CN112950500B - Hyperspectral denoising method based on edge detection low-rank total variation model - Google Patents

Abstract

The invention discloses a hyperspectral denoising method based on an edge detection low-rank total variation model, constructs an input signal model, and builds and optimizes an edge detection low-rank total variation model based on the input signal model; uses singular value shrinkage The method solves the first sub-problem divided in the low-rank total variational model of edge detection; divides the obtained second sub-problem based on the number of hyperspectral image bands, and uses an iterative gradient-based fast edge detection four-neighborhood The domain total variational algorithm solves all the second sub-problems; uses the soft threshold shrinkage operator to solve the obtained third sub-problem, and iterates the results of all the obtained sub-problems; Compare 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. After experimental verification and analysis, the denoising effect of the spectral image is improved.

Description

A hyperspectral denoising method based on low-rank total variational model for edge detection

technical field

The invention relates to the technical field of hyperspectral image data processing, in particular to a hyperspectral denoising method based on an edge detection low-rank total variation model.

Background technique

Hyperspectral imaging (HSI) technology can acquire two-dimensional images in a wide range of electromagnetic spectrum and higher spectral resolution, so it is used in archaeology and art conservation, vegetation and water resources control, food quality and safety control, forensics, surgery and Diagnosis, crime scene detection, biomedicine, military and other fields have been widely used.

However, due to its unique physical design, HSI is inevitably polluted by various noises during the acquisition process. Common types of polluted noise include Gaussian noise, impulse noise, dead pixels, and streak noise. In recent years, many scientists have proposed a variety of HSI denoising algorithms. Among them, the hyperspectral image restoration method based on low-rank matrix restoration (LRMR) and the hyperspectral image restoration method based on total variation regularized low-rank matrix decomposition (LRTV) are the most effective ones. The LRMR method utilizes the low-rank characteristic of hyperspectral images, and represents the main information of hyperspectral images with a low-rank matrix, thereby removing a large amount of redundant information in hyperspectral images. And most of the noise is also included in the redundant information, so the use of low-rank matrix to restore the hyperspectral image can achieve the effect of denoising. However, the denoising method based on low rank only studies the correlation between spectral bands, ignoring the spatial correlation of local neighborhood pixels, so it cannot achieve the best denoising effect. On the basis of low-rank characteristics, the LRTV method describes the spatial correlation and spatial smoothness of local neighborhood pixels, and its denoising effect is better than LRMR, but this method uses too little spatial correlation information of neighborhood pixels, and The protection of hyperspectral image edges during local neighborhood pixel smoothing is ignored. Therefore, the design method to improve the denoising effect of spectral images needs to be further introduced.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a hyperspectral denoising method based on a low-rank total variation model of edge detection, so as to improve the denoising effect of spectral images.

In order to achieve the above object, the present invention provides a hyperspectral denoising method based on a low-rank total variation model for edge detection, comprising the following steps:

constructing an input signal model, and constructing and optimizing an edge detection low-rank total variational model based on the input signal model;

Solve the first sub-problem divided in the edge detection low-rank total variation model by using the singular value shrinkage method;

Divide the obtained second sub-problems based on the number of hyperspectral image bands, and use an iterative gradient-based fast edge detection four-neighbor total variation algorithm to solve all the second sub-problems;

Solve the obtained third sub-problem by using the soft-threshold shrinkage operator, and iterate the results of all the obtained sub-problems;

The current iteration result is compared with the set iteration termination condition until the iteration termination condition is satisfied, and the corresponding peak signal-to-noise ratio and structural similarity value are calculated.

Wherein, constructing an input signal model, and constructing and optimizing an edge detection low-rank total variation model based on the input signal model, including:

Add the acquired original image to the randomly generated sparse noise and Gaussian noise in turn to obtain the input signal model;

Based on the input signal model, an edge detection low-rank total variation model is constructed, and the augmented Lagrangian function method is used to optimize the edge detection low-rank total variation model, and the main sub-problems are divided, among which, The divided sub-problems include a first sub-problem, a second sub-problem and a third sub-problem.

Wherein, the obtained second sub-problems are divided based on the number of hyperspectral image bands, and the iterative gradient-based fast edge detection four-neighbor total variation algorithm is used to solve all the second sub-problems, including:

Divide the obtained second sub-problem into multiple sub-problems according to the number of hyperspectral image bands;

Rewrite and iterate each of the band sub-problems, and in the iterative process, use the edge detection operator to assign values to the detected pixels;

Iteratively calculates the absolute values of the four-neighbor differences of all the pixel points that satisfy the condition after the assignment, until the set iterative condition is satisfied, and the solution of the corresponding second sub-problem is obtained.

Among them, iterative calculation is performed on the absolute value of the four-neighbor difference of all pixel points that satisfy the condition after assignment, until the set iterative condition is satisfied, and the solution of the corresponding second sub-problem is obtained, including:

Flip the value of the pixel point after the assignment to obtain the detection value;

Using the addition of the absolute value of the difference between the four neighborhoods of each pixel point, the result value of the constraint condition of the current calculation result and the result value of the constraint condition of the previous calculation result are calculated, and the absolute value of the obtained difference is divided by all the The result value of the constraint condition of the current calculation result, if the obtained calculation value is less than the set iteration condition, the iteration is terminated, and the result values of all frequency bands are added to obtain the solution of the second sub-problem.

Among them, the current iteration result is compared with the set iteration termination condition until the iteration termination condition is satisfied, and the corresponding peak signal-to-noise ratio and structural similarity value are calculated, including:

If the current calculation result does not satisfy the set iteration termination condition, the first sub-problem, the second sub-problem, the third sub-problem and all other sub-problems are re-solved until the set iteration termination condition is met, wherein , the other sub-problems are problems other than the first sub-problem, the second sub-problem and the third sub-problem;

After the set iteration termination condition is satisfied, the obtained hyperspectral denoised image is compared with the original image to obtain the corresponding peak signal-to-noise ratio and structural similarity value.

A hyperspectral denoising method based on a low-rank total variation model for edge detection of the present invention constructs an input signal model, and builds and optimizes a low-rank total variation model for edge detection based on the input signal model; using a singular value shrinkage method Solve the first sub-problem divided in the edge detection low-rank total variation model; divide the obtained second sub-problem based on the number of hyperspectral image bands, and use the iterative gradient-based fast edge detection four-neighborhood The total variational algorithm solves all the second sub-problems; uses the soft threshold shrinkage operator to solve the obtained third sub-problem, and iterates the results of all the obtained sub-problems; compares the current iteration result with The set iteration termination conditions are compared until the iteration termination conditions are met, and the corresponding peak signal-to-noise ratio and structural similarity values are calculated, and the edge detection four-neighborhood total variation algorithm is used to denoise the hyperspectral image, It not only strengthens the smoothness relationship between neighborhoods, but also protects the edge in the hyperspectral image, avoiding the edge being smoothed and affecting the denoising effect. After experimental verification and analysis, this method has better denoising effect.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

FIG. 1 is a schematic diagram of steps of a hyperspectral denoising method based on a low-rank total variation model of edge detection provided by the present invention.

Figure 2 is a clean original image provided by the present invention.

FIG. 3 is an image after adding noise provided by the present invention.

FIG. 4 is an image after LRMR denoising provided by the present invention.

FIG. 5 is an image after LRTV denoising provided by the present invention.

FIG. 6 is an image after EDTV denoising according to the technical solution provided by the present invention.

FIG. 7 is a comparison diagram of PSNR of each band provided by the present invention.

FIG. 8 is a comparison diagram of the SSIM of each band provided by the present invention.

Detailed ways

The following describes in detail the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary, and are intended to explain the present invention and should not be construed as limiting the present invention.

In the description of the present invention, "plurality" means two or more, unless otherwise expressly and specifically defined.

Referring to FIG. 1, the present invention provides a hyperspectral denoising method based on a low-rank total variation model for edge detection, comprising the following steps:

S101. Build an input signal model, and build and optimize a low-rank total variation model for edge detection based on the input signal model.

Specifically, construct the input signal model Y=X+S+N, where Y represents the input noise signal; X represents the clean original image; S represents sparse noise, which is used to describe impulse noise, dead pixels, stripe noise, etc.; N represents Gaussian noise.

According to the input signal model, a low-rank total variation model for edge detection is established:

表示高斯噪声的F范数的平方，去噪后使该项尽可能小，从而达到去噪效果；ε为一个尽可能小的数，用来约束优化项；rank(·)表示矩阵的秩；r为设定的矩阵秩大小，用来约束优化项，使其满足低秩性质；τ和λ均为正则项参数。Among them, min represents the value of X and S when the latter formula reaches the minimum value; || · || _* is the nuclear norm, which refers to the sum of the singular values of the matrix, which is used for convex approximate rank constraints and is used to describe the high low-rank characteristics of spectral images; ||X|| _EDTV represents piecewise smoothness of hyperspectral images; ||S|| ₁ represents sparse noise; st is subjectto, followed by constraints; ||·|| _F is Frobenius Norm, that is, the sum of the squares of the absolute values of the matrix elements and then the square root; in the constraint term

Represents the square of the F-norm of Gaussian noise. After denoising, make the item as small as possible to achieve the denoising effect; ε is a number as small as possible, which is used to constrain the optimization item; rank( ) represents the rank of the matrix; r is the set size of the matrix rank, which is used to constrain the optimization term to satisfy the low-rank property; τ and λ are both regular term parameters.

According to the established low-rank total variation model of edge detection, the model is optimized and solved:

The augmented Lagrangian function method (Augmented Lagrangian method, hereinafter referred to as ALM) is used to solve the above problem. First, rewrite the above problem equivalently, as follows:

L is equivalent to X before the equivalent rewriting, in order to facilitate the use of the subsequent ALM method.

Using the ALM method, the optimized augmented Lagrangian function is as follows:

s.t.rank(L)≤r

表示求关于L,X,S,Λ₁,Λ₂的函数的最小值函数；Λ₁,Λ₂为优化系数矩阵；<·,·>表示内积；μ为罚因子，初始值设置为1e-2。in,

Represents the function of finding the minimum value of the function about L, X, S, Λ ₁ , Λ ₂ ; Λ ₁ , Λ ₂ are the optimization coefficient matrix; <·,·> represents the inner product; μ is the penalty factor, and the initial value is set to 1e -2.

Divide the above problem into multiple sub-problems and solve them one by one iteratively:

表示式子*达到最小值时·的取值；k表示第k次迭代；*^(k+1)表示第k+1次迭代后*式的结果；*^(k)表示第k次迭代后*式的结果。in

Represents the value of the expression * when it reaches the minimum value; k represents the k-th iteration; * ^(k+1) represents the result of the * formula after the k+1-th iteration; * ^(k) represents the k-th iteration * formula result.

Thus, the problem is reduced to solving the three main first to third sub-problems of L, X, and S.

S102. Use the singular value shrinkage method to solve the first sub-problem divided in the low-rank total variational model for edge detection.

Specifically, the method of singular value contraction is used to solve the first sub-problem of L.

For a given matrix W, decompose it using singular value decomposition to get:

W=UE _r V ^* ,E _r =diag({σ _i } _1≤i≤r )

where U, V are the unitary matrices obtained by the singular value decomposition of W; V ^* is the conjugate transpose of V; E _r is a positive semi-definite diagonal matrix; diag( ) represents the construction of a diagonal matrix whose diagonal elements are ·; {σ _i } _1≤i≤r represents the set formed by the first r diagonal elements.

Then use the singular value contraction operator:

达到最小时且满足L的秩小于r时L的值；Among them, D _δ (W) is the formula

The value of L when the minimum is reached and the rank of L is less than r;

D _δ (W)=UD _δ (E _r )V ^* ,D _δ (E _r )=diag{max((σ _i -δ),0)}, where max(*,0) means that for each * and 0 comparison, take the maximum value of each comparison between the two.

S103. Divide the obtained second sub-problems based on the number of hyperspectral image bands, and use an iterative gradient-based fast edge detection four-neighbor total variation algorithm to solve all the second sub-problems.

Specifically, solve the second subproblem about X:

The problem is decomposed into p sub-problems according to the number of hyperspectral image bands p, namely

表示第k+1次迭代后第j个波段X的值；where j is an integer from 1 to p;

represents the value of the jth band X after the k+1th iteration;

After the assignment, the absolute value of the four-neighbor difference is iteratively calculated for all pixels that satisfy the condition that the pixel point is a non-edge pixel point and the four-neighborhood of the pixel point is a non-edge pixel point, until the set iterative condition is met, and the result is obtained The solution to the corresponding second subproblem.

The above problem is solved using an iterative gradient-based fast four-neighbor total variational algorithm for edge detection.

The subproblems for each band above can be rewritten as equivalent problems as follows:

其中，P_C为正交投影算子，L(p,q)为矩阵对算子，其中The solution to the above problem is

Among them, PC is the orthogonal projection operator, _L (p,q) is the matrix pair operator, where

L(p,q) _i,j =p _i,j +q _i,j -p _i-1,j -q _i,j-1 , i=1,...,m,j=1,... .,n

p _i,j =x _i,j -x _i+1,j , i=1,...,m-1,j=1,...,n

q _i,j =x _i,j -x _i,j+1 , i=1,...,m,j=1,...,n-1

Where x _{*, ·} is the value of the pixel whose abscissa is * ordinate is ·;

In the iterative process, X is continuously assigned, and it is constantly approaching the optimal solution. In each iteration process, the Sobel edge operator is used to perform edge detection on X. If the pixel is detected as an edge, the value is 1, otherwise it is 1. 0; the detected value δ _i,j is obtained by flipping its 0 and 1 values.

Then, the absolute value of the difference between the four neighborhoods of each pixel is added to describe the smoothness of the hyperspectral image. When an edge is detected, the pixel does not participate in the smoothness characterization, or when a certain point around the pixel is an edge, The neighborhood of this direction does not participate in the characterization of smoothness, so we get

in,

值与上一次迭代该式子的值相减的绝对值除以此次的值小于预设的迭代条件1e-4时，则停止迭代，从而求解得计算值X。When the iteration is satisfied this time

When the absolute value of the subtraction of the value from the previous iteration of the formula divided by the current value is less than the preset iteration condition 1e-4, the iteration is stopped, and the calculated value X is obtained.

The complete X is obtained by superimposing and restoring the calculated value X _j obtained from each band.

S104. Use a soft threshold shrinkage operator to solve the obtained third sub-problem, and iterate over the obtained results of all the sub-problems.

Specifically, the third sub-problem of S is solved by using the soft threshold shrinkage operator.

Shrinking operator by soft threshold

where x∈R, Δ>0; then the solution of the sub-problem in this step is:

Iterate to get Λ ₁

Iterate to get Λ ₂

S105. 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.

Specifically, the penalty factor is set at each amplification step ρ=1.5 and μ _max =1e6, and μ is iterated.

μ( ^k+1 )=min(ρμ, μ _max ), where min(*, ·) represents the value of comparing * and ·, whichever is smaller.

Judging the iteration termination conditions, if the conditions are met, the iteration is stopped. The iteration termination conditions are as follows:

Where ||·|| _∞ is the infinity norm, which represents the maximum value of the sum of the absolute values of the matrix row vectors; ε ₁ , ε ₂ is a number as small as possible, which is the constraint parameter.

If the iteration termination condition is not met, continue to return to solve the first sub-problem again, and perform a new round of iteration until the termination condition is met, and the solution of the existing model is obtained.

Calculate the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) parameters of the obtained hyperspectral denoised image X and the unnoised clean image to evaluate the superiority of the comparative denoising effect.

Case Analysis:

其中M、N为高光谱图像维度，本实例M＝145，N＝145；r＝10；ε₁＝ε₂＝1e-6；μ的初始值为1e-2。The hyperspectral image input in this example is a clean hyperspectral image of Indiana, USA, namely X, which has 224 bands and a dimension of 145*145*224. It is artificially added with noise. The added noise includes sparse noise (including salt and pepper noise) and Gaussian noise. After adding noise, the output is Y, and τ is 0.015; λ is

M and N are the dimensions of the hyperspectral image. In this example, M=145, N=145; r=10; ε ₁ =ε ₂ =1e-6; the initial value of μ is 1e-2.

The three-dimensional hyperspectral image after adding noise is sent to the model of this technical solution, and the obtained comparison diagram before and after denoising is shown in Figure 2-6. Figure 2-6 is a grayscale image, which represents the depth of black, and the darker the grayscale The smaller the gray value of the image, the clean original image in Figure 2, the image after adding noise in Figure 3, the image after denoising by LRMR method, Figure 5 is the image after denoising by LRTV method, and Figure 6 is The image after denoising of this technical solution; according to the comparison between Figure 2 and Figure 3, it can be observed that this experiment has added more serious noise, which can reflect the effectiveness of this technical solution; according to Figure 4, it can be observed that there are still Blurred points, compared to Figure 5 and Figure 6, the denoising effect is not good; observe Figure 5 and Figure 6 and observe that the denoising effect of Figure 6 is similar globally, but when looking closely at the details, Figure 6 denoises The effect is better than Fig. 5, that is, it can be observed that the model of the technical solution has a good denoising effect. Compared with the method of hyperspectral image restoration based on low-rank matrix restoration (LRMR) proposed by Hongyan Zhang and the method of hyperspectral image restoration based on total variation regularized low-rank matrix factorization (LRTV) proposed by Wei He, this technical scheme is removed. The PSNR and SSIM parameters of each frequency band after the noise are compared with the above-mentioned prior art solutions, and Figures 7-8 are obtained. Observe Figure 7. The curve (solid line) located at the top of the image is the PSNR parameter curve of the technical solution, and the curve located in the middle ( The dotted line) is the PSNR parameter curve of the LRTV technical solution, and the curve at the bottom (dotted line) is the PSNR parameter curve of the LRMR technical solution. The line type on the upper right of the image corresponds to the footnote of the technical solution; the higher the PSNR value, the better the denoising effect. Good; according to Fig. 7, it can be seen that the denoising effect of each band of PSNR of this technical solution is better than that of LRMR; the PSNR of this technical solution basically satisfies the denoising effect of all bands and is better than that of LRTV technical solution (there are very few bands that are slightly lower than LRTV). Compared with the LRTV technical solution, this technical solution avoids the deterioration of the denoising effect in individual bands; observe Figure 8, the curve at the top of the image (dotted line) is the SSIM parameter curve of the technical solution, the curve in the middle (dotted line) is the SSIM parameter curve of the LRTV technical solution, and the curve at the bottom (solid line) is the SSIM parameter curve of the LRMR technical solution, at the upper right of the image The line type corresponds to the footnote of the technical solution; the closer the SSIM parameter is to 1, the closer the similarity to the original image structure is, which means that the denoising effect is better, and a conclusion consistent with the observation in Figure 7 can be obtained. It is superior to the above-mentioned existing technical solutions.

Take the average value of each band PSNR and SSIM of the technical solution and the above-mentioned existing scheme, and record it as a result; repeat the above experiment 30 times, and obtain 30 results; then take the average of the 30 results to obtain the PSNR, SSIM parameters, the results are shown in Table 1, and it can be observed that the technical solution is better than the existing solution above.

Table 1 Comparison of denoising effects of each scheme for 30 times

A hyperspectral denoising method based on a low-rank total variation model for edge detection of the present invention constructs an input signal model, and builds and optimizes a low-rank total variation model for edge detection based on the input signal model; using a singular value shrinkage method Solve the first sub-problem divided in the edge detection low-rank total variation model; divide the obtained second sub-problem based on the number of hyperspectral image bands, and use the iterative gradient-based fast edge detection four-neighborhood The total variational algorithm solves all the second sub-problems; uses the soft threshold shrinkage operator to solve the obtained third sub-problem, and iterates the results of all the obtained sub-problems; compares the current iteration result with The set iteration termination conditions are compared until the iteration termination conditions are met, and the corresponding peak signal-to-noise ratio and structural similarity values are calculated, and the edge detection four-neighborhood total variation algorithm is used to denoise the hyperspectral image, It not only strengthens the smoothness relationship between neighborhoods, but also protects the edge in the hyperspectral image, avoiding the edge being smoothed and affecting the denoising effect. After experimental verification and analysis, this method has better denoising effect.

The above disclosure is only a preferred embodiment of the present invention, and of course, it cannot limit the scope of rights of the present invention. Those of ordinary skill in the art can understand that all or part of the process for realizing the above-mentioned embodiment can be realized according to the rights of the present invention. The equivalent changes required to be made still belong to the scope covered by the invention.

Claims (2)

1. A hyperspectral denoising method based on an edge detection low-rank total variation model is characterized by comprising the following steps:

constructing an input signal model, and constructing and optimizing an edge detection low-rank total variation model based on the input signal model;

solving a first sub-problem divided in the edge detection low-rank fully-variable model by using a singular value shrinkage method;

dividing the obtained second subproblems based on the number of wave bands of the hyperspectral image, and solving all the second subproblems by using an iterative gradient-based fast edge detection four-neighborhood total variation algorithm;

iterating the obtained results of all the sub-problems by using a soft threshold shrinkage operator;

comparing the current iteration result with a set iteration termination condition until the iteration termination condition is met, and calculating a corresponding peak signal-to-noise ratio and a corresponding structural similarity value;

an input signal model is built, and an edge detection low-rank total variation model is built and optimized based on the input signal model, and the method comprises the following steps:

constructing an input signal model Y which is X + S + N, wherein Y represents an input noise signal; x represents a clean original image; s represents sparse noise; n represents Gaussian noise;

according to an input signal model, establishing an edge detection low-rank total variation model:

wherein min represents the value of X and S when the formula reaches the minimum value; i | · | purple wind _* Is a kernel norm, refers to the sum of matrix singular values, is used for convex approximate rank constraint,the low-rank characteristic is used for describing a hyperspectral image; | X | non-conducting phosphor _EDTV Representing the piecewise smoothness of the hyperspectral image; | S | non-woven phosphor ₁ Representing sparse noise; s.t. objectto, with constraints indicated later; i | · | purple wind _F Is Frobenius norm, which is the square sum of the absolute values of the matrix elements and then the square of the square; in constraint term

Represents the square of the F-norm of gaussian noise; ε is used to constrain the optimization term; rank (·) denotes the rank of the matrix; r is the set matrix rank size and is used for constraining optimization items to meet the low-rank property; both tau and lambda are regular term parameters;

according to the established edge detection low-rank total variation model, optimizing and solving the model:

solving the problems by adopting an augmented Lagrange function method; the above problem is first equivalently rewritten as follows:

l is equivalent to X before equivalent rewriting;

by adopting the ALM method, the optimized augmented Lagrangian function is as follows:

s.t.rank(L)≤r

wherein, mini (L, X, S, Lambda) ₁ ,Λ ₂ ) Expression relating to L, X, S, Lambda ₁ ,Λ ₂ A minimum function of the function of (a); lambda ₁ ,Λ ₂ Optimizing a coefficient matrix;<·,·>represents the inner product; mu is a penalty factor, and the initial value is set to be 1 e-2;

dividing the problem into a plurality of sub-problems, and solving one of the sub-problems in an iterative manner:

Λ ₁ ^(k+1) ＝Λ ₁ ^(k) +μ(Y-L ^(k+1) -S ^(k+1) )

Λ ₂ ^(k+1) ＝Λ ₂ ^(k) +μ(X ^(k+1) -L ^(k+1) )

wherein

The value of the expression when the minimum value is reached is expressed; k represents the kth iteration; * ^(k+1) Represents the result of formula after the (k + 1) th iteration; * ^(k) Represents the result of formula after the k-th iteration;

thus solving L, X, S the three main first to third sub-problems;

dividing the obtained second subproblems based on the number of the wave bands of the hyperspectral image, and solving all the second subproblems by using an iterative gradient-based fast edge detection four-neighborhood total variation algorithm, wherein the method comprises the following steps:

solving a second sub-problem with respect to X:

the problem is decomposed into p band sub-problems according to the number p of bands of the hyperspectral image, i.e.

Wherein j is an integer from 1 to p; x _j ^(k+1) Represents the value of the jth band X after the (k + 1) th iteration;

after assignment, carrying out iterative computation on the four-neighbor domain difference absolute values of all the pixels which meet the condition that the pixel is a non-edge pixel and the four neighborhoods of the pixel are non-edge pixels until a set iteration condition is met, and obtaining a solution of a corresponding second subproblem;

solving the problem by using an iterative gradient-based fast edge detection four-neighborhood total variation algorithm;

for the sub-problem of each band described above, we can rewrite it as an equivalent problem, as follows:

the solution of the above problem is

Wherein, P _C For the orthographic projection operator, L (p, q) is a matrix pair operator, wherein

L(p,q) _i,j ＝p _i,j +q _i,j -p _i-1,j -q _i,j-1 ，i＝1,...,m,j＝1,...,n

p _i,j ＝x _i,j -x _i+1,j ，i＝1,...,m-1,j＝1,...,n

q _i,j ＝x _i,j -x _i,j+1 ，i＝1,...,m,j＝1,...,n-1

Wherein x is _*,· The value of a pixel point with the abscissa as x and the ordinate as · is defined;

continuously evaluating the value of X in the iteration process, continuously approaching to the optimal solution, carrying out edge detection on X by adopting a Sobel edge operator in each iteration process, if the pixel point is detected to be an edge, setting the value to be 1, and otherwise, setting the value to be 0; the 0, 1 value is turned over to obtain a detection value delta _i,j ；

And then, the smoothness of the hyperspectral image is depicted by adding the difference absolute values of four adjacent domains of each pixel point, when an edge is detected, the pixel point does not participate in the smoothness depiction, or when a certain point around the pixel point is an edge, the adjacent domain in the direction does not participate in the smoothness depiction, so that the smoothness depiction is obtained

Wherein,

when iterated to satisfy this

When the absolute value of the subtraction of the value and the value of the formula of the previous iteration is divided by the value of the current iteration to be less than the preset iteration condition 1e-4, stopping the iteration, and solving to obtain a calculated value X;

calculating value X obtained from each wave band _j And (5) overlapping and reducing to obtain complete X.

2. The hyperspectral denoising method based on the edge detection low-rank total variation model according to claim 1, wherein comparing the current iteration result with a set iteration termination condition until the iteration termination condition is satisfied, and calculating a corresponding peak signal-to-noise ratio and a corresponding structural similarity value comprises:

if the current calculation result does not meet the set iteration termination condition, solving the first subproblem, the second subproblem, the third subproblem and all other subproblems again until the set iteration termination condition is met, wherein the other subproblems are the problems except the first subproblem, the second subproblem and the third subproblem;

and after the set iteration termination condition is met, comparing the obtained hyperspectral denoised image with the original image to obtain a corresponding peak signal-to-noise ratio and a corresponding structural similarity value.

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