A hyperspectral unmixing method based on hypergraph learning and sparse weighting

Abstract

The application discloses a hyperspectral unmixing method based on hypergraph learning and sparse weighting, and comprises the following steps: step 1, band fusion of a hyperspectral image; step 2, hypergraph learning of the hyperspectral image; and step 3, sparse unmixing of the hyperspectral image. The method can accurately extract spatial information of the hyperspectral image based on a hypergraph learning strategy, and the spatial information can be fully utilized in the unmixing process, so that the quality of estimated abundance is effectively improved. In addition, the method has stronger robustness to Gaussian noise and sparse noise, and can well inhibit the two types of noise. Therefore, the application has the characteristics of strong practical application value and good reliability, and is suitable for promotion and use.

Description

Technical Field

[0001] This invention belongs to the research field of remote sensing technology and relates to a hyperspectral unmixing method, specifically a robust sparse unmixing method for hyperspectral images. Background Technology

[0002] Hyperspectral remote sensing technology originated in the early 1980s, with the development of the first generation of imaging spectrometers by organically combining spectral and imaging techniques. However, early imaging spectrometers were often limited by spatial resolution, resulting in images containing a large number of mixed pixels, which affected the accurate identification and analysis of surface materials. In recent years, with the rapid development of hyperspectral remote sensing technology, although related equipment has significantly improved in both spectral and spatial resolution, the problem of mixed pixels remains difficult to eradicate, especially at the boundaries of different material regions. This problem greatly limits its further application in related fields.

[0003] Hyperspectral unmixing, as a crucial tool for addressing this challenge, not only enables in-depth analysis and effective utilization of hyperspectral images but has also become a research hotspot in the field of hyperspectral image processing. The core of hyperspectral unmixing lies in decomposing mixed pixels in an image into the unique spectra and abundances of each substance within the scene. This unmixing process is essential because mixed pixels directly lead to the loss of important ground feature information. Therefore, mining sub-pixel information through hyperspectral unmixing is particularly important. Furthermore, the complex distribution of ground features in nature and their inherent material differences necessitate the use of hyperspectral unmixing to accurately distinguish and identify their spectra. In addition, the abundance information obtained through hyperspectral unmixing is not only significant for understanding the distribution and composition of land cover and its background features but is also closely related to physical parameters of ecological structures such as vegetation indices, vegetation cover, and surface temperature. These parameters lay a solid foundation for quantitative remote sensing applications and assessments, leading to widespread attention to hyperspectral unmixing technology across numerous fields. Summary of the Invention

[0004] This invention provides a hyperspectral unmixing method based on hypergraph learning and sparse weighting, taking advantage of the spatial structural relationships between pixels in remote sensing images. This method accurately extracts spatial information from hyperspectral images using a hypergraph learning strategy and fully utilizes this spatial information during the unmixing process, thereby effectively improving the quality of abundance estimation. Furthermore, the proposed method exhibits stronger robustness to both Gaussian and sparse noise, effectively suppressing these two types of noise. Therefore, this invention has strong practical application value and high reliability, making it suitable for widespread use.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A hyperspectral unmixing method based on hypergraph learning and sparse weighting includes the following steps:

[0007] Step 1: Band fusion of hyperspectral images:

[0008] Step 1.1: Observe the 3D hyperspectral image The image is segmented along the spectral dimension, dividing it into a set of images consisting of multiple adjacent band sub-images. ,in, The number of image sets, where each image set contains sub-images of multiple adjacent bands of the original image, i.e.: ,in, Indicates the relationship with the first A set consisting of adjacent sub-images in each band. Original 3D image The Sub-images of each band;

[0009] Step 1.2, Each image set The fusion process is performed according to the following formula:

[0010]

[0011] in, Indicates the size of the set. It contains a collection of images. Average spatial information in;

[0012] Step 2, Hypergraph learning of hyperspectral images:

[0013] Step 2.1, based on image set The image after band fusion is represented as a matrix. Each pixel is considered a node in the hypergraph;

[0014] Step 2.2, let the matrix Representation and matrix The corresponding clean hyperspectral image, each pixel is also considered as a node in the hypergraph;

[0015] Step 2.3: Complete the hypergraph learning process for the hyperspectral image iteratively using the following steps:

[0016] Step 2.3.1, in the... In the next iteration, using - The nearest neighbor method selects each hyperedge of the hypergraph. Find the nearest neighbor nodes and calculate the hyperedge weight matrix of the hypergraph. ,in This represents the diagonal operations of a matrix, and the diagonal vector. elements For super-edge The weights are calculated using the following formula:

[0017]

[0018] in, It is an exponential function. For Gaussian kernel scaling parameters, and Representing images respectively The and the 1 pixel, express The square of the norm;

[0019] Step 2.3.2, in the... In the next iteration, the hypergraph Laplacian matrix Calculate using the following formula:

[0020]

[0021] Among them, superscript For matrix inversion, superscript This is the transpose operation of a matrix. Indicates by and The correlation matrix formed by the elements and Let the node degree and hyperedge degree matrices represent the matrix respectively, and calculate them using the following formula:

[0022]

[0023] in, Indicates all elements are Column vectors;

[0024] Step 2.3.3, in the... In the next iteration, the image Update as follows:

[0025]

[0026] in, For regularization parameters, Representing dimension and The same unit matrix, Indicates the first During the next iteration value, Indicates the first The newly calculated value in the next iteration value;

[0027] Step 2.3.4, if the number of iterations... Then terminate the iteration and output. ,in Set the maximum number of iterations for the hypergraph learning process; otherwise, proceed to step 2.3.1 to continue.

[0028] Step 3: Sparse unmixing of hyperspectral images:

[0029] Step 3.1: Use the Laplacian matrix of the hypergraph learned in Step 2 to constrain the abundance matrix of the unmixing process. This further improves the estimated abundance. The quality;

[0030] Step 3.2: Introduce auxiliary variables , and and Lagrangian multipliers , and The sparse demixing process of hyperspectral images is achieved using an alternating optimization strategy in the following steps:

[0031] Step 3.2.1, in the... In the next iteration, the variables during the unmixing process Calculate using the following formula:

[0032]

[0033] in, Represents a known spectral library matrix. Representing dimension and The same unit matrix, The input hyperspectral image is represented as a 2-D matrix. Indicates the first During the next iteration The value, Indicates the first During the next iteration The value;

[0034] Step 3.2.2, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0035]

[0036] in, , express Norm, , Represented by matrix The A vector formed by rows, For matrix The number of rows, For penalty parameters, Indicates the first The newly calculated value in the next iteration value;

[0037] Step 3.2.3, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0038]

[0039] in, The Laplacian matrix of the hypergraph obtained in step 2. For regularization parameters;

[0040] Step 3.2.4, in the... In the next iteration, auxiliary variables during the unmixing process Calculated using the following formula:

[0041]

[0042] in, Represents a symbolic function. The operator "" represents element-based absolute value operations. " indicates an element-based product operator. For regularization parameters, and Represents the abundance matrix The applied sparse weighting matrix;

[0043] Step 3.2.5, in the... In the next iteration, the sparse weighted matrix and Calculate according to the following formulas:

[0044]

[0045] in, For hyperparameters, Represented by the abundance matrix The A row vector composed of row elements. Abundance matrix The number of rows, Abundance matrix The OK The absolute value of the elements in the column. Representation matrix The OK Column elements;

[0046] Step 3.2.6, in the... In the next iteration, the Lagrangian multipliers are calculated as follows:

[0047]

[0048] Step 3.2.7, if the number of iterations... Then terminate the iteration and output. ,in The maximum number of iterations is set for the unmixing process; otherwise, proceed to step 3.2.1. When iteration stops according to step 3.2.7, the output is... This is the abundance matrix that needs to be estimated.

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] 1. This invention employs a strategy that combines hypergraph smoothing filtering with noise reduction for hypergraph learning, which can more accurately and adaptively extract spatial information from hyperspectral images, thereby effectively improving the quality of abundance estimation.

[0051] 2. In the process of unmixing, the present invention applies a double-weighted sparsity constraint to the abundance matrix, which can simultaneously and effectively promote the two different sparsities of the estimated abundance, thereby further improving the quality of the estimated abundance.

[0052] 3. This invention, within the framework of the ADMM algorithm, decomposes the original problem into several simpler subproblems for alternating optimization and solution. Therefore, this invention has strong practical application value and good reliability, making it suitable for widespread use. Attached Figure Description

[0053] Figure 1 This is a flowchart of the unmixing method of the present invention;

[0054] Figure 2 Compared with six other similar demixing methods, SUnSAL, DRSU-TV, ReHGSU, SUnCNN, WSRSSU, and SGLRWRSU, the demixing method of this invention achieves a signal-to-noise ratio of [value missing] in Gaussian noise. The demixing performance under the given conditions is shown in the graph.

[0055] Figure 3Compared with six other similar demixing methods, namely SUnSAL, DRSU-TV, ReHGSU, SUnCNN, WSRSSU, and SGLRWRSU, the demixing method of this invention has a sparse noise ratio of [missing information]. The demixing performance under the given conditions is shown in the graph. Detailed Implementation

[0056] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0057] This invention provides a hyperspectral unmixing method based on hypergraph learning and sparse weighting. The method utilizes a hypergraph learning strategy to jointly optimize hypergraph learning and image denoising, adaptively extracting spatial structure information between pixels from hyperspectral images, thereby improving the accuracy of the hyperspectral unmixing method. Based on a robust sparse regression strategy, a weighting is applied to the reconstruction term in the optimization model. Constraints are implemented to effectively suppress the impact of Gaussian and sparse noise in hyperspectral images on unmixing accuracy. The robust sparse unmixing model is optimized and solved based on the ADMM algorithm framework to obtain the estimated abundance matrix. Experiments were conducted using simulated hyperspectral datasets, demonstrating that the proposed unmixing method is significantly superior to several other advanced sparse unmixing methods of the same type. Figure 1 As shown, the specific steps are as follows:

[0058] Step 1: Band fusion of hyperspectral images:

[0059] The relevant parameters are set as follows during the band fusion process of hyperspectral images:

[0060] In signal-to-noise ratio Settings under Gaussian noise conditions: Image set ;

[0061] In noise ratio Setting for sparse noise: Image set .

[0062] The specific implementation steps are as follows:

[0063] To reduce redundant information in the spectral domain of hyperspectral images and the computational cost of the hypergraph learning process, the 3-D observation hyperspectral images are first... The image is segmented along the spectral dimension, dividing it into a set of images consisting of multiple adjacent band sub-images. ,in This represents the number of image sets. Each image set contains sub-images of multiple adjacent bands of the original image, i.e.: ,in Indicates the relationship with the first A set consisting of adjacent sub-images in each band. Original 3D image The Sub-images of each band. Each image set The fusion process is performed according to the following formula:

[0064] (1)

[0065] in, Indicates the size of the set. It contains a collection of images. Average spatial information in.

[0066] Step 2, Hypergraph learning of hyperspectral images:

[0067] In the hypergraph learning process of hyperspectral images, the relevant variables and parameters are set as follows:

[0068] Clean image Initialization settings: ;

[0069] In signal-to-noise ratio Setting the number of neighboring nodes in Gaussian noise case Gaussian kernel scale parameters Regular expression parameters Number of iterations ;

[0070] In noise ratio Setting the number of neighboring nodes in sparse noise case: Gaussian kernel scale parameters Regular expression parameters Number of iterations .

[0071] The specific implementation steps are as follows:

[0072] Based on image set The image after band fusion is represented as a matrix. Each pixel is considered a node in the hypergraph. Let the matrix... Representation and matrix The corresponding clean hyperspectral image is also treated as a node in the hypergraph for each pixel. The hypergraph learning process for the hyperspectral image is then completed iteratively using the following steps.

[0073] Step 2.1, in the... In the next iteration, using - The nearest neighbor method selects each hyperedge of the hypergraph. Find the nearest neighbor nodes and calculate the hyperedge weight matrix of the hypergraph. ,in This represents the diagonal operations of a matrix, and the diagonal vector. elements For super-edge The weights are calculated using the following formula:

[0074] (2)

[0075] in It is an exponential function. For Gaussian kernel scaling parameters, and Representing images respectively The and the 1 pixel, express The square of the norm.

[0076] Step 2.2, in the... In the next iteration, the hypergraph Laplacian matrix Calculate using the following formula:

[0077] (3)

[0078] superscript -1 For matrix inversion, superscript T This is the transpose operation of a matrix. Indicates by and The correlation matrix formed by the elements and Let the node degree and hyperedge degree matrices represent the matrix respectively, and calculate them using the following formula:

[0079] (4)

[0080] in Indicates all elements are Column vectors.

[0081] Step 2.3, in the... In the next iteration, the image Update as follows:

[0082] (5)

[0083] in For regularization parameters, Representing dimension and The same unit matrix, Indicates the first During the next iteration value, Indicates the first The newly calculated value in the next iteration value.

[0084] Step 2.4, if the number of iterations... Then terminate the iteration and output. ,in Set the maximum number of iterations for the hypergraph learning process. Otherwise, proceed to step 2.1.

[0085] Step 3: Sparse unmixing of hyperspectral images:

[0086] In the sparse unmixing process of hyperspectral images, the relevant variables and parameters are set as follows:

[0087] primitive variables Initialization settings: ;

[0088] Auxiliary variables Initialization settings: ;

[0089] Auxiliary variables Initialization settings: ;

[0090] Auxiliary variables Initialization settings: ;

[0091] Lagrangian multiplier initialization settings: ;

[0092] Sparse weighted matrix and Initialization settings: ;

[0093] In signal-to-noise ratio Setting the regularization parameter in Gaussian noise case: and Penalty parameters Hyperparameters Number of iterations ;

[0094] In noise ratio Setting regularization parameters for sparse noise conditions and Penalty parameters Hyperparameters Number of iterations .

[0095] The specific implementation steps are as follows:

[0096] In the process of hyperspectral image unmixing, in order to fully utilize the spatial information of the hyperspectral image, the Laplacian matrix of the hypergraph learned in step 2 is used to constrain the abundance matrix of the unmixing process. This further improves the estimated abundance. The quality. Next, by introducing auxiliary variables. , and and Lagrangian multipliers , and The sparse demixing process of hyperspectral images is achieved using an alternating optimization strategy in the following steps:

[0097] Step 3.1, in the... In the next iteration, the variables during the unmixing process Calculate using the following formula:

[0098] (6)

[0099] in, Represents a known spectral library matrix. Representing dimension and The same unit matrix, The input hyperspectral image is represented as a 2-D matrix. Indicates the first During the next iteration The value, Indicates the first During the next iteration The value of .

[0100] Step 3.2, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0101] (7)

[0102] in, , express Norm, , Represented by matrix The A vector formed by rows, For matrix The number of rows, For penalty parameters, Indicates the first The newly calculated value in the next iteration value.

[0103] Step 3.3, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0104] (8)

[0105] in, The Laplacian matrix of the hypergraph obtained in step 2. For regularization parameters.

[0106] Step 3.4, in the In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula:

[0107] (9)

[0108] in Represents a symbolic function. The operator "" represents element-based absolute value operations. " indicates an element-based product operator. For regularization parameters, and Represents the abundance matrix The applied sparse weighting matrix.

[0109] Step 3.5, in the In the next iteration, the sparse weighted matrix and Calculate according to the following formulas:

[0110] (10)

[0111] in, For hyperparameters, Represented by the abundance matrix The A row vector composed of row elements. Abundance matrix The number of rows, Abundance matrix The OK The absolute value of the elements in the column. Representation matrix The OK The elements of the column.

[0112] Step 3.6, in the... In the next iteration, the Lagrangian multipliers are calculated as follows:

[0113] (11)

[0114] Step 3.7, if the number of iterations... Then terminate the iteration and output. ,in The maximum number of iterations set for the unmixing process. Otherwise, proceed to step 3.1. When iteration stops according to step 3.7, the output is... This is the abundance matrix that needs to be estimated.

[0115] To verify the effectiveness of the unmixing method proposed in this invention, six similar unmixing methods—SUnSAL, DRSU-TV, ReHGSU, SUnCNN, WSRSSU, and SGLRWRSU—were used, along with the method described in this invention (Proposed), to add signal-to-noise ratio to simulated hyperspectral image data. Gaussian noise and noise ratio The experiment was conducted using sparse noise. The simulated hyperspectral image contains... Each band consists of [number] bands, and each band is composed of [number] bands. Composed of pixels, containing Squares are arranged in a grid, where each square represents a homogeneous region whose pixels are composed of the same abundance.

[0116] The experimental results show the abundance maps corresponding to all endmembers in the dataset, where Reference is the reference abundance map. Figure 2 and 3 As shown in the figure, the abundance maps corresponding to each endmember estimated by the method proposed in this invention have a clearer spatial structure compared with other methods. This indicates that the method proposed in this invention can utilize the spatial information of hyperspectral images more accurately. Furthermore, the abundance maps estimated by various methods also show that the unmixing method of this invention effectively suppresses both Gaussian noise and sparse noise, which fully verifies the robustness of the method against different types of noise.

[0117] Furthermore, to further illustrate the effectiveness of the proposed method, SRE and RMSE are used to measure the unmixing accuracy of each method. These two metrics are widely used to measure the performance of hyperspectral unmixing methods. The signal reconstruction error SRE is defined as:

[0118] (12)

[0119] in, and These represent the reference abundance and the estimated abundance, respectively. Generally, a higher SRE value indicates better performance of the unmixing method. The root mean square error (RMSE) is defined as:

[0120] (13)

[0121] in, and Each is a matrix and The There are several column vectors. Generally, the smaller the RMSE value, the better the performance of the unmixing method. As can be seen from the experimental results in Table 1, the SRE and RMSE values ​​obtained by the method described in this invention are far superior to other similar comparative methods, which further verifies the effectiveness of the method described in this invention.

[0122]

Claims

1. A hyperspectral unmixing method based on hypergraph learning and sparse weighting, characterized in that... The method includes the following steps: Step 1: Band fusion of hyperspectral images: Step 1.1: Observe the 3D hyperspectral image The image is segmented along the spectral dimension, dividing it into a set of images consisting of multiple adjacent band sub-images. ,in, The number of image sets, where each image set contains sub-images of multiple adjacent bands of the original image, i.e.: ,in, Indicates the relationship with the first A set consisting of adjacent sub-images in each band. Original 3D image The Sub-images of each band; Step 1.2, Each image set The fusion process is performed according to the following formula: in, Indicates the size of the set. It contains a collection of images. Average spatial information in; Step 2, Hypergraph learning of hyperspectral images: Step 2.1, based on image set The image after band fusion is represented as a matrix. Each pixel is considered a node in the hypergraph, where... , Indicates the relationship with the first A set consisting of adjacent sub-images in each band. Original 3D image The Sub-images of each band, The number of images in the set; Step 2.2, let the matrix Representation and matrix The corresponding clean hyperspectral image also treats each pixel as a node in the hypergraph; Step 2.3: Complete the hypergraph learning process for the hyperspectral image iteratively using the following steps: Step 2.3.1, in the... In the next iteration, using The nearest neighbor method selects each hyperedge of the hypergraph. Find the nearest neighbor nodes and calculate the hyperedge weight matrix of the hypergraph. ,in This represents the diagonal operations of a matrix, and the diagonal vector. elements For super-edge The weights; Step 2.3.2, in the... In the next iteration, the hypergraph Laplacian matrix Calculate using the following formula: Among them, superscript For matrix inversion, superscript This is the transpose operation of a matrix. Indicates by and The correlation matrix formed by the elements and These represent the node degree and hyperedge degree matrices, respectively; Step 2.3.3, in the... In the next iteration, the image Update as follows: in, For regularization parameters, Representing dimension and The same unit matrix, Indicates the first During the next iteration value, Indicates the first The newly calculated value in the next iteration value; Step 2.3.4, if the number of iterations... Then terminate the iteration and output. ,in Set the maximum number of iterations for the hypergraph learning process; otherwise, proceed to step 2.3.1 to continue. Step 3: Sparse unmixing of hyperspectral images: Step 3.1: Use the Laplacian matrix of the hypergraph learned in Step 2 to constrain the abundance matrix of the unmixing process. This further improves the estimated abundance. The quality; Step 3.2: Introduce auxiliary variables , and and Lagrangian multipliers , and The sparse demixing process of hyperspectral images is achieved using an alternating optimization strategy in the following steps: Step 3.2.1, in the... In the next iteration, the variables during the unmixing process Calculate using the following formula: in, Represents a known spectral library matrix. Representing dimension and The same unit matrix, The input hyperspectral image is represented as a 2-D matrix. Indicates the first During the next iteration The value, Indicates the first During the next iteration The value; Step 3.2.2, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula: in, , express Norm, , Represented by matrix The A vector formed by rows, For matrix The number of rows, For penalty parameters, Indicates the first The newly calculated value in the next iteration value; Step 3.2.3, in the... In the next iteration, auxiliary variables during the unmixing process Calculate using the following formula: in, The Laplacian matrix of the hypergraph obtained in step 2. For regularization parameters; Step 3.2.4, in the... In the next iteration, auxiliary variables during the unmixing process Calculated using the following formula: in, Represents a symbolic function. The operator "" represents element-based absolute value operations. " indicates an element-based product operator. For regularization parameters, and Represents the abundance matrix The applied sparse weighting matrix; Step 3.2.5, in the... In the next iteration, the sparse weighted matrix and Calculate according to the following formulas: in, For hyperparameters, Represented by the abundance matrix The A row vector composed of row elements. Abundance matrix The number of rows, Abundance matrix The OK The absolute value of the elements in the column. Representation matrix The OK Column elements; Step 3.2.6, in the... In the next iteration, the Lagrangian multipliers are calculated as follows: Step 3.2.7, if the number of iterations... Then terminate the iteration and output. ,in The maximum number of iterations is set for the unmixing process; otherwise, proceed to step 3.2.

1. When iteration stops according to step 3.2.7, the output is... This is the abundance matrix that needs to be estimated.

2. The hyperspectral unmixing method based on hypergraph learning and sparse weighting according to claim 1, characterized in that... The Calculate using the following formula: in, It is an exponential function. For Gaussian kernel scaling parameters, and Representing images respectively The and the 1 pixel, express The square of the norm.

3. The hyperspectral unmixing method based on hypergraph learning and sparse weighting according to claim 1, characterized in that... The and Calculated by the following formula: in, Indicates all elements are Column vectors.

4. The hyperspectral unmixing method based on hypergraph learning and sparse weighting according to claim 1, characterized in that... In step 1, the relevant parameters are set as follows: In signal-to-noise ratio Settings under Gaussian noise conditions: Image set ; In noise ratio Setting for sparse noise: Image set .

5. The hyperspectral unmixing method based on hypergraph learning and sparse weighting according to claim 1, characterized in that... In step 2, the variable initialization and related parameter settings are as follows: Clean image Initialization settings: ; In signal-to-noise ratio Setting the number of neighboring nodes in Gaussian noise case: Gaussian kernel scale parameters Regular expression parameters Number of iterations ; In noise ratio Setting the number of neighboring nodes in sparse noise case Gaussian kernel scale parameters Regular expression parameters Number of iterations .

6. The hyperspectral unmixing method based on hypergraph learning and sparse weighting according to claim 1, characterized in that... In step 3, the variable initialization and related parameter settings are as follows: primitive variables Initialization settings: ; Auxiliary variables Initialization settings: ; Auxiliary variables Initialization settings: ; Auxiliary variables Initialization settings: ; Lagrangian multiplier initialization settings: ; Sparse weighted matrix and Initialization settings: ; In signal-to-noise ratio Setting the regularization parameter in Gaussian noise case: and Penalty parameters Hyperparameters Number of iterations ; In noise ratio Setting regularization parameters for sparse noise conditions and Penalty parameters Hyperparameters Number of iterations .

Images