Simulation data generation and evaluation method and system for hyperspectral unmixing algorithm performance

Abstract

The invention relates to the technical field of digital image processing, and discloses an analog data generation and evaluation method and system for hyperspectral unmixing algorithm performance, and the method comprises the steps: generating an initial random grid based on a random seed; processing the initial random grid to generate a virtual ground feature distribution scene graph; processing the virtual ground feature distribution scene graph to obtain an initial abundance graph; performing superposition and normalization processing on a plurality of initial abundance maps generated based on the same random seed and different filtering parameters to generate a final abundance map; screening a group of end member spectrums, and monitoring the spectrum similarity between the end members; performing spectrum variation modeling on the screened end member spectrums to generate an end member spectrum set; according to the final abundance graph and the end member spectrum set, generating preliminary simulation spectrum data; adding noise into the preliminary simulation spectrum data to generate a final hyperspectral simulation data set, and evaluating the performance of the hyperspectral unmixing algorithm by using the data set, so that the objectivity and comprehensiveness of evaluation can be improved.

Description

Technical Field

[0001] This application relates to the field of digital image processing technology, and in particular to a method for generating hyperspectral analog data, and a method and system for evaluating the performance of hyperspectral unmixing algorithms based on such analog data. Background Technology

[0002] With the continuous expansion of hyperspectral remote sensing applications in agriculture, environmental monitoring, mineral resource exploration, and security, hyperspectral data processing is becoming increasingly important. Among these applications, hyperspectral unmixing, a crucial step in extracting endmember spectra and their corresponding abundance information from mixed pixels, provides more refined information on the distribution of ground features and has become an indispensable part of hyperspectral image processing. Due to the limitations of sensor spatial resolution, each pixel in a real-world hyperspectral image often contains a mixed signal of multiple ground feature spectra. The unmixing task aims to decompose this mixed signal into a linear or nonlinear combination of pure substances (endmembers) and estimate the proportion (abundance) of each endmember in the pixel.

[0003] While existing hyperspectral unmixing algorithms have made significant progress, their performance evaluation systems still have obvious limitations, especially in terms of dataset construction and evaluation criteria. Currently, widely used evaluation datasets mainly fall into three categories: real-world scene datasets, datasets constructed in laboratory environments, and simulation datasets generated based on theoretical models. Real-world scene datasets (such as Urban, Jasper Ridge, Samson, The Washington DC Mall, and Cuprite) can reflect the actual ground cover mixing characteristics and complex imaging conditions, providing important reference value for the promotion of algorithms in practical applications. However, due to sensor resolution limitations and ground cover boundary blurring effects, the "ground truth" attached to these datasets often fails to accurately characterize the actual mixing situation, limiting their reliability as algorithm evaluation benchmarks. To compensate for the shortcomings of real-world data, researchers construct hyperspectral datasets in controlled experimental environments to provide more accurate reference information. For example, Min Zhao et al. constructed a dataset containing 36 mixtures, over 130,000 pixels, and covering the 400–1000 nm wavelength range using printed chessboards, mixed quartz sand, and vertical plates; Chunyang Cui et al. constructed a Real Mixed Miniature Scene (RMMS) dataset, including simple mixed planar materials and complex vegetation scenes with three-dimensional structures; Bikram Koirala et al. prepared 325 samples by uniformly mixing mineral powders and used multiple hyperspectral sensors to acquire spectral data from the visible light to the long-wave infrared band (350–15385 nm), supplemented by X-ray diffraction and fluorescence analysis to verify the sample homogeneity. Although these laboratory datasets provide high annotation accuracy, their scene and material types are still relatively limited, making it difficult to cover the complex phenological changes, lighting conditions, and material variations in real-world applications. The third category is simulation datasets generated based on spectral mixing models. Commonly used models include linear mixture models (LMM), generalized linear mixture models (GLMM), multi-mixed pixel models (MMP), generalized bilinear models (GBM), and polynomial post-nonlinear mixture models (PPNMM). These datasets possess explicit prior information on endmembers and abundance, facilitating algorithm verification and comparison. However, their construction process typically relies on idealized assumptions, making it difficult to effectively simulate nonlinear mixing effects, spectral variations, and spatial structural complexities in real-world scenarios.

[0004] In summary, existing datasets have shortcomings in annotation accuracy, scene coverage, and modeling of mixed complexity, making it difficult to objectively and comprehensively evaluate the performance differences of unmixing algorithms in key dimensions such as spectral variability, endmember similarity, and smoothness of abundance spatial distribution. Furthermore, due to the lack of universally accepted standards for evaluating the quality of simulated data, existing research struggles to establish a quantitative correlation between simulated data attributes and algorithm performance, further leading to systematic biases in algorithm evaluation. Summary of the Invention

[0005] The purpose of this invention is to address at least one deficiency in the existing technology and to provide a method and system for generating and evaluating simulated data of hyperspectral unmixing algorithm performance. This invention can improve the objectivity and comprehensiveness of hyperspectral unmixing algorithm evaluation.

[0006] To achieve the above objectives, in a first aspect, the present invention provides a method for generating hyperspectral simulation data, the method comprising the following steps: An initial random grid for generating a digital image is generated based on a random seed; The initial random grid is subjected to Gaussian filtering and then divided by a threshold to generate a virtual ground feature distribution scene map; The virtual ground feature distribution scene map is convolved and downsampled to simulate the spatial resolution effect of remote sensing imaging, and an initial abundance map is obtained. Multiple initial abundance maps generated based on the same random seed but with different filtering parameters are superimposed and normalized to generate a final abundance map with complex texture features. Select a set of endmember spectra from the spectral library and monitor the spectral similarity between the selected endmembers; The selected endmember spectra are modeled for spectral variation to generate an endmember spectrum set with variation characteristics; The final abundance map and the endmember spectrum set with variation characteristics are input into the unmixing model for calculation to generate preliminary simulated spectral data; Noise is added to the preliminary simulated spectral data to generate the final hyperspectral simulation dataset.

[0007] Furthermore, the predefined size of the digital image is M×N pixels, where M and N are positive integers, and the numerical range of the initial random grid is [0, 1].

[0008] Furthermore, the different filtering parameters are the standard deviations (Sigma) of Gaussian filtering.

[0009] Furthermore, the spectral variation modeling of the selected endmember spectra specifically includes: The selected endmember spectra are subjected to a vertical shift transformation to obtain the first intermediate spectrum. The transformation calculation formula is as follows:

[0010] in, For the selected endmember spectra, For wavelength variables, This is the vertical translation amount. This is the first intermediate spectrum; The first intermediate spectrum is subjected to wavelength shift transformation to obtain the second intermediate spectrum. The transformation calculation formula is as follows:

[0011] in, This is the wavelength offset. This is the second intermediate spectrum; The selective absorption or reflection characteristics of the second intermediate spectrum are locally amplitude modulated to obtain the third intermediate spectrum. The modulation formula is as follows:

[0012] in, The set of extreme points of the spectral curve, specifically represented as , It is a curvature sign function, and at the peak Take +1, at the trough Take -1; For extreme point orientation window function, Parameters that control the scaling magnitude at each extreme point. The third intermediate spectrum, for Wavelength variable at extreme points The number of extreme points. for ; A linearly and nonlinearly coupled global scaling transformation is performed on the third intermediate spectrum to obtain the variant spectrum. The transformation formula is as follows:

[0013] in, Linear scaling factor Non-linear scaling factor It is a variable spectrum; The reflectance values ​​of the variable spectrum are constrained to the physical range [0, 1], as follows:

[0014] In the formula, These represent the minimum and maximum values ​​of the wavelength variable, respectively.

[0015] Furthermore, the step of selecting a set of endmember spectra from the spectral library and monitoring the spectral similarity between the selected endmembers specifically includes: quantifying their similarity by calculating the spectral angular distance between the endmember spectra, and selecting the endmember combinations according to a preset spectral angular distance threshold.

[0016] Secondly, the present invention also provides a performance evaluation method for a hyperspectral unmixing algorithm based on simulated data. This performance evaluation method is based on the hyperspectral simulated data generation method described in the first aspect, and specifically includes: Based on the method for generating hyperspectral simulation data, a hyperspectral simulation dataset with specific data attributes is obtained, wherein the data attributes include at least one of endmember similarity, average spectral angular distance, and average maximum gradient. Multiple hyperspectral unmixing algorithms to be evaluated were applied to the hyperspectral simulation dataset, and the abundance estimates and endmember estimates output by each algorithm were obtained. The abundance estimates and endmember estimates are compared with the true values ​​in the hyperspectral simulation dataset to calculate the accuracy evaluation index of each algorithm. Based on the accuracy evaluation index, the performance differences and shortcomings of each algorithm under different data attribute conditions are analyzed.

[0017] Furthermore, the endmember similarity is used to evaluate the degree of similarity between endmember spectra, the average spectral angular distance is used to evaluate the overall variability of endmember spectra, and the average maximum gradient is used to evaluate the spatial complexity and smoothness of the abundance map. The formula for calculating the average spectral angular distance is as follows:

[0018] In the formula, The average spectral angular distance. The number of endmembers, For the actual value of the endmember, This is an estimate of the endmember. To Perform transposition; the formula for calculating endmember similarity is as follows:

[0019] In the formula, ES represents endmember similarity, and SAD represents spectral angular distance; the formula for calculating the average maximum gradient is as follows:

[0020] In the formula, It is to satisfy The total number of pixels, For a sliding window, the center pixel of the sliding window is The surrounding pixels are , It is the size of the sliding window. yes Maximum absolute gradient at coordinate pixel ,in, , .

[0021] Furthermore, the accuracy evaluation metrics include the root mean square error of abundance estimation and the spectral angular distance of endmember estimation.

[0022] Thirdly, the present invention also provides a performance evaluation system for a hyperspectral unmixing algorithm based on simulated data, the system being based on the performance evaluation method described in the second aspect, comprising: Generation module: configured to generate a hyperspectral simulation dataset with specific data attributes based on the hyperspectral simulation data, wherein the data attributes include at least one of endmember similarity, average spectral angular distance, and average maximum gradient; Acquisition module: configured to apply multiple hyperspectral unmixing algorithms to be evaluated to the hyperspectral simulation dataset, and acquire the abundance estimates and endmember estimates output by each algorithm; The calculation module is configured to compare the abundance estimates and endmember estimates with the true values ​​of the hyperspectral simulation dataset and calculate the accuracy evaluation index of each algorithm. Analysis module: configured to analyze the performance differences and defects of each algorithm under different data attribute conditions based on the accuracy evaluation index.

[0023] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method described in the second aspect.

[0024] Compared with the prior art, the technical advantages of the present invention are as follows: This invention employs data-driven spectral variation modeling, endmember similarity constraint screening, and multi-scale abundance map overlay and fusion techniques to generate highly complex and controllable simulated data. It overcomes the shortcomings of traditional simulated data being overly idealized, the inaccuracy of the "true value" of real data, and the limited scope of laboratory data scenarios. In the evaluation, three core quantitative indicators are proposed: endmember similarity, average spectral angular distance, and average maximum gradient. These indicators can accurately reveal the performance differences and inherent defects of different unmixing algorithms in dealing with specific challenges such as spectral variation, endmember similarity, and spatial complexity. This provides a clear decision-making basis for targeted optimization and selection of algorithms, effectively improving the objectivity and comprehensiveness of the evaluation. Attached Figure Description

[0025] Figure 1This is a flowchart of a method for generating hyperspectral simulation data according to Embodiment 1 of the present invention; Figure 2 This is a virtual land cover distribution scene map with the same random seed but different Sigma values, as shown in Embodiment 1 of the present invention. Figure 2 a is a virtual ground feature distribution scene map with a Sigma value of 15; Figure 2 b is a virtual ground feature distribution scene map with a Sigma value of 30; Figure 2 c represents a virtual ground feature distribution scene with a Sigma value of 45; Figure 2 d represents a virtual ground feature distribution scene with a Sigma value of 60; Figure 3 The initial abundance diagram of four pure substances with a Sigma value of 15 in Example 1 of the present invention; Figure 3 a is the initial abundance diagram of pure substance A with a Sigma value of 15; Figure 3 b is the initial abundance diagram of pure substance B with a Sigma value of 15; Figure 3 c is the initial abundance diagram of pure substance C with a Sigma value of 15; Figure 3 d represents the initial abundance diagram of pure substance D with a Sigma value of 15; Figure 4 The final abundance map is obtained by superimposing and normalizing initial abundance maps with the same random seed but different Sigma values ​​from Embodiment 1 of the present invention, wherein... Figure 4 a is the final abundance diagram of pure substance A after superposition and normalization; Figure 4 b is the final abundance diagram of pure substance B after superposition and normalization. Figure 4 c is the final abundance diagram of pure substance C after superposition and normalization. Figure 4 d is the final abundance diagram of pure substance T after superposition and normalization. Figure 5 This is a pseudo-color map of simulated data with a signal-to-noise ratio (SNR) of 10 added, as shown in Embodiment 1 of the present invention. Figure 5 a is a noise-free analog false-color image; Figure 5 b represents a noisy, simulated data false-color image; Figure 6This is a block diagram of a performance evaluation system for a hyperspectral unmixing algorithm based on simulated data, according to Embodiment 3 of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0027] Example 1 Please see Figure 1 A preferred embodiment of the present invention provides a method for generating hyperspectral simulation data, the method comprising the following steps: S1: An initial random grid for generating a digital image based on a random seed; S2: Perform Gaussian filtering on the initial random grid and divide it by threshold to generate a virtual ground feature distribution scene map; S3: Perform convolution and downsampling processing on the virtual ground feature distribution scene map to simulate the spatial resolution effect of remote sensing imaging and obtain an initial abundance map; S4: The multiple initial abundance maps generated based on the same random seed but with different filtering parameters are superimposed and normalized to generate a final abundance map with complex texture features; S5: Select a set of endmember spectra from the spectral library and monitor the spectral similarity between the selected endmembers; S6: Perform spectral variation modeling on the selected endmember spectra to generate an endmember spectrum set with variation characteristics; S7: Input the final abundance map and the endmember spectrum set with variation characteristics into the unmixing model for calculation to generate preliminary simulated spectral data; S8: Add noise to the preliminary simulated spectral data to generate the final hyperspectral simulation dataset.

[0028] This embodiment employs data-driven spectral variation modeling, endmember similarity constraint screening, and multi-scale abundance map overlay and fusion techniques to generate highly complex and controllable simulated data. This overcomes the shortcomings of traditional simulated data being too idealistic, real data having inaccurate "true values," and laboratory data having limited scenarios.

[0029] In an optional embodiment, in step S1, an initial random grid for a digital image is generated using a random seed, wherein the size of the digital image is M×N pixels, M and N are positive integers, and the numerical range of the initial random grid is [0, 1]. Defining the initial random grid values ​​in the [0,1] range is beneficial for subsequent thresholding and normalization processing.

[0030] In an optional embodiment, in step S2, Gaussian filtering can smooth the initial random grid. By setting an appropriate threshold, the smoothed initial random grid can be mapped to different material regions, thereby generating a virtual ground feature distribution map. The standard deviation Sigma of the Gaussian filter determines the density of the ground feature distribution. The larger the Sigma value, the wider the spatial range of the Gaussian filter and the higher the image smoothness, but details will be lost. Please refer to [link to relevant documentation]. Figure 2 This example illustrates virtual terrain distribution scenarios with the same random seed but Sigma values ​​of 15, 30, 45, and 60. In this embodiment, the threshold selection rule is as follows: the threshold is set based on the number of terrain categories (n) to be simulated, dividing the [0,1] interval into n equal parts, with thresholds of 1 / n, 2 / n, ..., (n-1) / n respectively. For example, assuming there are four pure substances, the thresholds can be set to 0.25, 0.5, and 0.75, thus dividing the random grid into four equal parts, each occupying the same area.

[0031] In an optional embodiment, in step S3, due to the limited spatial resolution of real-world remote sensing sensors, one pixel may cover an entire area of ​​ground features. S3 uses convolution and downsampling to process the virtual ground feature distribution map, obtaining a lower-resolution, more blurred initial abundance map. This simulates the insufficient resolution of remote sensing images. For example, if the initial random grid map is 1000×1000, using a 10×10 convolution kernel can obtain an initial abundance map of size 100×100. Please refer to [link to relevant documentation]. Figure 3 The initial abundance diagram of four pure substances in this embodiment of the invention. The four pure substances are assumed to be A, B, C, and D. A, B, C, and D can be any substance, such as soil and vegetation.

[0032] In an optional embodiment, in step S4, the different filtering parameters are the standard deviation Sigma of the Gaussian filter. It should be noted that in remote sensing images, many substances exhibit spectral or spatial overlap, usually due to the mixing of ground cover distributions, similarity of spectral characteristics, or limitations of sensor resolution. These substances include: soil and vegetation, water and suspended matter, various minerals, etc. To further simulate this phenomenon, this embodiment superimposes abundance maps with the same random seed but different Sigma values ​​(15, 30, 45, 60) and then normalizes them. The resulting abundance maps of four pure substances exhibit obvious texture characteristics and better smoothness, while also solving the defect of Gaussian distribution-synthesized abundance maps having only blocky distributions. For details, please refer to [link to relevant documentation]. Figure 4 .

[0033] In an optional embodiment, in step S5, an endmember screening mechanism is added when constructing the simulated dataset to monitor endmember similarity. This screening mechanism works by calculating the spectral angular distance (SAD) between any two candidate endmember spectra. If the SAD value between any two endmembers is less than a preset threshold T, one of them is randomly removed, and a new candidate endmember is added from the spectral library until the SAD between all endmembers is greater than the threshold T. It should be noted that existing studies generally use the USGS spectral library to randomly select endmembers, but this does not effectively consider the differences in spectral similarity between endmembers. If the selected spectral curves are too similar, the unmixing process will be challenging; while combinations of endmembers with significant spectral differences may reduce the difficulty of unmixing. This endmember selection method creates potential bias due to omitted variables, making the performance comparison of different algorithms less objective. This embodiment adds an endmember screening mechanism when constructing the simulated dataset, monitoring endmember similarity through Spectral Angle Distance (SAD). This method retains the convenience of the traditional experimental framework while eliminating the interference of endmember similarity on the evaluation results, more realistically reflecting algorithm performance.

[0034] In an optional embodiment, step S6 specifically includes: The selected endmember spectra are subjected to a vertical shift transformation to obtain the first intermediate spectrum. The transformation calculation formula is as follows:

[0035] in, For the selected endmember spectra, For wavelength variables, This represents the vertical translation amount, reflecting the overall reflectivity baseline shift. This is the first intermediate spectrum; The first intermediate spectrum is subjected to wavelength shift transformation to obtain the second intermediate spectrum. The transformation calculation formula is as follows:

[0036] in, This refers to the wavelength offset, simulating the wavelength calibration error or physical displacement effect of the spectrometer. This is the second intermediate spectrum; The selective absorption or reflection characteristics of the second intermediate spectrum are locally amplitude modulated to obtain the third intermediate spectrum. The modulation formula is as follows:

[0037] in, The set of extreme points of the spectral curve, specifically represented as , It is a curvature sign function, and at the peak Take +1, at the trough Take -1; For extreme point orientation window function, Parameters that control the scaling magnitude at each extreme point. The third intermediate spectrum, for Wavelength variable at extreme points The number of extreme points. for ; A linearly and nonlinearly coupled global scaling transformation is performed on the third intermediate spectrum to obtain the variant spectrum. The transformation formula is as follows:

[0038] in, Linear scaling factor Non-linear scaling factor It is a variable spectrum; The reflectance values ​​of the variable spectrum are constrained to the physical range [0, 1], as follows:

[0039] In the formula, These are the minimum and maximum values ​​of the wavelength variable, respectively. Remote sensing reflectivity is defined as the ratio of reflected radiation energy to incident radiation energy. Its physical range is strictly limited to [0,1]. Exceeding this range will lead to non-physical interpretation, so physical constraints must be added.

[0040] Furthermore, the step of selecting a set of endmember spectra from the spectral library and monitoring the spectral similarity between the selected endmembers specifically includes: quantifying their similarity by calculating the spectral angular distance between the endmember spectra, and selecting the endmember combinations according to a preset spectral angular distance threshold.

[0041] This embodiment proposes a data-driven spectral variation modeling method. Unlike traditional solutions that rely on prior physical models, this embodiment establishes a universal spectral variation characterization system, overcoming the pre-defined limitations of existing methods on spectral variation morphologies. The core of this method lies in systematically constructing variation patterns of endmember spectra from the data itself, specifically manifested as: vertical and wavelength shifts in spectral curves, local amplitude modulation of spectral absorption / reflection characteristics, and overall scaling of energy across the entire spectral band, where the scaling effect encompasses both linear and nonlinear effects. Finally, a randomization mechanism is introduced to randomly variate the spectrum of each pixel in the synthesis, simulating the widespread and unpredictable nature of spectral variation in real-world scenarios. In terms of parameter configuration, this embodiment differentiates settings based on the physical causes of different variation types. Translation effects mainly originate from wavelength calibration errors and geometric distortions, have a low probability of occurrence, and can be detected through calibration. Meanwhile, to avoid introducing unrealistic variations and ensure unchanged spectral characteristics, the position of the main absorption peak must be kept stable; therefore, it is recommended to control the wavelength shift within 30% of the sensor resolution. In contrast, the scaling effect is influenced by a variety of factors, including changes in illumination, spatial heterogeneity of material physicochemical properties, differences in atmospheric transport paths, and surface roughness, resulting in a wider range of variation and a higher frequency of occurrence. Therefore, it should be given a higher weight in parameter settings.

[0042] In an optional embodiment, in step S7, the unmixing model can be a linear model or a generalized bilinear model.

[0043] In an optional embodiment, in step S8, Gaussian noise is added to the preliminary simulated spectral data to simulate the electronic noise generated when real sensors acquire data. The signal-to-noise ratio (SNR) is a key control parameter that can generate data with different noise levels. For example, this embodiment uses data with an added SNR of 10 as an example; the pseudo-color map of the final simulated data is as follows. Figure 5 As shown.

[0044] This embodiment generates the final hyperspectral simulation dataset through a multi-dimensional parameter control mechanism: (1) Spatial resolution simulation: Data with different spatial resolutions can be generated by adjusting the image size and kernel size; (2) Scene complexity control: Different scene complexities can be simulated by adjusting the parameter sigma and superimposing virtual ground feature distribution scenes; (3) Endmember selection: Endmember combinations are optimized using spectral similarity thresholds; (4) Spectral variation simulation: An endmember spectral variation model is constructed using spectral perturbation parameters. This method supports multiple unmixing models and can generate simulation datasets covering different mixing mechanisms.

[0045] Furthermore, based on the hyperspectral simulation data generation method in steps S1-S8, this embodiment proposes a performance evaluation method for the hyperspectral unmixing algorithm based on simulation data. This method specifically includes: S101: Based on the hyperspectral simulation data generation method described in steps S1-S8, obtain a hyperspectral simulation dataset with specific data attributes, wherein the data attributes include at least one of endmember similarity, average spectral angular distance, and average maximum gradient. In an optional embodiment, in step S101, the endmember similarity is used to evaluate the similarity between endmember spectra, the average spectral angular distance is used to evaluate the overall variability of the endmember spectra, and the average maximum gradient is used to evaluate the spatial complexity and smoothness of the abundance map. The formula for calculating the average spectral angular distance is as follows:

[0046] In the formula, The average spectral angular distance. The number of endmembers, For the actual value of the endmember, This is an estimate of the endmember. To Perform transposition; the formula for calculating endmember similarity is as follows:

[0047] In the formula, ES represents endmember similarity, and SAD represents spectral angular distance; the formula for calculating the average maximum gradient is as follows:

[0048] In the formula, It is to satisfy The total number of pixels, For a sliding window, the center pixel of the sliding window is The surrounding pixels are , It is the size of the sliding window. yes Maximum absolute gradient at coordinate pixel ,in, , .

[0049] It should be noted that the Mean Maximum Gradient (MMG) metric is a statistical method for measuring the local gradient changes in an abundance map. This metric calculates the gradient change between the center value and surrounding values ​​pixel by pixel using a sliding window, extracts the maximum absolute gradient value within the local region, and then averages the maximum gradient values ​​of all pixels. A smaller MMG indicates better image smoothness. Furthermore, this metric reflects the local smoothness of the abundance map and is particularly suitable for analyzing the significance and distribution patterns of boundary features in the abundance map. Additionally, it only considers the edge smoothness of the abundance map, so pixels with a maximum gradient value of 0 are not included in the mean calculation, thus improving the robustness of the metric and the physical meaning of the results.

[0050] S102: Apply the various hyperspectral unmixing algorithms to be evaluated to the hyperspectral simulation dataset, and obtain the abundance estimates and endmember estimates output by each algorithm; S103: Compare the abundance estimates and endmember estimates with the true values ​​of the hyperspectral simulation dataset, and calculate the accuracy evaluation index of each algorithm; S104: Based on the accuracy evaluation index, analyze the performance differences and defects of each algorithm under different data attribute conditions.

[0051] This invention employs data-driven spectral variation modeling, endmember similarity constraint screening, and multi-scale abundance map overlay and fusion techniques to generate highly complex and controllable simulated data. It overcomes the shortcomings of traditional simulated data being overly idealized, the inaccuracy of the "true value" of real data, and the limited scope of laboratory data scenarios. In the evaluation, three core quantitative indicators are proposed: endmember similarity, average spectral angular distance, and average maximum gradient. These indicators can accurately reveal the performance differences and inherent defects of different unmixing algorithms in dealing with specific challenges such as spectral variation, endmember similarity, and spatial complexity. This provides a clear decision-making basis for targeted optimization and selection of algorithms, effectively improving the objectivity and comprehensiveness of the evaluation.

[0052] Example 2 To fully disclose and describe the technical solution of the present invention and demonstrate its beneficial effects, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment demonstrates how to apply the hyperspectral simulation data generation method and the data attribute-based algorithm evaluation method proposed in this invention to conduct a systematic and quantifiable performance evaluation of various types of hyperspectral unmixing algorithms. This embodiment aims to verify whether the method proposed in this invention can effectively solve the problems described in the background art, namely: by generating a simulation dataset with quantifiable indicators (ES, MSAD, MMG, SNR), establishing the correlation between data attributes and algorithm performance, thereby conducting a comprehensive and objective performance evaluation of unmixing algorithms based on different principles, and accurately revealing their performance differences and defects in different scenarios.

[0053] To achieve the above objectives, this experiment strictly follows the method and procedure proposed in this invention: I. Generating a Hyperspectral Simulation Dataset: Using the method described in Example 1, a set of standard simulation datasets (“standard set”) is first generated. Its key characteristic parameters are shown in Table 1, including endmember similarity (ES=50.06%), average spectral angular distance (MSAD=0.0501), average maximum gradient (MMG=0.2817), and signal-to-noise ratio (SNR=30 dB). II. Constructing Control Groups: To examine the algorithm's performance under different data attributes, other parameters were fixed, and only one specific attribute was systematically adjusted, generating five control group datasets: (1). Control group (signal-to-noise ratio of 20) and control group (signal-to-noise ratio of 10): used to test the algorithm's noise resistance.

[0054] (2). Control group (average spectral angular distance is) ): Used to test the algorithm's resistance to spectral variations.

[0055] (3). Control group (mean maximum gradient is) ): Used to test the sensitivity of an algorithm to the space complexity of abundance graphs.

[0056] (4). Control group (endmember similarity of 76.52%): used to test the algorithm’s ability to distinguish high-similar endmembers.

[0057] Other key characteristic parameters of the five control group datasets are shown in Table 1. Table 1: Key Characteristic Parameters of Standard and Control Groups

[0058] III. Selection of Evaluation Algorithms: For comprehensive evaluation, 10 representative unmixing algorithms covering five major categories were selected, as shown in Table 2, including geometric models (VCA, N-FINDR), sparse regression (SUnSAL-TV, Sparse HU), nonnegative matrix factorization (TV-RSNMF, RCONMF), tensor factorization (MVNTF, SeCoDe), and neural networks (DGMSSU, HapkeCNN).

[0059] Table 2: 10 Unmixing Algorithms

[0060] IV. Evaluation Metrics and Procedures: All algorithms underwent five repeated trials on each set of data to eliminate random errors, and the average value was used as the final result. Algorithm parameters were set to their default or general settings to ensure fairness and objectivity in the evaluation, accurately reflecting the algorithm's performance under identical conditions. Root mean square error (RMSE) and spectral angular distance (SAD) were used to quantify the accuracy of abundance estimation and endmember extraction, respectively. The RMSE was calculated as follows:

[0061] In the formula, express The number of elements in It is a true abundance matrix. It is an estimated abundance matrix.

[0062] V. Experimental Results and Analysis: After evaluation using the method in Example 1, the quantitative results are shown in Tables 3 and 4.

[0063] Table 3: Experimental results of spectral angular distance

[0064] Table 4: Experimental results of root mean square error

[0065] Based on these results, this embodiment can perform the following objective and in-depth analysis, accurately identifying the performance bottlenecks of various algorithms: 5.1 Performance analysis of algorithms for noise intensity and spectral variability (SNR & MSAD): This embodiment accurately reveals the essential differences in the anti-interference capabilities of various algorithms by controlling the SNR and MSAD parameters.

[0066] (1). Geometric model algorithms: Data shows that the VCA algorithm exhibits the strongest robustness with a SAD increase of only 0.1184 when SNR=10dB, thanks to its integrated PCA / SVD denoising module. In contrast, the N-FINDR algorithm shows a sharp increase in SAD to 0.3668 under the same conditions, proving that it lacks a built-in denoising mechanism and is most sensitive to noise and spectral variations.

[0067] (2). Sparse regression algorithms: The SUnSAL-TV algorithm maintains a stable RMSE in noisy environments (~0.048 for SNR=20 / 10dB), verifying the effectiveness of the TV regularizer. However, it relies on an external endmember library and has poor adaptability when facing hyperspectral variations, with SAD deteriorating to 0.4099. In contrast, the Sparse HU algorithm extracts endmembers directly from the data and is less affected by spectral variations (SAD changes from 0.3027 to 0.4099, a smaller increase than SUnSAL-TV).

[0068] (3) Nonlinear decomposition / tensor decomposition algorithms: Although they benefit from various regularization terms, due to their pixel-by-pixel unmixing characteristics, the error accumulation effect of pixel-level spectral variation is significant. When MSAD=0.0983, the RMSE of the TV-RSNMF algorithm increases from 0.2419 to 0.3272, and RCONMF increases from 0.1669 to 0.2023. The error increase even exceeds the impact of SNR=10dB noise.

[0069] (4). Neural network model: HapkeCNN algorithm shows excellent comprehensive anti-interference ability and has the smallest performance degradation under high noise and high spectral variation conditions (RMSE=0.2196 when SNR=10dB, SAD=0.2734 when MSAD=0.0983), and its performance is significantly better than DGMSSU.

[0070] 5.2 Performance analysis of the algorithm for smoothness of abundance map and space complexity (MMG): This embodiment quantifies space complexity by using the MMG index and finds that its impact on algorithm performance is closely related to the algorithm principle.

[0071] (1). The performance of geometric algorithms (VCA, N-FINDR) depends on the number of pure pixels. Although the reduction of MMG (from 0.2817 to 0.1864) leads to a decrease in the number of pure pixels (from 2141 to 959), its absolute number is still much greater than the number of endmembers (4), so its impact on performance is limited.

[0072] (2). SUnSAL-TV is not sensitive to changes in MMG, but its performance is limited by the quality of endmember extraction. The accuracy of Sparse HU decreases significantly with decreasing MMG (RMSE increases from 0.0661 to 0.0939), because the reduction in pure pixels leads to a decrease in the quality of the endmember bundle extracted by the VCA algorithm it relies on.

[0073] (3). The tensor decomposition algorithm SeCoDe benefits from the improved smoothness of the abundance map, and its RMSE drops from 0.1278 to 0.1132, proving that its convolutional tensor model can better fit the smooth spatial structure.

[0074] It should be noted that the accuracy of TV-RSNMF actually decreased when the abundance map was smoother (RMSE increased from 0.2419 to 0.2876). Analysis in this embodiment revealed that this was because the background noise (SNR=30) introduced during abundance map generation disrupted the sparsity and low-rank properties of the data, causing its weighted sparsity regularization term to fail. This finding highlights the ability of the method in this invention to diagnose algorithmic defects under complex coupling factors.

[0075] (4). The accuracy of HapkeCNN increases with smoothness (RMSE decreases from 0.1415 to 0.2044), while DGMSSU's performance decreases significantly due to its sensitivity to noise.

[0076] 5.3 Performance analysis of the endmember similarity (ES) algorithm: This invention effectively tested the algorithm's ability to distinguish similar features by constructing a dataset with high ES values ​​(76.52%).

[0077] (1) The performance of geometric model-based algorithms (VCA, N-FINDR) is significantly affected (the SAD of VCA increases from 0.0981 to 0.1136). Because it relies on the principle of geometric feature difference such as "maximum volume" or "projection iteration", these geometric feature differences become blurred when the endmembers are highly similar, resulting in the failure of endmember extraction.

[0078] (2). Sparse regression algorithms heavily rely on prior endmember libraries. Increased endmember similarity leads to a "cliff-like drop" in the performance of SUnSAL-TV, with its RMSE deteriorating sharply from 0.0480 to 0.5198.

[0079] (3) The overall accuracy of nonnegative matrix factorization and tensor factorization algorithms decreased, with SeCoDe's SAD increasing from 0.1598 to 0.2637. The main reason is that high-similarity endmembers lead to feature space redundancy, increasing the difficulty of decomposition. TV-RSNMF, on the other hand, improved its endmember extraction accuracy (SAD) (from 0.1819 to 0.1049), which proves that its strong sparsity constraint and dynamic weight mechanism have unique advantages in dealing with feature redundancy.

[0080] (4). The neural network models (HapkeCNN, DGMSSU) exhibited the best and most stable performance when dealing with high-similarity endmembers (SAD=0.1166, RMSE=0.1701 for HapkeCNN; SAD=0.0758, RMSE=0.1750 for DGMSSU). This is due to their ability to decouple and represent deep features through physical models (Hapke) or nonlinear mappings (autoencoders), as verified in this embodiment.

[0081] This embodiment fully demonstrates the entire process of evaluating the hyperspectral unmixing algorithm using Example 1. Through the simulated dataset generated by this invention, which contains precise quantitative indicators, this embodiment successfully established a scientific correlation between the algorithm's performance (RMSE, SAD) and the data's intrinsic attributes (ES, MSAD, MMG, SNR). The final analysis results show that the evaluation method provided by this invention can not only fairly and objectively compare the overall performance of different algorithms, but also deeply diagnose the specific advantages and disadvantages of each algorithm in different challenging scenarios (such as high noise, high spectral variability, high ground feature mixing complexity, and high-level meta-similarity). This provides a clear and reliable decision-making basis for algorithm selection, improvement, and application scenario planning, ultimately achieving the invention's objective.

[0082] Example 3 Please see Figure 6 This invention also provides a performance evaluation system for a hyperspectral unmixing algorithm based on simulated data, the system comprising: Generation module: configured to generate a hyperspectral simulation dataset with specific data attributes based on the hyperspectral simulation data, wherein the data attributes include at least one of endmember similarity, average spectral angular distance, and average maximum gradient; Acquisition module: configured to apply multiple hyperspectral unmixing algorithms to be evaluated to the hyperspectral simulation dataset, and acquire the abundance estimates and endmember estimates output by each algorithm; The calculation module is configured to compare the abundance estimates and endmember estimates with the true values ​​of the hyperspectral simulation dataset and calculate the accuracy evaluation index of each algorithm. Analysis module: configured to analyze the performance differences and defects of each algorithm under different data attribute conditions based on the accuracy evaluation index.

[0083] The system proposed in this embodiment is based on the method proposed in Embodiment 1. Therefore, the options proposed in Embodiment 1 are also applicable to this embodiment. To avoid repetition, they will not be described again here.

[0084] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0085] Obviously, the 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. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for generating hyperspectral simulation data, characterized in that, The method comprises the following steps: generating an initial random grid of a digital image based on a random seed; performing Gaussian filtering on the initial random grid and generating a virtual ground object distribution scene graph through threshold division; performing convolution and down-sampling processing on the virtual ground object distribution scene graph to simulate the spatial resolution effect of remote sensing imaging, thereby obtaining an initial abundance map; superimposing and normalizing a plurality of initial abundance maps generated based on the same random seed and different filtering parameters to generate a final abundance map with complex texture characteristics; selecting a group of endmember spectra from a spectral library and monitoring the spectral similarity between the selected endmembers; modeling the spectral variability of the selected endmember spectra to generate an endmember spectrum set with variability characteristics; inputting the final abundance map and the endmember spectrum set with variability characteristics into an unmixing model for calculation to generate preliminary simulated spectral data; adding noise to the preliminary simulated spectral data to generate a final hyperspectral simulated data set.

2. The method of claim 1, wherein, The predefined size of the digital image is MxN pixels, where M and N are positive integers, and the numerical interval of the initial random grid is [0, 1].

3. The method of claim 1, wherein, The different filtering parameters are the standard deviation Sigma of Gaussian filtering.

4. The method of claim 1-3, wherein, The spectral variability modeling of the selected endmember spectra specifically comprises: performing a vertical offset transformation on the selected endmember spectra to obtain a first intermediate spectrum, and the transformation calculation formula is as follows: wherein, is the selected endmember spectrum, is the wavelength variable, is the vertical shift, is the first intermediate spectrum; performing a wavelength offset transformation on the first intermediate spectrum to obtain a second intermediate spectrum, and the transformation calculation formula is as follows: wherein is a wavelength shift, is a second intermediate spectrum; performing local amplitude modulation on the selective absorption or reflection characteristics of the second intermediate spectrum to obtain a third intermediate spectrum, and the modulation formula is as follows: wherein, is a set of spectral curve extreme points, specifically represented as , is a curvature sign function, and at a wave peak , takes +1, and at a wave trough , takes -1; is an extreme point directional window function, is a parameter controlling the scaling amplitude of each extreme point, is a third intermediate spectrum, is a wavelength variable at an extreme point, is a number of extreme points, is ; performing overall scaling transformation of linear and nonlinear coupling on the third intermediate spectrum to obtain a variability spectrum, and the transformation formula is as follows: wherein a linear scaling factor, a non-linear scaling factor, is the variant spectrum; constraining the reflectivity value of the variability spectrum to the physical range [0, 1], and the representation is as follows: wherein respectively the minimum and maximum values of the wavelength variable.

5. The method of claim 1, wherein, The method specifically comprises: quantifying the similarity between endmember spectra by calculating the spectral angle distance between them, and selecting the endmember combination according to a preset spectral angle distance threshold.

6. A performance evaluation method of a hyperspectral unmixing algorithm based on simulated data, characterized in that, The performance evaluation method is based on the generation method of the hyperspectral simulation data according to any one of claims 1-5, and specifically comprises: based on the generation method of the hyperspectral simulation data, obtaining a hyperspectral simulation data set with specific data attributes, the data attributes at least including one of endmember similarity, average spectral angle distance, and average maximum gradient; applying a plurality of hyperspectral unmixing algorithms to be evaluated to the hyperspectral simulation data set, and obtaining abundance estimation values and endmember estimation values output by each algorithm; comparing the abundance estimation values and endmember estimation values with the true values of the hyperspectral simulation data set, and calculating the accuracy evaluation indexes of each algorithm; based on the accuracy evaluation indexes, analyzing the performance differences and defects of each algorithm under different data attributes.

7. The method of claim 6, wherein the method further comprises: The endmember similarity is used to evaluate the similarity between endmember spectra, the average spectral angle distance is used to evaluate the overall variation of endmember spectra, and the average maximum gradient is used to evaluate the spatial complexity and smoothness of the abundance map, wherein the calculation formula of the average spectral angle distance is as follows: wherein is the average spectral angle distance, is the number of endmembers, is the true value of the endmember, is the estimated value of the endmember, is the transpose of the matrix The formula for the endmember similarity is as follows: In the formula, ES is the endmember similarity, and SAD is the spectral angle distance; the calculation formula of the average maximum gradient is as follows: In the formula, is the total number of pixel points satisfying is a sliding window, the center pixel of the sliding window is , and the surrounding pixels are , is the size of the sliding window, is the maximum gradient absolute value at the coordinate pixel point , wherein,​ ， 。 8. The method of claim 6, wherein the method further comprises: The precision evaluation index includes the root mean square error of abundance estimation and the spectral angle distance of endmember estimation. 9.A performance evaluation system of a hyperspectral unmixing algorithm based on simulated data, characterized in that, The system is based on the performance evaluation method of any one of claims 6-8, comprising: A generation module configured to obtain a hyperspectral simulation data set with specific data attributes based on the generation method of the hyperspectral simulation data, wherein the data attributes at least include one of endmember similarity, average spectral angle distance and average maximum gradient; An acquisition module configured to apply a plurality of hyperspectral unmixing algorithms to be evaluated to the hyperspectral simulation data set, and acquire the abundance estimation value and the endmember estimation value output by each algorithm; A calculation module configured to compare the abundance estimation value and the endmember estimation value with the true value of the hyperspectral simulation data set, and calculate the precision evaluation index of each algorithm; An analysis module configured to analyze the performance difference and defects of each algorithm under different data attribute conditions based on the precision evaluation index.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method of any one of claims 6 to 8.

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