A shadow compensation method for hyperspectral images based on nonlinear pixel analysis

Abstract

The present invention discloses a method for shadow compensation of hyperspectral images based on nonlinear pixel analysis. The shadow compensation algorithm of the present invention can be divided into three parts: endmember extraction, abundance estimation and shadow area reconstruction. According to the multiple interactions of photons that may exist in the pixels in the shadow area of ​​the image, the present invention first extracts endmembers from the shadow area and non-shadow area of ​​the image, and estimates the abundance of the pixels in the shadow area using the endmembers in the shadow area and an unmixing algorithm based on a nonlinear mixing model. Finally, the pixels in the shadow area are reconstructed using the endmembers in the non-shadow area and the pixel abundance values ​​in the shadow area to compensate for the shadow part in the hyperspectral image. The present invention can use various nonlinear unmixing models to estimate the abundance of pixels in the shadow area and reconstruct the pixels in the shadow area.

Description

Technical Field

[0001] The invention belongs to the field of image processing, and in particular relates to a hyperspectral image shadow compensation method based on nonlinear pixel analysis. Background Art

[0002] Hyperspectral images have rich spectral information and high spectral resolution, and have attracted widespread attention in the field of remote sensing in recent years. The spectral range of hyperspectral images covers visible to near-infrared, including hundreds of spectral bands. Rich spectral information and fine spectral resolution help to analyze the materials in the scene using the spectral information in the image. Hyperspectral imaging is widely used in pollution monitoring, land use analysis, medical imaging processing, and target detection. However, in the process of remote sensing image imaging, due to the presence of vegetation, telephone poles, buildings, etc., shadow areas will be formed in the image. Therefore, for the same imaging material, the spectral characteristics of pixels in the shadow and non-shadow areas may be very different. The spectral intensity values ​​of pixels in the shadow area of ​​the hyperspectral image are lower than the intensity values ​​of pixels in the non-shadow area, which affects the accuracy of the hyperspectral image classification and target detection algorithms.

[0003] A lot of work has been done on removing shadows from hyperspectral images. Physical model-based shadow compensation methods analyze the shadow area of ​​the image by measuring the sun's altitude, azimuth or sensor parameters, and then remove the shadow. For example, the Retinex model uses the sun's azimuth information to compensate for the shadow area in the image. Hyperspectral images are usually acquired by airborne platforms or satellites, and it is difficult to directly measure prior knowledge such as geometry or atmospheric conditions, which limits the scope of use of this type of method. Multi-model shadow removal methods are similar to physical model-based shadow compensation methods, using additional sensors such as lidar and global positioning system (GPS) to remove shadows. The use of additional sensors limits the use of this type of method. Another type of shadow compensation method uses features such as color, illumination and geometry to analyze the difference between shadow and non-shadow areas in the image based on different attributes. For example, the color invariant space model uses color transformation theory and threshold method for shadow compensation. Recently, a study proposed the use of linear spectral unmixing to perform image shadow compensation, that is, using endmember information from non-shadow areas and pixel abundance scores from shadow areas to reconstruct the spectral information of shadow areas in the image. Although some progress has been made in shadow compensation methods based on spectral unmixing, it must be pointed out that the generation of shadows may involve multiple scattering of light, so that the high-order interaction of photons will introduce nonlinear effects in spectral mixing. Therefore, it is of great significance to use nonlinear pixel analysis for spectral unmixing and reconstruction in the study of shadow compensation methods. Summary of the invention

[0004] The purpose of the present invention is to overcome the above shortcomings and provide a hyperspectral image shadow compensation method based on nonlinear pixel analysis to model shadow scenes using a nonlinear mixed model and improve the accuracy of spectral shadow compensation. In the research of the present invention, only the shadow compensation algorithm is focused on, and the shadow area is considered to be known, and the detection method is no longer used for shadow detection.

[0005] In order to achieve the above object, the present invention comprises the following steps:

[0006] S1, obtaining a three-dimensional hyperspectral image of the shadow to be compensated, and reconstructing the three-dimensional hyperspectral image of the shadow to be compensated to obtain a two-dimensional hyperspectral image;

[0007] S2, estimating the number of endmembers of the two-dimensional hyperspectral image to obtain the number of endmembers;

[0008] S3, obtaining a partition label matrix of shadow and non-shadow regions of the shadow image to be compensated, and reconstructing the partition label matrix to obtain a one-dimensional partition label;

[0009] S4, dividing the two-dimensional hyperspectral image into a shadow area set and a non-shadow area set according to the one-dimensional partition label;

[0010] S5, using the vector component analysis endmember extraction method to estimate the endmembers of the shadow area, and obtain the endmember matrix of the shadow area;

[0011] S6, using the vector component analysis endmember extraction method to estimate the endmembers of the non-shadow area, and obtain the endmember matrix of the non-shadow area;

[0012] S7, using the endmember matrix extracted from the shadow area to estimate the abundance of the pixels in the shadow area;

[0013] S8, the reconstruction of the shadow area is completed by using the abundance estimation information of the shadow area and the corresponding end members extracted from the non-shadow area.

[0014] In S7, a nonlinear unmixing model is used to analyze the pixels in the shadow area, and the optimization problem is as follows:

[0015]

[0016] st

[0017] Among them, x is the image of the shaded area, Φ represents the nonlinear relationship between endmembers and abundance, E is the endmember, a is the abundance, and different nonlinear unmixing models are used to estimate the abundance of the shaded area.

[0018] The specific method in S7 is as follows:

[0019] S71, using the bilinear model to estimate the abundance of the shadow area, and obtaining the shadow area abundance estimation result a based on the bilinear model bilinear ;

[0020] S72, using p-order polynomials to account for higher-order interactions between photons, obtains the abundance estimation result of the shadow region based on the bilinear model a p ;

[0021] S73, using the K-Hype model to explain the higher-order interactions between photons, obtain the abundance estimation result of the shadow region based on the K-Hype model a K-Hype ;

[0022] S74, using multiple linear mixed models to estimate the abundance of shadow area pixels a MLM ;

[0023] S75, using the deep autoencoder unmixing method NAE to estimate the abundance of shadow areas a NAE .

[0024] In S71, the solution of the bilinear model is achieved by solving the following constrained quadratic problem:

[0025]

[0026] st

[0027] Among them, γ ij is the probability of interaction between end members, a i is the abundance corresponding to the ith end member, a j is the abundance corresponding to the jth end member, e i is the ith end member, e j is the jth end member, and ⊙ is the dot product.

[0028] In S72, the abundance estimation result of the shadow area based on the p-order polynomial model is a p , which is achieved by solving the following constrained quadratic problem:

[0029]

[0030] st

[0031] Among them, b ik is the weight coefficient, is the ith end member, and k is the power number.

[0032] In S73, the K-Hype model is as follows:

[0033]

[0034] in, represents the transpose of the lth row of e, ψ nlin is a real function defined in the reproducing kernel Hilbert space, k nlin is its reproducing kernel function, is the lth row of e, n l For the lth row of noise n, the kernel function is selected as follows:

[0035]

[0036]

[0037] in, is the p-th row of e, and σ is the noise standard deviation.

[0038] In S74, the multiple linear mixed model is expressed as follows:

[0039]

[0040] Where n is the noise, which is solved by solving the following optimization problem:

[0041]

[0042] st

[0043] Among them, e i is the ith end member.

[0044] In S75, the model of the shaded area is expressed as follows:

[0045] x=Ψ(Ea)+n

[0046] Among them, Ψ is the nonlinear relationship between end members and abundance. The training of the entire autoencoder network is achieved by minimizing the minimum mean square error between input pixels and reconstructed pixels, as shown in the following formula:

[0047]

[0048] Among them, x i is the i-th pixel, is the i-th estimated pixel.

[0049] The specific method of S8 is as follows:

[0050] S81, by finding the minimum spectral angle distance, each shadow region end member e i Correspond to its end members in the non-shaded area E′;

[0051] S82, reconstructing the spectrum of the shadow area by using the abundance vectors corresponding to the pixels in the shadow area and the end members matched from the non-shadow area.

[0052] In S81, the end element matrix E′ is the same as the end element e in the shaded area. i The end member vector with the minimum SAD value is e i The corresponding non-shaded end member e i ″, as shown below:

[0053]

[0054] The method of S82 is as follows:

[0055] x=Φ(E″,a)

[0056] where Φ is the nonlinear unmixing model used in abundance estimation.

[0057] Compared with the prior art, the shadow compensation algorithm of the present invention can be divided into three parts: endmember extraction, abundance estimation and shadow area reconstruction. According to the multiple interactions of photons that may exist in the shadow area pixels of the image, the present invention first extracts endmembers from the shadow area and non-shadow area of ​​the image, and estimates the abundance of the pixels in the shadow area using the endmembers in the shadow area and the unmixing algorithm based on the nonlinear mixing model. Finally, the pixels in the shadow area are reconstructed using the endmembers in the non-shadow area and the pixel abundance values ​​in the shadow area to compensate for the shadow part in the hyperspectral image. The present invention can use various nonlinear unmixing models to estimate the abundance of the pixels in the shadow area, obtain abundance information, and reconstruct the pixels in the shadow area. By using the labeled shadow image data collected in the laboratory and the real remote sensing data results, it can be seen that the use of nonlinear unmixing methods can effectively improve the effect of spectral image shadow compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the process of the present invention;

[0059] Figure 2 This is the Pavia University data experimental reconstruction diagram of the present invention; wherein, (a) is the Pavia University synthetic RGB image, (b) is the experimental area, (c) is the image reconstructed using FCLS, (d) is the image reconstructed using NCLS, (e) is the image reconstructed using the bilinear model, (f) is the image reconstructed using the p-order model, (g) is the image reconstructed using the K-Hype algorithm, (h) is the image reconstructed using MLM, and (i) is the image reconstructed using NAE. DETAILED DESCRIPTION

[0060] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention is further described in detail with reference to the following specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0061] Step 1: Obtain the three-dimensional hyperspectral image X of the shadow to be compensated 3D , treat the de-shadowed 3D hyperspectral image X 3D Perform reconstruction processing to obtain a two-dimensional hyperspectral image X;

[0062] Among them, the shadow three-dimensional hyperspectral image X 3D The expression is:

[0063]

[0064] The expression of the two-dimensional hyperspectral image X is:

[0065]

[0066] N=M×W

[0067] Among them, L is the number of spectral channels of the three-dimensional hyperspectral image to be compensated for shadows, M is the spatial dimension length of the three-dimensional hyperspectral image to be compensated for shadows; W is the spatial dimension width of the three-dimensional hyperspectral image to be compensated for shadows, and N is the total number of pixels in the two-dimensional hyperspectral image.

[0068] Step 2: Estimate the number of endmembers of the two-dimensional hyperspectral image X to obtain the number of endmembers R;

[0069] Specifically, the minimum error identification method is used to minimize the projection of the two-dimensional hyperspectral image X. The number of endmembers R of the two-dimensional hyperspectral image is determined in the orthogonal subspace by minimizing the sum of the noise energy of the projection and the projection signal error energy.

[0070] Step 3: Obtain the shadow and non-shadow area division label matrix A of the shadow image to be compensated 2D , partition the label matrix A 2D Reconstruct and obtain a one-dimensional partition label A;

[0071] Step 4: Divide the two-dimensional hyperspectral image X into a shadow area set S and a non-shadow area set according to the partition label A.

[0072] Step 5: Use the vector component analysis endmember extraction method to estimate the endmembers of the shadow area S and obtain the endmember matrix E of the shadow area;

[0073] Specifically, the pixel with the largest projection distance in the simplex is found in S and used as a candidate end member. By finding an orthogonal subspace and calculating the projection distance of each pixel in the orthogonal subspace, the pixel with the largest projection distance is found as the newly acquired end member, and the end member matrix is ​​continuously updated until R end members are found.

[0074] Step 6: Use the vector component analysis endmember extraction method to extract the non-shadow area Perform endmember estimation to obtain the endmember matrix E′ of the shadow area;

[0075] Specifically, in The pixel with the largest projection distance in the simplex is found and used as a candidate endmember. By finding an orthogonal subspace and calculating the projection distance of each pixel in the orthogonal subspace, the pixel with the largest projection distance is found as the newly acquired endmember, and the endmember matrix is ​​continuously updated until R endmembers are found.

[0076] Step 7: Use the endmember matrix E extracted from the shadow area to estimate the abundance of the shadow area pixels. This step uses a nonlinear unmixing model to analyze the shadow area pixels. The optimization problem is as follows:

[0077]

[0078] st

[0079] Among them, x is the image of the shaded area, Φ represents the nonlinear relationship between the endmember and the abundance, and E is the endmember. Different nonlinear unmixing models can be used to estimate the abundance of the shaded area.

[0080] Step 7-1: Use the bilinear model to estimate the abundance of the shadow area and obtain the shadow area abundance estimation result a based on the bilinear model bilinear , the solution of the bilinear model can be achieved by solving the following constrained quadratic problem:

[0081]

[0082] st

[0083] Among them, γ ij is the probability of interaction between end members, a i is the abundance corresponding to the ith end member, a j is the abundance corresponding to the jth end member, e i is the ith end member, e j is the jth end member, and ⊙ is the dot product.

[0084] Specifically, the problem can be solved by using the MATLAB optimization toolbox.

[0085] Step 7-2: Use a p-order polynomial to account for the higher-order interactions between photons and obtain the shadow region abundance estimation result a based on the bilinear model p ,The model can be realized by solving the following constrained quadratic problem:

[0086]

[0087] st

[0088] Among them, b ik is the weight coefficient, is the ith end member, and k is the power number.

[0089] Specifically, the problem can be solved by using the MATLAB optimization toolbox.

[0090] Step 7-3: Use the K-Hype model to explain the higher-order interactions between photons and obtain the abundance estimation result of the shadow region based on the K-Hype model a K-Hype , the model is shown as follows:

[0091]

[0092] in, represents the transpose of the lth row of e, ψ nlin is a real function defined in the reproducing kernel Hilbert space, k nlin is its reproducing kernel function, is the lth row of e, n l For the lth row of noise n, the kernel function can be selected as

[0093]

[0094]

[0095] in, is the p-th row of e, and σ is the noise standard deviation.

[0096] Step 7-4: Use multiple linear mixed models to estimate the abundance of shadow area pixels a MLM , the model can be expressed as follows:

[0097]

[0098] Where n is the noise, which can be solved by solving the following optimization problem:

[0099]

[0100] st

[0101] Among them, e i is the ith end member.

[0102] Step 7-5: Estimate the abundance of shadowed areas using a nonlinear hyperspectral unmixing method based on a deep autoencoder network NAE , the model can be expressed as follows:

[0103] x=Ψ(Ea)+n

[0104] Among them, Ψ is the nonlinear relationship between end members and abundance. The training of the entire autoencoder network is achieved by minimizing the minimum mean square error between input pixels and reconstructed pixels, as shown in the following formula:

[0105]

[0106] Among them, x i is the i-th pixel, is the i-th estimated pixel.

[0107] Specifically, the algorithm can be implemented using PyTorch and Torch frameworks.

[0108] Step 8: This step completes the reconstruction of the shadow area by using the abundance estimation information of the shadow area and the corresponding end members extracted from the non-shadow area.

[0109] Step 8-1: Separate each shadow region end member e by finding the minimum spectral angle distance i The end element matrix E′ corresponds to the end element e in the shaded area. i The end member vector with the minimum SAD value is e i The corresponding non-shaded end member e i ″, as shown below:

[0110]

[0111] Step 8-2: Reconstruct the spectrum of the shadow area by using the abundance vectors corresponding to the pixels in the shadow area and the endmembers matched from the non-shadow area.

[0112] x=Φ(E″,a)

[0113] where Φ is the nonlinear unmixing model used in abundance estimation.

[0114] The effect of the present invention is further described below in conjunction with specific experiments. Using labeled experimental data established in the laboratory and real remote sensing data, a shadow compensation experiment based on nonlinear unmixing was carried out. In the experiment, FCLS and NCLS unmixing algorithms based on linear unmixing, as well as bilinear models, p-order models (p=2), K-Hype algorithms, MLM unmixing algorithms and NAE algorithms based on nonlinear unmixing models were used to estimate abundance, and then the performance of the shadow compensation method proposed based on unmixing was evaluated. In this experiment, the K-Hype algorithm based on Gaussian kernel was used, in which μ=0.5 and σ=4 were set; for the NAE algorithm, the learning rate was set to 1×10 -4 The Adam optimizer is used to train the network. The batch size is set to 512, and all samples are trained 50 times in total. In the experiment, the two linear methods FCLS and NCLS are used as references for the results of nonlinear algorithms.

[0115] In order to quantitatively evaluate the experimental results, shadow and non-shadow data of 5 scenes were collected in a strictly controlled laboratory scene. In the experiment, a low-resolution mixture was simulated by using a checkerboard material as an imaging target, and then a plastic plate was placed next to the imaging target to form a shadow area. This experiment uses RMSE to evaluate the accuracy of abundance estimation, and RE is used to evaluate the accuracy of shadow spectrum reconstruction. The RMSE results of this experiment are shown in Table 1. These results show that the nonlinear unmixing method can effectively estimate the abundance of the shadow area. The experimental results of RE are shown in Table 2. From the experimental results, it can be seen that the shadow compensation method based on the nonlinear unmixing model is better than the one based on the linear unmixing model, especially the shadow compensation effect based on the K-Hype algorithm and the p-order unmixing model is better. These quantitative results prove the effectiveness of nonlinear unmixing in shadow compensation.

[0116] Table 1 Comparison of RMSE of abundance estimation of laboratory-created data

[0117]

[0118]

[0119] Table 2 Comparison of laboratory creation data RE

[0120] FCLS NCLS Bilinear p-order model K-Hype MLM NAE Scenario A 0.0081 0.0098 0.0077 0.0075 0.0070 0.0076 0.0084 Scenario B 0.0079 0.0108 0.0076 0.0071 0.0068 0.0076 0.0075 Scenario C 0.0087 0.0115 0.0084 0.0081 0.0074 0.0081 0.0083 Scenario D 0.0090 0.0122 0.0086 0.0082 0.0074 0.0082 0.0088 Scenario E 0.0084 0.0101 0.0080 0.0072 0.0078 0.0083 0.0074

[0121] The Pavia University dataset was used for shadow compensation experiments. This dataset was collected by the Reflection Optical System Imaging Spectrometer (ROSIS). The ROSIS-03 sensor contains 115 spectral channels ranging from 430 to 860 nm. In the data used in this study, 12 noise channels were removed, leaving 103 spectral channels. The spatial resolution of the image is 1.3 m / pixel. Figure 2 (a) shows the synthetic RGB image of the image. This experiment uses Figure 2 The sub-image shown in (b) is used to verify the algorithm. The spatial dimension of the sub-image is 120×106, and the shadow area is mainly caused by buildings.

[0122] In this experiment, the VCA method is used for endmember extraction. In this sub-image, we consider that the number of endmembers in the shadow area and the non-shadow area is 3. The reconstructed images obtained using different hybrid models are shown in Figure 2. Figure 2 As shown in (c)-(i), the experimental results show that the image reconstructed using the nonlinear unmixing algorithm is more consistent with the surrounding image and the image is smoother. In order to better demonstrate the superiority of the algorithm proposed in this paper, a classification strategy is used in the experiment to quantitatively evaluate the performance of the shadow compensation algorithm. According to the public classification labels of the image, a total of 6 different types of objects are marked in the area. In the experiment, 10% of the pixels are used as the training set of the support vector machine (SVM), and the classification accuracy is expressed by classification accuracy (CA). The CA experimental results are shown in Table 3, where "-" represents the classification results without removing the shadow. These results clearly show the effectiveness of nonlinear unmixing shadow compensation.

[0123] Table 3 CA experimental results

[0124] - FCLS NCLS Bilinear p-order model K-Hype MLM NAE CA 87.58％ 91.67％ 91.00％ 95.56％ 95.56％ 94.78％ 94.81％ 93.99％

[0125] See also Figure 2 , where RGB images are generated according to the CIE 1964 color space.

[0126] Compared with the existing methods, the hyperspectral image shadow compensation method system of the present invention uses a method based on hyperspectral unmixing for shadow compensation, which does not require additional prior information and can achieve shadow compensation based on the image's own characteristics. Compared with the use of linear unmixing methods for shadow compensation, the present invention uses a nonlinear mixing model for spectral unmixing to obtain the abundance information of the shadow area pixel, which can solve the multiple scattering problem in the shadow formation process and improve the shadow reconstruction effect.

[0127] The above embodiment is only one of the implementation methods that can realize the technical solution of the present invention. The scope of protection claimed by the present invention is not limited only to this embodiment, but also includes changes, replacements and other implementation methods that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention.

Claims

1. A hyperspectral image shadow compensation method based on nonlinear pixel analysis, characterized in that: The following steps are involved: S1, obtaining a three-dimensional hyperspectral image of the shadow to be compensated, and reconstructing the three-dimensional hyperspectral image of the shadow to be compensated to obtain a two-dimensional hyperspectral image; S2, estimating the number of endmembers of the two-dimensional hyperspectral image to obtain the number of endmembers; S3, obtaining a partition label matrix of shadow and non-shadow regions of the shadow image to be compensated, and reconstructing the partition label matrix to obtain a one-dimensional partition label; S4, dividing the two-dimensional hyperspectral image into a shadow area set and a non-shadow area set according to the one-dimensional partition label; S5, using the vector component analysis endmember extraction method to estimate the endmembers of the shadow area, and obtain the endmember matrix of the shadow area; S6, using the vector component analysis endmember extraction method to estimate the endmembers of the non-shadow area, and obtain the endmember matrix of the non-shadow area; S7, use the endmember matrix extracted from the shadow area to estimate the abundance of the pixels in the shadow area. The specific method is as follows: S71, using the bilinear model to estimate the abundance of the shadow area, and obtaining the shadow area abundance estimation result a based on the bilinear model bilinear ; S72, using p-order polynomials to account for higher-order interactions between photons, obtains the abundance estimation result of the shadow region based on the bilinear model a p ; S73, using the K-Hype model to explain the higher-order interactions between photons, obtain the abundance estimation result of the shadow region based on the K-Hype model a K-Hype ; S74, using multiple linear mixed models to estimate the abundance of shadow area pixels a MLM ; S75, using the deep autoencoder unmixing method NAE to estimate the abundance of shadow areas a NAE ; S8, the reconstruction of the shadow area is completed by using the abundance estimation information of the shadow area and the corresponding end members extracted from the non-shadow area.

2. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1 is characterized in that: In S7, a nonlinear unmixing model is used to analyze the pixels in the shadow area, and the optimization problem is as follows: Among them, x is the image of the shaded area, Φ represents the nonlinear relationship between endmembers and abundance, E is the endmember, a is the abundance, and different nonlinear unmixing models are used to estimate the abundance of the shaded area.

3. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1 is characterized in that: In S71, the solution of the bilinear model is achieved by solving the following constrained quadratic problem: Among them, γ ij is the probability of interaction between end members, a i is the abundance corresponding to the ith end member, a j is the jth end member pair The abundance of i is the ith end member, e j is the jth end member, and ⊙ is the dot product.

4. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1 is characterized in that: In S72, the abundance estimation result of the shadow area based on the p-order polynomial model is a p , which is achieved by solving the following constrained quadratic problem: Among them, b ik is the weight coefficient, is the ith end member, and k is the power number.

5. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1 is characterized in that: In S73, the K-Hype model is as follows: in, represents the transpose of the lth row of e, ψ nlin is a real function defined in the reproducing kernel Hilbert space, k nlin is its reproducing kernel function, is the lth row of e, n l For the lth row of noise n, the kernel function is selected as follows: in, is the p-th row of e, and σ is the noise standard deviation.

6. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1, characterized in that: In S74, the multiple linear mixed model is expressed as follows: Where n is the noise, which is solved by solving the following optimization problem: Among them, e i is the ith end member.

7. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1 is characterized in that: In S75, the model of the shaded area is expressed as follows: x=Ψ(Ea)+n Among them, Ψ is the nonlinear relationship between end members and abundance. The training of the entire autoencoder network is achieved by minimizing the minimum mean square error between input pixels and reconstructed pixels, as shown in the following formula: Among them, x i is the i-th pixel, is the i-th estimated pixel.

8. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 1, characterized in that: The specific method of S8 is as follows: S81, by finding the minimum spectral angle distance, each shadow region end member e i Correspond to its end members in the non-shaded area E′; S82, reconstructing the spectrum of the shadow area by using the abundance vectors corresponding to the pixels in the shadow area and the end members matched from the non-shadow area.

9. The hyperspectral image shadow compensation method based on nonlinear pixel analysis according to claim 8, characterized in that: In S81, the end element matrix E′ is the same as the end element e in the shaded area. i The end member vector with the minimum SAD value is e i The corresponding non-shaded end member e i ″, as shown below: The method of S82 is as follows: x=Φ(E″,a) where Φ is the nonlinear unmixing model used in abundance estimation.

Images