Hyperspectral mineral unmixing method and system based on complementary evidence and adaptive uncertainty modeling, and storage medium

Abstract

The application discloses a hyperspectral mineral unmixing method and system based on complementary evidence and adaptive uncertainty modeling and a storage medium, and particularly relates to the technical field of mineral unmixing; the method comprises the following steps: acquiring a hyperspectral image to be processed and a corresponding mineral spectral library; respectively calculating a first similarity matrix based on a spectral angle, a second similarity matrix based on matching of mineral endmember spectrum and pixel spectrum absorption valley characteristics, and a third similarity matrix based on reconstruction of a spectral background autoencoder; respectively converting the similarity matrices into basic probability assignment vectors through a basic probability assignment function; fusing the basic probability assignment matrices by using a step-by-step weighted Dempster combination rule; and performing uncertainty reassignment and abundance and normalization processing to generate a mineral abundance map, so that the accuracy and robustness of hyperspectral remote sensing mineral identification and mineral abundance inversion are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of mineral unmixing technology, and more specifically, to a hyperspectral mineral unmixing method, system, and storage medium based on complementary evidence and adaptive uncertainty modeling. Background Technology

[0002] Hyperspectral remote sensing imagery provides rich data support for geological and mineral identification by offering continuous, narrow-band spectral information of ground features. However, due to spatial resolution limitations in remote sensing imaging, in practical applications, a single pixel often contains multiple mineral endmembers, resulting in mixed spectral features. Furthermore, the spectral differences between different minerals are often subtle, especially when there is strong background interference, leading to overlapping spectral features that are difficult to distinguish effectively.

[0003] Existing hyperspectral mineral unmixing methods are mostly based on single feature information analysis and lack effective mechanisms for fusing and utilizing multiple feature information, making it difficult to accurately identify and quantify mineral abundance under complex background conditions. This results in limited mineral identification accuracy and poor stability of unmixing results.

[0004] To address the aforementioned problems, a technical solution is provided. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a hyperspectral mineral unmixing method, system, and storage medium based on complementary evidence and adaptive uncertainty modeling to address the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling includes the following steps: S1: Acquire the hyperspectral image to be processed and the corresponding mineral spectral library; S2: Based on the hyperspectral image and the corresponding mineral spectral library, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix; S3: Based on hyperspectral images and the corresponding mineral spectral library, the absorption valleys are detected by combining the endmember spectrum of each mineral and the spectrum of each image pixel. The feature matching similarity between the pixel and the mineral is calculated to obtain the second similarity matrix. S4: Based on hyperspectral images and the corresponding mineral spectral library, the background spectrum is reconstructed by a spectral background autoencoder to obtain the third similarity matrix; S5: Convert the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability allocation matrices using the basic probability allocation function; S6: The basic probability assignment matrix is ​​fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix; S7: Perform uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map.

[0007] In a preferred embodiment, S1 specifically refers to: Hyperspectral remote sensing data is acquired for the target area to generate hyperspectral images to be processed; Mineral spectral data corresponding to the characteristics of the target region are selected from a pre-set mineral spectral database to form a corresponding mineral spectral library.

[0008] In a preferred embodiment, S2 specifically refers to: Based on hyperspectral images and corresponding mineral spectral libraries, the spectral angle between each pixel of the hyperspectral image and each mineral endmember is calculated. The spectral angles of each pixel in the hyperspectral image and each mineral endmember are converted into similarity values ​​to obtain the first similarity matrix.

[0009] In a preferred embodiment, S3 specifically refers to: Based on hyperspectral images and the corresponding mineral spectral library, continuum removal is performed on the spectrum of each mineral endmember and the spectrum of each image pixel; All absorption valleys were detected in the spectrum after continuum removal, and the characteristic parameters of each absorption valley were calculated. The similarity of absorption position matching is calculated using global minimum error matching. The similarity of absorption depth matching is calculated using sequential alignment; Adaptively calculate the absorption shape matching similarity based on the availability of feature width and symmetry; The second similarity matrix is ​​obtained by calculating the comprehensive similarity based on the similarity of absorption position matching, absorption depth matching, and absorption shape matching.

[0010] In a preferred embodiment, S4 specifically refers to: Based on hyperspectral images and corresponding mineral spectral libraries, continuum removal is performed on the pure mineral spectra to locate absorption valleys. The spectral values ​​within the absorption valleys are then replaced with the corresponding continuum values ​​to obtain the background spectrum. For each mineral, noise is added to the corresponding background spectrum to generate a training set, and a shallow autoencoder is trained. For each pixel, the corresponding background spectrum is extracted, and the background of each pixel is reconstructed using an autoencoder for all mineral backgrounds. Calculate the weighted reconstruction error, and use the hyperbolic decay function to convert the weighted reconstruction error into background similarity to obtain the third similarity matrix.

[0011] In a preferred embodiment, S5 specifically refers to: Each row of the first similarity matrix, the second similarity matrix, and the third similarity matrix is ​​input into the basic probability allocation function, and normalized by the Softmax function controlled by the temperature parameter to obtain the probability distribution vector. Calculate the normalized entropy of the probability distribution vector; The uncertainty mass is dynamically calculated using the exponential decay function based on the normalized entropy. The uncertainty quality is assigned to the identification framework to form a basic probability assignment matrix.

[0012] In a preferred embodiment, S6 specifically refers to: Weights are assigned to the basic probability assignment matrices for spectral angle evidence, absorption feature evidence, and spectral background evidence, respectively. The basic probability allocation matrix of spectral angle evidence and the basic probability allocation matrix of absorption feature evidence are weighted and fused. The same row vector of the basic probability allocation matrix of spectral angle evidence and the basic probability allocation matrix of absorption feature evidence are extracted, and the first conflict coefficient between the vectors is calculated. If the first conflict coefficient exceeds the corresponding preset threshold, a weighted average is used for fusion; otherwise, the standard Dempster rule is used for fusion to obtain an intermediate fusion result. The intermediate fusion result is weighted and fused with the basic probability assignment matrix of spectral background evidence. The same row vector of the intermediate fusion result and the basic probability assignment matrix of spectral background evidence are extracted, and the second conflict coefficient between the vectors is calculated. If the second conflict coefficient exceeds the corresponding preset threshold, a weighted average is used for fusion; otherwise, the standard Dempster rule is used for fusion to obtain the fusion basic probability allocation vector and generate the fusion basic probability allocation matrix.

[0013] In a preferred embodiment, S7 specifically refers to: The confidence vector and uncertainty mass of each mineral are separated from the fused basic probability assignment matrix; For each cell, if the uncertainty mass is greater than zero and the sum of the confidence vectors of each mineral is greater than zero, then the ratio of each mineral confidence vector to the uncertainty mass is redistributed, and the mineral confidence is updated. The updated mineral confidence matrix was reshaped into a spatial three-dimensional abundance map; The abundance vector of each spatial cell in the spatial three-dimensional abundance map is normalized.

[0014] On the other hand, the present invention provides a hyperspectral mineral unmixing system based on complementary evidence and adaptive uncertainty modeling, comprising: Image acquisition module: Acquires the hyperspectral image to be processed and the corresponding mineral spectral library; Angle similarity module: Based on hyperspectral images and corresponding mineral spectral libraries, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix; Feature matching module: Based on hyperspectral images and corresponding mineral spectral libraries, it combines the absorption valley detection of each mineral endmember spectrum and each image pixel spectrum to calculate the feature matching similarity between pixels and minerals, and obtains the second similarity matrix; Background reconstruction module: Based on hyperspectral images and corresponding mineral spectral libraries, background spectral reconstruction is performed through a spectral background autoencoder to obtain a third similarity matrix; Probability Transformation Module: Converts the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability assignment matrices using the basic probability assignment function. Evidence fusion module: The basic probability assignment matrix is ​​fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix; Abundance Normalization Module: Performs uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map.

[0015] On the other hand, the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling.

[0016] The technical effects and advantages of the hyperspectral mineral unmixing method, system, and storage medium based on complementary evidence and adaptive uncertainty modeling provided by this invention are as follows: By acquiring the hyperspectral image to be processed and the corresponding mineral spectral library, the correspondence between mineral endmember information and image spectral information is ensured within the same analytical framework. A first similarity matrix is ​​obtained through spectral angle similarity, utilizing the overall shape difference of the spectrum to form a stable initial distinguishing criterion. A second similarity matrix is ​​obtained through absorption valley detection and feature matching, introducing the characterization of diagnostic absorption features of minerals to enhance the separability of similar minerals. A third similarity matrix is ​​obtained through background spectrum reconstruction using a spectral background autoencoder, introducing a description of spectral background trends to reduce the interference of background differences and noise on diagnostic information. The three similarity matrices are converted into corresponding basic probability allocation matrices using basic probability allocation functions, achieving a quantitative expression of evidence credibility and uncertainty. Then, a step-by-step weighted Dempster combination rule is used for fusion, reducing the impact of single evidence bias on the unmixing results and improving fusion stability. Finally, uncertainty redistribution and abundance normalization are performed on the fused basic probability allocation matrix to output a mineral abundance map that satisfies abundance constraints, thereby improving the consistency and interpretability of the mineral abundance inversion results. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling of the present invention; Figure 2 This is a schematic diagram of the structure of the hyperspectral mineral unmixing system based on complementary evidence and adaptive uncertainty modeling of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1 Figure 1 The present invention provides a hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling, which includes the following steps: S1: Acquire the hyperspectral image to be processed and the corresponding mineral spectral library; S2: Based on the hyperspectral image and the corresponding mineral spectral library, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix; S3: Based on hyperspectral images and the corresponding mineral spectral library, the absorption valleys are detected by combining the endmember spectrum of each mineral and the spectrum of each image pixel. The feature matching similarity between the pixel and the mineral is calculated to obtain the second similarity matrix. S4: Based on hyperspectral images and the corresponding mineral spectral library, the background spectrum is reconstructed by a spectral background autoencoder to obtain the third similarity matrix; S5: Convert the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability allocation matrices using the basic probability allocation function; S6: The basic probability assignment matrix is ​​fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix; S7: Perform uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map.

[0020] S1: Obtain the hyperspectral image to be processed and the corresponding mineral spectral library, including: Hyperspectral remote sensing data is acquired for the target area to generate hyperspectral images to be processed; First, determine the spatial geographic range of the target area. For example, select areas with specific geological structures or abundant mineral resources as the target area for hyperspectral remote sensing data acquisition. After determining the spatial geographic range, select a hyperspectral remote sensing sensor suitable for the spatial resolution requirements of the target area. The selection of the hyperspectral remote sensing sensor depends on the fineness of the spectral characteristics and spatial scale of the mineral species in the target area. For example, for areas with fine-grained mineral spatial distribution, a high-resolution hyperspectral remote sensing sensor with a spatial resolution of less than five meters is used; for areas with relatively uniform spatial distribution of minerals, a remote sensing sensor with a spatial resolution of around ten meters is selected.

[0021] The selection of the spectral range and number of bands for the hyperspectral remote sensing sensor is determined based on the accuracy requirements of mineral identification. For example, when the target minerals are diverse and have complex spectral characteristics, a hyperspectral remote sensing sensor with more than one hundred spectral bands and a wavelength coverage from visible light to shortwave infrared is used; when the spectral characteristics of minerals in the target area are relatively simple, a sensor with several dozen bands is selected. After selecting the hyperspectral remote sensing sensor, continuous spatial scanning is performed over the target area using airborne or satellite payloads. During the scanning process, the flight altitude, flight speed, and scan overlap rate are controlled to ensure the spatial and spectral consistency and continuity of the generated hyperspectral image data to be processed. For example, to ensure the spatial continuity of the image, the overlap rate between flight paths can be set to 30% to 50%.

[0022] After the hyperspectral remote sensing data acquisition is completed, the acquired hyperspectral remote sensing data is converted into hyperspectral image data to be processed. The conversion process includes: First, geometric correction is performed on the acquired raw hyperspectral remote sensing data to eliminate spatial displacement errors generated during the movement of the hyperspectral remote sensing sensor. The geometric correction method adopts orthorectification, that is, using the ground control point and GPS positioning data acquired simultaneously during acquisition, a mathematical transformation model between the raw hyperspectral remote sensing data and the geospatial coordinate system is established, and the remote sensing data is coordinately projected and spatially aligned. The geometrically corrected hyperspectral remote sensing data forms image data under a unified spatial coordinate system. Radiometric calibration is performed on the geometrically corrected image data, including establishing a linear relationship between the raw radiometric values ​​of the remote sensing image and the reference spectral radiometric values ​​based on the standard ground object reference spectral data measured simultaneously during acquisition, using linear interpolation, and then performing radiometric calibration on the remote sensing image data to obtain the hyperspectral image data to be processed in reflectance form.

[0023] After completing the geometric correction and radiometric calibration of the hyperspectral image data, noise removal processing is performed. Noise removal methods include, but are not limited to, principal component analysis (PCA) utilizing inter-band redundancy information, sliding window filtering along the spectral dimension, and adaptive threshold denoising based on wavelet transform. For example, using PCA, the covariance matrix of the hyperspectral image data is first calculated, the number of principal components contributing more than 95% is determined, the corresponding principal components are retained, and the remaining noisy components are removed to reconstruct the denoised hyperspectral image data.

[0024] Mineral spectral data corresponding to the characteristics of the target region are selected from a pre-set mineral spectral database to form a corresponding mineral spectral library; Based on the geological background, historical mineral survey results, and distribution characteristics of regional mineral resources in the target area, the types of minerals that may exist in the target area are determined. For example, if it is determined that clay minerals, carbonate minerals, and iron oxide minerals mainly exist in the target area, then the corresponding mineral spectral data of the minerals need to be screened; if the minerals are unknown or the mineral types are uncertain, a mineral spectral database with more comprehensive coverage of mineral types is used for preliminary screening to ensure that the mineral spectral library covers all mineral types that may exist in the target area.

[0025] After determining the range of possible mineral species, mineral spectral data is extracted from a pre-defined mineral spectral database. During extraction, the wavelength range, spectral resolution, and data quality of the spectral data need to be considered. For example, the mineral spectral database should cover the wavelength range from visible light to shortwave infrared to match the wavelength range of the hyperspectral image data; the spectral resolution should be similar to that of the acquired hyperspectral image data to ensure effective comparison between the mineral endmember spectral data and the hyperspectral image data to be processed.

[0026] The mineral spectral data extracted from the pre-defined mineral spectral database undergoes adaptive processing to ensure optimal matching of spectral features between the selected mineral spectral data and the hyperspectral image data to be processed. Adaptive processing methods include band interpolation, band resampling, and spectral data standardization. When the number of bands in the mineral spectral data differs from that in the hyperspectral image data, interpolation is used to adjust the number of bands in the mineral spectral data to perfectly match the hyperspectral image data. If the spectral resolution of the mineral spectral data is higher than that of the hyperspectral image data, band resampling is used to resample the hyperspectral data to the same spectral resolution as the hyperspectral image data. Finally, standardization is used to uniformly normalize the mineral spectral data to the same spectral scale. For example, maximum-minimum normalization is used to perform maximum-minimum normalization on each band of the mineral spectral data to eliminate intensity differences between different mineral spectra, thus constructing a mineral spectral library corresponding to the characteristics of the target region.

[0027] S2: Based on the hyperspectral image and the corresponding mineral spectral library, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix, including: Based on hyperspectral images and corresponding mineral spectral libraries, the spectral angle between each pixel of the hyperspectral image and each mineral endmember is calculated. The spectral angles of each pixel in the hyperspectral image and each mineral endmember are converted into similarity values ​​to obtain the first similarity matrix.

[0028] For example, input a hyperspectral image X ∈ R (22×38×221). Input a USGS mineral spectral library S_m ∈ R (27×221). Reshape the hyperspectral image X into a two-dimensional matrix X_2d ∈ R (836×221), where 836 = 22×38.

[0029] Calculate the spectral angle between each pixel and each mineral endmember in the hyperspectral image. ∈[0,π / 2]. Converting this to similarity, the calculation formula is: The first similarity matrix S_a∈R(836×27) is obtained; where, Let p be the spectral angle (in radians) between pixel p and mineral j. Let p be the similarity between pixel p and mineral j.

[0030] S3: Based on hyperspectral imagery and the corresponding mineral spectral library, combining the absorption valleys of each mineral endmember spectrum and each image pixel spectrum, the feature matching similarity between pixels and minerals is calculated to obtain the second similarity matrix, including: Based on hyperspectral images and the corresponding mineral spectral library, continuum removal is performed on the spectrum of each mineral endmember and the spectrum of each image pixel; All absorption valleys were detected in the spectrum after continuum removal, and the characteristic parameters of each absorption valley were calculated. The similarity of absorption position matching is calculated using global minimum error matching. The similarity of absorption depth matching is calculated using sequential alignment; Adaptively calculate the absorption shape matching similarity based on the availability of feature width and symmetry; The second similarity matrix is ​​obtained by calculating the comprehensive similarity based on the similarity of absorption position matching, absorption depth matching, and absorption shape matching.

[0031] For example, continuum removal is performed on the spectrum of each mineral endmember and the spectrum of each image pixel: ,in The reflectance after removing the continuum is . The original spectral reflectance, This is a continuum obtained by linear interpolation of convex hull points.

[0032] All absorption valleys are detected in the spectrum after continuum removal, and the characteristic parameters of each absorption valley are calculated: position λ, depth d, width wth, and symmetry sym; the pixel feature set is denoted as P, and the mineral feature set is denoted as M.

[0033] Calculate the feature matching similarity between pixels and minerals: The absorption position matching similarity calculation uses a global minimum error matching strategy, and the similarity is between [0,1].

[0034] Global minimum error matching, specifically: For the current pixel p, the set of absorption locations corresponding to its extracted absorption features is as follows: ,in It represents the absorption position of the k-th absorption feature in pixel p, where k represents the absorption feature index of pixel p, k=1,2,... , This represents the number of absorption features of pixel p; for the currently compared mineral endmember m, the set of corresponding absorption positions for its absorption features is... ,in This represents the absorption position of the l-th absorption feature of mineral endmember m, where l is the absorption feature index of mineral endmember m, l=1,2,... , This indicates the number of absorption features of the mineral endmember m.

[0035] Calculate the absolute positional error between each absorption feature of pixel p and all absorption features of mineral endmember m, forming a value of . The error matrix ER(p,m); the elements in the matrix This represents the absolute value of the error between the absorption position of the k-th absorption feature of pixel p and the absorption position of the l-th absorption feature of mineral endmember m, calculated using the following formula: .

[0036] Find the minimum value in the row containing the k-th absorption feature of pixel p in the error matrix ER(p,m), using the formula: This allows us to obtain the absorption feature of pixel p and the mineral endmember m. Global optimal position matching error among absorption features .

[0037] Find the pixel p using the method described above. The set of global optimal position matching errors for each absorption feature After arithmetic averaging, the average error of the global optimal position matching of pixel p is obtained. The formula is , which is the absorption position matching similarity as the absorption feature of pixel p. For the absorption feature of pixel p and the mineral endmember m The globally optimal position matching error among absorption features is the minimum error between the absorption position of the k-th absorption feature of pixel p and the absorption position of all absorption features of mineral endmember m; Spos(p) is the absorption position matching similarity of the absorption features of pixel p.

[0038] The above strategy ensures that each pixel feature can be matched with the closest feature in the mineral endmember spectrum, avoiding incorrect matching caused by inconsistent feature order or different numbers, thus achieving optimal similarity assessment at the feature level.

[0039] The absorption depth matching similarity calculation adopts an order alignment strategy.

[0040] The sequential alignment strategy is based on reasonable engineering assumptions. Before matching features such as depth and shape, the absorption features of pixels and mineral endmembers have already established a one-to-one correspondence in position through global minimum error matching. That is, for the k-th absorption feature of pixel p, it has been determined that it corresponds to the k-th absorption feature of mineral endmember m. One absorption characteristic, the formula is: .in, This represents the index of the absorption features of the k-th absorption feature of pixel p in the absorption features of mineral endmember m after the global minimum matching is determined.

[0041] When calculating absorption depth similarity, the absorption depths of the k-th absorption feature of pixel p are compared. With mineral end-member m Absorption depth of each absorption feature Calculate the absorption depth ratio The formula is .

[0042] Calculate the value of pixel p using the method described above. Set of absorption depth ratios for each absorption feature After arithmetic averaging, the average value of the absorption depth matching ratio of pixel p is obtained. The formula is , which is the absorption depth matching similarity as the absorption feature of pixel p. The absorption depth of the k-th absorption feature of pixel p is related to the absorption depth of the mineral endmember m. The ratio of absorption depth of each absorption feature.

[0043] While ensuring optimal location matching, sequential alignment simplifies the computational complexity of features, guarantees the physical consistency of comparison (i.e., it compares features of the same absorption valley that are closest in spatial location), and avoids erroneous comparisons of features between different absorption valleys.

[0044] The absorption shape matching similarity can be adaptively calculated based on feature availability.

[0045] For the matched pixel p, the k-th absorption feature and the mineral endmember m, the... Each absorption feature is analyzed, and its absorption width wth is extracted. This represents the absorption width of the k-th absorption feature in pixel p. Represents the mineral endmember m. Calculate the absorption width similarity of each absorption feature. The formula is The above calculations can effectively handle the differences in the width of absorption features at different depths.

[0046] For the matched feature pairs (k, The symmetry parameters of the k-th absorption feature of pixel p are extracted respectively. , and mineral end-member m Symmetry parameters of absorption features The symmetry parameter is obtained by calculating the correlation coefficient between the left half of the absorption feature and the flipped right half. The symmetry similarity of the k-th absorption feature... The calculation formula is The denominator 2 ensures that even at the two endpoints (such as 1 and -1), the similarity remains in the range of [0,1]. The larger the value, the closer the symmetry.

[0047] The comprehensive shape similarity requires testing the availability of width similarity and symmetry similarity. If both width similarity and symmetry similarity are available, then the comprehensive shape similarity of the k-th absorbing feature of pixel p is... The arithmetic mean of width similarity and symmetry similarity is given by the formula: If only width similarity is available, then If only symmetry similarity is available, then If both width similarity and symmetry similarity are unavailable (with a very low probability), then skip the feature pair. Finally, calculate the similarity of pixel p. The set of comprehensive shape similarities of each absorption feature After arithmetic averaging, the average similarity of the comprehensive shape matching of pixel p is obtained. The formula is , which is the absorption shape matching similarity as the absorption feature of pixel p. To efficiently compute the feature logarithm in terms of the availability of width and symmetry parameters.

[0048] When calculating the overall similarity, position and depth have the highest weights (0.4 each), reflecting their diagnostic importance, while shape has a lower weight (0.2). The overall similarity of absorption features of pixel p... The calculation formula is: Where, Sttotal(p) is the overall similarity of the absorption features of pixel p; Spos(p) is the similarity of the absorption position matching of the absorption features of pixel p; Sdepth(p) is the similarity of the absorption depth matching of the absorption features of pixel p; and Sshape(p) is the similarity of the absorption shape matching of the absorption features of pixel p. The second similarity matrix S_b∈R(836×27) is obtained by calculating pixel by pixel in this manner.

[0049] S4: Based on hyperspectral imagery and the corresponding mineral spectral library, background spectral reconstruction is performed using a spectral background autoencoder to obtain a third similarity matrix, including: Based on hyperspectral images and corresponding mineral spectral libraries, continuum removal is performed on the pure mineral spectra to locate absorption valleys. The spectral values ​​within the absorption valleys are then replaced with the corresponding continuum values ​​to obtain the background spectrum. For each mineral, noise is added to the corresponding background spectrum to generate a training set, and a shallow autoencoder is trained. For each pixel, the corresponding background spectrum is extracted, and the background of each pixel is reconstructed using an autoencoder for all mineral backgrounds. Calculate the weighted reconstruction error, and use the hyperbolic decay function to convert the weighted reconstruction error into background similarity to obtain the third similarity matrix.

[0050] For example, the spectrum of a pure mineral is subjected to continuum removal to locate the absorption valleys. The spectral values ​​within the absorption valleys are then replaced with the corresponding continuum values ​​to obtain the background spectrum b_j after "filling" the absorption valleys.

[0051] For each mineral j, noise (Gaussian, multiplicative, low-frequency) is added to its background spectrum b_j to generate a training set, and a shallow autoencoder is trained with encoding dimension d=20. The network forward propagation formula is: encoder hidden layer representation h=ReLU( ), with a size of 1×20; where, This is the encoder weight matrix, initially distributed according to a standard normal distribution, with a size of 221×20. This is the encoder bias vector, with a size of 1×20 and an initial value of 0.

[0052] A shallow autoencoder with a single hidden layer is employed. Both the encoder and decoder contain only one fully connected layer. The encoder's hidden layer uses the ReLU activation function, which provides non-linear expressive power and helps learn the sparse features of the spectral background. The decoder's output layer uses the Sigmoid activation function to compress the output values ​​to the (0,1) interval, consistent with the normalized spectral reflectance range, ensuring the physical reasonableness of the reconstructed values. Training samples are generated by adding one of the following three types of noise to the pure mineral background spectrum, each noise simulating a real variation: Additive Gaussian noise: The noise vector ns ~ N(0, σ²), where the standard deviation is randomly selected between 0.01 and 0.03; Multiplicative noise (simulating illumination changes): The noise form is (1+δ) *bj, where δ is uniformly distributed in the interval [-0.05, 0.05]. Low-frequency noise (simulating background trend changes): Add a low-frequency sine wave A*sin(2πkidx / L), where the amplitude A is controlled within 2%-5% of the original spectral value, and k... idx is the band index, and L is the total number of bands.

[0053] For each training sample, a noise type is randomly selected, and the corresponding noise parameters are randomly generated.

[0054] The Adam optimizer is used, whose adaptive learning rate is suitable for handling sparse gradients and can accelerate convergence.

[0055] The loss function uses mean squared error (MSE) loss, which directly minimizes the difference between the reconstructed spectrum and the original background spectrum.

[0056] The initial learning rate was set to 0.001.

[0057] It can converge after a maximum of 800 training cycles.

[0058] The encoding dimension is typically 1 / 10 of the number of bands.

[0059] By overlaying the original background spectrum with the reconstructed spectrum, we can visually verify that the shallow autoencoder can accurately reconstruct smooth background trends. Deep models tend to reconstruct absorbing features (leading to overlap with evidence of absorbing features), while shallow models focus on background trends, which aligns with the decoupling design goal.

[0060] Decoder reconstructs output x̂=Sigmoid( ), with a size of 1×221, This is the decoder weight matrix, initially set to a standard normal distribution with a size of 20×221. This is the decoder bias vector, with a size of 1×221 and an initial value of 0.

[0061] The loss function Loss is calculated using the mean squared error, and is Loss = ||b_j-x̂||².

[0062] Pixel background similarity calculation: For pixel p, extract its background spectrum x_pbg. Reconstruct x̂_pj using the autoencoder of the j-th mineral.

[0063] Calculate the weighted reconstruction error of pixel p after reconstruction by the autoencoder of mineral j. The formula is ; in, Let x_pbg and x̂_pj be the mean squared errors. Let x_pbg and x̂_pj be the gradient errors. This represents the low-frequency error between x_pbg and x̂_pj.

[0064] The weighted reconstruction error is calculated using the hyperbolic decay function. Convert to background similarity between pixel p and the j-th mineral The calculation formula is: ,in This is the scaling factor, which controls the discrimination.

[0065] The similarity vector between pixel p and all n mineral endmembers is calculated using the above method. After pixel-by-pixel calculation, the third similarity matrix S_c∈R(836×27) is obtained.

[0066] S5: Convert the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability assignment matrices using the basic probability assignment function, including: Each row of the first similarity matrix, the second similarity matrix, and the third similarity matrix is ​​input into the basic probability allocation function, and normalized by the Softmax function controlled by the temperature parameter to obtain the probability distribution vector. Calculate the normalized entropy of the probability distribution vector; The uncertainty mass is dynamically calculated using the exponential decay function based on the normalized entropy. The uncertainty quality is assigned to the identification framework to form a basic probability assignment matrix.

[0067] For example, each row of the first similarity matrix, the second similarity matrix, and the third similarity matrix is ​​input into the basic probability assignment function, including: Security processing ensures all similarity values ​​are positive: s_j is the j-th value in the input similarity row vector, and the processed value is s_j'. The processing formula is s_j'=max(s_j,10). -10 This method is used to perform security processing on all values ​​in the input similarity row vector.

[0068] Temperature τ scaling Softmax: , , Here, vj is the intermediate value of s_j' after temperature scaling; pj is the probability value obtained by normalizing vj, forming a probability distribution.

[0069] Parameter settings: spectral angle τ=0.08, absorption characteristic τ=0.05, spectral background τ=0.1.

[0070] Absorption features are diagnostic features for mineral identification. Differences in similarity have high discriminative power. Smaller absorption features can amplify subtle differences and enhance selectivity for key minerals. However, excessively small absorption features (e.g., <0.03) can lead to oversensitivity and be greatly affected by noise.

[0071] The spectral angle reflects the overall spectral shape, is sensitive to global changes but not to details, and a medium spectral angle balances shape matching and noise tolerance. The spectral angle is easily affected by factors such as illumination and atmosphere, and requires a certain degree of smoothness.

[0072] Spectral background is trend information after removing diagnostic features, and its discrimination is naturally low. A larger spectral background value produces a smoother probability distribution, avoiding information duplication and conflict with absorption feature evidence.

[0073] Based on extensive experiments and validation with different datasets, the absorption feature τ ranges from [0.03, 0.08]; the spectral angle τ ranges from [0.05, 0.12]; and the spectral background τ ranges from [0.08, 0.15].

[0074] The three τ values ​​should maintain a relative relationship: τ absorption characteristic < τ spectral angle < τ spectral background, and the temperature parameter needs to be adjusted in conjunction with the uncertainty parameters Umin and Umax.

[0075] Calculate dynamic uncertainty: Calculate the entropy H = -Σp_jln(p_j), and the maximum entropy H_max = ln(n).

[0076] Normalized entropy H_norm = H / H_max.

[0077] Uncertainty .in Minimum uncertainty when evidence is highly concentrated. The maximum uncertainty arises when evidence is highly dispersed. Reducing the scope makes the system more certain overall, but may ignore conflicting evidence. Increasing the scope makes the system more conservative and retains more uncertainty. As a decay rate parameter, increasing it causes uncertainty to increase faster with entropy, while decreasing it causes uncertainty to increase more gradually with entropy. This represents the normalized entropy, which measures the dispersion of evidence.

[0078] Parameter settings: spectral angle [U_min, U_max]=[0.10, 0.25]; absorption characteristics [0.05, 0.20]; spectral background [0.15, 0.30].

[0079] The ranking of physical diagnostic capabilities based on three types of evidence was determined through experimental optimization. Absorption features exhibit the strongest diagnostic and physical interpretability. In mixed pixels, absorption features in specific bands may still be retained even if the overall spectral shape changes. A weight of 0.4 emphasizes its decisive role in mineral identification.

[0080] The spectral angle is sensitive to global spectral variations, but is easily affected by non-target factors such as illumination conditions, atmospheric effects, and instrument calibration errors, leading to "different objects sharing the same spectrum." A weight of 0.25 is used to suppress the ambiguity it may introduce. The spectral background and absorption features are complementary and have strong noise resistance; a weight of 0.35 is slightly lower than that of the absorption features.

[0081] BPA allocation: ,in The assumption representing the j-th mineral, , For identification framework.

[0082] Finally, three basic probability assignment (BPA) matrices are obtained, namely the basic probability assignment matrix M_1 for spectral angle evidence, the basic probability assignment matrix M_2 for absorption feature evidence, and the basic probability assignment matrix M_3 for spectral background evidence, M_1, M_2, M_3∈R(836×28).

[0083] S6: The basic probability assignment matrices are fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix, including: Weights are assigned to the basic probability assignment matrices for spectral angle evidence, absorption feature evidence, and spectral background evidence, respectively. The first step is to perform weighted fusion on the basic probability allocation matrix of spectral angle evidence and the basic probability allocation matrix of absorption feature evidence, extract the same row vector of the basic probability allocation matrix of spectral angle evidence and the basic probability allocation matrix of absorption feature evidence, and calculate the first conflict coefficient between the vectors. If the first conflict coefficient exceeds the corresponding preset threshold, a weighted average is used for fusion; otherwise, the standard Dempster rule is used for fusion. This process is repeated row by row to obtain intermediate fusion results. The intermediate fusion result is weighted and fused with the basic probability assignment matrix of spectral background evidence in the second step. The same row vector of the intermediate fusion result and the basic probability assignment matrix of spectral background evidence are extracted, and the second conflict coefficient between the vectors is calculated. If the second conflict coefficient exceeds the corresponding preset threshold, a weighted average is used for fusion; otherwise, the standard Dempster rule is used for fusion. This process is repeated row by row to obtain the fusion basic probability allocation vector and generate the fusion basic probability allocation matrix.

[0084] For example, the evidence weights are set to w = [0.25, 0.40, 0.35]. M_1 and M_2 are merged row by row to obtain the intermediate matrix M_12. Extract the row vectors of the three evidence matrices corresponding to pixel p from matrices M_1, M_2, and M_3 respectively: , , That is, the basic probability assignment vector for each piece of evidence in pixel p. Using... and Calculate the conflict coefficient The formula is Where n represents the total number of mineral endmembers, It was the first piece of evidence assigned to the mineral. The basic probability mass, The second piece of evidence was assigned to the mineral. The basic probability mass. If If the probability distribution is greater than 0.8, then a weighted average method is used to directly fuse the basic probability distribution vectors of the two pieces of evidence to obtain the intermediate fused basic probability distribution vector. The formula is .in , The normalized weights calculated in step 1 when using weighted fusion, for example =0.25, =0.40.

[0085] Otherwise, using the standard Dempster rule, the basic probabilistic quality of intermediate fusions is obtained: ; ;in Assigning intermediate fusion evidence to The basic probability mass, The second piece of evidence was assigned to the mineral. The basic probability mass, , The first and second pieces of evidence were assigned to the identification framework, respectively. The basic probability mass, Assigning intermediate fused evidence to the identification framework The basic probability quality. Obtain the basic probability assignment vector for intermediate fusions after traversing n minerals.

[0086] Line-by-line fusion of M_12 and M_3: using the basic probability assignment vector of pixel p and Calculate the conflict coefficient The formula is: Where n represents the total number of mineral endmembers, Intermediate fusion evidence is assigned to the minerals The basic probability mass, The third piece of evidence was assigned to the mineral. The basic probability mass.

[0087] like If the probability is greater than 0.8, a weighted average method is used for fusion to obtain the final fused basic probability allocation vector. The calculation formula is: ,in , The normalized weights are those calculated when weighted fusion is used in step 2. =0.65, =0.35. Otherwise, Using standard Dempster rules: ,

[0088] in Assigning final fusion evidence to The basic probability mass, Assigning intermediate fusion evidence to The basic probability mass, The third piece of evidence was assigned to the mineral. The basic probability mass, , The intermediate fusion and the third evidence allocation to the identification framework are respectively: The basic probability mass, Assigning fused evidence to the identification framework The basic probability mass is obtained by traversing n minerals. The basic probability assignment vector of the final fusion is obtained, which forms the final fusion BPA matrix M_fused∈R(836×28).

[0089] S7: Perform uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map, including: The confidence vector and uncertainty mass of each mineral are separated from the fused basic probability assignment matrix; For each cell, if the uncertainty mass is greater than zero and the sum of the confidence vectors of each mineral is greater than zero, then the ratio of each mineral confidence vector to the uncertainty mass is redistributed, and the mineral confidence is updated. The updated mineral confidence matrix was reshaped into a spatial three-dimensional abundance map; The abundance vector of each spatial cell in the spatial three-dimensional abundance map is normalized.

[0090] For example, for the p-th row of M_fused: extract the mineral confidence vector bel_p∈R^27 and the uncertainty mass u_p=m(Θ).

[0091] Calculate the confidence level and S_p = Σbel_p. If u_p > 0 and S_p > 0, then update the confidence level: bel_p_new = bel_p * (1 + u_p / S_p). Otherwise, bel_p_new = bel_p, and the confidence matrix B_new is constructed after pixel-by-pixel calculation.

[0092] The updated confidence matrix B_new∈R^(836×27) is reshaped into a three-dimensional array A∈R^(22×38×27), which is the initial abundance map.

[0093] For each spatial location (r, c) in the initial abundance map A, calculate its sum. .like >0, then A(r,c,:)= a_rc. / Ensure that the sum of the abundance values ​​of each cell in the final abundance map is 1.

[0094] Using the above methods, the abundance distribution maps of 27 minerals in the 22×38 image space were obtained, and the mixed pixel decomposition was completed.

[0095] Example 2 The difference between Embodiment 2 and Embodiment 1 is that this embodiment introduces a hyperspectral mineral unmixing system based on complementary evidence and adaptive uncertainty modeling.

[0096] Figure 2 A schematic diagram of the hyperspectral mineral unmixing system based on complementary evidence and adaptive uncertainty modeling of the present invention is given. The hyperspectral mineral unmixing system based on complementary evidence and adaptive uncertainty modeling includes: Image acquisition module: Acquires the hyperspectral image to be processed and the corresponding mineral spectral library; Angle similarity module: Based on hyperspectral images and corresponding mineral spectral libraries, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix; Feature matching module: Based on hyperspectral images and corresponding mineral spectral libraries, it combines the absorption valley detection of each mineral endmember spectrum and each image pixel spectrum to calculate the feature matching similarity between pixels and minerals, and obtains the second similarity matrix; Background reconstruction module: Based on hyperspectral images and corresponding mineral spectral libraries, background spectral reconstruction is performed through a spectral background autoencoder to obtain a third similarity matrix; Probability Transformation Module: Converts the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability assignment matrices using the basic probability assignment function. Evidence fusion module: The basic probability assignment matrix is ​​fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix; Abundance Normalization Module: Performs uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map.

[0097] The present invention discloses a storage medium, characterized in that the storage medium stores an optimization program based on a performance model parameter simulation, and when the optimization program based on the performance model parameter simulation is executed by a processor, it implements the steps of the hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling as described above.

[0098] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling, characterized in that, Includes the following steps: S1: Acquire the hyperspectral image to be processed and the corresponding mineral spectral library; S2: Based on the hyperspectral image and the corresponding mineral spectral library, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix; S3: Based on hyperspectral images and the corresponding mineral spectral library, the absorption valleys are detected by combining the endmember spectrum of each mineral and the spectrum of each image pixel. The feature matching similarity between the pixel and the mineral is calculated to obtain the second similarity matrix. S4: Based on hyperspectral images and the corresponding mineral spectral library, the background spectrum is reconstructed by a spectral background autoencoder to obtain the third similarity matrix; S5: Convert the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability allocation matrices using the basic probability allocation function; S6: The basic probability assignment matrix is ​​fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix; S7: Perform uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map.

2. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 1, characterized in that, S1, specifically: Hyperspectral remote sensing data is acquired for the target area to generate hyperspectral images to be processed; Mineral spectral data corresponding to the characteristics of the target region are selected from a pre-set mineral spectral database to form a corresponding mineral spectral library.

3. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 2, characterized in that, S2, specifically: Based on hyperspectral images and corresponding mineral spectral libraries, the spectral angle between each pixel of the hyperspectral image and each mineral endmember is calculated. The spectral angles of each pixel in the hyperspectral image and each mineral endmember are converted into similarity values ​​to obtain the first similarity matrix.

4. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 3, characterized in that, S3, specifically: Based on hyperspectral images and the corresponding mineral spectral library, continuum removal is performed on the spectrum of each mineral endmember and the spectrum of each image pixel; All absorption valleys were detected in the spectrum after continuum removal, and the characteristic parameters of each absorption valley were calculated. The similarity of absorption position matching is calculated using global minimum error matching. The similarity of absorption depth matching is calculated using sequential alignment; Adaptively calculate the absorption shape matching similarity based on the availability of feature width and symmetry; The second similarity matrix is ​​obtained by calculating the comprehensive similarity based on the similarity of absorption position matching, absorption depth matching, and absorption shape matching.

5. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 4, characterized in that, S4, specifically: Based on hyperspectral images and corresponding mineral spectral libraries, continuum removal is performed on the pure mineral spectra to locate absorption valleys. The spectral values ​​within the absorption valleys are then replaced with the corresponding continuum values ​​to obtain the background spectrum. For each mineral, noise is added to the corresponding background spectrum to generate a training set, and a shallow autoencoder is trained. For each pixel, the corresponding background spectrum is extracted, and the background of each pixel is reconstructed using an autoencoder for all mineral backgrounds. Calculate the weighted reconstruction error, and use the hyperbolic decay function to convert the weighted reconstruction error into background similarity to obtain the third similarity matrix.

6. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 5, characterized in that, S5, specifically: Each row of the first similarity matrix, the second similarity matrix, and the third similarity matrix is ​​input into the basic probability allocation function, and normalized by the Softmax function controlled by the temperature parameter to obtain the probability distribution vector. Calculate the normalized entropy of the probability distribution vector; The uncertainty mass is dynamically calculated using the exponential decay function based on the normalized entropy. The uncertainty quality is assigned to the identification framework to form a basic probability assignment matrix.

7. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 6, characterized in that, S6, specifically: Weights are assigned to the basic probability assignment matrices for spectral angle evidence, absorption feature evidence, and spectral background evidence, respectively. The basic probability allocation matrix of spectral angle evidence and the basic probability allocation matrix of absorption feature evidence are weighted and fused. The same row vector of the basic probability allocation matrix of spectral angle evidence and the basic probability allocation matrix of absorption feature evidence are extracted, and the first conflict coefficient between the vectors is calculated. If the first conflict coefficient exceeds the corresponding preset threshold, a weighted average is used for fusion; otherwise, the standard Dempster rule is used for fusion to obtain an intermediate fusion result. The intermediate fusion result is weighted and fused with the basic probability assignment matrix of spectral background evidence. The same row vector of the intermediate fusion result and the basic probability assignment matrix of spectral background evidence are extracted, and the second conflict coefficient between the vectors is calculated. If the second conflict coefficient exceeds the corresponding preset threshold, a weighted average is used for fusion; otherwise, the standard Dempster rule is used for fusion to obtain the fusion basic probability allocation vector and generate the fusion basic probability allocation matrix.

8. The hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling according to claim 7, characterized in that, S7, specifically: The confidence vector and uncertainty mass of each mineral are separated from the fused basic probability assignment matrix; For each cell, if the uncertainty mass is greater than zero and the sum of the confidence vectors of each mineral is greater than zero, then the ratio of each mineral confidence vector to the uncertainty mass is redistributed, and the mineral confidence is updated. The updated mineral confidence matrix was reshaped into a spatial three-dimensional abundance map; The abundance vector of each spatial cell in the spatial three-dimensional abundance map is normalized.

9. A hyperspectral mineral unmixing system based on complementary evidence and adaptive uncertainty modeling, used to implement the hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling as described in any one of claims 1-8, characterized in that, include: Image acquisition module: Acquires the hyperspectral image to be processed and the corresponding mineral spectral library; Angle similarity module: Based on hyperspectral images and corresponding mineral spectral libraries, calculate the spectral angle between each pixel of the hyperspectral image and each mineral endmember, and convert it into similarity to obtain the first similarity matrix; Feature matching module: Based on hyperspectral images and corresponding mineral spectral libraries, it combines the absorption valley detection of each mineral endmember spectrum and each image pixel spectrum to calculate the feature matching similarity between pixels and minerals, and obtains the second similarity matrix; Background reconstruction module: Based on hyperspectral images and corresponding mineral spectral libraries, background spectral reconstruction is performed through a spectral background autoencoder to obtain a third similarity matrix; Probability Transformation Module: Converts the first similarity matrix, the second similarity matrix, and the third similarity matrix into their corresponding basic probability assignment matrices using the basic probability assignment function. Evidence fusion module: The basic probability assignment matrix is ​​fused using the step-by-step weighted Dempster combination rule to obtain the fused basic probability assignment matrix; Abundance Normalization Module: Performs uncertainty redistribution and abundance normalization on the fused basic probability distribution matrix to generate a mineral abundance map.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program or instructions that cause a computer to perform the hyperspectral mineral unmixing method based on complementary evidence and adaptive uncertainty modeling as described in any one of claims 1 to 9.

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