A hyperspectral mixed noise removal method based on double total variation

Abstract

The application provides a hyperspectral mixed noise removal method based on double total variation, acquires a hyperspectral image containing mixed noise, selects an SSTV regular term to describe the global sparse structure of the hyperspectral image, simultaneously designs a reweighted norm to constrain the local sparse structure of the spatial direction difference image of the principal component image of the hyperspectral image, introduces double constraints, selects more sparse global features and local features, uses a sparse regular term to isolate sparse noise, uses a norm to depict Gaussian noise of the image, constructs a hyperspectral image denoising model based on double total variation, introduces an auxiliary variable to optimize the hyperspectral image denoising model based on double total variation, uses an ALM algorithm framework to optimize the proposed model, converts a complex problem into multiple simple sub-problems to be solved by alternately iterating, and obtains a denoised hyperspectral image; and the application can effectively improve the applicability and precision of hyperspectral image denoising.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of remote sensing image processing, and more particularly relates to a hyperspectral mixed noise removal method based on double total variation. BACKGROUND

[0002] Hyperspectral remote sensing technology effectively combines advanced spectral technology and traditional two-dimensional imaging technology. Hyperspectral images have rich spectral information, and such images with high spectral resolution have wide application value in practice. In the imaging process, the collected hyperspectral images will be contaminated by various mixed noises due to electromagnetic interference, imaging environment and transmission process, including Gaussian noise, impulse noise, strip noise and dead line noise. Mixed noise reduces the image quality in the image and affects the accuracy and reliability of further application, such as classification, unmixing and target detection of hyperspectral images. Therefore, mixed noise removal has important research value in hyperspectral image processing.

[0003] At present, many denoising methods have been proposed at home and abroad, and good results have been achieved. Current hyperspectral denoising methods mainly include three types of spatial domain denoising method, spectral domain denoising method and model optimization denoising method. In recent years, sparse and low-rank models have been widely used in hyperspectral image denoising, and different angles are used to decompose and estimate the rank of the tensor, and the effects are also different. More suitable regularization constraints need to be selected to retain more useful and detailed information, and the effect of hyperspectral image denoising is further improved.

[0004] The remote sensing image is modeled and expressed as a tensor data, and then the to-be-solved variable is constrained to satisfy certain tensor properties and effective estimation of information restoration is realized. The two core problems of solving remote sensing image information restoration are to establish an effective tensor optimization model and to design an efficient algorithm for model solving. Therefore, it is an important task to design an efficient solving algorithm to find a satisfactory solution of the model. SUMMARY

[0005] In order to overcome the above problems existing in the prior art, the application proposes a hyperspectral mixed noise removal method based on double total variation.

[0006] The application is implemented by the following technical solutions:

[0007] A method for removing mixed hyperspectral noise based on double total variation. Hyperspectral image is a three-dimensional tensor data, i.e., two-dimensional spatial dimension and one-dimensional spectral dimension. Tucker decomposition is used to characterize the similarity of the overall structure of the high-dimensional image. The visual saliency map is used as a weighting factor to act on the original image and then added to the original image to enhance the saliency feature. The spatial patch smoothness prior of the image is another effective regularization term for mixed noise removal. The SSTV regularization term is selected to describe the global sparse structure of the hyperspectral image. At the same time, a reweighted L1 norm is designed to constrain the local sparse structure of the spatial direction difference image of the principal component map of the hyperspectral image. Dual constraints are introduced to select sparser global features and local features. The L1 sparse regularization term is used to isolate sparse noise. The F norm characterizes the Gaussian noise of the image. The established model uses the ALM algorithm framework to optimize the proposed model, converting complex problems into multiple simple sub-problems to be solved alternately and iteratively to obtain the denoised hyperspectral image. The steps of this method are as follows:

[0008] Step 1: Obtain a hyperspectral image Y containing mixed noise;

[0009] Step 2: Select the SSTV regularization term to describe the global sparse structure of the hyperspectral image, and at the same time design a reweighted L1 norm to constrain the local sparse structure of the spatial directional difference image of the principal component map of the hyperspectral image, introduce dual constraints, select sparser global features and local features, the L1 sparse regularization term is used to isolate sparse noise, the F norm characterizes the Gaussian noise of the image, introduce the sparse structure dual constraint, obtain more accurate local features and global features, better remove noise, restore the hyperspectral image, and combine tensor decomposition to construct a hyperspectral image denoising model based on double total variation;

[0010] Step 3: Introduce auxiliary variables Z, R1 and R2 to optimize the hyperspectral image denoising model based on double total variation in step 2. The introduction of auxiliary variables makes the problem of the hyperspectral image denoising model based on double total variation in step 2 separable, and the separated sub-problems are easier to solve, where X = Z, D w X = R1, DH = R2, Z is the hyperspectral image equal to X, R1 is the differential image of X, and R2 is the differential image of the principal component map;

[0011] Step 4: Use the ALM algorithm to solve the optimized double total variation-based hyperspectral image denoising model to obtain the denoised hyperspectral image.

[0012] Further technical solutions include:

[0013] The specific process of step 2 is:

[0014] The mathematical model for establishing a hyperspectral image denoising model based on prior information is:

[0015] Y=X+S+N;

[0016] Where Y represents the noisy hyperspectral image, is a real number space, I1 and I2 are the length and width of the hyperspectral image respectively, I3 is the number of spectra, X represents the clean hyperspectral image, S represents sparse noise, and N represents Gaussian noise. X, S, and N are the same size as Y. The goal of removing mixed noise from hyperspectral remote sensing images is to restore the true image X from the observed Y, which is an ill-posed inverse problem.

[0017] Construct a hyperspectral image denoising model based on double total variation:

[0018]

[0019] Among them, D w (·)=[w1×D x (·);w2×D y (·);w3D z (·)] is the anisotropic space-spectral difference operator, D(·)=[D x (·); D y (·)] is the principal component space difference operator, D x is the difference operator in the horizontal direction of space, D y is the vertical difference operator in space, D z is the difference operator in the spectral direction, G is the reweighting factor, λ1, λ2, and λ3 are non-negative positive parameters used to balance the weights between each item, ε is the variance of Gaussian noise, || ||1 represents the L1 norm of the tensor, || || F Represents the Frobenius norm of the tensor;

[0020] Set the sparse coefficients λ1 = λ2 = 1, λ3 = 10, and the isotropic difference coefficients w = [w1, w2, w3] to [1, 1, 0.6];

[0021] The x, y, and z directions represent the horizontal, vertical, and spectral directions of space, respectively, in high-dimensional remote sensing data. x 、D y 、D z Representing the difference operator of the three-dimensional tensor in three different directions and the value at any position (i, j, p) is defined as follows:

[0022]

[0023] Perform PCA dimensionality reduction on the hyperspectral image to obtain the principal component graph H. The edge information graph W of the principal component graph is obtained by horizontal and vertical differences. G is used as the reweighting factor and updated according to the following formula:

[0024]

[0025] Among them, eps is a very small number. In the implementation process, the MATLAB built-in function eps() is used to obtain this very small number to avoid the denominator being zero;

[0026] PCA dimensionality reduction is implemented using Matlab built-in functions, and the first three principal components are selected;

[0027] The specific process of step three is:

[0028] Introduce auxiliary variables Z, R1 and R2 to optimize the model, where X = Z, D w X = R1, DH = R2, the proposed hyperspectral image denoising model based on double total variation is equivalently expressed as the following model:

[0029]

[0030] The specific process of step four is:

[0031] Based on the ALM solution framework, the augmented Lagrangian function of the hyperspectral image denoising model based on double total variation is written as follows:

[0032]

[0033] Where μ is the penalty coefficient, Λ1, Λ2, Λ3, Λ4 are Lagrange multipliers;

[0034] Initialize X=Y, Z=R1=R2=S=Λ1=Λ2=Λ3=Λ4=0 tensors, μ=0;

[0035] Under the framework of ALM, we can perform alternating iterations to solve each variable while fixing other variables, initializing k = 0;

[0036] Step 4.1, fix other variables and update X k+1 :

[0037]

[0038] The subproblem is solved using the HOOI algorithm. When G k+1 and U i k+1 After obtaining it through the HOOI algorithm, the update of X is substituted back into the Tucker decomposition to obtain:

[0039] X k+1 =C k+1 ×1U1 k+1 ×2U2 k+1 ×3U3 k+1 ;

[0040] The tensor rank parameter in the HOOI algorithm is set to [120, 120, 10];

[0041] Step 4.2, fix other variables and update Z k+1 :

[0042]

[0043] The subproblem is a least squares problem, which is obtained by solving the following linear equation:

[0044] μ(I+D w T D w )Z=μX+Λ2+D w T (μR1-Λ3);

[0045] The above formula is solved using the Fast Fourier Transform:

[0046]

[0047] The Z of the current iteration process is obtained by the above formula k+1 Then, continue to Z k+1 Further compensation updates;

[0048] Perform SLIC superpixel segmentation on the principal component image H obtained in step 2 to obtain a visual saliency map M, which is used as a weighting factor and combined with the hyperspectral image Z of the current iteration process. k+1 Each band is element-wise multiplied and then multiplied with the hyperspectral image Z of the current iteration process. k+1 By adding, the significant features of the hyperspectral image are enhanced, and a hyperspectral smooth area with better restoration effect is obtained;

[0049] Z k+1 Bring in Z k+1 (:,:,i)+a×M×Z k+1 The result of (:,:,i) calculation is Z after compensation update k +1 ;

[0050] Where M is the visual saliency map, a is the coefficient of saliency feature enhancement, SLIC superpixel segmentation is implemented using Matlab built-in functions, the visual saliency map coefficient a is set in the range of [0, 1], the superpixel segmentation parameters are set to the default values, and the expected number of superpixels is in the range of [300, 600].

[0051] Step 4.3, fix other variables and update R1 k+1 :

[0052]

[0053] Using the soft threshold shrinkage operator, we get the following closed-form solution for R1:

[0054]

[0055] Wherein, Shrinkage is the soft threshold shrinkage operator, Shrinkage(m,n)=sign(m)max(|m|-n,0), sign(m) is the sign function, which is 1 when m>0, 0 when m=0, and -1 otherwise.

[0056] Step 4.4: Fix other variables and update R2 k+1 :

[0057]

[0058] Using the soft threshold shrinkage operator, we get the following closed-form solution for R2:

[0059]

[0060] Step 4.5, fix other variables and update S k+1 :

[0061]

[0062] Using the soft threshold shrinkage operator, we get the following closed-form solution for S:

[0063]

[0064] Step 4.6, fix other variables and update the Lagrange multiplier:

[0065]

[0066] Step 4.7, determine whether the iteration termination condition is met, relative change error When Rel≤10 -6 , then terminate the iteration and output a noise-free image; if Rel>10 -6 , then repeat steps 4.1 to 4.6 in step 4, and continue to iterate and update alternately until the iteration termination condition Rel≤10 is met -6 Or when the number of iterations k reaches the preset maximum number of iterations 40, the noise-free image X is output.

[0067] This paper proposes a method for removing mixed hyperspectral noise based on dual total variation. The SSTV regularization term is used to describe the global sparse structure of the hyperspectral image. The reweighted L1 norm is used to constrain the local sparse structure of the spatial difference image of the principal component graph of the hyperspectral image. This dual constraint is introduced to select sparser global and local features. The detailed information of hyperspectral images plays an important role in practical applications. Traditional SSTV regularization methods have poor restoration effects on local details of hyperspectral images that are severely contaminated by mixed noise. The addition of the reweighted L1 norm constraint selects sparser local features, improves the peak signal-to-noise ratio and structural similarity of the restored image, and thus obtains a hyperspectral restored image with better mixed noise removal. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 The overall block diagram of a method for removing mixed hyperspectral noise based on double total variation provided by the present invention;

[0069] Figure 2 This is the real image of the 160th band of the Indian Pines hyperspectral image;

[0070] Figure 3 This is the noise image of the 160th band of the IndianPines hyperspectral image;

[0071] Figure 4 This is the restored image of the 160th band of the Indian Pines hyperspectral image; DETAILED DESCRIPTION

[0072] The present invention will be further explained below with reference to the accompanying drawings.

[0073] This paper proposes a method for removing mixed-noise hyperspectral data based on dual total variation. The test image for this method is the internationally recognized Indian Pines hyperspectral image, with a size of 145×145×224. The Indian Pines hyperspectral image containing mixed noise serves as the model input, Y, and the test is performed according to the following technical scheme:

[0074] Step 1: Obtain a hyperspectral image Y containing mixed noise;

[0075] Step 2: Select the SSTV regularization term to describe the global sparse structure of the hyperspectral image, and at the same time design the reweighted L1 norm to constrain the local sparse structure of the spatial directional difference image of the principal component map of the hyperspectral image, introduce dual constraints, select sparser global features and local features, L1 sparse regularization term is used to isolate sparse noise, F norm characterizes the Gaussian noise of the image, introduces sparse structure dual constraints, obtains more accurate local features and global features, better removes noise, restores the hyperspectral image, and combines tensor decomposition to construct a hyperspectral image denoising model based on double total variation; the specific process is as follows:

[0076] The mathematical model for establishing a hyperspectral image denoising model based on prior information is:

[0077] Y=X+S+N;

[0078] Where Y represents the noisy hyperspectral image, is a real number space, I1 and I2 are the length and width of the hyperspectral image respectively, I3 is the number of spectra, X represents the clean hyperspectral image, S represents sparse noise, and N represents Gaussian noise. X, S, and N are the same size as Y. The goal of removing mixed noise from hyperspectral remote sensing images is to restore the true image X from the observed Y, which is an ill-posed inverse problem.

[0079] Construct a hyperspectral image denoising model based on double total variation:

[0080]

[0081]

[0082] Among them, D w (·)=[w1×D x (·);w2×D y (·);w3D z (·)] is the anisotropic space-spectral difference operator, D(·)=[D x (·); D y (·)] is the principal component space difference operator, D x is the difference operator in the horizontal direction of space, D y is the vertical difference operator in space, D z is the difference operator in the spectral direction, G is the reweighting factor, λ1, λ2, and λ3 are non-negative positive parameters used to balance the weights between each item, ε is the variance of Gaussian noise, || ||1 represents the L1 norm of the tensor, || || F Represents the Frobenius norm of the tensor;

[0083] Set the sparse coefficients λ1 = λ2 = 1, λ3 = 10, and the isotropic difference coefficients w = [w1, w2, w3] to [1, 1, 0.6];

[0084] The x, y, and z directions represent the spatial horizontal, spatial vertical, and spectral directions in high-dimensional remote sensing data, respectively. x 、D y 、D z Representing the difference operator of the three-dimensional tensor in three different directions and the value at any position (i, j, p) is defined as follows:

[0085]

[0086] Perform PCA dimensionality reduction on the hyperspectral image to obtain the principal component graph H. The edge information graph W of the principal component graph is obtained by horizontal and vertical differences. G is used as the reweighting factor and updated according to the following formula:

[0087]

[0088] Among them, eps is a very small number. In the implementation process, the MATLAB built-in function eps() is used to obtain this very small number to avoid the denominator being zero;

[0089] PCA dimensionality reduction is implemented using Matlab built-in functions, and the first three principal components are selected;

[0090] Step 3: Introduce auxiliary variables Z, R1 and R2 to optimize the hyperspectral image denoising model based on double total variation in step 2. The introduction of auxiliary variables makes the problem of the hyperspectral image denoising model based on double total variation in step 2 separable, and the separated sub-problems are easier to solve, where X = Z, D w X = R1, DH = R2, Z is the hyperspectral image equal to X, R1 is the differential image of X, and R2 is the differential image of the principal component map; the specific process is:

[0091] Introduce auxiliary variables Z, R1 and R2 to optimize the model, where X = Z, D w X = R1, DH = R2, the proposed hyperspectral image denoising model based on double total variation is equivalently expressed as the following model:

[0092]

[0093] Step 4: Use the ALM algorithm to solve the optimized double total variation-based hyperspectral image denoising model to obtain the denoised hyperspectral image; the specific process is as follows:

[0094] Based on the ALM solution framework, the augmented Lagrangian function of the hyperspectral image denoising model based on double total variation is written as follows:

[0095]

[0096] Where μ is the penalty coefficient, Λ1, Λ2, Λ3, Λ4 are Lagrange multipliers;

[0097] Initialize X=Y, Z=R1=R2=S=Λ1=Λ2=Λ3=Λ4=0 tensors, μ=0;

[0098] Under the framework of ALM, we can perform alternating iterations to solve each variable while fixing other variables, initializing k = 0;

[0099] Step 4.1, fix other variables and update X k+1 :

[0100]

[0101] The subproblem is solved using the HOOI algorithm. When G k+1 and U i k+1 After obtaining it through the HOOI algorithm, the update of X is substituted back into the Tucker decomposition to obtain:

[0102] X k+1 =C k+1 ×1U1 k+1 ×2U2 k+1 ×3U3 k+1 ;

[0103] The tensor rank parameter in the HOOI algorithm is set to [120, 120, 10];

[0104] Step 4.2, fix other variables and update Z k+1 :

[0105]

[0106] The subproblem is a least squares problem, which is obtained by solving the following linear equation:

[0107] μ(I+D w T D w )Z=μX+Λ2+D w T (μR1-Λ3);

[0108] The above formula is solved using the Fast Fourier Transform:

[0109]

[0110] The Z of the current iteration process is obtained by the above formula k+1 Then, continue to Z k+1Further compensation updates;

[0111] Perform SLIC superpixel segmentation on the principal component image H obtained in step 2 to obtain a visual saliency map M, which is used as a weighting factor and combined with the hyperspectral image Z of the current iteration process. k+1 Each band is element-wise multiplied and then multiplied with the hyperspectral image Z of the current iteration process. k+1 By adding, the significant features of the hyperspectral image are enhanced, and a hyperspectral smooth area with better restoration effect is obtained;

[0112] Z k+1 Bring in Z k+1 (:,:,i)+a×M×Z k+1 The result of (:,:,i) calculation is Z after compensation update k +1 ;

[0113] Where M is the visual saliency map, a is the coefficient of saliency feature enhancement, SLIC superpixel segmentation is implemented using the MATLAB built-in function, the value range of the visual saliency map coefficient a is set to [0, 1], the superpixel segmentation parameters are set to the default values, and the expected number of superpixels is in the range of [300, 600].

[0114] Step 4.3, fix other variables and update R1 k+1 :

[0115]

[0116] The subproblem can be solved using the soft threshold shrinkage operator to obtain the following closed-form solution to R1:

[0117]

[0118] Wherein, Shrinkage is the soft threshold shrinkage operator, Shrinkage(m,n)=sign(m)max(|m|-n,0), sign(m) is the sign function, which is 1 when m>0, 0 when m=0, and -1 otherwise.

[0119] Step 4.4: Fix other variables and update R2 k+1 :

[0120]

[0121] The subproblem can be solved using the soft threshold shrinkage operator to obtain the following closed-form solution to R2:

[0122]

[0123] Step 4.5, fix other variables and update S k+1 :

[0124]

[0125] The subproblem can be solved using the soft threshold shrinkage operator to obtain the following closed-form solution for S:

[0126]

[0127] Step 4.6, fix other variables and update the Lagrange multiplier:

[0128]

[0129] Step 4.7, determine whether the iteration termination condition is met, relative change error When Rel≤10 -6 , then terminate the iteration and output a noise-free image; if Rel>10 -6 , then repeat steps 4.1 to 4.6 in step 4, and continue to iterate and update alternately until the iteration termination condition Rel≤10 is met -6 Or when the number of iterations k reaches the preset maximum number of iterations 40, the noise-free image X is output.

[0130] In particular, each sub-problem in step 4 will be solved iteratively based on the ALM framework until Rel≤10 -6 Or when the number of iterations reaches the preset maximum number of iterations 40, the iteration is terminated, and the output X is the noise-free Indian Pines hyperspectral image, achieving the purpose of removing the mixed noise of the hyperspectral image.

[0131] The noise removal results of the present invention can be evaluated from different perspectives, including visual comparison and quantitative comparison. The quantitative comparison indicators, mean peak signal-to-noise ratio (MPSNR) and mean structural similarity (MSSIM), are used. The larger the value, the closer the denoised image is to the reference image, and the better the denoising effect.

[0132] This paper proposes a method for removing mixed noise from hyperspectral images based on double total variation. The experimental platform is implemented using MATLAB software. Both PCA principal component analysis and SLIC algorithm use MATLAB built-in functions. The case simulation experimental results are shown in the figure. Figure 2 This is the real image of the 160th band of the Indian Pines hyperspectral image. Figure 3 This is the noise-contaminated image of the 160th band of the Indian Pines hyperspectral image. Figure 4 This is the restored image of the 160th band of the Indian Pines hyperspectral image restored by this method. Figure 2 、 Figure 3 and Figure 4It can be seen that the image details recovered by the method are restored very clearly. The MPSNR of the Indian Pines hyperspectral noise image is 13.7389 dB, and the MSSIM is 0.2025. After the Indian Pines hyperspectral image is recovered by the method, the MPSNR is improved to 38.8024 dB, and the MSSIM is improved to 0.9848, which proves the effectiveness and feasibility of the method.

Claims

1. A method for removing mixed hyperspectral noise based on double total variation, characterized in that: The steps of this method are as follows: Step 1: Obtain a hyperspectral image Y containing mixed noise; Step 2: Select the SSTV regularization term to describe the global sparse structure of the hyperspectral image. At the same time, design a reweighted L1 norm to constrain the local sparse structure of the spatial directional difference image of the principal component map of the hyperspectral image. Introduce dual constraints to select sparser global features and local features. The L1 sparse regularization term is used to isolate sparse noise, and the F norm characterizes the Gaussian noise of the image. Combined with tensor decomposition, a hyperspectral image denoising model based on double total variation is constructed. The mathematical model for establishing a hyperspectral image denoising model based on prior information is: Y=X+S+N; in is a real number space, I1 and I2 are the length and width of the hyperspectral image respectively, I3 is the number of spectra, X represents the clean hyperspectral image, S represents sparse noise, N represents Gaussian noise, and X, S, N are the same size as Y; Construct a hyperspectral image denoising model based on double total variation: Among them, D w (·)=[w1×D x (·);w2×D y (·);w3D z (·)] is the anisotropic space-spectral difference operator, D(·)=[D x (·); D y (·)] is the principal component space difference operator, D x is the difference operator in the horizontal direction of space, D y is the vertical difference operator in space, D z is the difference operator in the spectral direction, G is the reweighting factor, λ1, λ2, and λ3 are non-negative positive parameters used to balance the weights between each item, ε is the variance of Gaussian noise, || ||1 represents the L1 norm of the tensor, || || F Represents the Frobenius norm of the tensor; Set the sparse coefficients λ1 = λ2 = 1, λ3 = 10, and the isotropic difference coefficients w = [w1, w2, w3] to [1, 1, 0.6]; The x, y, and z directions represent the horizontal, vertical, and spectral directions of space, respectively, in high-dimensional remote sensing data. x 、D y 、D z Representing the difference operator of the three-dimensional tensor in three different directions and the value at any position (i, j, p) is defined as follows: Perform PCA dimensionality reduction on the hyperspectral image to obtain the principal component graph H. The edge information graph W of the principal component graph is obtained by horizontal and vertical differences. G is updated according to the following formula: Here, eps is a very small number. We use the built-in function eps() in Matlab to obtain this very small number to avoid the denominator being zero. PCA dimensionality reduction is implemented using Matlab built-in functions, and the first three principal components are selected; Step 3: Introduce auxiliary variables Z, R1 and R2 to optimize the hyperspectral image denoising model based on double total variation in step 2. The introduction of auxiliary variables makes the problem of the hyperspectral image denoising model based on double total variation in step 2 separable, and the separated sub-problems are easier to solve, where X = Z, D w X = R1, DH = R2, Z is the hyperspectral image equal to X, R1 is the differential image of X, and R2 is the differential image of the principal component map; Step 4: Use the ALM algorithm to solve the optimized double total variation based hyperspectral image denoising model to obtain the denoised hyperspectral image; Based on the ALM solution framework, the augmented Lagrangian function of the hyperspectral image denoising model based on double total variation is written as follows: Where μ is the penalty coefficient, Λ1, Λ2, Λ3, Λ4 are Lagrange multipliers.

2. The method for removing mixed hyperspectral noise based on double total variation according to claim 1, characterized in that: Step 4 also includes: initializing X=Y, Z=R1=R2=S=Λ1=Λ2=Λ3=Λ4=0 tensors, μ=0; In the ALM framework, each variable is solved by alternating iterations while other variables are fixed, and k is initialized to 0; Step 4.1, fix other variables and update X k+1 : The subproblem is solved using the HOOI algorithm. When G k+1 and U i k+1 After obtaining it through the HOOI algorithm, the update of X is substituted back into the Tucker decomposition to obtain: X k+1 =C k+1 ×1U1 k+1 ×2U2 k+1 ×3U3 k+1 ; The tensor rank parameter in the HOOI algorithm is set to [120, 120, 10]; Step 4.2, fix other variables and update Z k+1 : The subproblem is a least squares problem, which is obtained by solving the following linear equation: μ(I+D w T D w )Z=μX+L2+D w T (μR1-Λ3); The above formula is solved using the Fast Fourier Transform: The Z of the current iteration process is obtained by the above formula k+1 Then, continue to Z k+1 Further compensation updates; Perform SLIC superpixel segmentation on the principal component image H obtained in step 2 to obtain a visual saliency map M, which is used as a weighting factor and combined with the hyperspectral image Z of the current iteration process. k+1 Each band is element-wise multiplied and then multiplied with the hyperspectral image Z of the current iteration process. k+1 By adding, the significant features of the hyperspectral image are enhanced, and a hyperspectral smooth area with better restoration effect is obtained; Z k+1 Bring in Z k+1 (:,:,i)+a×M×Z k+1 The result of (:,:,i) calculation is Z after compensation update k+1 ; Where M is the visual saliency map, a is the coefficient of saliency feature enhancement, SLIC superpixel segmentation is implemented using Matlab built-in functions, the visual saliency map coefficient a is set in the range of [0, 1], the superpixel segmentation parameters are set to the default values, and the expected number of superpixels is in the range of [300, 600]. Step 4.3, fix other variables and update R1 k+1 : Using the soft threshold shrinkage operator, we get the following closed-form solution for R1: Among them, Shrinkage is a soft threshold shrinkage operator, Shrinkage(m,n)=sign(m)max(|m|-n,0), sign(m) is the sign function, which is 1 when m>0, 0 when m=0, and -1 otherwise; Step 4.4: Fix other variables and update R2 k+1 : Using the soft threshold shrinkage operator, we get the following closed-form solution for R2: Step 4.5, fix other variables and update S k+1 : Using the soft threshold shrinkage operator, we get the following closed-form solution for S: Step 4.6, fix other variables and update the Lagrange multiplier: Step 4.7, determine whether the iteration termination condition is met, relative change error When Rel≤10 -6 , then terminate the iteration and output a noise-free image; if Rel>10 -6 , then repeat steps 4.1 to 4.6 in step 4, and continue to iterate and update alternately until the iteration termination condition Rel≤10 is met -6 Or when the number of iterations k reaches the preset maximum number of iterations 40, the noise-free image X is output.

Images