Hyperspectral Image Denoising Method and System Based on Low-Rank Tensor Decomposition and Adaptive Graph Total Variation

Abstract

The present invention discloses a hyperspectral image denoising method and system based on low-rank tensor decomposition and adaptive graph total variation. First, a hyperspectral denoising model is constructed; the augmented Lagrangian multiplier method is used to alternately solve the variables of the hyperspectral denoising model of tensor decomposition and adaptive graph total variation one by one; the classical HOOI algorithm is used to solve the first variable; the second variable is solved based on the number of bands of the hyperspectral image; the soft threshold shrinkage is used to solve the third variable; the fourth variable of the model is directly differentiated; and the results of all the obtained variables are iterated; the current iteration result is compared with the set iteration termination condition until the convergence condition is satisfied. The method provided by the present invention, compared with LRTV which uses Tucker decomposition, can well retain spatial and spectral correlation information, and compared with LRTDTV which uses more neighbor information of AWGTV, can well retain edge information, and this algorithm achieves the best denoising effect.

Description

Technical Field

[0001] The present invention relates to the technical field of hyperspectral data processing, and particularly to a hyperspectral image denoising method and system based on low-rank tensor decomposition and adaptive graph total variation. Background Art

[0002] Hyperspectral image (HSI) data is collected by an imaging spectrometer, which contains dozens or hundreds of continuous bands. The imaging spectrometer can obtain the spectral information of ground objects with nanometer-level spectral resolution, and organically combines the spectral information characterizing the attributes of ground objects with the spatial information characterizing the geometric position relationship of ground objects, making it possible for precise quantitative analysis and detail extraction of ground objects. HSI has been applied to many fields such as terrain classification, food safety, precision agriculture, cancer detection, and military monitoring.

[0003] However, due to being interfered by various factors during the imaging process, HSI is inevitably contaminated by various noises, such as Gaussian noise, impulse noise, stripe noise, etc. This noise limits the application of HSI. Therefore, HSI denoising is necessary. In recent years, scientists have proposed many HSI denoising methods; among them, the methods with relatively good denoising effects include the method of hyperspectral image restoration based on total variation regularized low-rank matrix decomposition (LRTV), the method of low-rank tensor decomposition based on total variation regularization (LRTDTV), etc. LRTV utilizes the low-rank characteristics of HSI data to characterize the spatial correlation and spatial smoothness of local neighborhood pixels, further improving the denoising effect. However, this method uses too little spatial correlation information of neighborhood pixels and ignores the protection of the HSI edges during the local neighborhood pixel smoothing process. LRTDTV combines Tucker decomposition on the basis of LRTV. This algorithm makes full use of spectral correlation information by using Tucker decomposition, and its denoising effect is significantly better than that of LRTV, but it ignores the protection of HSI edge information. Therefore, it is necessary to further propose a hyperspectral denoising algorithm. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a hyperspectral image denoising method and system based on low-rank tensor decomposition and adaptive graph total variation, which improves the denoising effect of hyperspectral images.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation provided by the present invention includes the following steps:

[0007] Model the input data, and construct a hyperspectral denoising model of tensor decomposition and adaptive graph total variation based on the data model;

[0008] Solve the variables of the hyperspectral denoising model of tensor decomposition and adaptive graph total variation one by one using the augmented Lagrangian multiplier method;

[0009] Use the classical HOOI algorithm to solve the first variable hyperspectral image of the model ;

[0010] Solve each band of the second variable hyperspectral image of the model based on the number of bands of the hyperspectral image ;

[0011] Use soft thresholding shrinkage to solve the third variable sparse noise of the model ;

[0012] By directly differentiating the fourth variable Gaussian noise of the model ; and iterating the results of all variables obtained;

[0013] Compare the current iteration result with the set iteration termination condition until the convergence condition of the iteration termination is satisfied.

[0014] Furthermore, the hyperspectral denoising model is established according to the following formula:

[0015] Construct a hyperspectral denoising model of tensor decomposition and adaptive graph total variation according to the signal model, and the expression is as follows:

[0016]

[0017]

[0018] Among them, represents the noisy hyperspectral image, represents the clean image, represents the sparse noise, represents the Gaussian noise; represents the graph total variation, represents the Frobenius-norm of the Gaussian noise, represents the l1-norm of the sparse noise, τ and λ are non-negative parameters; represents the Tucker decomposition of the clean image, represents the tensor core, U i (i = 1, 2, 3) represents the i-th factor matrix, and the operation symbol "× i (i = 1, 2, 3)" represents the product between the tensor and the matrix, represents U i transpose, I represents the identity matrix, τ and λ are non-negative parameters, used to balance the AWGTV term and the l1-norm term;

[0019] Introduce variables is equivalent to Then the hyperspectral denoising model is equivalent to the following optimization problem:

[0020]

[0021]

[0022] represents the clean hyperspectral data.

[0023] Furthermore, the optimization problem is solved by using the augmented Lagrangian multiplier method, and the augmented Lagrangian function is expressed as:

[0024]

[0025]

[0026] where ρ > 0 is the penalty parameter, Λ1 and Λ2 are Lagrangian multipliers, <*,*> is the inner product operation,

[0027] Furthermore, the variables in the augmented Lagrangian function are updated as follows:

[0028] 1) Update

[0029]

[0030] The above is equivalent to:

[0031]

[0032] represents the clean hyperspectral image, represents the result after the (k + 1)-th iteration; represents the sparse noise, represents the result after the k-th iteration; represents the Gaussian noise, represents the result after the k-th iteration; represents the clean hyperspectral image, represents the result after the k-th iteration; Λ1 represents the Lagrangian multiplier, represents the result of Λ1 after the k-th iteration; Λ2 represents the Lagrangian multiplier, represents the result of Λ2 after the k-th iteration;

[0033] By using the classical HOOI, it is easy to obtain and Then, it can be updated as follows:

[0034]

[0035] denotes the tensor core, denotes the result after the (k + 1)-th iteration; U i (i = 1, 2, 3) denotes the i-th factor matrix; denotes the result after the (k + 1)-th iteration.

[0036] Furthermore, the variables in the augmented Lagrangian function are updated in the following way:

[0037] 2) Update

[0038]

[0039] Matrixize the three-dimensional HSI data and the Λ2 matrix, that is, first vectorize each band, and then sort them column by column for each band. Let be denoted as Z = [z1, z1…, z ρ . To solve the above equation, we can first solve for X (k+1) :

[0040]

[0041] It can be solved band by band. The solution for the j-th band, that is, the j-th column of X, is expressed as:

[0042]

[0043] Then, matrixize z j into an M×N matrix The optimal solution to the unconstrained problem is:

[0044]

[0045] where, vec() represents the vectorization operator, and L(P (k) , Q (k) ) is the matrix pair operator. After solving all the sub-problems, we can obtain X (k+1) , and further obtain

[0046] P is a matrix, and the values in this matrix are the differences in pixel values in the horizontal direction of the image. P (k) is the result after the k-th iteration; Q is a matrix, and the values in this matrix are the differences in pixel values in the vertical direction of the image. Q (k) is the result after the k-th iteration; Denote the matrixization of the j-th band in Z; ||X j || (AWGTV,j) Denote the total variation of the j-th band of X;

[0047] Furthermore, the variables in the augmented Lagrangian function are updated as follows:

[0048] 3) Update

[0049]

[0050] By introducing the soft-thresholding operator:

[0051]

[0052] where and Δ > 0, denote variables; denote the set of real numbers; Δ denotes the threshold; the optimal solution of the problem can be expressed as:

[0053]

[0054] Furthermore, the variables in the augmented Lagrangian function are updated as follows:

[0055] 4) Update

[0056]

[0057] By taking the derivative, we can obtain:

[0058]

[0059] Based on the ALM algorithm, the update formula for the Lagrange multiplier is as follows:

[0060]

[0061]

[0062] Compare the current iteration result with the set iteration termination condition until the iteration termination condition is satisfied.

[0063] Furthermore, the convergence condition for the iteration termination is as follows:

[0064] and

[0065] where ε1 and ε2 are constraint parameters.

[0066] The hyperspectral image denoising system based on low-rank tensor decomposition and adaptive graph total variation provided by the present invention includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the above-mentioned method is implemented.

[0067] The beneficial effects of the present invention are as follows:

[0068] The hyperspectral image denoising method and system based on low-rank tensor decomposition and adaptive graph total variation provided by the present invention adopt Tucker decomposition compared with LRTV, which can well retain spatial and spectral correlation information. Compared with LRTDTV that adopts AWGTV with more neighbor information, it can well retain edge information, and this algorithm achieves the best denoising effect.

[0069] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, they will be obvious to those skilled in the art based on the study of the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following specification. Description of the Drawings

[0070] In order to make the objectives, technical solutions, and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0071] Figure 1 It is a flowchart of the hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation.

[0072] Figure 2 It is the clean hyperspectral image provided by the present invention.

[0073] Figure 3 It is the noisy hyperspectral image provided by the present invention.

[0074] Figure 4 It is the hyperspectral image after denoising by LRTV provided by the present invention.

[0075] Figure 5 It is the hyperspectral image after denoising by LRTDTV provided by the present invention.

[0076] Figure 6 It is the hyperspectral image after denoising by the technical solution LRTDGTV provided by the present invention.

[0077] Figure 7 It is the PSNR comparison chart of each band provided by the present invention.

[0078] Figure 8 It is the SSIM comparison chart of each band provided by the present invention. Detailed Embodiments

[0079] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments given are not intended to limit the present invention.

[0080] Embodiment 1

[0081] As Figure 1 shown, the hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation provided in this embodiment includes the following steps:

[0082] Model the input data and construct a hyperspectral denoising model of tensor decomposition and adaptive graph total variation based on the data model;

[0083] Use the augmented Lagrangian multiplier method to alternately solve the variables of the hyperspectral denoising model of tensor decomposition and adaptive graph total variation one by one;

[0084] Use the classical HOOI algorithm to solve the first variable of the model;

[0085] Solve the second variable of the model band by band based on the number of bands of the hyperspectral image;

[0086] Use soft thresholding shrinkage to solve the third variable of the model;

[0087] Derive the fourth variable of the model directly; and iterate on the results of all variables obtained;

[0088] Compare the current iteration result with the set iteration termination condition until the iteration termination condition is satisfied, and calculate the corresponding peak signal-to-noise ratio and structural similarity value.

[0089] The first variable in this embodiment refers to the clean hyperspectral image which belongs to the introduced variable; the second variable refers to the clean hyperspectral image The third variable refers to the sparse noise The fourth variable refers to the Gaussian noise

[0090] The hyperspectral denoising model is constructed as follows:

[0091]

[0092]

[0093] Among them, represents the adaptive weighted graph total variation of the clean image, which is used to describe the piecewise smooth characteristics of the hyperspectral image, The l1-norm representing sparse noise is used to characterize sparse noises such as salt-and-pepper noise, dead-line noise, and stripe noise. The Frobenius-norm representing Gaussian noise is used to separate Gaussian noise. The Tucker decomposition of the clean image, and the operation symbol "×" i represents the mode product. represents the transpose of U i , I represents the identity matrix; τ and λ are non-negative parameters used to balance the AWGTV term and the l1-norm term. In the model, edge detection technology is also used to preserve edge information. In addition, Performing Tucker decomposition on can characterize the correlation between the spatial and spectral bands of HSI data simultaneously.

[0094] represents the tensor kernel; U1 represents the first factor matrix; U2 represents the second factor matrix; U3 represents the second factor matrix; U i represents the i-th factor matrix; i represents the i-th; represents the transpose of U i , I represents the identity matrix;

[0095] The Tucker decomposition of the clean image, ×1 represents the product of the tensor and the first factor matrix; ×2 represents the product of the tensor and the second factor matrix; ×3 represents the product of the tensor and the third factor matrix;

[0096] HSI data p is the number of bands, and each band can be regarded as a grayscale image of M×N dimensions. An undirected graph can be represented as V = {1,…, N} represents the set of N nodes in the graph, E is the set of edges of the graph, A represents the weighted adjacency matrix of the graph, and the (i, j)-th element of A is denoted as a(i, j). This element represents the correlation between node i and node j. If there is an edge connecting node i and node j, then a(i, j) > 0; otherwise, a(i, j) = 0.

[0097] Among them, represents the adaptive weighted total variation of the graph, and its specific construction steps are as follows:

[0098] First, each band X of the three-dimensional hyperspectral data i is constructed into a graph, that is, the pixel points are modeled as signal values, and adjacent pixel points are characterized by edges. The weight of the edge is defined by a Gaussian kernel function, and the weight a(i, j) of the edge is calculated according to the following formula:

[0099]

[0100] Then, edge detection is performed using an edge detection operator. If node i is an edge pixel, the weight w(i,j) = 0; otherwise, w(i,j) = a(i,j). In this way, an adaptive corrected adjacency matrix W can be obtained.

[0101] According to the definition of total variation of a graph:

[0102] where x i is the signal value of the i-th node of the graph .

[0103] Finally, the adaptive weight is incorporated into the total variation of the graph to obtain the adaptive total variation of the b-th band

[0104]

[0105] Furthermore, the adaptive total variation of all bands can be calculated

[0106]

[0107] The Tucker decomposition is as follows:

[0108] The Tucker decomposition is a high-order principal component analysis that decomposes a tensor into the form of the product of a tensor core and factor matrices. Each factor matrix can be regarded as the principal component in different dimensions. For example, for a third-order tensor The Tucker decomposition can be expressed as

[0109]

[0110] In the formula, and are factor matrices, considered as the principal components in each dimension, is called the tensor core, which shows the degree of interaction between different components. The operation symbol represents the outer product of vectors, which means that each element of the tensor is the product of the corresponding vector elements.

[0111] I represents the first dimension of the tensor ; J represents the second dimension of the tensor ; K represents the third dimension of the tensor ; Q represents the first dimension of the tensor core ; R represents the second dimension of the tensor core ; S represents the third dimension of the tensor core ; b represents the element of the factor matrix B; c represents the element of the factor matrix C; d represents the element of the factor matrix D; o qrs represents the element of the tensor core .

[0112] In this embodiment, the hyperspectral image denoising method is specifically carried out according to the following steps:

[0113] Model the salt-and-pepper noise, dead-line noise, and stripe noise as sparse noise, then the noisy HSI data can be expressed as:

[0114]

[0115] Among them, represents the noisy hyperspectral image, represents the clean image, represents the sparse noise, represents the Gaussian noise.

[0116] According to the signal model, construct a hyperspectral denoising model of tensor decomposition and adaptive graph total variation, and the expression is as follows:

[0117]

[0118]

[0119] To facilitate the solution, introduce the variable is equivalent to The above-mentioned hyperspectral denoising model (i.e., the denoising model) is equivalent to the following optimization problem:

[0120]

[0121]

[0122] represents the clean hyperspectral data

[0123] The above optimization problem can be solved by the augmented Lagrangian multiplier method, and the augmented Lagrangian function can be expressed as:

[0124]

[0125]

[0126] Among them, ρ>0 is the penalty parameter, Λ1 and Λ2 are the Lagrangian multipliers, <*,*> is the inner product operation, and the variables in the above formula are alternately optimized. In the (k + 1)-th iteration, the variables can be specifically updated as follows:

[0127] 1) Update

[0128]

[0129] The above formula can be equivalent to:

[0130]

[0131] represents the clean hyperspectral image, represents the result after the (k + 1)-th iteration; represents the sparse noise, represents the result after the k-th iteration; represents the Gaussian noise, represents the result after the k-th iteration; represents the clean hyperspectral image, represents the result after the k-th iteration; Λ1 represents the Lagrange multiplier, represents the result of Λ1 after the k-th iteration; Λ2 represents the Lagrange multiplier, represents the result of Λ2 after the k-th iteration;

[0132] By using the classical HOOI algorithm, it is easy to obtain and Then, can be updated as follows:

[0133]

[0134] represents the tensor kernel, represents the result after the (k + 1)-th iteration; U i (i = 1, 2, 3) represents the i-th factor matrix; represents the result after the (k + 1)-th iteration.

[0135] 2) Update

[0136]

[0137] For the convenience of solution, first matrixize the three-dimensional HSI data and the ∧2 matrix, that is, first vectorize each band, and then sort them column by column for each band. Let be denoted as Z = [z1, z1…, z ρ , and to solve the above equation, we can first solve X (k+1) :

[0138]

[0139] can be solved band by band. The solution of the j-th band, that is, the j-th column of X, can be expressed as:

[0140]

[0141] Then, matrixize z j into an M×N matrix The optimal solution of the unconstrained problem is:

[0142]

[0143] where vec() represents the vectorization operator, and L(P (k) , Q (k) ) is the matrix pair operator. After solving all sub-problems, X (k+1) can be obtained, and then

[0144] P is a matrix, and the values in this matrix are the differences of pixel values in the horizontal direction of the image. P (k) is the result after the k-th iteration; Q is a matrix, and the values in this matrix are the differences of pixel values in the vertical direction of the image. Q (k) is the result after the k-th iteration; represents the matrixization of the j-th band in Z; ||X j || (AWGTV，j) represents the total variation of the j-th band map of X;

[0145] 3) Update

[0146]

[0147] By introducing the soft-thresholding shrinkage operator:

[0148]

[0149] where and Δ > 0, represents the variable; represents the set of real numbers; Δ represents the threshold; the optimal solution of the problem can be expressed as:

[0150]

[0151] 4) Update

[0152]

[0153] By taking the derivative, we can get:

[0154]

[0155] Based on the ALM algorithm, the update formula of the Lagrange multiplier is as follows:

[0156]

[0157]

[0158] Compare the current iteration result with the set iteration termination condition until the iteration termination condition is satisfied, and calculate the corresponding peak signal-to-noise ratio and structural similarity value.

[0159] Specifically, check the convergence condition for iteration termination:

[0160] and

[0161] where ε1 and ε2 are constraint parameters, which are numbers as small as possible. If the convergence condition is not satisfied, the variables are continuously updated until the convergence condition is satisfied to obtain the optimal solution of the model. Finally, calculate the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) between the denoised hyperspectral image and the clean hyperspectral image without noise.

[0162] Example 2

[0163] The HSI dataset in this example is the clean hyperspectral image of Indian Pines in Indiana, USA Its data size is 145 * 145 * 224. To simulate noise data, artificial noise is added, including sparse noise (including salt-and-pepper noise, stripe noise, dead line noise), Gaussian noise, and the output after adding noise is the noisy hyperspectral image The value of τ is 0.008; the value of λ is 0.11.

[0164] Send the three-dimensional noisy hyperspectral image y into the LRTDGTV model, and the output is the denoised hyperspectral image as Figure 6 shown, Figure 2 represents the hyperspectral image without noise, Figure 3 is the noisy hyperspectral image, Figure 4 is the hyperspectral image after LRTV denoising, Figure 5 is the hyperspectral image after LRTDTV denoising. By comparing Figure 2 with Figure 3 of the comparison, it can be observed that relatively severe noise is added in this experiment, which can reflect the effectiveness of the technical solution; according to Figure 4 and Figure 5 it can be observed that there is edge blurring in the image, Figure 4 and Figure 5The denoising effect diagrams of LRTV and LRTDTV are shown respectively. It can be easily seen that LRTV and LRTDTV can effectively remove noise, but there is loss of edge information in the HSI image, while LRTDGTV can overcome these problems to achieve the best denoising effect. Compared with LRTV which adopts Tucker decomposition, this method can well preserve the spatial and spectral correlation information. Compared with LRTDTV which adopts AWGTV with more neighbor information, it can well preserve the edge information, and this algorithm achieves the best denoising effect.

[0165] while Figure 6 can overcome this problem, that is, it can be observed that the denoising effect of the technical solution model of the present invention is better. Figure 7 and Figure 8 The figure shows the comparison diagrams of the PSNR and SSIM parameters of each band after denoising of the technical solution of the present invention with the existing LRTV and TRTDTV technical solutions. It can be found from Figure 7 that the PSNR value of the technical solution of the present invention is basically higher than that of the LRTV and LRTDTV technical solutions in each band, and only a very small number are lower than the LRTDTV technical solution, but the difference is not significant. The higher the PSNR value, the better the denoising effect. According to Figure 8 observation, the denoising effect of the PSNR of each band of the technical solution of the present invention is better than that of the LRTV and LRTDTV technical solutions; the closer the SSIM value is to 1, the better the denoising effect. In summary, it can be observed that the technical solution of the present invention is superior to the above-mentioned existing technical solutions.

[0166] The average peak signal-to-noise ratio MPSNR and the average structural similarity MSSIM parameters obtained by averaging the PSNR and SSIM of each band of the technical solution of the present invention and the above-mentioned existing solutions are shown in Table 1. It can be observed that the technical solution of the present invention is superior to the above-mentioned existing solutions.

[0167]

[0168] This embodiment uses low-rank tensor decomposition and adaptive graph total variation for hyperspectral image denoising, which not only strengthens the piecewise smoothness characteristics of HSI, but also preserves the edge information in the hyperspectral image, avoiding the edges from being smoothed and affecting the denoising effect. Through experimental verification and analysis, this method has a better denoising effect.

[0169] The above-described embodiments are only preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims

1. A hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation, characterized in that: Including the following steps: Model the input data and construct a hyperspectral denoising model based on tensor decomposition and adaptive graph total variation using the data model; Use the augmented Lagrangian multiplier method to solve the variables of the hyperspectral denoising model of tensor decomposition and adaptive graph total variation alternately one by one; Solve the first variable hyperspectral image of the model using the classical HOOI algorithm ; Solve the second variable hyperspectral image of the model one by one according to the number of bands of the hyperspectral image Solve band by band; Using soft thresholding shrinkage to solve the sparse noise of the third variable of the model for solution; By directly taking the derivative of the Gaussian noise of the fourth variable of the model and iterating the results of all variables obtained; Compare the current iteration result with the set iteration termination condition until the convergence condition for the iteration termination is satisfied.

2. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation as claimed in claim 1, wherein: The hyperspectral denoising model is established according to the following formula: According to the signal model, construct a hyperspectral denoising model of tensor decomposition and adaptive graph total variation, and the expression is as follows: Among them, represents the noisy hyperspectral image, represents the clean image, represents the sparse noise, represents the Gaussian noise; represents the total variation of the image, represents the Frobenius - norm of the Gaussian noise, represents the l1 - norm of the sparse noise, τ and λ are non - negative parameters; represents the Tucker decomposition of the clean image, represents the tensor kernel, U i (i = 1, 2, 3) represents the i - th factor matrix, the operation symbol "× i " represents the product between the tensor and the matrix, represents U i 's transpose, I represents the identity matrix, τ and λ are non - negative parameters used to balance the AWGTV term and the l1 - norm term; Introduce variables Is equivalent to Then the hyperspectral denoising model is equivalent to the following optimization problem: Represents clean hyperspectral data.

3. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive total variation on graphs according to claim 2, wherein: The optimization problem is solved using the augmented Lagrangian multiplier method, and the augmented Lagrangian function is expressed as: Where ρ>0 is the penalty parameter, Λ1 and Λ2 are Lagrangian multipliers, and <*,*> is the inner product operation.

4. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation according to claim 3, characterized in that: The variables in the augmented Lagrangian function are updated in the following manner: 1) Update The above formula is equivalent to: represents a clean hyperspectral image, represents the result after the (k + 1)-th iteration; represents sparse noise, represents the result after the k-th iteration; represents Gaussian noise, represents the result after the k-th iteration; represents a clean hyperspectral image, represents the result after the k-th iteration; Λ1 represents the Lagrange multiplier, represents the result of Λ1 after the k-th iteration; Λ2 represents the Lagrange multiplier, represents the result of Λ2 after the k-th iteration; By using the classical HOOI algorithm, it can be easily obtained that and Then can be updated as follows: represents a tensor core, represents the result after the (k + 1)-th iteration; U i represents the i-th factor matrix; represents the result after the (k + 1)-th iteration.

5. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation as claimed in claim 3, wherein: The variables in the augmented Lagrangian function are updated in the following manner: 2) Update The three-dimensional HSI data and the Λ2 matrix are formed. That is, each band is first vectorized, and then sorted column by column for each band. Let be denoted as Z = [z1, z1…, z ρ . To solve the above equation, X (k+1) can be solved first: It can be solved band by band. The solution of the j-th band, that is, the j-th column of X, is expressed as: Then, transform z j into an M×N matrix The optimal solution of the unconstrained problem is: where, vec() represents the vectorization operator, and L(P (k) , Q (k) ) is the matrix pair operator. After solving all sub-problems, X (k+1) can be obtained, and then P is a matrix, and the values in this matrix are the differences of pixel values in the horizontal direction of the image, P (k) is the result after the k-th iteration; Q is a matrix, and the values in this matrix are the differences of pixel values in the vertical direction of the image, Q (k) is the result after the k-th iteration; represents the matrixization of the j-th band in Z; ||X j || (AWGTV,j) represents the total variation of the j-th band image of X.

6. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation according to claim 3, characterized in that: The variables in the augmented Lagrangian function are updated in the following manner: 3) Update By introducing a soft thresholding operator: Among them, and Δ > 0, represent variables; represents the set of real numbers; Δ represents a threshold; the optimal solution of the problem can be expressed as:

7. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive total variation on graphs according to claim 3, wherein: The variables in the augmented Lagrangian function are updated in the following manner: 4) Update By taking the derivative, we can get: Based on the ALM algorithm, the update formula for the Lagrangian multiplier is as follows: Compare the current iteration result with the set iteration termination condition until the iteration termination condition is satisfied.

8. The hyperspectral image denoising method based on low-rank tensor decomposition and adaptive graph total variation according to claim 7, characterized in that: The convergence condition for the iteration termination is as follows: and Where v1 and v2 are constraint parameters.

9. A hyperspectral image denoising system based on low-rank tensor decomposition and adaptive graph total variation, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method described in any one of claims 1 to 8 above.

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