Hyperspectral image compression reconstruction method based on Hankel rank increase tensor decomposition

Abstract

The invention discloses a hyperspectral image compression and reconstruction method based on Hankel rank increase tensor decomposition, which belongs to the technical field of image processing and spectral remote sensing, and comprises the following steps: step 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; step 2, constructing a high-order tensor based on Hankel transformation; step 3, aiming at the high-order tensor obtained in the step 2, constructing a regular term based on Hankel rank increase tensor decomposition; 4, replacing the sparse regular term of the basic compression reconstruction model in the step 1 with the regular term of Hankel rank increase tensor decomposition constructed in the step 3 to form a final hyperspectral image compression reconstruction model; and 5, solving the hyperspectral image compression reconstruction model constructed in the step 4 by adopting an alternating optimization method. 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 Hankel rank increasing tensor decomposition. 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 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 Hankel rank increasing tensor decomposition, 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 Hankel rank-increasing tensor decomposition 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 higher-order tensor based on the Hankel transform; Step 3: For the higher-order tensors obtained in Step 2, construct regularization terms based on Hankel rank-increasing tensor decomposition; Step 4: Replace the sparse regularization term of the basic hyperspectral image compression and reconstruction model in Step 1 with the regularization term of the Hankel rank increasing tensor decomposition constructed in Step 3 to form 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 vector form of a hyperspectral image is: ; Obtained through compressed sensing model Compression measurement : (1) in, For compression operators, , Compression rate ; Under the constraint of isometry, the sparsest signal is sought. Formula (1) can be transformed into the following form: (2) in, This indicates a sparse regularization term.

[0010] Furthermore, in step 2, the construction of the higher-order tensor based on the Hankel transform includes: For hyperspectral images Given 3 replication matrices ,in, ; , , , ; Then, the Hankelized higher-order tensor is obtained based on the multipath delay embedding transform: (3) in, To delay the length of the embedding operator, For the Hankel operator, The operator means to upgrade a 3rd-order tensor to a 6th-order tensor.

[0011] Furthermore, in step 3, the expression for constructing the regularization term based on Hankel rank increasing tensor decomposition is: , (4) in, It is a dictionary matrix; This is a relation tensor used to represent the association between different dictionary matrices; It is the identity matrix; This represents the product of the relation tensor and the dictionary matrix in the i-th dimension.

[0012] Furthermore, in step 4, the expression for the final hyperspectral image compression and reconstruction model is: (5) in, Denotes the Frobenius norm. is the regularization parameter of the tensor.

[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: The final hyperspectral image compression and reconstruction model is decomposed into three independent sub-problems. By fixing other variables, the dictionary matrix, relation tensor, and image vector are iteratively updated respectively, and the reconstructed hyperspectral image is finally output.

[0014] Furthermore, the expression for the dictionary matrix subproblem is: (6) When updating the dictionary matrix, the upgraded higher-order tensor is expanded along each dimension, and then the effective eigenvectors of each dimension are extracted through singular value decomposition to form the corresponding orthogonal dictionary matrix; where the singular value decomposition expression is: ,in, Describes a left singular matrix. , This represents the matrix expansion operator along the i-th dimension.

[0015] Furthermore, the expression for the relational tensor quantum problem is: (7) When updating the relation tensor, based on the current higher-order tensor and dictionary matrix, the optimal solution of the relation tensor is obtained through the pattern product operation between the higher-order tensor and the dictionary matrix. Its closed-form solution is: (8) With other variables fixed, update using formula (8) .

[0016] Furthermore, the image vector subproblem is expressed as follows: (9) When updating the image vector, the corresponding optimization subproblem is transformed into a system of linear equations. The conjugate gradient method is used to solve this system of linear equations to obtain the updated image vector. The expression for the system of linear equations is: (10) in, , for transpose, This indicates that the tensor is expanded into a vector.

[0017] Furthermore, during the iteration process, the rank of each dimension of the tensor is initialized to the minimum value. After each round of variable update, the rank of each dimension is gradually increased until the reconstruction error converges or the preset number of iterations is reached. Finally, the updated image vector is inversely expanded into tensor form to obtain the reconstructed hyperspectral image.

[0018] The beneficial effects of this invention are: This invention provides a hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition. First, it enhances the representation of structural information in hyperspectral images through multi-path delay embedding transform and Hankel transform. Second, it introduces Fourier transform to diagonalize higher-order images, enhancing the linear correlation of data and significantly reducing computational complexity. Then, it uses a rank-increasing stepwise approach to obtain the optimal low-rank approximation, and performs an inverse Hankel transform on the low-rank approximation to obtain the optimal estimate of the potential data. Finally, it incorporates this approximation into a hyperspectral image compression and reconstruction model, and solves the model using an alternating iterative method. This invention effectively overcomes the shortcomings of traditional methods that ignore the multidimensional structure of hyperspectral images and are prone to reconstruction distortion. It can accurately restore image details, effectively preserve edge information, and significantly suppress spectral distortion. While ensuring compression efficiency, it greatly improves reconstruction accuracy and is suitable for compressed sensing and acquisition scenarios involving multiple frames of data, such as hyperspectral imaging and nuclear magnetic resonance imaging. Attached Figure Description

[0019] Figure 1 A flowchart of the hyperspectral image compression and reconstruction method based on Hankel rank increasing tensor decomposition 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 Hankel rank-increasing tensor decomposition, 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 higher-order tensor based on the Hankel transform; Step 3: For the higher-order tensors obtained in Step 2, construct regularization terms based on Hankel rank-increasing tensor decomposition; Step 4: Replace the sparse regularization term of the basic hyperspectral image compression and reconstruction model in Step 1 with the regularization term of the Hankel rank increasing tensor decomposition constructed in Step 3 to form 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 vector form of a hyperspectral image is: ; Obtained through compressed sensing model Compression measurement : (1) in, For compression operators, , M <N Compression rate ; Under the constraint of isometry, the sparsest signal is sought. Formula (1) can be transformed into the following form: (2) in, Represents sparse regularization terms, for example, based on l 0、 l 1. Sparse regularization of nuclear norm.

[0024] Specifically, in step 2, a higher-order tensor based on the Hankel transform is constructed, including: For hyperspectral images Given 3 replication matrices ,in, ; , , , ; Then, the Hankelized higher-order tensor is obtained based on the multipath delay embedding transform: (3) in, To delay the length of the embedding operator, For the Hankel operator, The operator means to upgrade a 3rd-order tensor to a 6th-order tensor.

[0025] Specifically, in step 3, the expression for constructing the regularization term based on Hankel rank-increasing tensor decomposition is as follows: , (4) in, It is a dictionary matrix; This is a relation tensor used to represent the association between different dictionary matrices; It is the identity matrix; This represents the product of the relation tensor and the dictionary matrix in the i-th dimension.

[0026] Specifically, in step 4, the final expression for the hyperspectral image compression and reconstruction model is: (5) in, Denotes the Frobenius norm. is the regularization parameter of the tensor.

[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: The final hyperspectral image compression and reconstruction model is decomposed into three independent sub-problems. By fixing other variables, the dictionary matrix, relation tensor, and image vector are iteratively updated respectively, and the reconstructed hyperspectral image is finally output.

[0028] The dictionary matrix subproblem is expressed as follows: (6) When updating the dictionary matrix, the upgraded higher-order tensor is expanded along each dimension, and then the effective eigenvectors of each dimension are extracted through singular value decomposition to form the corresponding orthogonal dictionary matrix; where the singular value decomposition expression is: ,in, Describes a left singular matrix. , This represents the matrix expansion operator along the i-th dimension.

[0029] The expression for the relational tensor quantum problem is: (7) When updating the relation tensor, based on the current higher-order tensor and dictionary matrix, the optimal solution of the relation tensor is obtained through the pattern product operation between the higher-order tensor and the dictionary matrix. Its closed-form solution is: (8) The image vector subproblem is expressed as follows: (9) When updating the image vector, the corresponding optimization subproblem is transformed into a system of linear equations. The conjugate gradient method is used to solve this system of linear equations to obtain the updated image vector. The expression for the system of linear equations is: (10) in, , for transpose, This indicates that the tensor is expanded into a vector.

[0030] During the iteration process, the rank of each dimension of the tensor is initialized to the minimum value. After each round of variable update, the rank of each dimension is gradually increased until the reconstruction error converges or the preset number of iterations is reached. Finally, the updated image vector is inversely expanded into tensor form to obtain the reconstructed hyperspectral image. The process is shown in Table 1.

[0031] Table 1 Optimization process of hyperspectral image compression and reconstruction model

[0032] To further describe the effects of this application, this embodiment uses the method of this application to reconstruct compressed images. Simultaneously, four classic compressed sensing methods—StOMP, Kronecker Compressive Sensing (KCS), Reweighted Laplace Prior for Hyperspectral Compressive Sensing (RLPHCS), and Promoting Structured Sparsity for Hyperspectral Compressive Sensing (PSSHCS)—are selected as comparative methods, and the reconstruction results of these comparative methods are compared with the results of this invention.

[0033] 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.

[0034] To quantitatively and qualitatively evaluate the fusion effect, this embodiment uses peak signal-to-noise ratio (PSNR) as the evaluation index, and the results are shown in Table 2.

[0035] Table 2. Comparison of PSNR for different compression reconstruction methods at different sampling rates.

[0036] As shown in Table 2, compared with the four comparative methods, the method of this application has a higher PSNR value, which 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.

[0037] 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 Hankel rank-incrementing tensor decomposition constraint of this application.

[0038] 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 and reconstruction method based on Hankel rank-increasing tensor decomposition, characterized in that, 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 higher-order tensor based on the Hankel transform; Step 3: For the higher-order tensors obtained in Step 2, construct regularization terms based on Hankel rank-increasing tensor decomposition; Step 4: Replace the sparse regularization term of the basic hyperspectral image compression and reconstruction model in Step 1 with the regularization term of the Hankel rank increasing tensor decomposition constructed in Step 3 to form 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.

2. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 1, characterized in that, 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, include: Let the spatial resolution of the hyperspectral image be... Spectral bands are The hyperspectral image is then represented as: The vector form of a hyperspectral image is: ; Obtained through compressed sensing model Compression measurement : ；（1） in, For compression operators, , Compression rate ; Under the constraint of isometry, the sparsest signal is sought. Formula (1) can be transformed into the following form: ；（2） in, This indicates a sparse regularization term.

3. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 2, characterized in that, In step 2, the construction of the higher-order tensor based on the Hankel transform includes: For hyperspectral images Given 3 replication matrices ,in, ; , , , ; Then, the Hankelized higher-order tensor is obtained based on the multipath delay embedding transform: ；（3） in, To delay the length of the embedding operator, For the Hankel operator, The operator means to upgrade a 3rd-order tensor to a 6th-order tensor.

4. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 3, characterized in that, In step 3, the expression for constructing the regularization term based on Hankel rank increasing tensor decomposition is: ， ；（4） in, It is a dictionary matrix; This is a relation tensor used to represent the association between different dictionary matrices; It is the identity matrix; This represents the product of the relation tensor and the dictionary matrix in the i-th dimension.

5. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 4, characterized in that, In step 4, the expression for the final hyperspectral image compression and reconstruction model is: ；（5） in, Denotes the Frobenius norm. is the regularization parameter of the tensor.

6. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 5, characterized in that, In step 5, the hyperspectral image compression and reconstruction model constructed in step 4 is solved using an alternating optimization method, and the reconstructed hyperspectral image is finally output, including: The final hyperspectral image compression and reconstruction model is decomposed into three independent sub-problems. By fixing other variables, the dictionary matrix, relation tensor, and image vector are iteratively updated respectively, and the reconstructed hyperspectral image is finally output.

7. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 6, characterized in that, The expression for the dictionary matrix subproblem is: ；（6） When updating the dictionary matrix, the upgraded higher-order tensor is expanded along each dimension, and then the effective eigenvectors of each dimension are extracted through singular value decomposition to form the corresponding orthogonal dictionary matrix; where the singular value decomposition expression is: ,in, Describes a left singular matrix. , This represents the matrix expansion operator along the i-th dimension.

8. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 6, characterized in that, The expression for the relational tensor quantum problem is: ；（7） When updating the relation tensor, based on the current higher-order tensor and dictionary matrix, the optimal solution of the relation tensor is obtained through the pattern product operation between the higher-order tensor and the dictionary matrix. Its closed-form solution is: ；（8） With other variables fixed, update using formula (8) .

9. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 6, characterized in that, The expression for the image vector subproblem is: ；（9） When updating the image vector, the corresponding optimization subproblem is transformed into a system of linear equations. The conjugate gradient method is used to solve this system of linear equations to obtain the updated image vector. The expression for the system of linear equations is: ；（10） in, , for transpose, This indicates that the tensor is expanded into a vector.

10. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 6, characterized in that, During the iteration process, the rank of each dimension of the tensor is initialized to the minimum value. After each round of variable update, the rank of each dimension is gradually increased until the reconstruction error converges or the preset number of iterations is reached. Finally, the updated image vector is inversely expanded into tensor form to obtain the reconstructed hyperspectral image.

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