Hyperspectral image compression reconstruction method based on hankel rank increasing tensor decomposition

Abstract

The application discloses a hyperspectral image compression reconstruction method based on Hankel rank increasing tensor decomposition, and belongs to the technical fields of image processing and spectral remote sensing, and comprises the following steps: step 1, a basic hyperspectral image compression reconstruction model based on a regular term constraint is constructed to obtain a compression measurement value of the hyperspectral image; step 2, a high-order tensor based on a Hankel transformation is constructed; step 3, a regular term based on Hankel rank increasing tensor decomposition is constructed for the high-order tensor obtained in step 2; step 4, the regular term of the Hankel rank increasing tensor decomposition constructed in step 3 is substituted into a sparse regular term of the basic compression reconstruction model in step 1 to form a final hyperspectral image compression reconstruction model; and step 5, an alternating optimization method is used to solve the hyperspectral image compression reconstruction model constructed in step 4. The application can effectively solve the problems of large data volume of the hyperspectral image, storage and transmission difficulties and the problem that the existing compression reconstruction method ignores multi-dimensional structure information.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of image processing and spectral remote sensing, and particularly relates to a hyperspectral image compression and reconstruction method based on Hankel rank increasing tensor decomposition. BACKGROUND

[0002] As a special image type with both spatial and spectral dimension information, hyperspectral image (HSI) can accurately capture the fine features of different materials in the scene, and plays an important role in scene classification, target detection, environmental monitoring, resource exploration and many other fields due to its rich information dimension. However, the high information density of hyperspectral image also brings the problem of large data volume. Compared with traditional images, HSI contains tens or even hundreds of spectral bands, resulting in an exponential increase in data volume, which poses a serious challenge to the storage and transmission of limited resource platforms such as unmanned aerial vehicle remote sensing systems, satellite data transmission links and portable detection devices, greatly limiting their promotion and application in resource-constrained scenarios.

[0003] To solve this problem, the industry has proposed a variety of hyperspectral image compression methods, such as classic compression techniques such as wavelet transform and JPEG2000. However, these traditional methods essentially treat hyperspectral images as a collection of multiple independent single-band images for processing, failing to fully exploit and utilize the spatial and spectral dimension redundancy information present in HSI, resulting in limited compression efficiency and loss of critical information during compression, making it difficult to meet the quality requirements of compressed data in high-precision application scenarios. Therefore, how to build a compression and reconstruction model that takes into account compression efficiency and reconstruction accuracy and can fully utilize the inherent characteristics of HSI has become a core problem that needs to be solved in the current hyperspectral image processing field.

[0004] In recent years, the rise of compressive sensing (CS) theory has provided a new technical path for the compression and acquisition of hyperspectral images. This theory only needs to capture a small amount of incoherent measurement data during imaging, and the complete hyperspectral image can be recovered through subsequent reconstruction methods. Compared with traditional compression methods, the hyperspectral image compression scheme based on CS theory can significantly reduce the hardware complexity of imaging devices, while reducing resource consumption during data storage and transmission, exhibiting significant technical advantages. To promote the application of CS theory in HSI processing, researchers have proposed various technical means to convert hyperspectral images into sparse signals, but how to accurately reconstruct high-quality hyperspectral images from limited measurement data still poses a great challenge.

[0005] In essence, the compressed sensing reconstruction of hyperspectral image belongs to a pathological underdetermined problem, and the core solution idea is to convert the HSI into a description form with sparse characteristics by introducing appropriate sparse priors, so as to realize stable solution. l 0、 l 1With l p (0 p<2) sparse norm, but such methods only focus on the sparsity of the signal, ignoring the complex structural information contained in the hyperspectral image. The regularization-based method is the current mainstream reconstruction framework, and this kind of method usually incorporates prior knowledge into the observation model to form a unified framework. For this kind of method, the key problem is how to design a suitable regularization term to represent the sparsity of HSI, for example, using the sparsity of the abundance matrix in the spectral unmixing framework; constructing group sparsity constraints based on spatial / spectral redundancy structure; and describing the sparsity of the gradient domain of HSI based on piecewise smooth structure. However, these techniques describe the sparsity of HSI in vector space, simplify the multi-dimensional HSI data to one-dimensional vector for processing, and do not consider the multi-dimensional structure of HSI. This simplified processing method inevitably leads to the loss of important structural information in the hyperspectral image, and further causes distortion of the reconstructed image, which is difficult to meet the requirements of high-precision applications for image quality.

[0006] In summary, the existing hyperspectral image compression reconstruction method still has obvious deficiencies in utilizing the internal structural information of the data and balancing the compression efficiency and reconstruction accuracy, and it is urgent to propose a compression reconstruction scheme that can fully exploit the multi-dimensional structural characteristics and internal correlation of HSI to solve the defects of the existing technology. SUMMARY

[0007] In view of the problems existing in the prior art, the present application provides a hyperspectral image compression reconstruction method based on Hankel rank increasing tensor decomposition, which aims to solve the problems of large amount of hyperspectral image data, difficult storage and transmission, and ignoring of multi-dimensional structural information by existing compression reconstruction methods.

[0008] To achieve the above object, the present application provides the following technical scheme:

[0009] The hyperspectral image compression reconstruction method based on Hankel rank increasing tensor decomposition comprises the following steps:

[0010] Step 1, constructing a basic hyperspectral image compression reconstruction model based on regularization term constraint, and obtaining the compressed measurement value of the hyperspectral image;

[0011] Step 2, based on the hyperspectral image in step 1, constructing a high-order tensor based on Hankel transform;

[0012] Step 3, for the high-order tensor obtained in step 2, a regular term based on Hankel rank increasing tensor decomposition is constructed;

[0013] Step 4, the regular term of Hankel rank increasing tensor decomposition constructed in step 3 is substituted for the sparse regular term of the basic hyperspectral image compression reconstruction model in step 1 to form a final hyperspectral image compression reconstruction model;

[0014] Step 5, the hyperspectral image compression reconstruction model constructed in step 4 is solved by using an alternating optimization method, and a reconstructed hyperspectral image is finally output.

[0015] Further, in step 1, the construction of the basic hyperspectral image compression reconstruction model based on the regular term constraint to obtain the compression measurement value of the hyperspectral image comprises:

[0016] Let the spatial resolution of the hyperspectral image be , and the spectral band be , then the hyperspectral image is represented as: , and the vector form of the hyperspectral image is: ;

[0017] The compression measurement value of the hyperspectral image is obtained through a compression sensing model :

[0018] ; (1)

[0019] Wherein, is a compression operator, , ; the compression rate is ;

[0020] Under the constraint of the equidistance property condition, by seeking the sparsest signal , formula (1) is transformed into the following form:

[0021] ; (2)

[0022] Wherein, represents a sparse regular term.

[0023] Further, in step 2, the construction of the high-order tensor based on the Hankel transform comprises:

[0024] For the hyperspectral image , three replication matrices are given, wherein, ; , , , ; Then, the Hankelized high-order tensor is obtained according to the multi-path delay embedding transformation:

[0025] (3)

[0026] wherein, is the length of the delay embedding operator, is the Hankel operator, the operator represents the up-ordering of the 3-order tensor to the 6-order tensor.

[0027] Further, in step 3, the expression of the regular term based on the Hankel rank increasing tensor decomposition is constructed as:

[0028] (4)

[0029] wherein, is the dictionary matrix; is the relationship tensor, used for representing the correlation between different dictionary matrices; is the unit matrix; represents the product of the relationship tensor and the dictionary matrix in the i-th dimension.

[0030] Further, in step 4, the expression of the final hyperspectral image compression reconstruction model is:

[0031] (5)

[0032] wherein, represents the Frobenius norm, is the regularization parameter of the tensor.

[0033] Further, in step 5, the hyperspectral image compression reconstruction model constructed in step 4 is solved by using the alternating optimization method, and finally the reconstructed hyperspectral image is output, including:

[0034] The final hyperspectral image compression reconstruction model is decomposed into three independent sub-problems, and by fixing other variables, the dictionary matrix, the relationship tensor and the image vector are iteratively updated respectively, and finally the reconstructed hyperspectral image is output.

[0035] Further, the expression of the dictionary matrix sub-problem is:

[0036] (6)

[0037] When updating the dictionary matrix, the up-ordered high-order tensor is respectively matrix unfolded along each dimension, and then the effective eigenvector of each dimension is extracted through singular value decomposition to form the corresponding orthogonal dictionary matrix; wherein, the singular value decomposition expression is: ​wherein, denotes a left-singular matrix, , denotes a matrix unfolding operator along the i-th dimension.

[0038] Further, the relationship tensor sub-problem expression is:

[0039] ; (7)

[0040] When updating the relationship tensor, based on the current high-order tensor and the dictionary matrix, the optimal solution of the relationship tensor is obtained through the mode product operation of the high-order tensor and the dictionary matrix, and the closed-form solution is:

[0041] ; (8)

[0042] Fixing other variables, the formula (8) is used to update .

[0043] Further, the image vector sub-problem expression is:

[0044] ; (9)

[0045] When updating the image vector, the corresponding optimization sub-problem is converted into a linear equation set, the conjugate gradient method is used to solve the linear equation set, and the updated image vector is obtained; wherein, the expression of the linear equation set is:

[0046] ; (10)

[0047] wherein, , is the transpose of , denotes unfolding the tensor into a vector.

[0048] Further, in the iteration process, the ranks of each dimension of the tensor are initialized as the minimum value, the ranks of each dimension are gradually increased after completing a round of variable updating each time, until the reconstruction error converges or the preset iteration number is reached, finally the updated image vector is inversely unfolded into a tensor form, and the reconstructed hyperspectral image is obtained.

[0049] The beneficial effects of the present application are:

[0050] The application provides a hyperspectral image compression reconstruction method based on Hankel rank increasing tensor decomposition, which first enhances the structural information representation of the hyperspectral image through multi-path delay embedding transformation and Hankel transformation; secondly, the Fourier transformation is introduced to diagonalize the high-order image, which not only enhances the linear correlation of the data, but also greatly reduces the calculation complexity; then, the optimal low-rank approximation is obtained by gradually increasing the rank, and the inverse Hankel transformation is performed on the low-rank approximation to obtain the optimal estimation of the latent data; finally, the method is introduced into the hyperspectral image compression reconstruction model, and the model is solved by using the alternating iteration method. The application effectively overcomes the defects of the traditional method, such as ignoring the multi-dimensional structure of the hyperspectral image and being prone to loss of detail in reconstruction, and can not only accurately restore the image details and effectively retain the edge information, but also significantly suppress the spectral distortion, greatly improve the reconstruction accuracy while ensuring the compression efficiency, and is suitable for compression sensing and acquisition of scenes of multi-frame data such as hyperspectral imaging and nuclear magnetic resonance imaging. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 A flowchart of the hyperspectral image compression reconstruction method based on Hankel rank increasing tensor decomposition provided by the application is shown in the figure.

[0052] Figure 2 The compression reconstruction experimental results obtained by using the method of the application and the prior art are shown in the figure. DETAILED DESCRIPTION

[0053] The embodiments of the technical solutions of the application will be described in detail below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the application, and therefore only serve as examples, and cannot limit the protection scope of the application. Those skilled in the art should understand that the application can also be implemented without some specific details. In some other embodiments, methods, means, apparatuses and steps familiar to those skilled in the art are not described in detail, in order to highlight the main idea of the application.

[0054] Unless otherwise specified, in the application, the directions or positional relationships indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", "x direction", "y direction", "z direction" and the like are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the directions or positional relationships in the application are only used for illustrative purposes, and cannot be understood as limiting the patent, and those skilled in the art can understand the specific meanings of the above terms in combination with the drawings and according to the specific circumstances.

[0055] Embodiment one

[0056] See the attached Figures 1-2 . The embodiment provides a hyperspectral image compression reconstruction method based on Hankel rank increasing tensor decomposition, and a flowchart thereof is shown in the figure, including the following steps: Figure 1

[0057] Step 1, constructing a basic hyperspectral image compression reconstruction model based on a regular term constraint, and obtaining a compression measurement value of the hyperspectral image;

[0058] Step 2, constructing a high-order tensor based on the hyperspectral image in step 1 based on Hankel transformation;

[0059] Step 3, constructing a regular term based on Hankel rank increasing tensor decomposition for the high-order tensor obtained in step 2;

[0060] Step 4, replacing the sparse regular term of the basic hyperspectral image compression reconstruction model in step 1 with the regular term of Hankel rank increasing tensor decomposition constructed in step 3 to form a final hyperspectral image compression reconstruction model;

[0061] 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.

[0062] Specifically, in step 1, the basic hyperspectral image compression reconstruction model based on the regular term constraint is constructed, and the compression measurement value of the hyperspectral image is obtained, including:

[0063] Supposing that the spatial resolution of the hyperspectral image is , the spectral band is , the hyperspectral image is represented as: , and the vector form of the hyperspectral image is: ;

[0064] The compression measurement value of is obtained through a compression sensing model:

[0065] ; (1)

[0066] wherein is a compression operator, , M < N ; the compression rate is ;

[0067] Under the constraint of the equidistance property condition, by seeking the sparsest signal , formula (1) is converted into the following form:

[0068] ; (2) ​

[0069] wherein, denotes a sparse regularization term, for example, based on l 0, l 1, a sparse regularization term of the nuclear norm.

[0070] Specifically, in step 2, a high-order tensor based on Hankel transform is constructed, including:

[0071] For a hyperspectral image , three replication matrices are given, wherein, ; , , , ; ; then a high-order tensor of Hankelization is obtained according to a multi-path delay embedding transform:

[0072] ; (3)

[0073] wherein, is the length of the delay embedding operator, is a Hankel operator, the operator represents upgrading a 3-order tensor to a 6-order tensor.

[0074] Specifically, in step 3, the expression of the regularization term based on Hankel rank increasing tensor decomposition is constructed as:

[0075] , ; (4)

[0076] wherein, is a dictionary matrix; is a relationship tensor, used to represent the correlation between different dictionary matrices; is an identity matrix; denotes the product of the relationship tensor and the dictionary matrix in the i-th dimension.

[0077] Specifically, in step 4, the expression of the final hyperspectral image compression reconstruction model is:

[0078] ; (5)

[0079] wherein, denotes the Frobenius norm, is a regularization parameter of the tensor.

[0080] Specifically, in step 5, an alternating optimization method is used to solve the hyperspectral image compression reconstruction model constructed in step 4, and finally the reconstructed hyperspectral image is output, including:

[0081] The final hyperspectral image compression reconstruction model is disassembled into three independent sub-problems, and the dictionary matrix, the relationship tensor and the image vector are iteratively updated by fixing other variables, and finally the reconstructed hyperspectral image is output.

[0082] The dictionary matrix sub-problem expression is:

[0083] ; (6)

[0084] When updating the dictionary matrix, the upgraded high-order tensor is respectively matrix unfolded along each dimension, and then the effective eigenvector of each dimension is extracted by singular value decomposition to form the corresponding orthogonal dictionary matrix; wherein the singular value decomposition expression is: , , , , ,

[0085] The relationship tensor sub-problem expression is:

[0086] ; (7)

[0087] When updating the relationship tensor, based on the current high-order tensor and the dictionary matrix, the optimal solution of the relationship tensor is obtained by high-order tensor and dictionary matrix mode multiplication operation, and the closed-form solution is:

[0088] ; (8)

[0089] The image vector sub-problem expression is:

[0090] ; (9)

[0091] When updating the image vector, its corresponding optimization sub-problem is converted into a linear equation system, and the conjugate gradient method is used to solve the linear equation system to obtain the updated image vector; wherein the expression of the linear equation system is:

[0092] ; (10)

[0093] , , , , , ,

[0094] In the iteration process, the ranks of each dimension of the tensor are initialized as the minimum value, and the ranks of each dimension are gradually increased after each round of variable update is completed until the reconstruction error converges or the preset number of iterations is reached. Finally, the updated image vector is inversely unfolded into a tensor form to obtain the reconstructed hyperspectral image. The process is shown in Table 1.

[0095] Table 1 Optimization process of hyperspectral image compression reconstruction model

[0096]

[0097] To further describe the effect of the present application, the present application method is used to reconstruct the compressed image, and four classic compressed sensing methods: Stagewise Orthogonal Matching Pursuit (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 comparison methods. The reconstruction results of these comparison methods and the results of the present application are compared.

[0098] The image data Toy used in the present application comes from the public Cave data set, and the spatial resolution of the data is 512x512 and the spectral band is 31. In the experiment, three sampling rates of 0.10, 0.15 and 0.20 are selected, and a 300x300 image area is selected for testing.

[0099] In order to quantitatively and qualitatively evaluate the fusion effect, the Peak Signal to Noise Ratio (PSNR) is used as an evaluation index in the present embodiment, and the results are shown in Table 2.

[0100] Table 2 PSNR comparison table of each compression reconstruction method under different sampling rates

[0101]

[0102] From Table 2, compared with the four comparison methods, the method of the present application has a higher PSNR value, which indicates that the method of the present application has obvious advantages in the reconstruction of structural information, and is also superior to other methods in suppressing spectral distortion.

[0103] The visual comparison results of the compressed reconstruction on Toy data when the sampling rate is 0.20 are shown in FIG. 6. Figure 2 As can be seen from the enlarged areas, all the methods can obtain good restoration results, but the method of the present application not only has good detail reconstruction performance, but also has obvious advantages in preserving the edges of the image, which verifies the effectiveness of the Hankel rank increasing tensor decomposition constraint of the present application.

[0104] The above embodiments are only used to illustrate the technical solutions of the present application but not limit the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalently replaced without departing from the spirit and scope of the present application, and all of them should be covered in the scope of the claims of the present application. The technical, shape and structure parts not described in detail in the present application are all 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. 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, Represents sparse regularization terms; 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 represents the process of upgrading a 3rd-order tensor to a 6th-order tensor. 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. ; In step 4, the expression for the final hyperspectral image compression and reconstruction model is: ；（5） in, Denotes the Frobenius norm. The regularization parameter of the tensor; 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.

2. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 1, 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.

3. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 1, 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) .

4. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 1, 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.

5. The hyperspectral image compression and reconstruction method based on Hankel rank-increasing tensor decomposition according to claim 1, 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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