Hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint

Abstract

The invention discloses a hyperspectral image compression and reconstruction method based on graph tensor structure sparse constraint, and belongs to the technical field of image processing and spectral remote sensing, and the method comprises the steps: 1, constructing a basic hyperspectral image compression and reconstruction model based on regular term constraint, and obtaining a compression measurement value of a hyperspectral image; 2, constructing a sparse constraint regular term based on a tensor structure; step 3, constructing a non-linear smooth regular term based on the graph tensor; 4, fusing a tensor structure sparse constraint regular term and an image tensor nonlinear smooth regular term, replacing a sparse regular term of the basic hyperspectral image compression and reconstruction model in the step 1, and forming a final hyperspectral image compression and reconstruction model; and 5, solving the hyperspectral image compression reconstruction model constructed in the step 4 by adopting an alternating optimization method, and finally outputting a reconstructed hyperspectral image. The method can effectively solve the problems that a hyperspectral image is large in data size and difficult to store and transmit, and an existing compression reconstruction method neglects multi-dimensional structure information.

Description

Technical Field

[0001] This invention relates to the fields of image processing and spectral remote sensing technology, specifically to a hyperspectral image compression and reconstruction method based on sparse constraints of graph tensor structure. Background Technology

[0002] Hyperspectral images (HSI), as a special image type that combines spatial and spectral dimensions, can accurately capture the fine features of different materials in a scene. Due to their rich information dimensions, they play a crucial role in many fields such as scene classification, target detection, environmental monitoring, and resource exploration. However, the high information density of hyperspectral images also brings the problem of massive data volume. Compared to traditional images, HSI contains dozens or even hundreds of spectral bands, resulting in an exponential increase in data volume. This poses a severe challenge to the storage and transmission of data on resource-constrained platforms such as UAV remote sensing systems, satellite data transmission links, and portable detection devices, greatly limiting their promotion and application in resource-constrained scenarios.

[0003] To address this issue, various hyperspectral image compression methods have been proposed, such as wavelet transform and JPEG2000, classic compression techniques. However, these traditional methods essentially treat hyperspectral images as a collection of multiple independent single-band images, failing to fully exploit and utilize the spatial and spectral redundancy information inherent in HSI. This results in limited compression efficiency and a tendency to lose crucial information during compression, making it difficult to meet the quality requirements of high-precision applications. Therefore, how to construct a compression and reconstruction model that balances compression efficiency and reconstruction accuracy while fully utilizing the inherent characteristics of HSI has become a core problem urgently needing to be solved in the field of hyperspectral image processing.

[0004] In recent years, the rise of Compressive Sensing (CS) theory has provided a novel technological approach for the compression and acquisition of hyperspectral images. This theory requires only capturing a small amount of incoherent measurement data during the imaging stage, allowing for the reconstruction of a complete hyperspectral image through subsequent methods. Compared to traditional compression methods, CS-based hyperspectral image compression schemes significantly reduce the hardware complexity of imaging equipment and decrease resource consumption during data storage and transmission, demonstrating substantial technological advantages. To promote the application of CS theory in HSI processing, researchers have proposed various techniques to convert hyperspectral images into sparse signals; however, accurately reconstructing high-quality hyperspectral images from limited measurement data remains a significant challenge.

[0005] Essentially, compressed sensing reconstruction of hyperspectral images is an ill-conditioned, undetermined problem. Its core solution lies in introducing appropriate sparsity priors to transform the HSI into a sparse descriptive form, thereby achieving a stable solution. For example, based on... l 0、 l 1 and l p (0) While methods focusing on the sparsity norm of HSI (p<2) only consider the sparsity of the signal, they neglect the complex structural information inherent in hyperspectral images. Regularization-based methods are currently the mainstream reconstruction framework, typically incorporating prior knowledge into the observation model to form a unified framework. A key challenge for these methods is designing a suitable regularization term to characterize the sparsity of HSI. Examples include utilizing the sparsity of the abundance matrix within a spectral unmixing framework; constructing group sparsity constraints based on spatial / spectral redundancy structures; and characterizing the sparsity of the gradient domain of HSI based on piecewise smoothing structures. However, these techniques all describe the sparsity of HSI in vector space, simplifying multidimensional HSI data into a one-dimensional vector for processing, without considering the multidimensional structure of HSI. This simplification inevitably leads to the loss of important structural information in hyperspectral images, resulting in image distortion in the reconstructed image and failing to meet the image quality requirements of high-precision applications.

[0006] In summary, existing hyperspectral image compression and reconstruction methods still have significant shortcomings in utilizing the inherent structural information of the data and balancing compression efficiency and reconstruction accuracy. There is an urgent need to propose a compression and reconstruction scheme that can fully exploit the multidimensional structural characteristics and inherent correlations of HSI to address the deficiencies of existing technologies. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a hyperspectral image compression and reconstruction method based on graph tensor structure sparse constraints, which aims to solve the problems of large data volume, difficult storage and transmission of hyperspectral images, and the neglect of multidimensional structural information by existing compression and reconstruction methods.

[0008] To achieve the above objectives, the present invention provides the following technical solution: The hyperspectral image compression and reconstruction method based on graph tensor structure sparse constraints includes the following steps: Step 1: Construct a basic hyperspectral image compression and reconstruction model based on regularization constraints, and obtain the compression measurement value of the hyperspectral image; Step 2: Based on the hyperspectral image from Step 1, construct a tensor structure sparse constraint regularization term; Step 3: Based on the hyperspectral image from Step 1, construct a graph tensor-based nonlinear smoothing regularization term; Step 4: The tensor structure sparse constraint regularization term described in Step 2 and the graph tensor nonlinear smoothing regularization term described in Step 3 are fused together to replace the sparse regularization term of the basic hyperspectral image compression and reconstruction model in Step 1, forming the final hyperspectral image compression and reconstruction model. Step 5: The hyperspectral image compression and reconstruction model constructed in Step 4 is solved using the alternating optimization method, and the reconstructed hyperspectral image is finally output.

[0009] Furthermore, in step 1, the construction of a basic hyperspectral image compression and reconstruction model based on regularization constraints, and the acquisition of compression measurements of the hyperspectral image, includes: Let the spatial resolution of the hyperspectral image be... Spectral bands are The hyperspectral image is then represented as: The one-dimensional column vector form of a hyperspectral image is: ,in ; Obtained through compressed sensing model Compression measurement : (1) in, , As an observation dimension, ; For compression operators, the compression rate is... ; Under the constraint of isometry, the sparsest signal is sought. Formula (1) can be transformed into the following form: (2) in, Indicates based on l Sparse regularization terms of the 1-norm.

[0010] Furthermore, in step 2, the construction of the tensor structure sparse constraint regularization term includes: The initialized hyperspectral image is segmented to obtain a three-dimensional full-band image patch; For spatial location The central cube, search within a local window. A number of similar cubes; The central cube and the searched similar cubes are each expanded along the spectral dimension into corresponding two-dimensional matrices; by stacking similar two-dimensional matrices, a new third-order tensor is obtained, and so on, the following is constructed: A third-order tensor , Based on the above Using three third-order tensors, construct a sparse constraint regularization term based on tensor structure; the expression for the sparse constraint regularization term based on tensor structure is: (3) in , and The factor matrix is ​​orthogonal. It is the identity matrix. For sparse constraint terms, , refer to The number of non-zero elements in the neutron. express l 0 norm, This refers to the kernel tensor of the p-th dimension; Let represent the product of the kernel tensor and the factor matrix in the i-th dimension, where ; Based on l The 0-constraint kernel sparsity relaxation is , For weighted l The 1-norm, formula (3) is transformed into the following form: (4) in, Describing the Frobenius norm, and These are weight parameters.

[0011] Furthermore, in step 3, the expression for constructing the graph tensor-based nonlinear smoothing regularization term is: (5) in, This represents a matrix expansion along the spatial and spectral dimensions, taking all data in the nth dimension; This is the corresponding graph Laplace matrix. .

[0012] Furthermore, in step 4, the expression for the final hyperspectral image compression and reconstruction model is: (6) in, represents the regularization parameter for the graph tensor term.

[0013] Furthermore, in step 5, the alternating optimization method is used to solve the hyperspectral image compression and reconstruction model constructed in step 4, and the final output is the reconstructed hyperspectral image, including: Introducing auxiliary variables , making Its expression is: (7) in, It is a non-negative constant. It is the global multiplier vector; The final hyperspectral image compression and reconstruction model is decomposed into four independent sub-problems, and each variable is iteratively updated by fixing other variables, ultimately outputting the reconstructed hyperspectral image.

[0014] Furthermore, The subproblem expression is: (8) renew When, the solution is obtained through singular value decomposition. , and .

[0015] Furthermore, The subproblem expression is: (9) With other variables fixed, update using formula (9) .

[0016] Furthermore, The expression is: (10) renew When we take the derivative of formula (10), we get: (11) in, Represents overall data The nth dimension; Global multiplier vector The nth multiplier element; with other variables fixed, update using formula (11). , .

[0017] Furthermore, The subproblem expression is: (12) renew When the corresponding optimization subproblem is transformed into a system of linear equations, the conjugate gradient method is used to solve the system of linear equations to obtain the updated solution. The expression for the system of linear equations is: (13) in, , for transpose, This means expanding the tensor into a vector. This refers to the kernel tensor.

[0018] The beneficial effects of this invention are: This invention provides a hyperspectral image compression and reconstruction method based on graph tensor structure sparse constraints. First, a basic framework for hyperspectral image compression and reconstruction constrained by regularization terms is constructed. Then, tensor structure sparse constraint regularization terms and graph tensor nonlinear smoothing regularization terms are specifically designed. Through fusion and replacement, the final model of graph tensor structure sparse constraints is constructed. Finally, an alternating optimization method is used for efficient solution. This method fully exploits the spatial nonlocal similarity, local correlation, and global spectral correlation of hyperspectral images, and accurately characterizes the nonlinear smoothing structure of the spatial spectral domain. It effectively solves problems such as loss of multidimensional structural information, unreasonable sparse constraints, and unstable solutions in traditional methods, significantly improving the accuracy and stability of compression and reconstruction. Simultaneously, it balances compression efficiency and reconstruction quality, meeting the dual needs of storage and transmission on resource-constrained platforms and high-precision application scenarios, and has significant practical application value. Attached Figure Description

[0019] Figure 1 A flowchart of the hyperspectral image compression and reconstruction method based on graph tensor structure sparse constraints provided by the present invention; Figure 2 The image shows the experimental results of compression reconstruction obtained using the method of this invention and existing technologies. Detailed Implementation

[0020] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore merely examples and should not be used to limit the scope of protection of the present invention. Those skilled in the art should understand that the present invention can be implemented even without certain specific details. In some other embodiments, methods, means, equipment, and steps well known to those skilled in the art are not described in detail in order to highlight the spirit of the present invention.

[0021] Unless otherwise specified, in this invention, terms such as "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," "x-direction," "y-direction," and "z-direction" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe orientation or positional relationships in this invention are for illustrative purposes only and should not be construed as limiting this patent. For those skilled in the art, the specific meaning of the above terms can be understood in conjunction with the accompanying drawings and according to the specific circumstances.

[0022] Example 1 See attached Figures 1-2 This embodiment provides a hyperspectral image compression and reconstruction method based on graph tensor structure sparse constraints, the process of which is as follows: Figure 1 As shown, it includes the following steps: Step 1: Construct a basic hyperspectral image compression and reconstruction model based on regularization constraints, and obtain the compression measurement value of the hyperspectral image; Step 2: Based on the hyperspectral image from Step 1, construct a tensor structure sparse constraint regularization term; Step 3: Based on the hyperspectral image from Step 1, construct a graph tensor-based nonlinear smoothing regularization term; Step 4: The tensor structure sparse constraint regularization term from Step 2 and the graph tensor nonlinear smoothing regularization term from Step 3 are fused together to replace the sparse regularization term of the basic hyperspectral image compression and reconstruction model in Step 1, forming the final hyperspectral image compression and reconstruction model. Step 5: The hyperspectral image compression and reconstruction model constructed in Step 4 is solved using the alternating optimization method, and the reconstructed hyperspectral image is finally output.

[0023] Specifically, in step 1, a basic hyperspectral image compression and reconstruction model based on regularization constraints is constructed to obtain compression measurements of the hyperspectral image, including: Let the spatial resolution of the hyperspectral image be... Spectral bands are The hyperspectral image is then represented as: The one-dimensional column vector form of a hyperspectral image is: ,in ; Obtained through compressed sensing model Compression measurement : (1) in, , As an observation dimension, ; For compression operators, the compression rate is... ; Under the constraint of isometry, the sparsest signal is sought. Formula (1) can be transformed into the following form: (2) in, Indicates based on l Sparse regularization terms of the 1-norm.

[0024] Specifically, in step 2, a sparse constraint regularization term based on tensor structure is constructed, including: To fully exploit the structural sparsity in hyperspectral images, the initial hyperspectral image is first segmented to obtain three-dimensional full-band image patches; then, for spatially located... The central cube, search within a local window. Similar cubes; for example, in The local window is searched using the k-Nearest Neighbor (k-NN) method. A number of similar cubes are identified; then, to avoid disrupting the spatial-spectral correlation, the central cube and the searched similar cubes are expanded along the spectral dimension into corresponding two-dimensional matrices; by stacking the similar two-dimensional matrices, a new third-order tensor is obtained, and the following is constructed: A third-order tensor , The third-order tensor constructed in this way can simultaneously preserve spatial local sparsity, nonlocal similarity, and high spectral correlation. Based on this, a tensor structure-based sparsity constraint regularization term is proposed. The expression for the tensor structure-based sparsity constraint regularization term is: (3) in , and The factor matrix is ​​orthogonal. It is the identity matrix. For sparse constraint terms, , refer to The number of non-zero elements in the neutron. express l 0 norm, This refers to the kernel tensor of the p-th dimension; Let represent the product of the kernel tensor and the factor matrix in the i-th dimension, where ; Based onl The 0-constraint kernel sparsity relaxation is , For weighted l The 1-norm, formula (3) is transformed into the following form: (4) in, and These are the weight parameters. Essentially, all factor matrices are orthogonal dictionaries along the local and non-local spatial dimensions and the spectral dimension. It can be seen that the tensor sparse representation model, through adaptive multi-dictionary learning, represents the non-local spatial similarity and global spectral correlation of HSI in different dimensions. Compared to matrix sparse models, the advantage of tensor modeling is that it can represent not only the spatial-spectral correlation in HSI, but also the correlation of non-local similar blocks in HSI.

[0025] Specifically, in step 3, a graph tensor-based nonlinear smoothing regularization term is constructed, including: For hyperspectral images, due to factors such as multiple scattering and occlusion effects between substances during imaging, pixel spectra often exhibit nonlinear combinations of endmembers. Furthermore, factors such as illumination conditions and atmospheric absorption lead to nonstationarity of spatial spectral information. Hyperspectral images possess nonlinear structural information in the spatial spectral domain. Combining this with the high-dimensional structure of the data, a nonlinear smoothing regularization term based on graph tensors is constructed, with the following expression: (5) in, This represents a matrix expansion along the spatial and spectral dimensions, taking all data in the nth dimension; This is the corresponding graph Laplace matrix. .

[0026] Specifically, in step 4, the final expression for the hyperspectral image compression and reconstruction model is: (6) in, represents the regularization parameter for the graph tensor term.

[0027] Specifically, in step 5, the alternating optimization method is used to solve the hyperspectral image compression and reconstruction model constructed in step 4, and the final output is the reconstructed hyperspectral image, including: Introducing auxiliary variables , making Its expression is: (7) in, It is a non-negative constant. It is the global multiplier vector; The final hyperspectral image compression and reconstruction model is decomposed into four independent sub-problems, and each variable is iteratively updated by fixing other variables, ultimately outputting the reconstructed hyperspectral image.

[0028] in, The subproblem expression is: (8) renew When, the solution is obtained through singular value decomposition. , and .

[0029] in, The subproblem expression is: (9) With other variables fixed, update using formula (9) The solution can be obtained using a tensor-based weighted shrinkage threshold method.

[0030] in, The expression is: (10) renew When we take the derivative of formula (10), we have ,get: (11) in, Represents overall data The nth dimension; Global multiplier vector The nth multiplier element; with other variables fixed, update using formula (11). , .

[0031] in, The subproblem expression is: (12) renew When the corresponding optimization subproblem is transformed into a system of linear equations, the conjugate gradient method is used to solve the system of linear equations to obtain the updated solution. The expression for the system of linear equations is: (13) in, , for transpose, This means expanding the tensor into a vector. This refers to the kernel tensor.

[0032] Table 1 Optimization process of hyperspectral image compression and reconstruction model

[0033] To further describe the effects of this application, this embodiment uses the method of this application to reconstruct compressed images. Simultaneously, three classic compressed sensing methods are selected as comparison methods: Bayesian Compressive Sensing (BCS), Kronecker Compressive Sensing (KCS), TV Minimization by Augmented Lagrangian and Alternating Direction Algorithms (TVAL3), and Joint Tensor Regularization and Total Variation (JTRTV). The reconstruction results of these comparison methods are then compared with the results of this invention.

[0034] The image data Toy used in this application comes from the publicly available Cave dataset, which has a spatial resolution of 512×512 and 31 spectral bands. In the experiment, three sampling rates were selected: 0.10, 0.15, and 0.20, and a 300×300 image region was selected for testing.

[0035] To quantitatively and qualitatively evaluate the fusion effect, this embodiment uses five quality evaluation indicators: Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), Feature Similarity Index Measure (FSIM), Relative Average Spectral Error (ERGAS), and Spectral Angle Mapper (SAM). The quantitative analysis results are shown in Table 2.

[0036] Table 2. Comparison of quality evaluation of various compression reconstruction methods at different sampling rates.

[0037] As shown in Table 2, compared with the four comparative methods, the method of this application has higher PSNR, SSIM and FSIM, and smaller ERGAS and SAM values. This indicates that the method of this application has a significant advantage in the reconstruction of structural information and is also superior to other methods in suppressing spectral distortion.

[0038] When the sampling rate is 0.20, the visual contrast results of compressed reconstruction on the Toy data are as follows: Figure 2 As shown, it is easy to see that all methods can achieve good restoration results. However, from the magnified area, it can be seen that the method of this application not only has better detail reconstruction performance, but also shows a significant advantage in preserving the edges of the image. This verifies the effectiveness of the sparse constraint of the graph tensor structure in this application.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention. Technical aspects, shapes, and structures not described in detail in this invention are all well-known technologies.

Claims

1. A hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint, characterized in that, The method comprises the following steps: Step 1, constructing a basic hyperspectral image compression reconstruction model based on a regular term constraint to obtain a compression measurement value of the hyperspectral image; Step 2, constructing a tensor structure sparse constraint regular term based on the hyperspectral image in step 1; Step 3, constructing a graph tensor nonlinear smoothing regular term based on the hyperspectral image in step 1; Step 4, fusing the tensor structure sparse constraint regular term in step 2 and the graph tensor nonlinear smoothing regular term in step 3 to replace the sparse regular term of the basic hyperspectral image compression reconstruction model in step 1, thereby forming a final hyperspectral image compression reconstruction model; Step 5, solving the hyperspectral image compression reconstruction model constructed in step 4 by using an alternating optimization method, and finally outputting a reconstructed hyperspectral image.

2. The hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint according to claim 1, characterized in that, In step 1, the basic hyperspectral image compression reconstruction model based on the regular term constraint is constructed to obtain the compression measurement value of the hyperspectral image, comprising: Let the spatial resolution of the hyperspectral image be , and the spectral band be . The hyperspectral image is represented as: The one-dimensional column vector form of the hyperspectral image is: where ; obtained by a compressive sensing model of a compressed measurement value : （1） wherein , is the observation dimension, ; is the compression operator, and the compression rate is ; Under the constraint of the isometry property, the sparsest signal is sought Equation (1) is transformed into the following form: （2） wherein, denotes a sparse regularizer based on l 1-norm.

3. The hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint according to claim 2, characterized in that, In step 2, the construction of the regular term based on the tensor structure sparse constraint comprises: Segmenting the initialized hyperspectral image to obtain a three-dimensional full-band image block; For a center cube with spatial position , search for similar cubes in the local window. The central cube and the searched similar cubes are each expanded along the spectral dimension into corresponding two-dimensional matrices; by stacking similar two-dimensional matrices, a new third-order tensor is obtained, and so on, the following is constructed: A third-order tensor , Based on the above Using three third-order tensors, construct a sparse constraint regularization term based on tensor structure; the expression for the sparse constraint regularization term based on tensor structure is: （3） wherein , and are orthogonal factor matrices, is an identity matrix, is a sparse constraint term, , denotes the number of non-zero elements in , l the 0-norm, denotes the p-th dimension of the core tensor; denotes the product of the core tensor and the factor matrices in the i-th dimension, where ; will be based on l 0 constrained nuclear sparsity relaxation is , is a weighted l 1 norm, formula (3) is transformed into the following form: （4） wherein, denotes the Frobenius norm, and are weight parameters.

4. The hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint according to claim 3, characterized in that, In step 3, the expression of the graph tensor nonlinear smoothing regular term is: （5） wherein, represents the matrix unfolding along the space and the spectrum, taking all data of the nth dimension; is the corresponding graph Laplacian matrix; .

5. The method of claim 4, wherein the method is a hyperspectral image compression reconstruction method based on graph-tensor structured sparsity constraints. In step 4, the expression of the final hyperspectral image compression reconstruction model is: （6） wherein, is a regularization parameter for the graph tensor term.

6. The method of claim 5, wherein the method is a hyperspectral image compression reconstruction method based on graph-tensor structured sparsity constraints. In step 5, the solving of the hyperspectral image compression reconstruction model constructed in step 4 by using the alternating optimization method to finally output the reconstructed hyperspectral image comprises: Introducing auxiliary variables such that whose expression is （7） wherein is a non-negative constant, is a global multiplier vector; The final hyperspectral image compression reconstruction model is disassembled into four independent sub-problems, and each variable is iteratively updated by fixing other variables, and finally the reconstructed hyperspectral image is output.

7. The method of claim 6, wherein the method is a hyperspectral image compression reconstruction method based on graph-tensor structured sparsity constraints. The sub-problem expression is: （8） update by singular value decomposition , and .

8. The method of claim 6, wherein the method is a hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint. The sub-problem expression is: （9） Update using equation (9) with other variables fixed .

9. The method of claim 6, wherein the method is a hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint. The expression is: （10） updating Taking the derivative of equation (10) with respect to time gives: （11） wherein, represent the n-th dimension in the middle; is a global multiplier vector is the n-th multiplier element in the middle; fix other variables, update , .

10. The method of claim 6, wherein the method is a hyperspectral image compression reconstruction method based on graph tensor structure sparse constraint. The sub-problem expression is: （12） update At this time, the corresponding optimization sub-problem is converted into a linear equation system, the conjugate gradient method is used to solve the linear equation system, and an updated ; wherein the expression of the linear equation system is: （13） wherein , is the transpose of denotes the expansion of a tensor into a vector, refers to the kernel tensor.

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