CN106651778A - Spectral imaging method based on self-adaptive coupling observation and non-linear compressed learning - Google Patents

Abstract

The invention discloses a spectral imaging method based on adaptive coupling observation and nonlinear compression learning, which mainly solves the problem that the prior art cannot ensure that the observation matrix is not correlated with the learned dictionary. The implementation steps are as follows: 1. Project the signal in the original space onto the feature space; 2. Use the KPCA method to learn the dictionary in the feature space to obtain a sparse dictionary; 3. Randomly initialize the observation matrix, and use the sparse dictionary The perception matrix formed by the product of the initial observation matrix is iteratively trained to obtain a coupling-optimized observation matrix; 4. Realize nonlinear compressed sensing spectral imaging through the method of nuclear compressed sensing; 5. Use the pre-image method to restore the original signal. Experimental results show that: under different sampling rates, the present invention has better reconstruction effect than the existing method using Gaussian random matrix as the observation matrix, and can be used for low-cost and high-quality acquisition of hyperspectral images.

Description

Spectral Imaging Method Based on Adaptive Coupled Observation and Nonlinear Compressive Learning

technical field

The invention belongs to the technical field of image processing, and in particular relates to a compressed spectral imaging method, which can be used for low-cost and high-quality acquisition of hyperspectral images.

Background technique

Compressed sensing is a new sampling theory developed in the field of signal processing technology in recent years. Using the sparse characteristics of the signal, it can realize the accurate recovery of information under the condition of much smaller than the traditional Nyquist sampling rate. Existing compressed sensing methods are all based on explicit linear sparse representation models. The linear sparse representation model has the advantages of being simple, intuitive, easy to understand, and easy to operate. However, the actual scene information is more complicated, and it is difficult to obtain a sufficiently sparse representation under the linear sparse representation model. If a linear sparse representation model is used, the sparseness of the sparse coefficients obtained is lower, which makes more measurements required to restore the original signal. On the other hand, for the application of compressed sensing technology in compressed imaging, designing a better observation system can improve the imaging quality. Most of the existing compression imaging methods are based on random observations, and the observation matrix is selected as a Gaussian random matrix or a Bernoulli random matrix. However, this kind of random observation matrix can be uncorrelated with most orthogonal dictionaries and satisfy the condition of finite equidistant properties. However, the random observation matrix is still a non-adaptive observation matrix. Although it is universal, it is not suitable for different signals , because the information of the signal is not fully mined, and it is not adaptive and optimal, it is impossible to obtain high-quality compressed imaging results with a small number of sensors.

Contents of the invention

The purpose of the present invention is to address the deficiencies of the above-mentioned prior art, and propose a spectral imaging method based on adaptive coupling observation and nonlinear compression learning, so that the observation matrix and the learned dictionary have better non-correlation. Improve the quality of compressed imaging with a small number of observations.

The technical scheme of the present invention is to project the signal in the original space onto the feature space through the nonlinear kernel function, and perform dictionary learning in the feature space; through a method similar to K-SVD, the sparse dictionary and the initial observation matrix The perceptual matrix composed of the product of , is iteratively trained to obtain a coupling-optimized observation matrix; the nonlinear compressive sensing spectral imaging is realized through the method of kernel compressive sensing. Its implementation steps include the following:

(1) Select three groups of n ₁ ×n ₂ ×n ₃ hyperspectral images, randomly select n spectral segments except the 10th spectral segment to construct the training sample matrix Y=[y ₁ ,y ₂ ,…,y _j ,… ,y _n ], where n ₁ ×n ₂ is the size of the hyperspectral image, n ₃ is the number of total bands, y _j is the column vector drawn from the jth spectral segment, j=1,2,…, n, n is the number of training samples;

(2) Use the training sample matrix Y to train the dictionary, and use the method of kernel principal component analysis (KPCA) to obtain the sparse dictionary of the training sample, which is denoted as n is the number of samples, and K is the number of atoms in the obtained sparse dictionary;

(3) Set the number of measured points as m, and randomly generate a Gaussian random matrix as the initial observation matrix i=1,2,...,m, φ _i is the row vector of initialization observation matrix Φ ₀ ;

(4) According to the sparse dictionary A, combined with the training sample matrix Y and the initial observation matrix Φ ₀ , the perception matrix G=f(Φ ₀ ^T ) ^T f(Y)A is obtained, and the perception matrix G is trained to obtain the final observation matrix Φ , where f is a nonlinear mapping function, and T represents transposition;

(5) Three groups of images of the 10th spectral segment are pulled into column vectors as test samples, which are recorded as e ₁ , e ₂ , e ₃ respectively;

(6) According to the observation matrix Φ obtained in (4) above, perform nonlinear compression imaging on the three test samples e ₁ , e ₂ , and e ₃ in (5), and obtain the measured value m=f _k (<Φ, e _i >), where e _i represents the i-th group of test samples, i is from 1 to 3, and f _k is the selected kernel function;

(7) Calculating the sparse coefficients using the least squares method in represents the pseudo-inverse;

(8) According to the sparse coefficient β and the sparse dictionary A, use the pre-image method to reconstruct the original image in The recovered image for group i.

Compared with the prior art, the present invention has the following advantages:

1. The adaptive coupling optimization algorithm in the kernel space proposed by the present invention makes the observation matrix and the sparse dictionary obtained through dictionary learning have higher non-correlation, and can better meet the restricted equidistant characteristic conditions of the compressed sensing theory.

2. The present invention performs coupling optimization based on the sparse dictionary obtained by dictionary learning to obtain an observation matrix, which can fully mine signal information and is more adaptive, thereby obtaining a better reconstruction effect.

Description of drawings

Fig. 1 is the realization flowchart of the present invention;

Fig. 2 is to use the method of the present invention and with Gaussian random matrix as the method for observation matrix when the sampling rate is 10% to the reconstruction effect contrast figure of test image IndianPines;

Fig. 3 is the mean square error curve figure of reconstructing the restored image to the test image IndianPines when the sampling rate is 10% with the method of the present invention and with the Gaussian random matrix as the observation matrix;

Fig. 4 is to use the method of the present invention and take Gaussian random matrix as the method for observation matrix when the sampling rate is 10% to the reconstruction effect contrast figure of test image Moffet;

Fig. 5 is to use the method of the present invention and the method with Gaussian random matrix as the observation matrix when sampling rate is 10% to carry out the mean square error curve figure of reconstructing the restored image to test image Moffet;

Fig. 6 is to use the method of the present invention and take Gaussian random matrix as the method for observation matrix when the sampling rate is 10% to the reconstruction effect contrast figure of test image WashtonDC;

Fig. 7 is a curve diagram of the mean square error of the reconstructed test image WashtonDC using the method of the present invention and the method of using a Gaussian random matrix as the observation matrix when the sampling rate is 10%.

Specific implementation method

With reference to Fig. 1, the concrete realization steps of the present invention are as follows:

Step 1. Build the training sample matrix.

Get three sets of n ₁ ×n ₂ ×n ₃ hyperspectral images from the image library, use the image of the 10th spectral segment of each group of hyperspectral images as a test sample, and the other n spectral segments as training samples, and use the training samples Each spectral segment image of is pulled into a column vector to form a training sample matrix of size w×n: Y=[y ₁ ,y ₂ ,…,y _j ,…,y _n ], where w=n ₁ ×n ₂ y _j represents the column vector drawn by each spectral segment, j=1,2,...,n.

Step 2. Use the training sample Y to train the dictionary.

In nonlinear compression imaging, the method of training dictionary has methods such as nuclear principal component analysis, nuclear K-SVD and nuclear independent component analysis, and the time of nuclear principal component analysis method training dictionary is relatively short, so the present invention adopts nuclear principal component analysis The KPCA method trains the training samples and finds the sparse dictionary, the steps are as follows:.

2a) The selected kernel function is a polynomial kernel function k(x, y) = f _k (<x, y>) = (<x, y>+c) ^d , where x, y are the input variables of the kernel function, c Be the intercept parameter of kernel function, its value is c=0.5, and d is the exponent parameter, and its value is d=5;

2b) Use the kernel function selected in 2a) to find the kernel matrix of the sample matrix Y:

C=k(Y,Y)=(<Y,Y>+c) ^d

in n is the number of samples;

2c) Decompose the eigenvalue of the kernel matrix C, that is, C=VΣV ^T , where Σ is a diagonal matrix, V is the eigenvector matrix corresponding to the eigenvalue, and T represents transposition;

2d) Set the contribution degree Z=0.9, calculate the contribution rate of each positive eigenvalue in the sum of all positive eigenvalues in the diagonal matrix Σ, and accumulate the contribution of the positive eigenvalues according to the order of the eigenvalues in descending order rate, stop when the accumulated sum is greater than the contribution rate Z, and record the number of accumulated eigenvalues as p;

2e) Obtain the corresponding eigenvector matrix V _p according to the eigenvectors of the first p largest eigenvalues, then the sparse dictionary A=V _p .

Step 3. Generate an initial observation matrix Φ ₀ .

Assuming that the number of measurement points is m, a Gaussian random matrix of size m×w is randomly generated as the initial observation matrix: φ _i is the i-th row vector of the initialization observation matrix Φ ₀ , i=1,2,...,m.

Step 4. According to the sparse dictionary A, the perception matrix G is obtained by combining the training sample matrix Y and the initial observation matrix Φ ₀ .

Multiply the sparse dictionary A, the training sample matrix Y, and the initial observation matrix Φ ₀ to obtain the perception matrix: G=f(Φ ₀ ^T ) ^T f(Y)A, where f represents the nonlinear mapping function, and T represents the transformation place.

Step 5. Train the perception matrix G to obtain the final observation matrix Φ.

5a) The selected kernel function is a polynomial kernel function k(x,y)=f _k (<x,y>)=(<x,y>+c) ^d , c is the intercept parameter of the kernel function, and its value is c=0.5, d is an index parameter, and its value is d=5;

5b) Calculate the Gram matrix G ^T G of the perception matrix G, and solve the following optimization problem to obtain the observation matrix with the least correlation with the sparse dictionary in the feature space:

where I _K is an identity matrix with a size of K×K, and F represents the Frobenius norm of the matrix;

5c) Transform the above optimization problem into G ^T G≈I _K , substitute the perceptual matrix G=f(Φ ₀ ^T ) ^T f(Y)A into G ^T G≈I _K , and multiply the sparse dictionary A to the left on both sides , multiplied right by its transpose A ^T , to get the following relationship:

AA ^T f(Y) ^T f(Φ ₀ ^T )f(Φ ₀ ^T ) ^T f(Y)AA ^T ≈AA ^T ;

5d ^{) Singular value decomposition is performed on the above AAT, that is, AAT = VΛV T , where} , is the orthogonal matrix obtained after singular value decomposition, Is a diagonal matrix, n is the number of training samples;

5e) Substituting AAT = ^{VΛV T into} the formula in 5c), the following relationship is obtained:

VΛV ^T f(Y) ^T f(Φ ₀ ^T )f(Φ ₀ ^T ) ^T f(Y)VΛV ^T ≈VΛV ^T

5f) According to the sample matrix Y and the initialization observation matrix Φ ₀ , combined with the kernel function, calculate the transition kernel matrix K _nm :

5g) simplify the formula of 5e) to:

Among them, the intermediate variable

5h) Write the diagonal matrix Λ as diag(λ ₁ ,…,λ _n ), write the intermediate variable Γ _mn as the row vector form Γ _mn =[τ ₁ ,…,τ _m ] ^T , and write the objective function transform into Among them, v _i =[λ ₁ τ _i,1 ,…,λ _n τ _i,n ];

5i) will expands to:

At the same time, define the error matrix as:

5j) According to the transition kernel matrix K _nm and the orthogonal matrix V, use the following formula to initialize Γ _mn :

5k) The maximum value of the number of cycles t is set to be m, and t starts to cycle from 1;

5l) In the tth cycle, calculate the error matrix E _t , and perform eigenvalue decomposition on it to obtain the largest eigenvalue ξ _t and its corresponding eigenvector u _t ;

5m) According to the following formula, update For each row vector of :

5n) By looping m times, the intermediate variable with the minimum correlation can be obtained

5o) Calculate transition kernel matrix

5p) Solve the following formula to obtain the observation matrix Φ after coupling optimization:

where k(x,y)=f _k (<x,y>).

Step 6. Acquire a test image.

Take the image of the 10th spectral segment of the three sets of hyperspectral images as the test image, and pull it into a column vector, denoted as e ₁ , e ₂ , e ₃ respectively.

Step 7. According to the dictionary A obtained in the above step 2 and the observation matrix Φ obtained in the step 4, the three test images e ₁ , e ₂ , and e ₃ in the step 5 are subjected to nonlinear compression imaging using the method of nuclear compressed sensing .

7a) According to the form of the compressed observation equation M=Gβ, calculate the measured value vector M and the perception matrix G:

7b) According to the calculated measured value vector M and perception matrix G, use the least squares algorithm to obtain the sparse coefficient

Step 8. Reconstruct the original image according to the sparse coefficient β and the sparse dictionary A

Using the pre-image method, the original image is reconstructed by the following formula i=1,2,3:

Among them, u _p represents the p-th column of the unit orthogonal basis, p=1,2,…,w, w is the number of pixels in the hyperspectral image, Aβ=[c ₁ ,c ₂ ,…,c _j , …,c _n ] ^T , c _j represents the jth element of Aβ, f _k is the previously selected polynomial kernel function, is the inverse function of f _k .

Effect of the present invention can be further illustrated by following experiments:

1) Experimental conditions

The three sets of hyperspectral images used in this experiment are typical AVIRIS hyperspectral data: IndianPines, Moffet and WashingtonDC. The IndianPines data was obtained by imaging the agricultural area of northwest Indiana with the AVIRIS sensor in 1992, and the Moffet image was obtained by imaging the Moffett area in California with the AVIRIS sensor in August 1992; the wavelength range of the two sets of images is 0.4um～2.5um, There are 224 spectral segments in total, and there are 200 spectral segments after removing all bands whose pixels are 0 and opaque, and the spatial resolution is 20m. The WashtonDC image is imaged by the HYDICE spectrometer in the Washington DC Mall area. The wavelength range is 0.4um to 2.5um, with a total of 210 spectral bands. After preprocessing, 191 bands are selected, and the spatial resolution is 2.8m. The IndianPines image has a size of 145×145×200, the Moffet image has a size of 145×145×200, and the WashtonDC image has a size of 145×145×191.

Experimental simulation environment: the software MATLAB 2012R is used as the simulation tool, the CPU is AMD A8-5550M, the main frequency is 2.10GHz, the memory is 16G, and the operating system is Windows 7 Ultimate Edition.

Randomly select the 10th spectral segment from each group of hyperspectral images as a test image, and take images of other spectral segments of each group of hyperspectral images as training samples.

2) Simulation content

Simulation 1: Under different sampling rates of 0.1% to 20%, respectively adopt the method of the present invention and the existing method using Gaussian random matrix as the observation matrix to carry out nonlinear compressed sensing simulation experiments on the test image, and the experimental results are shown in Table 1 .

Table 1 Experimental comparison of the two methods at different sampling rates

It can be seen from Table 1 that as the sampling rate continues to increase, the PSNR of the two methods continues to rise, indicating that the reconstruction effect is steadily improving, but the method of the present invention has the largest improvement. Under the same sampling rate, the method of the present invention has the highest PSNR and the best reconstruction effect.

Simulation 2: Under the sampling rate of 10%, the method of the present invention and the existing method using Gaussian random matrix as the observation matrix are respectively used to carry out the compressed sensing simulation experiment on the test image IndianPines, and the experimental results are shown in Figure 2 and Figure 3, where :

Figure 2(a) is the original image of the 10th band of the test image IndianPines;

Figure 2(b) is a reconstructed image using the existing Gaussian random matrix as the observation matrix method, and its PSNR is 34.8322dB;

Fig. 2 (c) is the reconstructed image adopting the method of the present invention, and its PSNR is 37.3694dB;

Figure 3 is the mean square error curves of the two methods at different sampling rates.

Simulation 3: Under the sampling rate of 10%, the method of the present invention and the existing method using Gaussian random matrix as the observation matrix are respectively used to carry out the compressed sensing simulation experiment on the test image Moffet, and the experimental results are shown in Figure 4 and Figure 5, where :

Figure 4(a) is the original image of the 10th spectral segment of the test image Moffet;

Figure 4(b) is the reconstructed image using the existing Gaussian random matrix as the observation matrix method, and its PSNR is 47.2954dB;

Fig. 4 (c) is the reconstructed image adopting the method of the present invention, and its PSNR is 49.9599dB;

Figure 5 is the mean square error curves of the two methods at different sampling rates.

Simulation 4: Under the sampling rate of 10%, respectively adopt the method of the present invention and the existing method using Gaussian random matrix as the observation matrix to carry out the compressed sensing simulation experiment on the test image WashtonDC, the experimental results are shown in Figure 6 and Figure 7, where :

Figure 6(a) is the original image of the 10th band of the test image WashingtonDC;

Figure 6(b) is the reconstructed image using the existing Gaussian random matrix as the observation matrix method, and its PSNR is 44.1374dB;

Fig. 6 (c) is the reconstructed image adopting the method of the present invention, and its PSNR is 46.4503dB;

Figure 7 is the mean square error curves of the two methods at different sampling rates.

From the experimental results in Fig. 2, Fig. 4 and Fig. 6, it can be seen that at the same sampling rate, compared with the existing method using Gaussian random matrix as the observation matrix, the present invention has higher PSNR and the best reconstruction effect .

As can be seen from the graphs of Fig. 3, Fig. 5 and Fig. 7, as the sampling rate increases, the mean square error of the two methods all presents a downward trend; The mean square error of the image is smaller, which illustrates the superiority of the method of the present invention.

Claims (3)

1. A spectral imaging method based on adaptive coupling observation and nonlinear compression learning, comprising the steps of: (1) Select three groups of n ₁ ×n ₂ ×n ₃ hyperspectral images, and randomly select n spectral segments except the 10th spectral segment to construct a sample matrix: Y=[y ₁ ,y ₂ ,…,y _j ,… ,y _n ], where n ₁ ×n ₂ represents the size of the hyperspectral image, n ₃ is the total band number of the hyperspectral image, y _j represents the column vector drawn from the jth spectral segment, j=1,2 ,...,n, n is the number of training samples; (2) Use the training sample matrix to train the dictionary, and use the method of kernel principal component analysis (KPCA) to obtain the sparse dictionary of the training sample, denoted as n is the number of samples, and K is the number of atoms in the obtained sparse dictionary; (3) Set the number of measured points as m, and randomly generate a Gaussian random matrix as the initial observation matrix i=1,2,...,m, φ _i is the row vector of initialization observation matrix Φ ₀ ; (4) According to the sparse dictionary A, combined with the training sample matrix Y and the initial observation matrix Φ ₀ , the perception matrix G=f(Φ ₀ ^T ) ^T f(Y)A is obtained, and the perception matrix G is trained to obtain the final observation matrix Φ , where f is a nonlinear mapping function, and T represents transposition; (5) Three groups of images of the 10th spectral segment are pulled into column vectors as test samples, which are recorded as e ₁ , e ₂ , e ₃ respectively; (6) According to the observation matrix Φ obtained in (4) above, perform nonlinear compression imaging on the three test samples e ₁ , e ₂ , and e ₃ in (5), and obtain the measured value M=f _k (<Φ, e _i >), where e _i represents the i-th group of test samples, i is from 1 to 3, and f _k is the selected kernel function; (7) Calculating the sparse coefficients using the least squares method in represents the pseudo-inverse; (8) According to the sparse coefficient β and the sparse dictionary A, use the pre-image method to reconstruct the original image in The recovered image for group i. 2. The method according to claim 1, wherein in the step (4), the perception matrix G is trained, as follows: 2a) The selected kernel function is a polynomial kernel function k(x,y)=f _k (<x,y>)=(<x,y>+c) ^d , c is the intercept parameter of the kernel function, and its value is c=0.5, d is an index parameter, and its value is d=5; 2b) Calculate the Gram matrix of the perception matrix G, namely G ^T G, and solve the following optimization problems to obtain the observation matrix with the least correlation with the sparse dictionary in the feature space: $\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>$ where I _K is an identity matrix with a size of K×K, and F represents the Frobenius norm of the matrix; 2c) Transform the above optimization problem into G ^T G≈I _K , bring the perceptual matrix G=f(Φ ₀ ^T ) ^T f(Y)A into (G) ^T G≈I _K , and multiply left on both sides Sparse dictionary A, right multiplied by its transpose A ^T , to get the following relationship: AA ^T f(Y) ^T f(Φ ₀ ^T )f(Φ ₀ ^T ) ^T f(Y)AA ^T ≈AA ^T 2d ^{) Singular value decomposition is performed on the above AAT, that is, AAT = VΛV T , where} , is the orthogonal matrix obtained after singular value decomposition, Is a diagonal matrix, n is the number of training samples. 2e) Substituting AAT = ^{VΛV T into} the relational expression in 3c), the following relational expression is obtained: VΛV ^T f(Y) ^T f(Φ ₀ ^T )f(Φ ₀ ^T ) ^T f(Y)VΛV ^T ≈VΛV ^T 2f) According to the sample matrix Y and the initialization observation matrix Φ ₀ , combined with the kernel function, calculate the transition kernel matrix K _nm : 2g) Simplify the relational expression of 3e) to: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; V\&Lambda;V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; V\&Lambda;V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&ap;</span>{\mathrm{<span\; class="notranslate">\; V\&Lambda;V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&Lambda;\&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; no</span>}}\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}<span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}\end{array}<span\; class="notranslate">\; ,</span>$ in, 2h) Write the diagonal matrix Λ as diag(λ ₁ ,…,λ _n ), write Γ _mn as a row vector form Γ _mn =[τ ₁ ,…,τ _m ] ^T , and write the objective function transform into: Among them, v _i =[λ ₁ τ _i,1 ,…,λ _n τ _i,n ] ^T ; 2i) Put the above expands to: At the same time, define the error matrix as: ${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Lambda;</span>}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; t</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ;</span>$ 2j) According to the transition kernel matrix K _nm and the orthogonal matrix V, use the following formula to initialize Γ _mn : ${\mathrm{<span\; class="notranslate">\; \&Gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; V</span>}$ 2k) The maximum value of the number of cycles t is set to be m, and t starts to cycle from 1; 2l) In the tth cycle, calculate the error matrix E _t , and perform eigenvalue decomposition on it to obtain the largest eigenvalue ξ _t and its corresponding eigenvector u _t , 2m) Using the following formula, update For each row vector of : $\sqrt{{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ 2n) cycle m times, you can get the minimum correlation 2o) Calculate transition kernel matrix 2p) Solve the following formula to obtain the coupling-optimized observation matrix Φ: where k(x,y)=f _k (<x,y>). 3. The method according to claim 1, wherein said step (8) is to use the pre-image method to reconstruct the original image according to the sparse coefficient β and the sparse dictionary A By the following formula: ${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; w</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; w</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}$ Among them, u _p represents the pth column of the unit orthogonal basis, p=1,2,…,w, w is the number of hyperspectral image pixels, Aβ=[c ₁ ,c ₂ ,…,c _j ,… ,c _n ] ^T , c _j represents the jth element of Aβ, f _k is the previously selected polynomial kernel function, and f _k ^-1 is the inverse function of f _k .