Hyperspectral end member extraction method based on leading edge surface exploration
By constructing an initial population and Pareto front using an evolutionary algorithm, and combining bi-objective learning and perturbation strategies, hyperspectral endmember extraction is optimized, solving the accuracy problem of existing methods under noise and outliers, and achieving efficient endmember extraction.
Patent Information
- Application Number
- CN202511930632.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-19
- Publication Date
- 2026-03-03
AI Technical Summary
Existing methods for extracting endmembers from hyperspectral images struggle to accurately extract endmembers in the presence of noise or outliers, and deep learning-based methods require labeled samples for training, leading to high remixing errors.
A hyperspectral endmember extraction method based on evolutionary algorithms is adopted. By constructing an initial population, a multi-objective function, and a Pareto front, and combining a dual-objective learning strategy, an endmember pool solution generation strategy, and perturbation operations, the endmember extraction process is optimized.
It improves the accuracy and diversity of endmember extraction, and can provide multiple endmember combination schemes in a single run, which is significantly better than existing algorithms.
Smart Images
Figure CN121600285A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of hyperspectral image processing technology, specifically a hyperspectral endmember extraction method based on frontier exploration. Background Technology
[0002] Hyperspectral images (HSI) contain rich spectral information, characterized by high spectral resolution for each pixel. Each pixel typically covers a continuous spectral band from visible light to near-infrared and even thermal infrared wavelengths. However, due to spatial resolution limitations, mixed pixels inevitably appear in hyperspectral images, posing a significant challenge to their further analysis and utilization. Spectral unmixing can effectively address the mixed pixel problem, and endmember extraction (EE) is a crucial step in the unmixing process. The goal of endmember extraction is to identify pure pixels from a given hyperspectral image, representing regions containing only a single substance. This is achieved by transforming the unmixing results into decomposing mixed pixels into extracted endmembers with different weights (abundance).
[0003] Currently, algorithms used to solve the endmember extraction problem can be mainly divided into five categories: minimum volume model-based EE algorithms, pure pixel-based EE algorithms, spatial information-based EE algorithms, statistical model-based EE algorithms, and deep learning-based EE algorithms. In minimum volume model-based EE algorithms, a simplex is first designed in the feature space such that all pixels in the input image can be located inside this simplex. The optimization task then transforms into finding the smallest such simplex. In pure pixel-based EE algorithms, the assumption is that pure pixels of ground features exist in the hyperspectral image, and data projection is used to locate these endmembers. In spatial information-based EE algorithms, the endmember extraction process considers the strong spatial correlation between pixels in the hyperspectral image and designs metrics or processing techniques based on spatial correlation to obtain good endmember extraction results. In statistical model-based EE algorithms, based on the assumption that different spectral components are statistically independent, an unsupervised method based on independent component analysis (ICA) is used to extract endmembers. Furthermore, due to the nonnegativity of endmember spectral density and abundance, nonnegative matrix factorization (NMF) has been introduced to address the hyperspectral unmixing problem. Deep learning-based EE algorithms have demonstrated significant performance in endmember extraction tasks.
[0004] While these EE algorithms can extract endmembers from hyperspectral images, most methods are based on geometric or statistical assumptions. When noise or outliers are present in the hyperspectral image, these methods struggle to extract accurate endmembers effectively. Furthermore, since the extracted endmembers are constructed from neural networks rather than actual pixels in the hyperspectral image, deep learning-based endmember extraction algorithms require labeled samples to train the deep learning model, resulting in relatively high remixing errors. Therefore, a hyperspectral endmember extraction method based on frontal exploration is needed. Summary of the Invention
[0005] This application provides a method and apparatus for extracting hyperspectral endmembers based on frontier exploration, which solves the technical problem of low accuracy in existing endmember extraction methods.
[0006] To achieve the above objectives, this application adopts the following technical solution: Firstly, a hyperspectral endmember extraction method based on frontier exploration is provided, including: Acquire the original hyperspectral image and construct the initial population; Establish a multi-objective function for the initial population evolution and generate the Pareto front. Endmember extraction is performed based on the Pareto front to obtain the endmember set.
[0007] With the development of evolutionary algorithms, their application in endmember extraction problems has received increasing attention. Benefiting from their powerful global search capabilities, evolutionary algorithms are well-suited for comprehensively exploring spectral datasets to identify endmembers. Different evolutionary algorithm frameworks, such as genetic algorithms, particle swarm optimization, ant colony optimization, differential evolution, and the firefly algorithm, have been employed to optimize objective functions, such as root mean square error (RMSE), volume inverse, or both. Notably, methods based on multi-objective evolutionary algorithms can simultaneously optimize both volume inverse and RMSE, and can provide multiple optimal solutions in a single run to meet diverse needs in practical applications.
[0008] Based on the above technical solution, in the hyperspectral endmember extraction method based on front exploration provided in this application, the following steps are taken: First, an original hyperspectral image is acquired, and an initial population is constructed. Then, a multi-objective function for the evolution of the initial population is established, and a Pareto front is generated. Endmembers are extracted based on the Pareto front to obtain an endmember set. Using the endmember information in Pareto front individuals, high-quality offspring individuals are generated in each generation through learning, aggregation, and perturbation operations. In the global search phase, a dual-objective learning strategy guides non-Pareto front individuals to evolve towards reliable regions containing high-quality endmembers. Simultaneously, an endmember pool is constructed by integrating endmembers from Pareto front individuals using a solution generation strategy based on the endmember pool. A super-individual is generated using a simple formation growth algorithm, and perturbation of this super-individual generates diverse offspring individuals with similar characteristics. In the local optimization phase, a perturbation strategy is used to improve the quality of Pareto front individuals obtained in the global search phase, thereby improving the accuracy of endmember extraction.
[0009] In conjunction with the first aspect above, one possible implementation of constructing the initial population includes: The original pixel space of the original hyperspectral image is obtained. A set number of distinct pixels are randomly selected from the original pixel space to form an individual. An initial population is constructed based on several individuals, and the initial population is encoded. The individual is an endmember set.
[0010] Specifically, pixels are randomly selected from the original pixel space R to form the initial population pop. ， The population is then encoded. Suppose the hyperspectral image has N pixels, and M endmembers need to be extracted. M distinct pixels are randomly selected from the N pixels to form an individual, and NP individuals are constructed to form a population pop. For encoding the pop population, each individual is encoded using binary 0-1 encoding; where 1 indicates that the current pixel is selected, and 0 indicates that it is not selected.
[0011] In conjunction with the first aspect above, in one possible implementation, the establishment of the multi-objective function for the initial population evolution and the generation of the Pareto front include: Construct the volume inverse objective optimization function and the reconstruction error objective optimization function for the initial population; construct a multi-objective optimization function based on the volume inverse objective optimization function and the reconstruction error objective optimization function, calculate the Pareto solution set of the multi-objective optimization function, and obtain the Pareto front, wherein the Pareto front is the objective space corresponding to the Pareto solution set; One expression of the inverse volume objective function is as follows: ; Where E represents the endmember combination, and M represents the number of extracted endmembers. This represents the pixels after principal component analysis. One expression for the reconstruction error objective optimization function is as follows: ; in, The spectral reconstruction fidelity between the original hyperspectral image (HSI) and its linear approximation using extracted endmembers was evaluated; and Let represent the original spectrum and reconstructed spectrum of the i-th pixel in the hyperspectral image, respectively; note that... It is obtained by remixing endmembers with abundance, where X is a binary-encoded decision vector used to indicate whether each pixel is an endmember; One form of the multi-objective optimization function is as follows: ; in, The objective function is the inverse volume optimization function. To reconstruct the error objective optimization function.
[0012] For ease of understanding, we establish a minimum objective function and solve for a set of equilibrium solutions. Specifically, we minimize the objective function as follows: Where X is the set of endmembers; minF(X) is the objective function to be minimized; f(x) is the objective function; and n is the number of objective functions. If X is not dominated by any other decision vector, then X is a Pareto optimal solution, and the Pareto solution set is the set of all Pareto optimal solutions.
[0013] In conjunction with the first aspect above, in one possible implementation, the endmember extraction based on the Pareto front to obtain the endmember set includes: During the global search phase, individuals on the non-Pareto frontier are updated based on a dual-objective learning strategy, and the next generation of the population is generated. Obtain the number of iterations and determine whether the number of iterations is G times the set interval number of algebras, where G = 1, 2, ...; If yes, then the individuals on the Pareto front are integrated based on the solution generation strategy of the endmember pool to generate the next generation of the population; then proceed to the next iteration. No, proceed to the next iteration; In the local optimization stage, the individuals obtained in the global search stage are optimized based on perturbation measurement to obtain the final endmember set; the global search stage is the stage where the number of iterations is less than or equal to K times the set iteration threshold; the local optimization stage is the stage where the number of iterations is greater than K times the iteration threshold, where K∈(0,1).
[0014] In the global search phase, a dual-objective learning strategy is adopted to guide non-Pareto front individuals to evolve towards reliable regions where high-quality endmembers reside. Simultaneously, a solution generation strategy based on the endmember pool integrates endmembers from Pareto front individuals to construct an endmember pool, uses the simple growth algorithm to generate super individuals, and generates diverse offspring individuals with similar characteristics by perturbing the super individuals. In the local optimization phase, a perturbation strategy is adopted to improve the quality of Pareto front individuals obtained in the global search phase.
[0015] In conjunction with the first aspect above, in one possible implementation, the step of updating individuals on the non-Pareto front based on the dual-objective learning strategy and generating the next generation population includes the following steps: Two individuals on the Pareto front are randomly selected as learning targets, and one individual on a non-Pareto front is randomly selected as the learner. Two individuals are randomly selected on the Pareto front as learning targets, denoted as Pa and Pb respectively; an individual is selected on the non-frontier as the learner, denoted as Q; it is understandable that if there is only one individual on the frontier, then the other individual is randomly selected from the second frontier. Obtain the decision vector, and based on the encoding order in the decision vector, obtain the positions of a pair of corresponding endmembers contained in the learning target Pa and the learning target Pb; define the learnable region corresponding to the learner Q in the two-dimensional image domain based on the positions, the learnable region includes the expanded region Ra obtained by expanding based on the corresponding endmember positions in the learning target Pa and the expanded region Rb obtained by expanding based on the corresponding endmember positions in the learning target Pb; the expanded region is obtained by expanding the corresponding region by a set number of pixels around the position of the corresponding endmember. The same learning process is performed on each individual on the non-frontier surface. After all individuals have been updated, the offspring population is obtained. Environmental selection is performed based on the population and the offspring population to obtain the next generation population, which consists of the best individuals selected from the population and the offspring population.
[0016] In conjunction with the first aspect above, in one possible implementation, the learning process includes at least: When the corresponding extended regions Ra and Rb in the learnable region overlap, the endmember position of the learner Q after learning will be adjusted to the overlapping region. This is because the overlapping region contains endmember information of two learning targets, indicating that the region is more reliable. The algorithm will randomly select a position from the overlapping region as the adjusted position of the learner after learning. When the expansion regions Ra and Rb in the learnable region do not overlap, and the endmember position of learner Q is not located in expansion regions Ra and Rb, the endmember position of learner Q after learning will be randomly adjusted to expansion region Ra or expansion region Rb. When the expansion regions Ra and Rb in the learnable region do not overlap, and the endmember position of learner Q is located in either expansion region Ra or expansion region Rb, the endmember position of learner Q will remain unchanged after learning. The endmember positions in Q obtained after learning will be based on the original endmember positions and the expanded region. and expansion area The relationship between the three factors determines the outcome.
[0017] In conjunction with the first aspect above, in one possible implementation, the endmember pool-based solution generation strategy integrates individuals on the Pareto front to generate the next generation population, including the following steps: Collect all endmembers from the preface individuals, remove duplicate endmembers, and construct an endmember pool, denoted as . n represents the number of endwords in the endword pool. Apply the simple length-forming algorithm to the endmembers in the endmember pool to obtain the endmembers with the largest corresponding volume; The extraction process terminates when the number of endmembers extracted, i, reaches the required number of endmembers, M. The endmembers extracted from the endmember pool at this point are represented as follows: The endmembers in the endmember pool are converted into individuals and denoted as super individuals. Local perturbations are applied to the super individuals to generate offspring populations. Pareto front individuals are selected from the offspring populations as the output of the solution generation scheme for the endmember pool. Environmental selection is performed on the output results and the population to obtain the next generation population; the next generation population consists of the output results and the best individuals selected from the population; that is, the best NP individuals are selected from the output results and the population as the next generation population.
[0018] In conjunction with the first aspect above, in one possible implementation, the simplex growth algorithm, simplex The volume is: ;in, The term is an endmember extracted from the endmember pool, p represents a candidate endmember in the endmember pool, and the superscripts of p and q indicate the spectral dimensions after principal component analysis of the original endmember spectra. The goal of this algorithm is to maximize the... Let be the volume of the simplex at the vertex. Specifically, the search process proceeds step by step: First, a random number is generated. The first endmember is determined by searching the endmember pool in the one-dimensional space after principal component analysis, maximizing the volume defined by the formula. The second endmember is also determined in the one-dimensional principal component analysis space, i.e., the one-dimensional PCA space, and the first endmember is used as another vertex. The i-th endmember is determined in the (i-1)-dimensional space after PCA dimensionality reduction, and the previous (i-1) endmembers are used as other vertices.
[0019] In conjunction with the first aspect above, in one possible implementation, the step of optimizing the individuals obtained in the global search phase based on perturbation measurement to obtain the final endmember set includes: Obtain the individuals on the frontier surface corresponding to each generation of the population; Extract the position of the i-th endmember of an individual. In the rectangular region of the hyperspectral image Randomly select one pixel as the updated endmember, where... To set the area range parameters; After each endmember is updated, a new individual corresponding to the individual is generated, and the new individuals corresponding to each individual are added to the population. Environmental selection is performed to obtain a new population. When the number of iterations is less than the set iteration threshold, the iteration continues until the number of iterations reaches the set iteration threshold. The solution of the Pareto front in the new population is selected as the final endmember set.
[0020] This application provides a hyperspectral endmember extraction method based on frontier exploration. Compared with existing technologies, the advantages of this application include: 1. The process involves acquiring raw hyperspectral images and constructing an initial population; establishing a multi-objective function for the initial population's evolution and generating a Pareto front; extracting endmembers based on the Pareto front to obtain an endmember set; utilizing endmember information from Pareto front individuals, generating high-quality offspring individuals in each generation through learning, aggregation, and perturbation operations; in the global search phase, a dual-objective learning strategy guides non-Pareto front individuals to evolve towards reliable regions containing high-quality endmembers; simultaneously, a solution generation strategy based on the endmember pool integrates endmembers from Pareto front individuals to construct an endmember pool, using a simple formation growth algorithm to generate super individuals, and perturbing these super individuals to generate diverse offspring individuals with similar characteristics; in the local optimization phase, a perturbation strategy is used to improve the quality of Pareto front individuals obtained in the global search phase, thereby enhancing the accuracy of endmember extraction.
[0021] 2. This invention designs a two-stage evolutionary algorithm to complete the hyperspectral endmember extraction task. In the global search stage, the algorithm can fully explore the feasible solution space; in the local optimization stage, the algorithm performs a refined search around the leading solution to enhance the quality of individuals in the population.
[0022] 3. This invention can obtain multiple different endmember combinations through a single run, providing decision-makers with a variety of options. Experimental results show that, on three common hyperspectral image test sets, this method has significant performance advantages compared with five state-of-the-art hyperspectral endmember extraction algorithms.
[0023] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description
[0024] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0025] Figure 1 This is a schematic diagram of the steps in the hyperspectral endmember extraction method of this application; Figure 2 This is a schematic diagram illustrating an example of the dual-objective learning strategy in this application; Figure 3 This is a schematic diagram illustrating an example of the solution generation strategy for the end-member pool in this application; Figure 4 This is a schematic diagram illustrating an example of a local optimization strategy for perturbation in this application. Detailed Implementation
[0026] The technical solutions of this application will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0027] Please see Figure 1 The first aspect of this application provides a method for extracting hyperspectral endmembers based on frontier exploration, comprising the following steps: Step 1: Population initialization; Randomly select pixels from the original pixel space R to form the initial population pop, and encode the population; Suppose the hyperspectral image has N pixels, and M endmembers need to be extracted. Randomly select M different pixels from the N pixels to form an individual, and construct NP individuals to form the population pop. For encoding the pop population, each individual is encoded using binary 0-1 encoding; where 1 indicates that the current pixel is selected, and 0 indicates that it is not selected. Step Two: Multi-Objective Optimization; Multi-objective optimization problems aim to simultaneously maximize or minimize multiple objectives, thereby finding a set of equilibrium solutions. A multi-objective optimization framework for minimization problems can be defined as follows: Minimize the objective function: .
[0028] Where X is the set of endmembers; minF(X) is the objective function to be minimized; f(X) is the objective function; and n is the number of objective functions. Suppose we have two decision vectors X1 and X2. If all objectives satisfy fi(X1)≤fi(X2), then for all i, X1 dominates X2 or X2 is dominated by X1, which is expressed as X1>X2. If a decision vector X is not dominated by any other decision vector, then X is a Pareto optimal solution. The Pareto solution set is the set of all Pareto optimal solutions, which is represented as the Pareto front in the objective space.
[0029] Step 3: Hyperspectral endmember extraction method based on frontier exploration; specifically including the following steps: S1. For the initial population pop, establish a multi-objective function for population evolution. ;in, It is the inverse objective function for volume. It is the objective function for reconstructing the error; Inverse volume objective function:
[0030] Where E represents the endmember combination, and M represents the number of extracted endmembers. This represents the endmembers, or pixels, after processing by principal component analysis. Reconstruct the error objective function:
[0031] The spectral reconstruction fidelity between the original hyperspectral image and its linear approximation using extracted endmembers was evaluated. and Let represent the original spectrum and reconstructed spectrum of the i-th pixel in the hyperspectral image, respectively; note that... It is obtained by remixing endmembers with abundance; X is a binary-coded decision vector used to indicate whether each pixel is an endmember.
[0032] S2, Global Exploration Phase, based on a dual-objective learning strategy; When the number of iterations is less than or equal to K When `maxgen` is used, it represents a set threshold for the number of iterations; it is in the global exploration phase; two individuals on the frontier are randomly selected as learning targets to guide the mutation of other individuals and generate new solutions. The newly generated individuals are merged with the previous generation population. The merged population uses the traditional NSGA-II framework, employing environmental selection based on frontier level and crowding distance to obtain a new population; if the number of iterations is less than K... If maxgen is reached, the iteration continues. In one possible implementation, individuals on the non-Pareto front are updated based on a dual-objective learning strategy to generate the next generation population, including the following steps: randomly selecting two individuals on the Pareto front as learning targets, and randomly selecting one individual on the non-Pareto front as the learner. Two individuals are randomly selected on the Pareto front as learning targets, denoted as Pa and Pb respectively; an individual is selected on the non-frontier as the learner, denoted as Q; it is understandable that if there is only one individual on the frontier, then the other individual is randomly selected from the second frontier. Obtain the decision vector. Based on the encoding order in the decision vector, obtain the positions of a pair of corresponding endmembers contained in the learning targets Pa and Pb. Based on these positions, define the learnable region corresponding to the learner Q in the two-dimensional image domain. The learnable region includes an expanded region Ra obtained by expanding the corresponding endmember positions in the learning target Pa and an expanded region Rb obtained by expanding the corresponding endmember positions in the learning target Pb. The expanded region is obtained by expanding the region around the corresponding endmember position by a set number of pixels. Specifically, according to the encoding order in the decision vector, for a pair of corresponding endmember positions pos1 and pos2 contained in the learning targets Pa and Pb, define a region around the endmember position in the two-dimensional image domain. The extended regions Ra and Rb of the pixel constitute the learnable regions of the corresponding endmembers in the learner Q. The same learning process is performed on each individual on the non-frontier surface. After all individuals have been updated, a offspring population is obtained. Environmental selection is then performed based on the population and the offspring population to obtain the next generation population, which consists of the best individuals selected from the population and the offspring population. Specifically, each individual on the non-frontier surface undergoes the same learning process. Once all individuals have been updated, the offspring population is formed. Subsequently, environmental selection is performed on the merged population (the union of the population and the offspring population), and the best NP individuals are selected as the next generation population.
[0033] In one possible implementation, the learning process includes at least the following: when the corresponding extended regions Ra and Rb in the learnable region overlap, the endmember position of the learner Q after learning will be adjusted to the overlapping region; this is because the overlapping region has endmember information of two learning targets, indicating that the region is more reliable; the algorithm will randomly select a position from the overlapping region as the adjusted position of the learner after learning. When the expansion regions Ra and Rb in the learnable region do not overlap, and the endmember position of learner Q is not located in expansion regions Ra and Rb, the endmember position of learner Q after learning will be randomly adjusted to expansion region Ra or expansion region Rb. When the expansion regions Ra and Rb in the learnable region do not overlap, and the endmember position of learner Q is located in either expansion region Ra or expansion region Rb, the endmember position of learner Q will remain unchanged after learning. The endmember position in Q obtained after learning will be determined based on the original endmember position and the relationship between the extended region Ra and the extended region Rb.
[0034] Please refer to the details. Figure 2 The learning strategy based on dual objectives involves the following steps: Step A1: For population pop, randomly select two individuals on the frontier as learning targets. If there is only one individual on the frontier, then the other individual is randomly selected from the second frontier. The two individuals are learning target Pa and learning target Pb, respectively. Then, select an individual from the non-frontier as learner Q. Step A2: Based on the encoding order in the decision vector, for a pair of corresponding endmember positions pos1 and pos2 contained in the learning target Pa and learning target Pb, define a path centered on this endmember position in the two-dimensional image domain. The extended regions Ra and Rb of a pixel constitute the learnable region of the corresponding endmember in learner Q. The learned endmember position in learner Q is determined by the original endmember position and the relationship between the extended regions Ra and Rb. This learning process can be summarized into the following three cases: When the expansion regions Ra and Rb overlap, the endmember position pos in the learner Q after learning will be adjusted to the overlapping region. This is because the overlapping region contains endmember information from both learning targets, indicating that the region is more reliable. The algorithm randomly selects a position from the overlapping region as the adjusted endmember position pos. When the expansion regions Ra and Rb do not overlap, and the end-member position pos is neither located in the expansion region Ra nor in the expansion region Rb, the algorithm will randomly select a new position from Ra or Rb as the new position of pos. When the expansion regions Ra and Rb do not overlap, but the end-member position pos is already located in one of the expansion regions Ra and Rb, the position of the end-member position pos remains unchanged. Step A3: Each non-frontier individual undergoes the same learning process. Once all individuals have been updated, the offspring population offa is formed. Subsequently, the merged population pop∪offa undergoes environmental selection, and the best NP individuals are selected as the next generation population pop. S3, Global Exploration Phase: Solution Generation Strategy Based on End-Member Pool; During the global exploration phase, at predetermined generations, endmembers of all individuals on the frontier of the population are selected to form an endmember pool. The Simple Forming Growth Algorithm (SFA) is used to extract superior endmembers from this pool to generate super-individuals. These super-individuals are then perturbed to obtain diverse offspring. The diverse offspring are then merged with the previous generation, and environmental selection is performed on the merged population to obtain a new population.
[0035] The endmember pooling-based solution generation strategy integrates individuals on the Pareto front to generate the next generation population. This includes the following steps: collecting endmembers from all individuals on the front, removing duplicate endmembers, and constructing an endmember pool, denoted as . n represents the number of endwords in the endword pool. Apply the simple length-forming algorithm to the endmembers in the endmember pool to obtain the endmembers with the largest corresponding volume; The extraction process terminates when the number of endmembers extracted, i, reaches the required number of endmembers, M. The endmembers extracted from the endmember pool at this point are represented as follows: The endmembers in the endmember pool are converted into individuals and denoted as super individuals. Local perturbations are applied to the super individuals to generate offspring populations. Pareto front individuals are selected from the offspring populations as the output of the solution generation scheme for the endmember pool. Specifically, the extraction process terminates when the number of extracted endpoints i reaches the required number of endpoints M. At this point, the endpoints extracted from the endpoint pool are represented as follows: These extracted endmembers are then transformed into individuals, i.e., super-individuals (os). For each endmember in the super-individual os, a local perturbation is performed within a 3×3 rectangular region centered on the endmember's current position. Through NP-fold local perturbations, a offspring population is constructed. NP represents the set number of perturbations; from Select its Pareto frontier individuals This serves as the output of the solution generation scheme based on the end-member pool. Environmental selection is performed on the output and the population to obtain the next generation population; the next generation population consists of the output and the best individuals selected from the population; that is, the NP best individuals are selected from the output and the population as the next generation population. In one possible implementation, in the simplex growth algorithm, simplex The volume is: ;in, The term is an endmember extracted from the endmember pool, p represents a candidate endmember in the endmember pool, and the superscripts of p and q indicate the spectral dimensions after principal component analysis of the original endmember spectra. The goal of this algorithm is to maximize the... Let be the volume of the simplex at the vertex. Specifically, the search process proceeds step by step: First, a random number is generated. The first endmember is determined by searching the endmember pool in the one-dimensional space after principal component analysis, maximizing the volume defined by the formula. The second endmember is also determined in the one-dimensional principal component analysis space, i.e., the one-dimensional PCA space, and the first endmember is used as another vertex. The i-th endmember is determined in the (i-1)-dimensional space after PCA dimensionality reduction, and the previous (i-1) endmembers are used as other vertices.
[0036] Please refer to the details. Figure 3 The solution generation strategy based on the end-member pool involves the following steps: Step B1: Collect all endmembers from all front surface individuals, remove duplicate endmembers, and construct an endmember pool, denoted as . , where n represents the number of endpoints in the endpoint pool; Step B2: Apply the simplex growth algorithm to the endmembers in the endmember pool to obtain the endmembers with the largest corresponding volume. It is important to note that in the simplex growth algorithm, the simplex... The volume is defined as: .
[0037] in The term "q" represents the identified endmembers, and "p" represents the candidate endmembers in the endmember pool. The superscripts of "p" and "q" indicate the spectral dimensions after principal component analysis of the original endmember spectra. The goal of this algorithm is to maximize the spectral dimensions of the endmember spectra. Let be the volume of the simplex at the vertex. The search process proceeds step by step: First, a random number is generated. The first endmember is determined by searching the endmember pool in the one-dimensional space after principal component analysis, maximizing the volume defined by the formula. The second endmember is also determined in the one-dimensional PCA space, with the first endmember as another vertex. The i-th endmember is determined in the (i-1)-dimensional space after PCA dimensionality reduction, with the previous (i-1) endmembers as other vertices.
[0038] Step B3: When the number of extracted endpoints i reaches the required number of endpoints M, the extraction process terminates. At this point, the endpoints extracted from the endpoint pool are represented as follows: These extracted endmembers are then transformed into individuals, i.e., super-individuals (os). For each endmember in the os, a local perturbation is performed within a 3×3 rectangular region centered on its current position. Through NP-fold local perturbations, a offspring population is constructed. .from Select its Pareto frontier individuals This serves as the output of the solution generation scheme based on the end-member pool.
[0039] Step B4: Perform environmental selection on the output results and the population to obtain the next generation population; the next generation population consists of the output results and the best individuals selected from the population; that is, select the best NP individuals from the output results and the population as the next generation population. S4, Local optimization stage, based on perturbation-based local optimization strategy; When the number of iterations is greater than K During the `maxgen` phase, the system is in a local optimization phase. In this phase, for each frontier individual, a perturbation is applied to each endmember of each individual to generate a new solution. This new solution is then merged with the previous generation's population, and environmental selection is performed to obtain a new population. If the number of iterations is less than the iteration threshold, the iteration continues until the iteration threshold is reached.
[0040] In one possible implementation, the individuals obtained in the global search phase are optimized based on perturbation measurement to obtain the final set of endmembers, including: obtaining the individuals on the frontier surface corresponding to each generation of the population; Extract the position of the i-th endmember of an individual. In the rectangular region of the hyperspectral image Randomly select one pixel as the updated endmember, where... To set the area range parameters; After each endmember is updated, a new individual corresponding to the previous individual is generated. These new individuals are then added to the population for environmental selection, resulting in a new population. If the number of iterations is less than a set threshold, iteration continues until the threshold is reached. The solution to the Pareto front in the new population is then selected as the final endmember set. Please refer to the details. Figure 4 The perturbation-based local optimization strategy has the following specific steps: For each individual on the Pareto front, in terms of parameters A perturbation is applied within a defined region; specifically, for each endmember in a Pareto front individual, denoted as (pos(x), pos(y)), we apply a perturbation to a rectangular region in the hyperspectral image. A new endmember is randomly selected from the population. After each endmember is updated, a new individual is generated and merged into the parent population. Subsequently, an environment selection operation is performed to select populations of size NP for the next generation, until an iteration threshold is reached. Finally, in the output phase, the solution of the first frontier in the pop population is selected as the set of extracted endmembers.
[0041] This invention defines the hyperspectral endmember extraction problem as a multi-objective optimization problem, simultaneously optimizing the volume inverse and reconstruction error of the selected endmember set. To obtain an endmember set with low redundancy, high purity, and high classification accuracy, this invention employs a combination of global search and local optimization search, using leading-edge individuals to guide the evolution of non-leading-edge individuals to obtain high-quality individuals; simultaneously, a solution generation strategy based on an endmember pool is designed to fully mine high-quality endmembers in leading-edge individuals; finally, a perturbation strategy is used to explore around existing leading-edge individuals to further improve population quality; compared with state-of-the-art hyperspectral endmember extraction algorithms, the obtained endmember set exhibits better performance for different standard hyperspectral datasets.
[0042] Some of the data in the above formula are calculated by removing dimensions and taking their numerical values. The formula is the closest to the real situation obtained by software simulation of a large amount of collected data. The preset parameters and preset thresholds in the formula are set by those skilled in the art according to the actual situation or obtained through simulation of a large amount of data.
[0043] How this application works: The process involves acquiring raw hyperspectral images and constructing an initial population; establishing a multi-objective function for the initial population's evolution and generating a Pareto front; extracting endmembers based on the Pareto front to obtain an endmember set; utilizing endmember information from Pareto front individuals, generating high-quality offspring individuals in each generation through learning, aggregation, and perturbation operations; in the global search phase, a dual-objective learning strategy guides non-Pareto front individuals to evolve towards reliable regions containing high-quality endmembers; simultaneously, a solution generation strategy based on the endmember pool integrates endmembers from Pareto front individuals to construct an endmember pool, using a simple formation growth algorithm to generate super individuals, and perturbing these super individuals to generate diverse offspring individuals with similar characteristics; in the local optimization phase, a perturbation strategy is used to improve the quality of Pareto front individuals obtained in the global search phase, thereby enhancing the accuracy of endmember extraction.
[0044] The above embodiments are only used to illustrate the technical methods of this application and are not intended to limit it. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of this application without departing from the spirit and scope of the technical methods of this application.
Claims
1. A method for extracting hyperspectral endmembers based on frontier exploration, characterized in that, include: Acquire the original hyperspectral image and construct the initial population; Establish a multi-objective function for the initial population evolution and generate the Pareto front. Endmember extraction is performed based on the Pareto front to obtain the endmember set.
2. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 1, characterized in that, One method for constructing the initial population includes: The original pixel space of the original hyperspectral image is obtained. A set number of distinct pixels are randomly selected from the original pixel space to form an individual. An initial population is constructed based on several individuals, and the initial population is encoded. The individual is an endmember set.
3. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 1, characterized in that, The process of establishing a multi-objective function for the initial population evolution and generating a Pareto front includes: Construct the volume inverse objective function and the reconstruction error objective function for the initial population; construct a multi-objective optimization function based on the volume inverse objective function and the reconstruction error objective function, calculate the Pareto solution set of the multi-objective optimization function, and obtain the Pareto front.
4. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 1, characterized in that, The terminology-based endmember extraction, performed on the Pareto front, yields an endmember set, including: During the global search phase, individuals on the non-Pareto frontier are updated based on a dual-objective learning strategy, and the next generation of the population is generated. Obtain the number of iterations and determine whether the number of iterations is G times the set interval number of algebras, where G = 1, 2, ...; If yes, then the individuals on the Pareto front are integrated based on the solution generation strategy of the endmember pool to generate the next generation of the population; then proceed to the next iteration. No, proceed to the next iteration; In the local optimization stage, the individuals obtained in the global search stage are optimized based on perturbation measurements to obtain the final endmember set.
5. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 4, characterized in that, The method of updating individuals on the non-Pareto front and generating the next generation population based on the dual-objective learning strategy includes the following steps: Two individuals on the Pareto front are randomly selected as learning targets, and one individual on a non-Pareto front is randomly selected as the learner. Two individuals are randomly selected on the Pareto front as learning targets, denoted as Pa and Pb respectively; an individual is selected on the non-frontier as the learner, denoted as Q. Obtain the decision vector, and according to the encoding order in the decision vector, obtain the positions of a pair of corresponding endmembers contained in the learning target Pa and the learning target Pb; based on the positions, define the learnable region corresponding to the learner Q in the two-dimensional image domain, the learnable region includes the expanded region Ra obtained by expanding based on the corresponding endmember positions in the learning target Pa and the expanded region Rb obtained by expanding based on the corresponding endmember positions in the learning target Pb. The same learning process is performed on each individual on the non-frontier surface. After all individuals have been updated, the offspring population is obtained. Environmental selection is performed based on the population and the offspring population to obtain the next generation population, which consists of the best individuals selected from the population and the offspring population.
6. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 5, characterized in that, The learning process includes at least: When the corresponding extended regions Ra and Rb in the learnable region overlap, the endmember position of learner Q after learning will be adjusted to the overlapping region. When the expansion regions Ra and Rb in the learnable region do not overlap, and the endmember position of learner Q is not located in expansion regions Ra and Rb, the endmember position of learner Q after learning will be randomly adjusted to expansion region Ra or expansion region Rb. When the expansion regions Ra and Rb in the learnable region do not overlap, and the endmember position of learner Q is located in either expansion region Ra or expansion region Rb, the endmember position of learner Q will remain unchanged after learning.
7. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 4, characterized in that, The solution generation strategy based on endmember pooling integrates individuals on the Pareto front to generate the next generation population, including the following steps: Collect all endmembers from the preface individuals, remove duplicate endmembers, and construct an endmember pool, denoted as . n represents the number of endwords in the endword pool. Apply the simple length-forming algorithm to the endmembers in the endmember pool to obtain the endmembers with the largest corresponding volume; The extraction process terminates when the number of endmembers extracted, i, reaches the required number of endmembers, M. The endmembers extracted from the endmember pool at this point are represented as follows: The endmembers in the endmember pool are converted into individuals and denoted as super individuals. Local perturbations are applied to the super individuals to generate offspring populations. Pareto front individuals are selected from the offspring populations as the output of the solution generation scheme for the endmember pool. Environmental selection is performed on the output results and the population to obtain the next generation population; the next generation population consists of the output results and the best individuals selected from the population.
8. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 7, characterized in that, In the simplex growth algorithm described above simplex The volume is: ； in, The term is an endmember extracted from the endmember pool. p represents a candidate endmember in the endmember pool. The superscripts of p and q indicate the spectral dimensions after principal component analysis of the original endmember spectra.
9. The method for extracting hyperspectral endmembers based on frontier exploration according to claim 4, characterized in that, The final endmember set is obtained by optimizing the individuals obtained in the global search phase based on perturbation measurement, including: Obtain the individuals on the frontier surface corresponding to each generation of the population; Extract the position of the i-th endmember of an individual. In the rectangular region of the hyperspectral image Randomly select one pixel as the updated endmember, where... To set the area range parameters; After each endmember is updated, a new individual corresponding to the individual is generated, and the new individuals corresponding to each individual are added to the population. Environmental selection is performed to obtain a new population. When the number of iterations is less than the set iteration threshold, the iteration continues until the number of iterations reaches the set iteration threshold. The solution of the Pareto front in the new population is selected as the final endmember set.