wherein, Indicates the number of bands in a high spatial resolution multispectral image; Indicates the number of bands in a low spatial resolution hyperspectral image; and These represent the width and height of a high spatial resolution multispectral image, respectively.

[0025] S22: High spatial resolution multispectral images The divided cubic image patches are clustered into K clusters using K-means;

[0026] S23: Assume that a high spatial resolution hyperspectral image of the target exists. The target high spatial resolution hyperspectral image is divided into multiple overlapping cubic image blocks in the same way as the high spatial resolution multispectral image;

[0027] S24: Based on the spatial correspondence between the cubic image blocks of the target high spatial resolution hyperspectral image and the high spatial resolution multispectral image, divide the cubic image blocks of the target high spatial resolution hyperspectral image into the corresponding clusters;

[0028] S25: Expand all cube image patches of the target high spatial resolution hyperspectral image in each cluster into two-dimensional matrices along the band dimension, and superimpose the expanded two-dimensional matrices to obtain the nonlocal similarity cube tensor of the target high spatial resolution hyperspectral image. ;in, Indicates the first The nonlocal similarity cube tensor of the target high spatial resolution hyperspectral image corresponding to each cluster; Indicates the width of the cube image block; Indicates the height of the cube image block; Indicates the first The number of cubic image blocks of the high spatial resolution hyperspectral image of the target in each cluster.

[0029] In this embodiment, the high spatial resolution multispectral tensor is first... Divided into sizes 1. K-means clustering is used to group all cubic image patches with 4 adjacent overlapping voxels into 10 clusters; 2. Assuming the target has a high spatial resolution hyperspectral tensor. If it exists, divide it into cubic image blocks according to the same segmentation and overlap rules, and then, based on the correspondence of empty space positions, The image patches are categorized into Within the corresponding clusters after clustering; then within each cluster All cube image patches are unfolded into two-dimensional matrices along the spectral band dimension. The unfolded matrices within the same cluster are then superimposed along the sample dimension to obtain the first... The nonlocally similar cube tensor corresponding to each cluster This is used to construct the nonlocal similarity cube tensor of the target high spatial resolution hyperspectral image.

[0030] S3: Based on the probability distribution model, construct a spatial observation model from a high spatial resolution multispectral image to a target high spatial resolution hyperspectral image, and a spectral observation model from a low spatial resolution hyperspectral image to a target high spatial resolution hyperspectral image using the maximum a posteriori probability criterion;

[0031] Preferably, the spatial observation model for transforming the high spatial resolution multispectral image into a target high spatial resolution hyperspectral image includes:

[0032]

[0033] in, A spatial observation model representing the transformation from a high spatial resolution multispectral image to a target high spatial resolution hyperspectral image; Represents high spatial resolution multispectral images; Represents a high spatial resolution hyperspectral image of the target; Residual tensors representing high spatial resolution hyperspectral images and high spatial resolution multispectral images of the target; Let F be the square of the F-norm; Represents the regularization parameter; Represents the spectrum upsampling function; Represents the spatial gradient operator; Represents the constraints observed in the probability distribution model; Representing the residual tensor The spatial gradient features follow a probability distribution type.

[0034] In this embodiment, a spatial spectrum observation model is constructed based on a Gaussian probability distribution model and using the maximum a posteriori probability criterion, targeting high spatial resolution multispectral tensors. Through spectral upsampling function After completing the spectral dimension expansion, a spatial observation model containing F-norm terms and spatial gradient constraint terms is constructed. ; where, regularization parameter residual tensor The spatial gradient characteristics follow a Gaussian distribution;

[0035] Preferably, the spectral observation model for transforming the low spatial resolution hyperspectral image into a target high spatial resolution hyperspectral image includes:

[0036]

[0037] in, Representing low spatial resolution hyperspectral images High spatial resolution hyperspectral image of the target Spectral observation model; Indicates the spatial sampling function; Let F be the square of the F-norm; This represents the residual tensor between the upsampled low spatial resolution hyperspectral image and the target high spatial resolution hyperspectral image; Represents the spectral gradient operator; Represents the regularization parameter; Represents the constraints observed in the probability distribution model; Representing the residual tensor The probability distribution type that the spectral gradient characteristics follow; and This represents the width and height of a low spatial resolution hyperspectral image.

[0038] In this embodiment, the low spatial resolution hyperspectral tensor is targeted. Through spatial upsampling function After scaling up the spatial dimensions, a spectral observation model containing F-norm terms and spectral gradient constraint terms is constructed. Regularization parameters residual tensor The spectral gradient features follow a Gaussian distribution. At the same time, the spectral scale transformation of the spatial observation model and the spatial scale transformation of the spectral observation model are both completed on the original image at the input stage, rather than being performed during the iterative process of image fusion.

[0039] By advancing the scaling transformation to the input stage, the large amount of redundant computation caused by repeatedly performing scaling transformation during iterations in traditional methods is completely avoided, significantly reducing the computational cost of the fusion process and improving the overall computational efficiency. The observation model constructed based on probability distribution and maximum a posteriori probability criterion has clear statistical significance and can flexibly and accurately characterize the differences and correlations in the spatial-spectral features of multi-source remote sensing images, adapting to the modal features of different fusion tasks. At the same time, the feature constraints on the residual tensor are strengthened through gradient constraint terms, improving the fitting accuracy of the observation model and laying a precise foundation for the construction of subsequent fusion models.

[0040] S4: The nonlocal similarity cube tensor expression of the target high spatial resolution hyperspectral image is transformed into a circular convolution form of subspace tensor and coefficient tensor using t-tensor product, and an adaptive tensor decomposition model is constructed by combining the mixture norm constraint.

[0041] Preferably, the adaptive tensor decomposition model includes:

[0042]

[0043]

[0044]

[0045] in, This represents an adaptive tensor decomposition model; This indicates finding the minimum value; The first high spatial resolution hyperspectral image of the target A nonlocally similar cube tensor; express The corresponding subspace tensor; express The corresponding coefficient tensor, Indicates intermediate parameters; Represents the circular convolution operator; Representation subspace tensor of Mixture norm; Represents the coefficient tensor Mixture norm; Denotes the Euclidean norm; Representation subspace tensor Along the second dimension One slice; Represents coefficient tensor Along the first dimension One slice; This represents the first dimension; This indicates the second dimension.

[0046] In this embodiment, the t-tensor product is used to transform the nonlocal similarity cube tensor of the high spatial resolution hyperspectral image of each cluster of targets. Convert to subspace tensor With coefficient tensor The circular convolution form, let ,in, Pick 1 / 3 and rounded down; simultaneously set the mixed norm order. ; combination Hybrid norm for constructing adaptive tensor decomposition models Through the Slice along the second dimension The Euclidean norm is calculated and summed along slices of the first dimension to constrain the sparsity of the two tensors. To optimize the objective, an adaptive tensor decomposition model was constructed. Cyclic convolution decomposition of tensors was achieved through t-tensor product, which better reflects the spatial spectral tensor structure characteristics of remote sensing images and can accurately extract low-dimensional subspace information from the data. The adaptive decomposition model, combined with mixture norm constraints, can impose sparsity constraints on the decomposed subspace tensors and coefficient tensors, laying the core model foundation for dynamically retaining non-zero slices and achieving adaptive estimation of tensor rank in subsequent iterations. This also avoids the adaptation problem caused by manually pre-setting the rank, making the model more closely resemble the true low-dimensional structure of remote sensing data.

[0047] S5: Based on the spatial observation model from high spatial resolution multispectral image to target high spatial resolution hyperspectral image, the spectral observation model from low spatial resolution hyperspectral image to target high spatial resolution hyperspectral image, and the adaptive tensor decomposition model, a remote sensing image fusion model is constructed using hyper-Laplace prior constraints.

[0048] Preferably, the remote sensing image fusion model includes:

[0049]

[0050]

[0051] in, and This represents a regularization parameter greater than 0; This represents the hyperLaplace prior constraint term; Indicates the distribution order parameter; , This represents the extraction of the k-th nonlocal similar cube tensor from a hyperspectral image with elevation spatial resolution. The operation symbols, Indicates transpose; Indicates the inverse operation; Indicates constraint terms; Represents the norm.

[0052] The space observation model constructed in this embodiment With spectral observation model Adaptive Tensor Decomposition Model To achieve fusion, a hyper-Laplace prior constraint term is introduced. Construct a complete remote sensing image fusion model and set regularization parameters. , ; Hyper-Laplace distribution order parameter ,by , , , , To optimize variables, a remote sensing image fusion model was constructed. This model integrates the advantages of a spatial-spectral observation model and an adaptive tensor decomposition model, while also introducing hyper-Laplace prior constraints. This enables the joint utilization of nonlocal similarity and global spatial-spectral structure prior information, thus improving the characterization of the spatial-spectral features of remote sensing images. Through multi-model fusion and multi-constraint superposition, the constructed fusion model not only closely matches the spatial-spectral data characteristics of multi-source remote sensing images but also effectively constrains the optimization process, preventing model overfitting. This lays a solid model foundation for subsequent accurate solution of the optimal tensor and generation of high-quality fused images.

[0053] S6: The remote sensing image fusion model is optimized by using proximal alternating minimization to estimate the optimal subspace tensor and coefficient tensor;

[0054] Preferably, the optimization solution of the remote sensing image fusion model using proximal alternation minimization includes:

[0055] S61: Initialize the maximum number of iterations T and the convergence threshold Proximal weight parameters and subspace tensor dimension ; Indicates rounding down;

[0056] S62: Obtain a high spatial resolution hyperspectral image of the target. Initialized as an upsampled low spatial resolution hyperspectral image Based on the target's high spatial resolution hyperspectral image Initialize the nonlocal similarity cube tensor of the high spatial resolution hyperspectral image of the target using step S2. ;

[0057] S63: Tensors for nonlocally similar cubes The third dimension Perform a Fast Fourier Transform to obtain a tensor ; for tensors Perform singular value decomposition on each front slice and take the first n... The maximum singular value yields the truncated value. , and ;make , ; Indicates conjugate transpose; for and Performing the third-dimensional inverse Fourier transform yields the subspace tensor. and coefficient tensor ;

[0058] S64: The remote sensing image fusion model is iteratively solved using proximal alternating minimization. The solution process is as follows:

[0059]

[0060] in, Indicates the number of iterations; This represents a remote sensing image fusion model; Indicates the weight.

[0061] In this embodiment, the maximum number of iterations is first initialized to 80, and the convergence threshold is set. Proximal weight parameters Subspace tensor dimension ; target hyperspectral tensor Initialized to The upsampled low spatial resolution hyperspectral image is then used to calculate the result in step S2. ,right Perform a Fast Fourier Transform on the third dimension, and then perform singular value decomposition on the frontal slices of the transformed tensor (corresponding to the two-dimensional slices along the third dimension, yielding each slice). , and Perform singular value decomposition and take the first-to-last value. The largest singular value is used to obtain the truncated value. , and After assigning values, perform an inverse Fourier transform to obtain the initial subspace tensor. and coefficient tensor Subsequently, an iterative solution using a proximal alternating minimization framework was adopted, sequentially solving for... , , , and Perform alternating optimization and updates, retaining only Update the dimensions by slicing non-zero levels until the maximum number of iterations is reached or the convergence threshold is met, to obtain the optimal subspace tensor. and coefficient tensor During the optimization process, when the coefficient tensor When constrained by the mixing norm, some of the level slices rapidly become zero in each optimization iteration. Therefore, a method of retaining only non-zero level slices is adopted for the coefficient tensor. Update the coefficient tensor. As the number of iterations increases, the coefficient tensor... Dimensions This dynamically reduces the rank of the target image and allows for rapid adaptive approximation. In this process, the remote sensing image fusion method based on adaptive tensor decomposition can adaptively find dimensions close to the rank. This enables more effective mining and utilization of prior knowledge in target images, improving the performance of the fusion model. Its computational cost also increases with dimensionality. The reduction in the amount of [something] decreases the efficiency of fusion.

[0062] The proximal alternating minimization framework is adopted to achieve stepwise optimization of multiple variables, which reduces the overall solution complexity and makes the optimization of the fusion model easier to converge. By dynamically retaining non-zero slices of coefficient tensors to achieve adaptive dimensionality reduction, it not only accurately approximates the true rank of remote sensing image tensors and solves the adaptation problem of manually preset ranks, but also continuously reduces the amount of iterative computation, greatly improves the efficiency of fusion solution, and ensures the accuracy of optimization results.

[0063] S7: Obtain the target high spatial resolution hyperspectral image based on the optimal subspace tensor and coefficient tensor.

[0064] Preferably, obtaining the target high spatial resolution hyperspectral image based on the optimal subspace tensor and coefficient tensor includes:

[0065]

[0066] in, This represents a high spatial resolution hyperspectral image of the target.

[0067] Another aspect of the present invention provides a remote sensing image fusion system based on adaptive tensor decomposition, the system comprising a memory and a processor; the memory is used to store an application program; the processor is used to run the application program and execute the aforementioned remote sensing image fusion method based on adaptive tensor decomposition.

[0068] Another aspect of the present invention provides a computer storage medium storing a computer program, which, when executed by a processor, implements the aforementioned remote sensing image fusion method based on adaptive tensor decomposition.

[0069] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0070] In summary, this invention achieves adaptive estimation of tensor rank through hybrid norm constraints and dynamic preservation of non-zero coefficient tensor slices, accurately matching the true low-dimensional structure of remote sensing data, fully mining data information, and improving fusion accuracy. By advancing the scale transformation to the input stage and combining it with a dynamic reduction strategy for coefficient tensor dimensions, redundant computation is significantly reduced, computational overhead is significantly lowered, and fusion efficiency is improved. Furthermore, by jointly utilizing nonlocal similarity and global hyperLaplace prior information, the spatial-spectral structure characterization is improved, effectively alleviating problems such as spectral distortion and loss of spatial details in the fused image. The generated high spatial resolution hyperspectral fused image can provide more accurate ground feature information support for fields such as environmental monitoring and resource exploration, and has good practical application value.

[0071] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A remote sensing image fusion method based on adaptive tensor decomposition, characterized in that, include: S1: Acquire low spatial resolution hyperspectral images and high spatial resolution multispectral images, and represent them as three-dimensional tensors; S2: Construct a nonlocal similarity cube tensor expression for the target high spatial resolution hyperspectral image based on the spatial consistency between the high spatial resolution multispectral image and the target high spatial resolution hyperspectral image; S3: Based on the probability distribution model, construct a spatial observation model from a high spatial resolution multispectral image to a target high spatial resolution hyperspectral image, and a spectral observation model from a low spatial resolution hyperspectral image to a target high spatial resolution hyperspectral image using the maximum a posteriori probability criterion; S4: The nonlocal similarity cube tensor expression of the target high spatial resolution hyperspectral image is transformed into a circular convolution form of subspace tensor and coefficient tensor using t-tensor product, and an adaptive tensor decomposition model is constructed by combining the mixture norm constraint. S5: Based on the spatial observation model from high spatial resolution multispectral image to target high spatial resolution hyperspectral image, the spectral observation model from low spatial resolution hyperspectral image to target high spatial resolution hyperspectral image, and the adaptive tensor decomposition model, a remote sensing image fusion model is constructed using hyper-Laplace prior constraints. S6: The remote sensing image fusion model is optimized by using proximal alternating minimization to estimate the optimal subspace tensor and coefficient tensor; S7: Obtain the target high spatial resolution hyperspectral image based on the optimal subspace tensor and coefficient tensor. 2.The remote sensing image fusion method based on adaptive tensor decomposition according to claim 1, characterized in that, The nonlocal similarity cube tensor expression for constructing the target high spatial resolution hyperspectral image includes: S21: a high spatial resolution multi-spectral image is divided into a plurality of overlapping cubic image blocks of the same size; wherein, two adjacent cubic image blocks overlap a fixed voxel; wherein, denotes the number of bands of the high spatial resolution multi-spectral image; denotes the number of bands of the low spatial resolution hyper-spectral image; denotes the number of bands of the low spatial resolution hyper-spectral image; and denote the width and height of the high spatial resolution multi-spectral image, respectively; S22: obtaining high spatial resolution multi-spectral images The divided cubic image blocks are clustered into K clusters by K-means. S23: Assuming there is a target high spatial resolution hyperspectral image The target high spatial resolution hyperspectral image is divided into a plurality of overlapping cubic image blocks in the same way as the high spatial resolution multispectral image; S24: Based on the spatial correspondence between the cubic image blocks of the target high spatial resolution hyperspectral image and the high spatial resolution multispectral image, divide the cubic image blocks of the target high spatial resolution hyperspectral image into the corresponding clusters; S25: Expand all cube image patches of the target high spatial resolution hyperspectral image in each cluster into two-dimensional matrices along the band dimension, and superimpose the expanded two-dimensional matrices to obtain the nonlocal similarity cube tensor of the target high spatial resolution hyperspectral image. ;in, Indicates the first The nonlocal similarity cube tensor of the target high spatial resolution hyperspectral image corresponding to each cluster; Indicates the width of the cube image block; Indicates the height of the cube image block; Indicates the first The number of cubic image blocks of the high spatial resolution hyperspectral image of the target in each cluster.

3. The remote sensing image fusion method based on adaptive tensor decomposition according to claim 2, characterized in that, The spatial observation model from the high spatial resolution multispectral image to the target high spatial resolution hyperspectral image includes: wherein, represents a spatial observation model of high spatial resolution multispectral images to a target high spatial resolution hyperspectral image; represents a high spatial resolution multispectral image; represents a target high spatial resolution hyperspectral image; represents a residual tensor of a target high spatial resolution hyperspectral image and a high spatial resolution multispectral image; represents the square of the F-norm; represents a regularization parameter; represents a spectral upsampling function; represents a spatial gradient operator; represents a constraint condition observed by a probability distribution model; represents a probability distribution type to which a spatial gradient feature of a residual tensor is subjected.

4. The remote sensing image fusion method based on adaptive tensor decomposition according to claim 3, characterized in that, The spectral observation model for transforming a low spatial resolution hyperspectral image into a target high spatial resolution hyperspectral image includes: wherein, denotes a low spatial resolution hyperspectral image to a target high spatial resolution hyperspectral image a spectral observation model; denotes a spatial upsampling function; denotes the square of the F-norm; denotes a residual tensor between the upsampled low spatial resolution hyperspectral image and the target high spatial resolution hyperspectral image; denotes a spectral gradient operator; denotes a regularization parameter; denotes a constraint condition observed by the probabilistic distribution model; denotes a residual tensor a probabilistic distribution type that the spectral gradient features of the residual tensor and denotes the width and height of the low spatial resolution hyperspectral image.

5. The remote sensing image fusion method based on adaptive tensor decomposition according to claim 4, characterized in that, The adaptive tensor decomposition model includes: in, This represents an adaptive tensor decomposition model; This indicates finding the minimum value; The first high spatial resolution hyperspectral image of the target A nonlocally similar cube tensor; express The corresponding subspace tensor; express The corresponding coefficient tensor, Indicates intermediate parameters; Represents the circular convolution operator; Representation subspace tensor of Mixture norm; Represents the coefficient tensor Mixture norm; Denotes the Euclidean norm; Representation subspace tensor Along the second dimension One slice; Represents the coefficient tensor Along the first dimension One slice; This represents the first dimension; This indicates the second dimension.

6. The remote sensing image fusion method based on adaptive tensor decomposition according to claim 5, characterized in that, The remote sensing image fusion model includes: in, and This represents a regularization parameter greater than 0; This represents the hyperLaplace prior constraint term; Indicates the distribution order parameter; , This indicates the extraction of the first [item] from a hyperspectral image with elevation spatial resolution. Nonlocally similar cube tensors The operation symbols, Indicates transpose; Indicates the inverse operation; Indicates constraint terms; Represents the norm.

7. The remote sensing image fusion method based on adaptive tensor decomposition according to claim 6, characterized in that, The optimization solution of the remote sensing image fusion model using proximal alternation minimization includes: S61: Initialize the maximum number of iterations T and the convergence threshold Proximal weight parameters and subspace tensor dimension ; Indicates rounding down; S62: Obtain a high spatial resolution hyperspectral image of the target. Initialized as an upsampled low spatial resolution hyperspectral image Based on the target's high spatial resolution hyperspectral image Initialize the nonlocal similarity cube tensor of the high spatial resolution hyperspectral image of the target using step S2. ; S63: Tensors for nonlocally similar cubes The third dimension Perform a Fast Fourier Transform to obtain a tensor ; for tensors Perform singular value decomposition on each front slice and take the first n... The maximum singular value yields the truncated value. , and ;make , ; Indicates conjugate transpose; for and Performing the third-dimensional inverse Fourier transform yields the subspace tensor. and coefficient tensor ; S64: The remote sensing image fusion model is iteratively solved using proximal alternating minimization. The solution process is as follows: in, Indicates the number of iterations; This represents a remote sensing image fusion model; Indicates the weight.

8. The remote sensing image fusion method based on adaptive tensor decomposition according to claim 6, characterized in that, The process of obtaining the target high spatial resolution hyperspectral image based on the optimal subspace tensor and coefficient tensor includes: in, This represents a high spatial resolution hyperspectral image of the target.

9. A remote sensing image fusion system based on adaptive tensor decomposition, characterized in that, The system includes a memory and a processor; the memory is used to store an application program; the processor is used to run the application program and execute a remote sensing image fusion method based on adaptive tensor decomposition as described in any one of claims 1 to 8.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer program, which, when executed by a processor, implements a remote sensing image fusion method based on adaptive tensor decomposition as described in any one of claims 1 to 8.

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