A multi-target multi-space collaborative hyperspectral unmixing method and system considering spectral variability

Abstract

This invention relates to the field of hyperspectral remote sensing technology and discloses a multi-objective, multi-spatial collaborative hyperspectral unmixing method and system considering spectral variability. The method includes the following specific steps: constructing a spectral feature subspace set based on the spectral difference characteristics of land cover types in hyperspectral images; constructing a multi-objective, multi-spatial collaborative endmember extraction model based on the spectral feature subspace set; iteratively optimizing and solving the multi-spatial collaborative model; and outputting the obtained endmember bundles as the unmixing result. This invention solves the problem of insufficient accuracy in existing endmember bundle extraction techniques and has the characteristics of improving the completeness of endmember bundle extraction and avoiding individual degradation and crowding distance failure problems.

Description

Technical Field

[0001] This invention relates to the field of hyperspectral remote sensing technology, and more specifically, to a multi-target, multi-spatial collaborative hyperspectral demixing method and system that takes into account spectral variability. Background Technology

[0002] Hybrid pixel decomposition methods can be broadly categorized into two types based on their workflow. The first type treats endmember extraction and abundance estimation as two independent steps, performing endmember extraction first, followed by abundance estimation. Common endmember extraction methods include those based on convex geometry theory, projection-based methods, spatial-spectral joint methods, error analysis methods, and optimization-based methods. Meanwhile, abundance estimation typically employs methods based on constrained least squares and sparse regression. The second type integrates these two stages, primarily using methods based on nonnegative matrix factorization and deep learning.

[0003] Hybrid pixel decomposition methods can be further classified based on whether or not they consider intra-class endmember variability. One type of method considers this variability, while another does not. Methods that do not consider endmember variability use a single endmember to represent a class of land cover in the hybrid model; this approach is relatively straightforward in both understanding and implementation. However, in real-world hyperspectral scenes, complex endmember variability issues often exist, meaning that spectral differences exist within a single land cover class. This variability is caused by factors such as intra-class material differences, lighting conditions, topographic variations, and phenological periods. Therefore, an increasing number of studies are addressing the endmember variability problem.

[0004] Some methods for addressing endmember variability utilize existing endmember libraries and apply abundance estimation algorithms such as multi-endmember spectral mixture analysis or sparse unmixing to perform mixed pixel decomposition. These abundance estimation algorithms select the most suitable set of endmembers from the endmember library for abundance estimation. However, in practical applications, the adaptability and usability of the endmember library cannot be guaranteed. Therefore, a more feasible approach is to automatically extract these endmembers from the image, extracting several endmembers for each land class to form an "endmember bundle," which should include as many intraclass variations as possible. This type of method is called an endmember bundle extraction algorithm.

[0005] Currently, only a limited number of endmember bundle extraction algorithms have been developed. Spatial local extraction is one of the most popular approaches in endmember bundle extraction. For example, a hyperspectral image can be spatially divided into subsets, and endmembers can be extracted within each subset. In this method, the number of endmembers in each subset is first estimated based on the Gram matrix method, and then traditional endmember extraction algorithms are used for endmember extraction. Finally, the endmembers obtained from all subsets are integrated to output the endmember bundle. Other approaches include randomly selecting pixels from the global image to form subsets, as proposed by the EBE algorithm, or dividing the image into multiple subsets using multi-scale interval sampling, as proposed by the MSREBE algorithm. However, these endmember bundle extraction methods have certain drawbacks, such as the inability to handle cases where the material categories within the subsets are incomplete, the consideration of only spectral information, and the limitations of traditional endmember extraction algorithms due to convex geometry theory, resulting in inaccurate endmember extraction.

[0006] In addition, some endmember bundle extraction methods utilize spatial information or spectral curve shape information for endmember bundle extraction. One such method is Spatial and Spectral Feature-Based Endmember Bundle Extraction (SSEBE), which uses traditional endmember extraction algorithms to extract endmembers from hyperspectral images and develops a post-processing strategy based on the heterogeneity index to remove candidate endmembers located in heterogeneous regions. This method is also limited by the finite accuracy of traditional endmember extraction algorithms based on convex geometry theory. Another example is Spectral Curve-Based Endmember Extraction (SCEE). This method uses pixels with the largest or smallest wavelet transform coefficients within a certain band to form a candidate endmember set, and uses a connected component labeling method to remove pixels in smaller connected regions within the candidate endmember set to obtain the final endmember set. This algorithm has a significant drawback: when obtaining the complete endmember set, a large number of redundant and noisy pixels are selected, leading to a severe decrease in endmember bundle extraction accuracy.

[0007] Essentially, endmember extraction is a combinatorial optimization problem that requires searching for the optimal combination of endmembers in an image. In recent years, multi-objective optimization algorithms have made significant progress in endmember bundle extraction due to their powerful global search capabilities. Existing methods, such as the MOEBE algorithm, construct endmember extraction models in different feature spaces based on the assumption that endmembers have different relative positions, and obtain endmember bundles through multi-objective optimization. These methods utilize the differences in data distribution across different feature spaces to expose more endmembers to the convex geometric boundaries formed by pixels, thereby improving the richness of endmember extraction. However, these techniques typically coarsely divide the original hyperspectral image into three spectral subsets along the spectral dimension, treating each subset as a different feature space. This approach ignores the unique spectral features of different landforms and fails to fully utilize the potential of spectral subspaces. Furthermore, these techniques directly employ a general evolutionary algorithm framework in multi-objective optimization. In the combinatorial optimization problem of endmember extraction, this general evolutionary algorithm framework suffers from individual degradation. Currently, there is an urgent need for a more effective multi-objective optimization-based endmember bundle extraction framework, and for improved optimization algorithms tailored to the specific characteristics of the endmember bundle extraction task. Achieving comprehensive endmember bundles using multi-objective optimization algorithms remains an unsolved challenge.

[0008] In summary, existing hyperspectral image unmixing methods suffer from insufficient accuracy in extracting endmember bundles. Therefore, how to invent a high-precision endmember bundle extraction and unmixing method based on multi-objective optimization algorithms is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0009] To address the problem of insufficient accuracy in endmember beam extraction in existing technologies, this invention provides a multi-target, multi-spatial collaborative hyperspectral demixing method that considers spectral variability. This method is characterized by improving the completeness of endmember beam extraction and avoiding individual degradation and crowding distance failure issues.

[0010] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0011] A multi-objective, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability includes the following specific steps:

[0012] Based on the spectral difference characteristics of land cover types in hyperspectral images, a set of spectral feature subspaces is constructed.

[0013] Based on the spectral feature subspace set, a multi-target, multi-space collaborative endmember extraction model is constructed.

[0014] Iterative optimization is used to solve the multi-space collaborative model;

[0015] Output the endmember bundle obtained from the solution as the unmixing result.

[0016] Preferably, based on the spectral differences in land cover types, a spectral feature subspace is constructed, and the specific steps are as follows:

[0017] The k-medios clustering algorithm is used to cluster the hyperspectral image into P pixel clusters in the spatial dimension, resulting in subdata. Where P is the number of end-member categories, L is the number of bands, and N is the number of bands. i The number of pixels contained in the i-th pixel cluster;

[0018] On the sub-data of each cluster, a fast clustering unsupervised band selection algorithm with enhanced density peaks is used to obtain the selected band numbers of group P.

[0019] Based on the obtained P groups of band number combinations, the subdata is split into P parts along the spectral dimension to obtain the subdata.

[0020] Use minimum noise separation transform on Y j Perform dimensionality reduction to obtain the dimensionality-reduced data.

[0021] Will Divide each set of M data points into a group to obtain the subspace set of all possible combinations.

[0022] Furthermore, based on the spectral feature subspace set, a multi-target, multi-spatial collaborative endmember extraction model is constructed, specifically as follows:

[0023] Construct a multi-objective optimization function based on the maximum volume theory:

[0024]

[0025] in, for The endmember matrix in the i-th subspace, vol(A) i ) represents finding A i The volume of the simplex formed;

[0026] Based on the multi-objective optimization function, a multi-objective optimization algorithm based on the improved NSGA-II is constructed;

[0027] Based on internal and external loops, a multi-target, multi-spatial collaborative endmember extraction model for endmember bundle extraction is constructed:

[0028] In the inner loop, the population is iteratively optimized through a multi-objective optimization algorithm to maximize the multi-objective function and extract the optimal endmember bundle;

[0029] The inner loop is terminated when the number of iterations of the optimization algorithm reaches the set maximum number of iterations.

[0030] In the outer loop, subspace combinations are selected sequentially and input into the multi-objective optimization algorithm each time, serving as the feature space for extracting and calculating the objective function at the end of the inner loop;

[0031] The optimal endmember bundle extracted from all spectral feature subspace combinations is used as the termination condition for the outer loop. Furthermore, based on a multi-objective optimization function, the specific steps of the multi-objective optimization algorithm are as follows:

[0032] S1: Initialize the input endmember bundle to a population containing NP individuals; randomly initialize the individual indices and initialize P gene pools;

[0033] S2: Using a gene segment allocation strategy, individuals in the population are randomly grouped into pairs to form mating pools; in the mating pools, simulated binary crossover and polynomial mutation are used to generate offspring populations, and the parent populations and offspring populations in the mating pools are merged into p', and the gene pool is updated through p'.

[0034] S3: Calculate the spatial crowding degree of each individual; select m individuals in p' using an elite retention environment selection method based on spatial crowding degree to update the population, output the updated population as an endmember bundle, and further update the gene pool based on the updated population.

[0035] S4: Return to step S2 and continue iterating the population until the set number of iterations is reached.

[0036] Furthermore, in step S1, the individual's sequence number is randomly initialized and P gene pools are initialized, specifically as follows:

[0037] Encode all individuals in the input endmember bundle using random cell indices:

[0038] X=(g1,g2,...,g P )

[0039] g i (i = 1, ..., P) represents the index of the i-th endmember in the i-th pixel cluster, where the pixel cluster is the Y obtained by clustering algorithm during the construction of the spectral feature subspace. i Each X record contains a set of endmembers, and all X records are encoded to obtain NP sequence numbers.

[0040] Encode each individual's endmember combinations into a chromosome, where each gene represents an endmember, and initialize P gene pools:

[0041]

[0042] pool k (k=1,...,P) represents the k-th gene pool constructed by the algorithm. This represents the k-th gene segment in the n-th individual.

[0043] Furthermore, the calculation of spatial crowding involves the following steps:

[0044] Convert the pixel indices of all individuals in the NP populations into spatial coordinates;

[0045] The corresponding gene segments are assigned to the corresponding spatial coordinates based on the spatial coordinates of each individual.

[0046] Each gene pool adaptively creates a corresponding adaptive grid based on the range of its spatial coordinates;

[0047] In each gene pool, the number of gene segments contained in each grid cell is used as the crowding degree of these gene segments;

[0048] The crowding of all gene segments contained in each individual is summed, and the sum is used as the spatial crowding of that individual.

[0049] Furthermore, an elite preservation environment selection method based on spatial crowding is used to select m individuals from p'. The specific steps are as follows:

[0050] Perform a non-dominated sort on p', dividing the individuals in p' into several different levels according to their dominance relationships;

[0051] Based on the non-dominated ranking, if there are individuals at the same level, then the individuals at the same level are ranked again based on spatial crowding.

[0052] Keep the first m sorted individuals and discard the rest.

[0053] Furthermore, a replacement mechanism to prevent duplicate extraction is implemented between inner loops, the specific steps of which are as follows:

[0054] In the inner loop, after each iteration extracts the endmember bundles of the subspace, the spectral angular distance between each extracted endmember and all pixels of the original hyperspectral image is calculated.

[0055] If the spectral angular distance of a pixel is less than the set threshold, then that pixel is replaced with the spectral mean of its endmember bundle.

[0056] Furthermore, the spectral angular distance between each extracted endmember and all pixels of the original hyperspectral image is calculated, specifically:

[0057]

[0058] Where 'a' represents the reference endmember spectrum. This indicates the extraction of endmember spectra.

[0059] A multi-objective, multi-spatial, collaborative hyperspectral unmixing system considering spectral variability includes a cascaded spectral feature subspace construction module, a multi-spatial collaborative model construction module, and an optimization solution module.

[0060] The spectral feature subspace construction module is used to construct a set of spectral feature subspaces based on the spectral difference features of land cover types in hyperspectral images.

[0061] The aforementioned multi-space collaborative model construction module is used to construct a multi-objective multi-space collaborative end-member extraction model based on the spectral feature subspace set;

[0062] The optimization solution module is used to iteratively optimize and solve the multi-space collaborative model, and outputs the obtained endmember bundle as the unmixing result.

[0063] The beneficial effects of this invention are as follows:

[0064] This invention discloses a multi-objective, multi-spatial collaborative hyperspectral unmixing method that considers spectral variability. By constructing a spectral feature subspace based on the spectral differences of land types, and constructing a multi-objective, multi-spatial collaborative endmember extraction model based on the set of spectral feature subspaces, the completeness of endmember bundle extraction is improved, the problem of insufficient accuracy of extracted endmember bundles is solved, and the multi-spatial collaborative model is solved by iterative optimization, avoiding individual degradation and crowding distance failure problems. Attached Figure Description

[0065] Figure 1 This is a flowchart illustrating a multi-target, multi-spatial, collaborative hyperspectral demixing method that considers spectral variability according to the present invention.

[0066] Figure 2 This is a block diagram illustrating the technical roadmap of the multi-target, multi-spatial, collaborative hyperspectral unmixing method of the present invention, which considers spectral variability, in Example 2.

[0067] Figure 3 This is the computational spatial crowding distance map of the multi-target, multi-spatial collaborative hyperspectral unmixing method of the present invention, which considers spectral variability, in Example 2.

[0068] Figure 4 This is a flowchart illustrating the multi-objective optimization algorithm of the multi-objective, multi-spatial collaborative hyperspectral unmixing method of the present invention, which considers spectral variability, in Example 2.

[0069] Figure 5 This is a schematic diagram illustrating the replacement mechanism of the multi-target, multi-spatial collaborative hyperspectral unmixing method of the present invention, which considers spectral variability, to improve the richness of variable spectral extraction in Example 2. Detailed Implementation

[0070] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0071] Example 1

[0072] like Figure 1 As shown, a multi-objective, multi-spatial collaborative hyperspectral unmixing method considering spectral variability includes the following specific steps:

[0073] Based on the spectral difference characteristics of land cover types in hyperspectral images, a set of spectral feature subspaces is constructed.

[0074] Based on the spectral feature subspace set, a multi-target, multi-space collaborative endmember extraction model is constructed.

[0075] Iterative optimization is used to solve the multi-space collaborative model;

[0076] Output the endmember bundle obtained from the solution as the unmixing result.

[0077] Example 2

[0078] More specifically, such as Figure 2 As shown, in a specific embodiment, considering the differential spectral features among land cover types in hyperspectral images distributed in different spectral subspaces, a spectral feature subspace is constructed based on the differential spectral features of land cover types. The specific steps are as follows:

[0079] The k-medios clustering algorithm is used to cluster the hyperspectral image into P pixel clusters in the spatial dimension, resulting in subdata. Where P is the number of end-member categories, L is the number of bands, and N is the number of bands. i The number of pixels contained in the i-th pixel cluster;

[0080] On the subdata of each cluster, the enhanced fast density-peak-based clustering (E-FDPC) algorithm is used to obtain the selected band numbers of group P.

[0081] Based on the obtained P groups of band number combinations, the subdata is split into P parts along the spectral dimension to obtain the subdata.

[0082] Use minimum noise separation transform on Y j Perform dimensionality reduction to obtain the dimensionality-reduced data.

[0083] Will Divide each set of M data points into a group to obtain the subspace set of all possible combinations.

[0084] In this embodiment, M is 3.

[0085] In one specific embodiment, according to the linear mixture model, a hyperspectral image can be decomposed into pure spectra (endmembers) of each geographic type constituting the pixels and matrices recording their corresponding proportions (abundance). Maximum volume theory treats the distribution of a hyperspectral image in a high-dimensional spectral space as a convex geometric body, with endmembers often located at the vertices of this convex body. To accurately extract the rich set of endmembers with variable spectra for constructing a spectral variation model, a multi-objective, multi-spatial collaborative endmember extraction model is constructed based on the spectral feature subspace set, specifically as follows:

[0086] Construct a multi-objective optimization function based on the maximum volume theory:

[0087]

[0088] in, for The endmember matrix in the i-th subspace, vol(A) i ) represents finding A i The volume of the simplex formed;

[0089] Based on the multi-objective optimization function, a multi-objective optimization algorithm based on the improved NSGA-II is constructed;

[0090] Based on internal and external loops, a multi-target, multi-spatial collaborative endmember extraction model for endmember bundle extraction is constructed:

[0091] In the inner loop, the population is iteratively optimized through a multi-objective optimization algorithm to maximize the multi-objective function and extract the optimal endmember bundle;

[0092] The inner loop is terminated when the number of iterations of the optimization algorithm reaches the set maximum number of iterations.

[0093] In the outer loop, subspace combinations are selected sequentially and input into the multi-objective optimization algorithm each time, serving as the feature space for extracting and calculating the objective function at the end of the inner loop;

[0094] In this embodiment, three spectral subspace combinations are selected sequentially as an endmember bundle in each iteration, and all possible combinations are sequentially input into the multi-objective optimization algorithm.

[0095] In this embodiment, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is known for its simplicity and efficiency, and is one of the most commonly used multi-objective optimization algorithms. The endmember bundle extraction task can be viewed as a combinatorial optimization problem, and NSGA-II can be used to obtain a set of Pareto optimal solutions. However, directly applying existing general-purpose multi-objective optimization algorithms such as NSGA-II to image endmember spatial combinatorial optimization problems can lead to individual degradation and crowding distance failure, affecting the accuracy of endmember bundle extraction. This invention introduces the concepts of gene recombination and spatial crowding to specifically improve the NSGA-II method to optimize the multi-objective function.

[0096] The optimal endmember bundle under the combination of all spectral feature subspaces is used as the outer loop termination condition.

[0097] In one specific embodiment, such as Figure 4 As shown, based on the multi-objective optimization function, the specific steps of the multi-objective optimization algorithm are as follows:

[0098] S1: Initialize the input endmember bundle to a population containing NP individuals; randomly initialize the individual indices and initialize P gene pools;

[0099] S2: Using a gene segment allocation strategy, individuals in the population are randomly grouped into pairs to form mating pools; in the mating pools, simulated binary crossover and polynomial mutation are used to generate offspring populations, and the parent populations and offspring populations in the mating pools are merged into p', and the gene pool is updated through p'.

[0100] S3: Calculate the spatial crowding degree of each individual; select m individuals in p' using an elite retention environment selection method based on spatial crowding degree to update the population, output the updated population as an endmember bundle, and further update the gene pool based on the updated population.

[0101] S4: Return to step S2 and continue iterating the population until the set number of iterations is reached.

[0102] In the multi-objective optimization algorithm, step S1 involves randomly initializing the individual's index and initializing P gene pools, specifically as follows:

[0103] Encode all individuals in the input endmember bundle using random cell indices:

[0104] X=(g1,g2,...,g P )

[0105] g i (i = 1, ..., P) represents the index of the i-th endmember in the i-th pixel cluster, where the pixel cluster is the Y obtained by clustering algorithm during the construction of the spectral feature subspace.i Each X record contains a set of endmembers, and all X records are encoded to obtain NP sequence numbers.

[0106] In this embodiment, population optimization is linked to the search for the optimal endmember combination. Furthermore, using this encoding method, each gene locus will search for endmembers in its corresponding cluster, greatly reducing the search space and increasing search efficiency (the gene locus is the sequence number of the gene segment in the individual's encoding).

[0107] Encode each individual's endmember combinations into a chromosome, where each gene represents an endmember, and initialize P gene pools:

[0108]

[0109] pool k (k=1,...,P) represents the gene pool constructed by the algorithm. This represents the k-th gene segment in the n-th individual.

[0110] In this embodiment, each gene pool stores all gene segments at corresponding gene loci for all individuals in the population. At the start of each iteration, the individuals in the population undergo a complete reorganization and update, meaning that all gene segments contained in an individual are randomly selected from the corresponding gene pool, and gene segments in the gene pool are not reassigned. The gene pool is updated after each population update.

[0111] In one specific embodiment, such as Figure 3 As shown, the specific steps for calculating space crowding are as follows:

[0112] Convert the pixel indices of all individuals in the NP populations into spatial coordinates;

[0113] The corresponding gene segments are assigned to the corresponding spatial coordinates based on the spatial coordinates of each individual.

[0114] In this embodiment, the spatial coordinates are the row and column numbers in the two-dimensional space of the image.

[0115] Each gene pool adaptively creates a corresponding adaptive grid based on the range of its spatial coordinates;

[0116] In each gene pool, the number of gene segments contained in each grid cell is used as the crowding degree of these gene segments;

[0117] The crowding of all gene segments contained in each individual is summed, and the sum is used as the spatial crowding of that individual.

[0118] In one specific embodiment, an elite retention environment selection method based on spatial crowding is used to select m individuals from p'. The specific steps are as follows:

[0119] Perform a non-dominated sort on p', dividing the individuals in p' into several different levels according to their dominance relationships;

[0120] Based on the non-dominated ranking, if there are individuals at the same level, then the individuals at the same level are ranked again based on spatial crowding.

[0121] Keep the first m sorted individuals and discard the rest.

[0122] In one specific embodiment, a replacement mechanism to prevent duplicate extraction is also provided between the inner loops, the specific steps of which are as follows:

[0123] In the inner loop, after each iteration extracts the endmember bundles of the subspace, the spectral angular distance between each extracted endmember and all pixels of the original hyperspectral image is calculated.

[0124] If the spectral angular distance of a pixel is less than the set threshold, then that pixel is replaced with the spectral mean of its endmember bundle.

[0125] In this embodiment, the proposed anti-duplication extraction strategy is executed between each inner loop iteration. Specifically, the spectral angular distance (SAD) between the endmember extracted in the current inner loop and all pixels in the original hyperspectral image is calculated. Pixels with an SAD less than a set threshold are replaced with the spectral mean of the cluster to which that pixel belongs. Figure 5 As shown, mean replacement ensures that the pixel is updated to a mixed pixel, preventing it from being extracted repeatedly and exposing other endmembers that constitute the simplex body. Furthermore, mean-replaced pixels contain feature information of a certain type of land cover, preventing the extraction of mixed pixels of multiple types when all clean pixels are replaced. At the algorithm optimization level, extracted endmembers will not interfere with the optimization process as local optima.

[0126] In summary, the beneficial effects of the present invention include:

[0127] A multi-objective, multi-spatial collaborative endmember extraction model was constructed: Existing endmember bundle extraction algorithms based on multi-objective optimization only roughly divide the original image into three equal parts along the spectral dimension, without considering the spectral differences between land cover types, and thus failing to fully utilize spectral information. This invention, to fully utilize image spectral information, carefully designs a feature space construction method, aiming to represent the spectral variability of endmembers from different land cover types as much as possible through multiple feature spaces. Considering the significant differences in the distribution of endmembers in different spectral subspaces, the spectral subspaces constructed based on the characteristics of each land cover type can better expose the endmembers of different land cover types outside the data boundaries, facilitating extraction. Specifically, the original image is first clustered into P clusters in the spatial dimension (P being the number of land cover types). Then, band selection is performed on each pixel cluster to obtain a set of bands containing the band features of each land cover type, thereby dividing the image into P subsets in the spectral dimension. In this embodiment, every three spectral subsets are treated as a combination, and endmember bundle extraction is performed sequentially under all possible combinations.

[0128] This invention employs a multi-strategy integrated multi-objective optimization algorithm: Existing endmember bundle extraction algorithms based on multi-objective optimization directly use general optimization algorithms to optimize the model. These general optimization algorithm frameworks are designed to solve mathematical optimization problems; directly applying them to spatial image combination optimization problems like endmember bundle extraction leads to individual degradation and crowding distance failure. Taking genetic algorithms as an example, in genetic algorithms, endmember combinations are encoded as chromosomes, where each gene segment represents an endmember. If gene segments from two parent chromosomes at the same gene locus represent different types of endmembers, crossover operations will result in two endmembers of the same type on the offspring chromosomes. This indicates that the offspring chromosomes record duplicate endmember types, resulting in incomplete endmember categories and individual degradation. To address this problem, this invention introduces a gene recombination strategy, constructing a gene pool for each land cover type. Chromosomes randomly select gene segments from these gene pools, ensuring that all chromosomes record consistent endmember types at the same gene locus, thus avoiding individual degradation. Furthermore, since even subtle differences in gene segments can significantly affect the objective function value in multi-objective optimization, traditional crowding distance based on the objective function is ineffective in endmember bundle extraction tasks. Therefore, this invention proposes a crowding degree calculation strategy based on the two-dimensional spatial distance between candidate endmembers in the image. This strategy avoids the failure of crowding distance, ensures population diversity, and enhances the algorithm's global search capability.

[0129] This invention also employs a strategy to prevent duplicate extraction: existing methods extract a large number of endmembers at once, inevitably resulting in duplicate endmembers in the results. In this invention, a small number of accurate endmembers are extracted in each outer loop and added to the result set, reducing the risk of redundant extraction. Furthermore, to prevent unintentional duplicate extraction that may occur between multiple outer loops, this invention proposes a replacement-based strategy to prevent duplicate extraction. During the sequential extraction process of different spectral subspace sets, any pixel in the original image that is similar to a subsequently extracted endmember is replaced with the mean of its corresponding pixel cluster. This operation has two major advantages for improving the endmember bundle extraction algorithm. First, it avoids the extraction of duplicate endmembers in subsequent iterations. Second, it moves the extracted endmembers from the data convex boundary to the interior, exposing other endmembers outside the boundary. This change can avoid interference from local optima during the optimization process, improving the richness of the endmember bundle extraction.

[0130] Example 3

[0131] A multi-objective, multi-spatial, collaborative hyperspectral unmixing system considering spectral variability includes a cascaded spectral feature subspace construction module, a multi-spatial collaborative model construction module, and an optimization solution module.

[0132] The spectral feature subspace construction module is used to construct a set of spectral feature subspaces based on the spectral difference features of land cover types in hyperspectral images.

[0133] The aforementioned multi-space collaborative model construction module is used to construct a multi-objective multi-space collaborative end-member extraction model based on the spectral feature subspace set;

[0134] The optimization solution module is used to iteratively optimize and solve the multi-space collaborative model, and outputs the obtained endmember bundle as the unmixing result.

[0135] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A multi-objective, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability, characterized in that: The specific steps include the following: Based on the spectral difference characteristics of land cover types in hyperspectral images, a set of spectral feature subspaces is constructed. Based on the spectral feature subspace set, a multi-objective, multi-spatial collaborative endmember extraction model is constructed, including: Based on the multi-objective optimization function, an improved multi-objective optimization algorithm based on NSGA-II is constructed: S1: Initialize the input endmember bundle to include A population of individuals; randomly initialize the individual indices and initialize... Gene banks: Encode all individuals in the input endmember bundle using random cell indices: Indicates the first The terminal in the first The index of a pixel cluster, where the pixel cluster is obtained using a clustering algorithm during the construction of the spectral feature subspace. each Record a set of endpoints to encode all ,get One serial number; Each individual's endmember combinations are encoded into a chromosome, where each gene represents an endmember. Initialization... Gene banks: in The algorithm constructs the first... A gene pool, Indicates the first The first of the individuals One gene segment; S2: Using a gene segment allocation strategy, individuals in the population are randomly paired to form mating pools; simulated binary crossover and polynomial mutation are used in the mating pools to generate offspring populations, and the parent populations and offspring populations in the mating pools are merged. ,pass Update the gene pool; S3: Calculate the spatial crowding degree for each individual; employ an elite retention environment selection method based on spatial crowding degree in... Select m individuals to update the population, output the updated population as an endmember bundle, and further update the gene pool based on the updated population. S4: Return to step S2 and continue iterating the population until the set number of iterations is reached; Based on inner and outer loops, a multi-objective, multi-spatial collaborative endmember extraction model is constructed for endmember bundle extraction: In the inner loop, the population is iteratively optimized through a multi-objective optimization algorithm to maximize the multi-objective function and extract the optimal endmember bundle; the inner loop terminates when the number of iterations of the optimization algorithm reaches the set maximum number of iterations; In the outer loop, subspace combinations are selected sequentially and input into the multi-objective optimization algorithm each time, serving as the feature space for calculating the objective function of the inner loop endmember bundle extraction; The optimal endmember bundle extracted under all spectral feature subspace combinations is used as the outer loop termination condition. Iterative optimization is used to solve the multi-space collaborative model; Output the endmember bundle obtained from the solution as the unmixing result.

2. The multi-target, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability according to claim 1, characterized in that: Based on the spectral differences in land cover types, a spectral feature subspace is constructed. The specific steps are as follows: The k-medios clustering algorithm is used to cluster hyperspectral images into groups based on their spatial dimension. Pixel clusters, to obtain sub-data ,in For the number of endmember categories, L For the number of bands, For the first The number of pixels contained in a pixel cluster; On the sub-data of each cluster, a fast clustering unsupervised band selection algorithm with enhanced density peaks is used to obtain... The selected band number for the group; According to the obtained Group band number combinations, in the spectral dimension, split the sub-data into , obtain sub-data ; Use minimum noise separation transform to Perform dimensionality reduction to obtain the dimensionality-reduced data. ; Will Divide each set of M data points into a group to obtain the subspace set of all possible combinations. ).

3. The multi-objective, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability according to claim 2, characterized in that, The multi-objective optimization function is expressed as: in, for The Middle Endmember matrices in each subspace Expressing the request The volume of the simplex formed.

4. The multi-objective, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability according to claim 1, characterized in that: The specific steps for calculating space crowding are as follows: Will The pixel indices of all individuals in a population are converted into spatial coordinates; The corresponding gene segments are assigned to the corresponding spatial coordinates based on the spatial coordinates of each individual. Each gene pool adaptively creates a corresponding adaptive grid based on the range of its spatial coordinates; In each gene pool, the number of gene segments contained in each grid cell is used as the crowding degree of these gene segments; The crowding of all gene segments contained in each individual is summed, and the sum is used as the spatial crowding of that individual.

5. The multi-objective, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability according to claim 4, characterized in that: An elite preservation environment selection method based on spatial crowding is adopted in Selecting m individuals from the pool, the specific steps are as follows: right Perform a non-dominated sort, and sort according to the dominance relationship. The individuals are divided into several different levels and sorted accordingly; Based on the non-dominated ranking, if there are individuals at the same level, then the individuals at the same level are ranked again based on spatial crowding. Keep the first m sorted individuals and discard the rest.

6. The multi-objective, multi-spatial, collaborative hyperspectral demixing method considering spectral variability according to claim 5, characterized in that: There is also a replacement mechanism to prevent duplicate extractions between the inner loops, and the specific steps are as follows: In the inner loop, after each iteration extracts the endmember bundles of the subspace, the spectral angular distance between each extracted endmember and all pixels of the original hyperspectral image is calculated. If the spectral angular distance of a pixel is less than the set threshold, then that pixel is replaced with the spectral mean of its endmember bundle.

7. The multi-objective, multi-spatial, collaborative hyperspectral unmixing method considering spectral variability according to claim 6, characterized in that: Calculate the spectral angular distance between each extracted endmember and all pixels in the original hyperspectral image, specifically: in, Indicates the reference endmember spectrum. This indicates the extraction of endmember spectra.

8. A multi-objective, multi-spatial, collaborative hyperspectral demixing system considering spectral variability, characterized in that: Includes a cascaded spectral feature subspace construction module, a multi-space collaborative model construction module, and an optimization solution module: The spectral feature subspace construction module is used to construct a set of spectral feature subspaces based on the spectral difference features of land cover types in hyperspectral images. The multi-spatial collaborative model construction module is used to construct a multi-objective, multi-spatial collaborative endmember extraction model based on a set of spectral feature subspaces, including: Based on the multi-objective optimization function, an improved multi-objective optimization algorithm based on NSGA-II is constructed: S1: Initialize the input endmember bundle to include A population of individuals; randomly initialize the individual indices and initialize... Gene banks: Encode all individuals in the input endmember bundle using random cell indices: Indicates the first The terminal in the first The index of a pixel cluster, where the pixel cluster is obtained using a clustering algorithm during the construction of the spectral feature subspace. each Record a set of endpoints to encode all ,get One serial number; Each individual's endmember combinations are encoded into a chromosome, where each gene represents an endmember. Initialization... Gene banks: in The algorithm constructs the first... A gene pool, Indicates the first The first of the individuals One gene segment; S2: Using a gene segment allocation strategy, individuals in the population are randomly paired to form mating pools; simulated binary crossover and polynomial mutation are used in the mating pools to generate offspring populations, and the parent populations and offspring populations in the mating pools are merged. ,pass Update the gene pool; S3: Calculate the spatial crowding degree for each individual; employ an elite retention environment selection method based on spatial crowding degree in... Select m individuals to update the population, output the updated population as an endmember bundle, and further update the gene pool based on the updated population. S4: Return to step S2 and continue iterating the population until the set number of iterations is reached; Based on inner and outer loops, a multi-objective, multi-spatial collaborative endmember extraction model is constructed for endmember bundle extraction: In the inner loop, the population is iteratively optimized through a multi-objective optimization algorithm to maximize the multi-objective function and extract the optimal endmember bundle; the inner loop terminates when the number of iterations of the optimization algorithm reaches the set maximum number of iterations; In the outer loop, subspace combinations are selected sequentially and input into the multi-objective optimization algorithm each time, serving as the feature space for calculating the objective function of the inner loop endmember bundle extraction; The optimal endmember bundle extracted under all spectral feature subspace combinations is used as the outer loop termination condition. The optimization solution module is used to iteratively optimize and solve the multi-space collaborative model, and outputs the obtained endmember bundle as the unmixing result.

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