Hyperspectral sparse unmixing method based on spatial structure prior characteristics

Abstract

The invention discloses a spatial structure priori feature-based hyperspectral sparse unmixing method. The method comprises the following steps of S1, establishing a spectral linear mixing model; s2, based on a spectral linear mixing model, sparse unmixing is introduced into hyperspectral image unmixing, and an initial objective function is constructed; s3, obtaining a coarse-scale hyperspectral image by using the SLIC, and unmixing the coarse-scale hyperspectral image to obtain abundance estimation under the coarse scale for constructing a superpixel space weighting factor S; s4, constructing a gradient weighting coefficient total variation (GWCTV) regularization item; and S5, obtaining a sparse unmixing model based on spatial structure prior characteristics, and solving an abundance matrix A by adopting an alternating direction multiplier method. According to the method, space structure information can be better mined, pixels with the same or similar spectral information can be more accurately classified into a homogeneous region, and interference of complex mixed noise is effectively dealt with.

Description

Technical Field

[0001] The present invention belongs to the technical field of hyperspectral image processing in the field of remote sensing, and in particular relates to a hyperspectral sparse unmixing method based on spatial structure prior features. Background Art

[0002] Hyperspectral remote sensing images are a type of image data obtained using remote sensing technology. They collect information in multiple bands of the electromagnetic spectrum, especially visible light, near infrared, mid-infrared, and thermal infrared bands. By simultaneously acquiring spectral information and spatial image information from multiple bands, hyperspectral remote sensing images can carefully reflect the spatial distribution of material characteristics and the differences between different objects. However, the spatial resolution of existing spectral sensors is limited, which leads to a large number of mixed pixels in hyperspectral remote sensing images. Spectral unmixing technology is a method for processing hyperspectral remote sensing images, which aims to analyze the pure object components (endmembers) contained in the pixels in the image and their relative proportions (abundance).

[0003] Difficulties of sparse unmixing technology for hyperspectral images: 1. Hyperspectral images have high spectral dimensions and serious data redundancy, which increases computational complexity; 2. Pixels in hyperspectral images are often not isolated, and there is usually a strong spatial correlation between adjacent pixels. Ignoring these spatial relationships may lead to unstable unmixing results, especially in edge or texture areas; 3. Although hyperspectral images carry rich ground object information, due to the spatial resolution limitations of the spectral imager and the complexity of the ground objects themselves, the noise generated during the imaging process will cause mixing between pixels. This mixing not only includes spectral signals of multiple substances (i.e., end members), but also increases the spectral differences between adjacent pixels, destroying the original spatial consistency between pixels, thereby further increasing the difficulty of the unmixing task.

[0004] Therefore, in order to address the above difficulties, especially the destruction of the spatial information of hyperspectral images by complex noise and the insufficient mining of hyperspectral spatial spectral information, it is necessary to design a new hyperspectral sparse unmixing method. Summary of the invention

[0005] The purpose of the present invention is to provide a hyperspectral sparse unmixing method based on spatial structure prior features to solve the problem that the hyperspectral image mentioned in the background technology contains mixed pixels of multiple substances, and to cope with the insufficient mining of spectral information and spatial information in the hyperspectral image under the interference of complex noise (such as Gaussian noise, sparse noise, etc.) and possible degradation phenomena such as pixel defects.

[0006] To achieve the above object, the present invention provides a hyperspectral sparse unmixing method based on spatial structure prior features, comprising the following steps:

[0007] S1. Define the input hyperspectral matrix Y, endmember spectrum matrix L, abundance matrix A, noise or error matrix N, and establish a spectral linear mixed model;

[0008] S2, based on the spectral linear mixture model, sparse unmixing is introduced into the hyperspectral image unmixing to construct the initial objective function;

[0009] S3, using the superpixel segmentation algorithm (SLIC) to obtain a coarse-scale hyperspectral image, unmixing the coarse-scale hyperspectral image to obtain the abundance estimation at the coarse scale, and constructing the superpixel spatial weighting factor S;

[0010] S4, applying the nuclear norm constraint to the gradient differences of the hyperspectral image in three dimensions, assigning weights to the three dimensions, and constructing the gradient weighted coefficient total variation (GWCTV) regularization term;

[0011] S5. Introduce the GWCTV regularization term and the superpixel spatial weighting factor S into the initial objective function to obtain a sparse unmixing model based on spatial structure prior features, and use the alternating direction multiplier method to solve the abundance matrix A.

[0012] In a specific implementation, in step S1, the matrix form of the spectral linear mixed model is expressed as: Y = LA + N

[0013] Where Y = [y1,...,y p ]∈R b×p , represents a hyperspectral image containing b bands and p pixels, L = [l1,...,l m ]∈R b×m represents an overcomplete spectral library, containing m pure spectral features, and the corresponding abundance matrix is ​​A = [a1,...,a p ]∈R m×p , and N∈R b×p represents model error and noise interference.

[0014] In a specific implementation, in step S2, the initial objective function is expressed as Among them, the parameter λ>0 is the regularization parameter, min represents the minimization function, ||·|| F represents the F-norm of the matrix, ||·|| 1,1 represents the l1 norm.

[0015] In a specific implementation, in step S3, a super pixel segmentation algorithm (SLIC) is used to obtain a coarse-scale hyperspectral image, specifically referring to:

[0016] The hyperspectral image is segmented into homogeneous regions using the SLIC algorithm, and then all pixels in each homogeneous region are averaged. The hyperspectral image obtained after processing is defined as a coarse-scale hyperspectral image.

[0017] Y∈R b×p represents the original hyperspectral image, represents the hyperspectral image after superpixel segmentation, where K represents the total number of superpixel blocks, and p t Y t The number of pixels in , let y k ∈R b×1 Represents Y t Any pixel in, that is, a column vector, the above averaging obtains a coarse-scale image The operation can be defined as:

[0018]

[0019] in, represents the average coarse-scale image A column within.

[0020] In a specific implementation, in step S3, obtaining the abundance estimate at a coarse scale specifically refers to:

[0021] The SUnSAL algorithm is used to analyze the coarse-scale hyperspectral image. Unmixing can obtain the abundance estimation matrix at a coarse scale

[0022] In a specific implementation, in step S3, the superpixel spatial weighting factor S is constructed, specifically by using the obtained abundance estimation at the coarse scale to construct the superpixel spatial weighting factor S.

[0023] The calculation process is expressed by the following formula:

[0024]

[0025] Among them, S (i,j) represents the element in the i-th row and j-th column of the matrix S, is the crude abundance estimation matrix For the i-th row of , ε is a very small non-zero value to avoid division by zero.

[0026] In a specific implementation, in step S4, the gradient weighted coefficient total variation (GWCTV) regularization term is:

[0027]

[0028] Among them, ||·|| *represents the nuclear norm of the matrix, G i represents the gradient difference of the i-th dimension of the hyperspectral image, α i Represents the gradient difference weight of the i-th dimension.

[0029] In a specific implementation, in step S5, the sparse unmixing model based on the spatial structure prior feature is:

[0030]

[0031] Where ⊙ represents the Hadamard product of two variables, S is the superpixel spatial weighting factor; GWCTV(·) represents the GWCTV regularization term; is the main data fitting term, λ||S⊙A|| 1,1 is a sparsity-promoting regularization term, which is used to improve the sparsity of the abundance matrix; GWCTV GWCTV(LA) is used to fully exploit the underlying spatial structure of hyperspectral images and effectively smooth the estimated abundance map.

[0032] In a specific implementation, the termination condition for solving the abundance matrix A using the alternating direction multiplier method is: the number of iterations reaches 300 or the error between the abundance matrix A twice is less than a threshold ε.

[0033] In a specific embodiment, the threshold ε is 10 -5 .

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention combines the GWCTV regularization term with the spatial weighting factor S at the superpixel scale to make more in-depth use of the spatial information in the hyperspectral data cube. The GWCTV regularization term applies the nuclear norm constraint to the sparse gradient information map, making full use of the low-rank structure in the gradient map. This method can measure the difference in the sparsity of gradient information in the spatial and spectral dimensions of hyperspectral images, and more effectively resist the interference of complex noise. The superpixel spatial weighting factor is used to maintain the original spatial information of the hyperspectral image, enhancing the spatial correlation between pixels and the row sparseness of the abundance solution.

[0036] Through experimental verification with multiple sets of real data, the present invention can better mine spatial structural information, so that pixels with the same or similar spectral information can be more accurately classified into homogeneous areas, thereby effectively dealing with the interference of complex mixed noise. Therefore, the method of the present invention can significantly improve the ability to estimate the abundance of mixed features in various application scenarios, especially under low signal-to-noise ratio conditions, and its performance is better than other advanced unmixing algorithms in terms of the accuracy and stability of abundance estimation, and is suitable for promotion and application.

[0037] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention is further described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0039] Figure 1 is a flow chart of an embodiment of the present invention;

[0040] Figure 2 is the true abundance map of the nine end members in the data cube DC1;

[0041] Figure 3 In the simulated data set DC1, when the signal-to-noise ratio of Gaussian noise is 10 dB, 10% salt-and-pepper noise is added in the 70 to 80 band, and a dead line interference is added to each band in the 170 to 180 band, the abundance estimation diagram of end member #6 by different unmixing methods;

[0042] Figure 4 It is a detailed classification diagram of the different mineral components in the Cuprite mining area;

[0043] Figure 5 It means using ADSpLRU, S 2 Abundance estimation diagram of real data by WSU, DRSU-TV, SUSRLR-TV and the unmixing algorithm of the present invention. DETAILED DESCRIPTION

[0044] The embodiments of the present invention are described in detail below. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0045] A hyperspectral sparse unmixing method based on spatial structure prior features of the present invention comprises the following steps:

[0046] S1. Define the input hyperspectral matrix Y, endmember spectral matrix L, abundance matrix A, noise or error matrix N, and establish a spectral linear mixed model.

[0047] In step S1, the matrix form of the spectral linear mixed model is expressed as: Y = LA + N

[0048] Where Y = [y1,...,y p ]∈R b×p , represents a hyperspectral image containing b bands and p pixels, L = [l1,...,l m ]∈Rb×m represents an overcomplete spectral library, containing m pure spectral features, and the corresponding abundance matrix is ​​A = [a1,...,a p ]∈R m×p , and N∈R b×p represents model error and noise interference.

[0049] S2. Based on the spectral linear mixture model, sparse unmixing is introduced into the hyperspectral image unmixing to construct the initial objective function.

[0050] In step S2, the initial objective function is expressed as Among them, the parameter λ>0 is the regularization parameter, min represents the minimization function, ||·|| F represents the F-norm of the matrix, ||·|| 1,1 express Norm.

[0051] S3. A coarse-scale hyperspectral image is obtained by using a superpixel segmentation algorithm (SLIC). The coarse-scale hyperspectral image can be unmixed to obtain the abundance estimation at the coarse scale, and a superpixel spatial weighting factor S is constructed.

[0052] In step S3, a super pixel segmentation algorithm (SLIC) is used to obtain a coarse-scale hyperspectral image, specifically:

[0053] The hyperspectral image is segmented into homogeneous regions using the SLIC algorithm, and then all pixels in each homogeneous region are averaged. The hyperspectral image obtained after processing is defined as a coarse-scale hyperspectral image.

[0054] Y∈R b×p represents the original hyperspectral image, represents the hyperspectral image after superpixel segmentation, where K represents the total number of superpixel blocks, and p t Y t The number of pixels in , let y k ∈R b×1 Represents Y t Any pixel in, that is, a column vector, the above averaging obtains a coarse-scale image The operation can be defined as:

[0055]

[0056] in, represents the average coarse-scale image The coarse-scale hyperspectral image reconstructs all elements in each homogeneous area of ​​the original image based on the average value, which can effectively reduce the impact of noise.

[0057] In step S3, obtaining the abundance estimation at a coarse scale specifically refers to:

[0058] The SUnSAL algorithm is used to analyze the coarse-scale hyperspectral image. Unmixing can obtain the abundance estimation matrix at a coarse scale

[0059] In step S3, a superpixel spatial weighting factor S is constructed, specifically, the superpixel spatial weighting factor S is constructed using the obtained abundance estimation at a coarse scale.

[0060] The calculation process is expressed by the following formula:

[0061]

[0062] Among them, S (i,j) represents the element in the i-th row and j-th column of the matrix S, is the crude abundance estimation matrix For the i-th row of , ε is a very small non-zero value to avoid division by zero.

[0063] S4. The nuclear norm constraint is applied to the gradient differences of the hyperspectral image in three dimensions, and weights are assigned to the three dimensions to construct the gradient weighted coefficient total variation (GWCTV) regularization term.

[0064] In step S4, the gradient weighted coefficient total variation (GWCTV) regularization term is:

[0065]

[0066] Among them, ||·||* represents the nuclear norm of the matrix, G i represents the gradient difference of the i-th dimension of the hyperspectral image, α i Represents the gradient difference weight of the i-th dimension.

[0067] S5. Introduce the GWCTV regularization term and the superpixel spatial weighting factor S into the initial objective function to obtain a sparse unmixing model based on spatial structure prior features, and use the alternating direction multiplier method to solve the abundance matrix A.

[0068] In step S5, the sparse unmixing model based on the spatial structure prior feature is:

[0069]

[0070] Where ⊙ represents the Hadamard product of two variables, S is the superpixel spatial weighting factor; GWCTV(·) represents the GWCTV regularization term; is the main data fitting term, λ||S⊙A|| 1，1is a sparsity-promoting regularization term, which is used to improve the sparsity of the abundance matrix; GWCTV GWCTV(LA) is used to fully exploit the underlying spatial structure of hyperspectral images and effectively smooth the estimated abundance map.

[0071] The termination condition for solving the abundance matrix A using the alternating direction multiplier method is: the number of iterations reaches 300 or the error between the two abundance matrix A is less than the threshold ε. The threshold ε is 10 -5 .

[0072] Example 1

[0073] The present invention provides a hyperspectral sparse unmixing method based on spatial structure prior features, and the specific steps are as follows:

[0074] Step S1, constructing a spectral linear mixing model: define the input hyperspectral image as Y, arrange the spectral vectors of the hyperspectral image pixels in a matrix form, and establish a hyperspectral image description model based on sparse unmixing: Y = LA + N

[0075] Where Y = [y1,...,y p ]∈R b×p , represents a hyperspectral image containing b bands and p pixels, L = [l1,...,l m ]∈R b×m represents an overcomplete spectral library, containing m pure spectral features, and the corresponding abundance matrix is ​​A = [a1,...,a p ]∈R m×p , and N∈R b×p represents model error and noise interference.

[0076] Step S2: Based on the spectral linear mixing model, sparse unmixing is introduced into the hyperspectral image unmixing to establish an initial objective function Among them, the parameter λ>0 is the regularization parameter, min represents the minimization function, ||·|| F represents the F-norm of the matrix, ||·|| 1，1 represents the l1 norm.

[0077] Step S3: In order to fully explore the spatial feature information of the hyperspectral image, the SLIC algorithm is used to segment the hyperspectral image into homogeneous regions, and then all pixels in each homogeneous region are averaged to obtain a coarse-scale hyperspectral image.

[0078]

[0079] in, represents the average coarse-scale image The coarse hyperspectral image reconstructs all elements in each homogeneous area of ​​the original image according to the average value, which can effectively reduce the impact of noise.

[0080] The coarse-scale hyperspectral image is processed using the classic SUnSAL algorithm. Unmixing provides coarse-scale abundance estimates

[0081] The abundance matrix A obtained based on the above solution is used to construct the superpixel spatial weighting factor S, and its calculation expression is:

[0082]

[0083] Among them, S (i,j) represents the element in the i-th row and j-th column of the matrix S, is the crude abundance estimation matrix For the i-th row of , ε is a very small non-zero value to avoid division by zero.

[0084] Step S4: In order to fully explore the underlying spatial structure and rich contextual information in the hyperspectral image, a new gradient weighted coefficient total variation (GWCTV) regularization term is introduced. The nuclear norm constraint is applied to the gradient difference of the hyperspectral image in three dimensions, and different weights are assigned to these dimensions. The expression of GWCTV(·) is:

[0085]

[0086] Among them, ||·|| * represents the nuclear norm of the matrix, G i represents the gradient difference of the i-th dimension of the hyperspectral image, α i Represents the gradient difference weight of the i-th dimension, which is appropriately adjusted according to the gradient sparsity of different data sets in each dimension.

[0087] Step S5: Based on the above content, the superpixel spatial weighting factor S and the gradient weighted coefficient total variation (GWCTV) regularization term are introduced into the sparse unmixing model to construct a new objective function:

[0088]

[0089] Where ⊙ represents the Hadamard product of two variables, S is the superpixel spatial weighting factor, and GWCTV(·) represents the GWCTV regularization term. is the main data fitting part, λ||S⊙A|| 1，1 It is a regularization term that promotes sparsity, and its function is to enhance the sparsity of the abundance matrix; GWCTVGWCTV(LA) aims to fully explore the underlying spatial structure of hyperspectral images and effectively smooth the estimated abundance maps.

[0090] The alternating direction multiplier method is used to solve the constructed new objective function, and the ANC constraint is incorporated into the formula, that is:

[0091]

[0092] in, when a i Its value is 0 when non-negative, otherwise it is positive infinity.

[0093] Introduce auxiliary variables U, V1, V2, V3, V4, V5 for variable replacement, and transform the formula into the following minimization problem:

[0094]

[0095] st:U=A,V1=LU,V2=U,V 3,i =LU, V5=U,i=1,2,3

[0096] According to the alternating direction multiplier method, the augmented Lagrange multiplier D is introduced to convert the formula into the following form:

[0097]

[0098] in G=(L,I,L,0,I) T , V≡(V1,V2,V3,V4,V5) T .

[0099] Assume the number of iterations k = 0, constant λ,λ GWCTV ,ε,μ>0, initialize U (0) , Fix other variables and calculate the values ​​of variables U, V1, V2, V3, V4, V5, D1, D2, D3, D4, and D5 respectively.

[0100] The variable U in the unmixing process is calculated as follows:

[0101]

[0102] The variables V1, V2, and V5 in the unmixing process are calculated as follows:

[0103]

[0104] During the unmixing process, variables V3 and V4 are calculated as follows:

[0105]

[0106] The Lagrange multiplier in the unmixing process is updated as follows:

[0107]

[0108] Let the number of iterations k = k + 1, and repeat the above solution process for variables U, V1, V2, V3, V4, V5, D1, D2, D3, D4, D5 until the termination condition is met. The termination condition is the maximum number of iterations k = 300 or the error of variable U before and after twice. The threshold value ε is 10 -5 .

[0109] That is, the termination condition for solving the abundance matrix A by using the alternating direction multiplier method is: the number of iterations reaches 300 or the error between the two abundance matrix A is less than the threshold ε, and the threshold ε is 10 -5 .

[0110] The present invention uses two evaluation indicators, signal reconstruction error (SRE) and success probability (ps), to quantitatively analyze the unmixing performance of each algorithm. Among them, SRE is used to measure the effectiveness of the unmixing method in accurately reconstructing the abundance matrix. The specific definition of SRE is:

[0111]

[0112] Among them, E(·) represents the expected function, α and They are the true abundance and estimated abundance results respectively. The larger the SRE value, the better the performance of the unmixing method.

[0113] p s It is an estimate of the probability that the relative error power is less than a certain threshold, which is used to measure the stability of the demixing algorithm and is defined as:

[0114]

[0115] The threshold here is usually set to 3.16, which is equivalent to 5dB. The unmixing result can be considered correct.

[0116] The beneficial effects of the present invention are verified by comparative experiments as follows.

[0117] In order to verify the effectiveness of the unmixing method proposed in the present invention, the alternating direction sparse and low-rank unmixing algorithm ADSpLRU (Alternating Direction Sparse and Low-Rank Unmixing) and the space-spectrum weighted sparse unmixing algorithm S2 Four sparse unmixing methods, namely WSU (Spectral-Spatial Weighted Sparse Unmixing), DRSU-TV (Hyperspectral Unmixing Using Double Reweighted Sparse Regression and Total Variation), and SUSRLR-TV (Superpixel-Based Reweighted Low-Rank and Total Variation Sparse Unmixing for Hyperspectral Remote Sensing Imagery), and the unmixing method (SSPSU) described in the present invention, use a synthetic simulated dataset DC1 and a real copper ore (Cuprite) dataset for unmixing processing.

[0118] The spectral library L1 was selected from the end-member spectral library of USGS, which contains the spectral characteristics of 240 minerals and 224 bands. Nine end-members were selected from L1 to create a 100×100 pixel data cube DC1.

[0119] In the real data experiment, a 350×350 pixel subset of the classic AVIRIS Cuprite dataset was used, with 224 bands per pixel. After removing bands 1-2, 105-115, 150-170, and 223-224 with low signal-to-noise ratio and strong water absorption, 188 bands were retained for analysis. The endmember spectral library used in the experiment is the same as DC1, but the interfering bands are removed. Figure 4 The results of mineral classification for the Cuprite mine are shown.

[0120] In the experiment, Gaussian noise with a signal-to-noise ratio of 10dB was added to the simulated data set DC1. On the basis of Gaussian interference, a set of experiments with different degrees of sparse noise interference were also added, that is, 10% salt and pepper noise was added in the 70-80 band, and a dead line interference was added to each band in the 170-180 band to form a more complex mixed noise interference. 2 Four sparse unmixing methods, WSU, DRSU-TV, SUSRLR-TV, and the unmixing method (SSPSU) described in the present invention, are used to unmix the simulated data set DC1 with noise added. The SRE values ​​and p s The values ​​are shown in Table 1.

[0121] Table 1 shows the SRE and P obtained after applying different algorithms to the data set DC1 for unmixing s value

[0122]

[0123] Note: Since the copper ore data is real hyperspectral image data, there is no real abundance value as a reference, so there is no table listing the performance values ​​of the copper ore dataset.

[0124] In the experiment, the third end member abundance map was selected as the representative for the DC1 dataset; three minerals, alunite, feldspar and chalcedony, were selected as the representatives for the real copper ore dataset, and ADSpLRU, S 2 The unmixing performances of the four sparse unmixing methods WSU, DRSU-TV, SUSRLR-TV and the unmixing method (SSPSU) described in the present invention on each data set are shown in the figure below: Figure 3 and Figure 5 As shown in the figure, the mineral abundance estimation results of each algorithm are generally consistent with the information provided by the USGS Tricorder classification map, which shows that these algorithms are suitable for this data set. However, in the ammonium feldspar abundance map, the ADSpLRU algorithm has obvious noise problems, and when estimating the chalcedony abundance map, the algorithm lacks many abundance details; the SUSRLR-TV algorithm has over-smoothing. In contrast, DRSU-TV, S 2 The WSU and SSPSU algorithms can better reproduce the spatial distribution of minerals. In particular, the chalcedony abundance map generated by the SSPSU algorithm proposed in the present invention has a high similarity with the reference map. Therefore, from a qualitative analysis perspective, it can be considered that the SSPSU algorithm is effective in processing the unmixing task of real hyperspectral data, and can also significantly improve the accuracy of the unmixing results.

[0125] It can be seen from the experimental results that the method of the present invention basically obtains the best SRE and p under different degrees of complex mixed noise environments. s Compared with the method without introducing the TV regularization term and the superpixel spatial weighting factor S, the present invention shows strong robustness in processing noise, accurately mines the low-rank and smooth parts and their sparse structures in the hyperspectral image, thereby fully revealing the underlying spatial structure information in the hyperspectral image, thereby improving the algorithm's unmixing accuracy.

[0126] The present invention firstly constructs a sparse unmixing framework which can fully mine the spatial structure prior information of hyperspectral images, and uses the superpixel segmentation algorithm (SLIC) to obtain a coarse-scale image Y. The coarse-scale hyperspectral image can be unmixed to obtain the abundance estimation at the coarse scale, thereby constructing the superpixel spatial weighting factor S. At the same time, the gradient differences of the hyperspectral image in three dimensions are quantified, and different weights are assigned to these dimensions. A new gradient weighted coefficient total variation (GWCTV) regularization term is proposed. By introducing the GWCTV regularization term and the superpixel-scale spatial weighting factor S, the underlying spatial structure in the image can be more comprehensively mined and the interference of complex noise can be more effectively resisted.

[0127] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions and substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A hyperspectral sparse unmixing method based on spatial structure prior features, characterized in that: The steps include: S1. Define the input hyperspectral matrix Y, endmember spectrum matrix L, abundance matrix A, noise or error matrix N, and establish a spectral linear mixed model; S2, based on the spectral linear mixture model, sparse unmixing is introduced into the hyperspectral image unmixing to construct the initial objective function; S3, using the superpixel segmentation algorithm (SLIC) to obtain a coarse-scale hyperspectral image, unmixing the coarse-scale hyperspectral image to obtain the abundance estimation at the coarse scale, and constructing the superpixel spatial weighting factor S; S4, applying the nuclear norm constraint to the gradient differences of the hyperspectral image in three dimensions, assigning weights to the three dimensions, and constructing the gradient weighted coefficient total variation (GWCTV) regularization term; S5. Introduce the GWCTV regularization term and the superpixel spatial weighting factor S into the initial objective function to obtain a sparse unmixing model based on spatial structure prior features, and use the alternating direction multiplier method to solve the abundance matrix A.

2. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S1, the matrix form of the spectral linear mixed model is expressed as: Y = LA + N Where Y = [y1,...,y p ]∈R b×p , represents a hyperspectral image containing b bands and p pixels, L = [l1,...,l m ]∈R b×m represents an overcomplete spectral library, containing m pure spectral features, and the corresponding abundance matrix is ​​A = [a1,...,a p ]∈R m×p , and N∈R b×p represents model error and noise interference.

3. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S2, the initial objective function is expressed as Among them, the parameter λ>0 is the regularization parameter, min represents the minimization function, ||·|| F represents the F-norm of the matrix, ||·|| 1,1 represents the l1 norm.

4. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S3, a super pixel segmentation algorithm (SLIC) is used to obtain a coarse-scale hyperspectral image, specifically: The hyperspectral image is segmented into homogeneous regions using the SLIC algorithm, and then all pixels in each homogeneous region are averaged. The hyperspectral image obtained after processing is defined as a coarse-scale hyperspectral image. Y∈R b×p represents the original hyperspectral image, represents the hyperspectral image after superpixel segmentation, where K represents the total number of superpixel blocks, and p t Y t The number of pixels in , let y k ∈R b×1 Represents Y t Any pixel in, that is, a column vector, the above averaging obtains a coarse-scale image The operation can be defined as: in, represents the average coarse-scale image A column within.

5. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S3, obtaining the abundance estimation at a coarse scale specifically refers to: The SUnSAL algorithm is used to analyze the coarse-scale hyperspectral image. Unmixing can obtain the abundance estimation matrix at a coarse scale 6. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S3, a superpixel spatial weighting factor S is constructed, specifically, the superpixel spatial weighting factor S is constructed using the obtained abundance estimation at a coarse scale. The calculation process is expressed by the following formula: Among them, S (i,j) represents the element in the i-th row and j-th column of the matrix S, is the crude abundance estimation matrix For the i-th row of , ε is a very small non-zero value to avoid division by zero.

7. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S4, the gradient weighted coefficient total variation (GWCTV) regularization term is: Among them, ||·|| * represents the nuclear norm of the matrix, G i represents the gradient difference of the i-th dimension of the hyperspectral image, α i Represents the gradient difference weight of the i-th dimension.

8. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1 is characterized in that: In step S5, the sparse unmixing model based on the spatial structure prior feature is: Where ⊙ represents the Hadamard product of two variables, S is the superpixel spatial weighting factor; GWCTV(·) represents the GWCTV regularization term; is the main data fitting term, λ||S⊙A|| 1,1 is a sparsity-promoting regularization term, which is used to improve the sparsity of the abundance matrix; λ GWCTV GWCTV(LA) is used to fully exploit the underlying spatial structure of hyperspectral images and effectively smooth the estimated abundance map.

9. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 1, characterized in that: The termination condition for solving the abundance matrix A using the alternating direction multiplier method is: the number of iterations reaches 300 or the error between the abundance matrix A before and after is less than the threshold ε.

10. The hyperspectral sparse unmixing method based on spatial structure prior features according to claim 9, characterized in that: The threshold ε is 10 -5 .

Images