Hyperspectral remote sensing abnormal small target detection method based on multi-aperture spectral information fusion

Abstract

The invention belongs to the technical field of target detection, and discloses a hyperspectral remote sensing abnormal small target detection method based on multi-aperture spectral information fusion. The method comprises the following steps: dividing a target region into n target sub-regions; collecting hyperspectral data of each target sub-region; converting each piece of hyperspectral data into a spectral data cube, and extracting spatial spectral feature data; extracting difference data from each piece of hyperspectral data; performing anomaly detection according to the spatial spectrum characteristic data and the difference data; according to the invention, through block processing and multi-aperture information fusion of hyperspectral data, the robustness of anomaly detection under spectrum aliasing interference is enhanced; a deep learning technology is introduced, so that higher detection precision and a lower false alarm rate are realized; the LSTM neural network is integrated, so that the dynamic target processing capability is improved; and model parameters are adjusted by adopting a clone selection algorithm, so that the accuracy and robustness of an anomaly detection result are further ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of target detection, and more specifically, to a method for detecting abnormal small targets in hyperspectral remote sensing by fusing multi-aperture spectral information. Background Art

[0002] Hyperspectral remote sensing technology is widely used in the fields of national defense and military security, environmental pollution monitoring, and mineral resource exploration because it can simultaneously obtain spatial and spectral information of objects. However, with the improvement of observation accuracy, the complex distribution of objects, the diversity of object types, and the ambiguity of spectral characteristics have brought new challenges to the existing hyperspectral anomaly small target detection technology. The existing hyperspectral anomaly detection technology can generally be divided into the following three categories:

[0003] Anomaly detection based on spectral features: This type of method maps high-dimensional spectral data to low-dimensional space and separates the target from the background through the abnormality of spectral features. However, the complex spectral aliasing phenomenon makes it difficult to find a suitable spectral mixing model, especially in the absence of prior knowledge, the accuracy and reliability of the detection results are difficult to guarantee; Anomaly detection based on spatial distribution features: This type of method usually uses Gaussian statistical models or other spatial modeling methods to characterize background features, thereby realizing the detection of abnormal targets. However, with the complexity of the types and distribution characteristics of land objects, traditional Gaussian models are difficult to effectively describe spectral aliasing phenomena, which increases the difficulty of anomaly detection; Anomaly detection based on structural features: This type of method does not need to inversely solve the composition ratio of land objects or perform background feature modeling, but uses pure data-driven methods such as self-organizing clustering or machine learning to separate background and anomalies. However, this type of method relies on a large number of assumptions, and how to construct effective measurement indicators and optimization algorithms remains a challenge.

[0004] Although current computer vision systems and hyperspectral sensors have powerful data processing capabilities, they still have many limitations in dealing with complex pathological blind signal detection problems. In contrast, although the visual system of flies relies on limited brain cells and low resolution, it can quickly and accurately detect and avoid abnormal targets in complex backgrounds, which provides a new idea for solving the problems in hyperspectral remote sensing anomaly detection. For example, the Chinese patent with authorization announcement number CN103293523B discloses a hyperspectral remote sensing abnormal small target detection method based on multi-aperture information processing; including: data observation-simulation of multi-aperture asynchronous mapping mechanism for hyperspectral remote sensing data Distributed parallel block information processing; using data acquisition chips to perform block data acquisition for hyperspectral remote sensing, simulating the multi-aperture information acquisition and mapping mechanism of the fly visual system, decomposing and recombining the hyperspectral remote sensing spectral data based on the "small eye" mapping function, forming a spectral data cube about local objects, and constructing a distributed parallel block information processing model; information processing - simulating the "cartridge" structure of the fly visual system to achieve redundant compression and super-sensitive fusion of massive spectral data; target detection - simulating the adaptive perception mechanism of the fly visual system's higher-order neurons, through the adaptive abnormal small target detection algorithm, combined with global anomaly and local anomaly discrimination to obtain anomaly detection results.

[0005] Although the above technology realizes spectral processing and target detection through bionic mechanisms, it still has the following limitations when facing complex environments: First, the lack of automatic feature extraction capability makes it impossible to fully extract target features under complex spectral backgrounds, which is prone to missed detection or false detection, affecting the accuracy and reliability of detection; second, the ability to process time series data of dynamic targets is insufficient, especially in rapidly changing dynamic environments, and the response is slow, and the target's changing characteristics cannot be captured in time, affecting the effectiveness of real-time detection; in addition, when faced with large-scale hyperspectral data, the ability to compress redundant information is insufficient, which increases the system's computational complexity and reduces the processing speed, making it difficult to meet the needs of efficient real-time detection.

[0006] In view of this, the present invention proposes a hyperspectral remote sensing abnormal small target detection method based on multi-aperture spectral information fusion to solve the above problems. Summary of the invention

[0007] In order to overcome the above-mentioned defects of the prior art and achieve the above-mentioned purpose, the present invention provides the following technical solution: a method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information, comprising:

[0008] S1: Divide the target area into n target sub-areas;

[0009] S2: Collect hyperspectral data of each target sub-area;

[0010] S3: Convert each hyperspectral data into a spectral data cube and extract spatial spectral feature data;

[0011] S4: extracting difference data from each hyperspectral data;

[0012] S5: Perform anomaly detection based on the spatial spectral feature data and the difference data.

[0013] Furthermore, the method for performing anomaly detection includes:

[0014] Obtain historically calculated spatial spectral feature data and difference data and mark them as historical data; based on historical data, adjust model parameters and train anomaly detection model; the anomaly detection model is based on variational autoencoder and integrates LSTM; model parameters include learning rate, forget gate weight, weight matrix, bias term and time step; weight matrix includes input gate weight matrix and output gate weight matrix, and bias term includes input gate bias term and output gate bias term;

[0015] The spatial spectral feature data and difference data corresponding to each target sub-region are respectively input into the trained anomaly detection model, and the detection label is output. The detection label is a digital label corresponding to the detection result, and the detection result includes normal detection and abnormal detection.

[0016] Furthermore, the step of adjusting the model parameters includes:

[0017] Step 1: Construct M parameter sets, set different numerical labels for different parameter sets, and mark them as parameter labels, where M is an integer greater than 1;

[0018] Step 2: Randomly generate an initial antibody group, where the antibodies in the initial antibody group correspond one to one with the parameter labels;

[0019] Step 3: Determine the fitness function;

[0020] Step 4: Calculate the fitness of each antibody in the initial antibody group, and perform antibody screening to generate a memory antibody group;

[0021] Step 5: Calculate the corresponding clone size for each antibody in the memory antibody group, and clone it to generate a clone antibody group;

[0022] Step 6: Calculate the selection probability of each antibody in the cloned antibody group, and determine whether to select the antibody based on the selection probability to generate a selected antibody group;

[0023] Step 7: Perform cloud adaptive mutation on each antibody in the selected antibody group using a cloud adaptive mutation operator to generate a mutant antibody group;

[0024] Step 8: Using an interpolation method to generate new antibodies for the antibodies in the variant antibody group to generate an interpolated antibody group;

[0025] Step 9: Recombining the antibodies in the variant antibody group to generate a recombinant antibody group;

[0026] Step 10: merging the interpolated antibody group and the recombinant antibody group to generate a merged antibody group;

[0027] Step 11: Determine whether the iteration is finished; if so, calculate the fitness of each antibody in the combined antibody group, and obtain the parameter set corresponding to the parameter label of the antibody with the largest fitness; if not, perform antibody screening on the combined antibody group, regenerate the memory antibody group, and return to step 5.

[0028] Furthermore, in step 1, a parameter range corresponding to each parameter in the model parameters is obtained, a value is randomly selected from each parameter range, a parameter set is constructed, and a total of M parameter sets are constructed, and the M parameter sets are all different;

[0029] In step 2, the initial antibody group X(0) = {X1, X2, X3, ... X q}, X q is the qth antibody, that is, the size of the initial antibody population is q; the range of antibodies is M parameter sets; the number of iterations t of the initial antibody population is 0;

[0030] In step 3, the fitness function is expressed as: f=zq; wherein f is the fitness and zq is the accuracy; the accuracy is obtained by using the parameter set and historical data corresponding to the antibody as analysis data, inputting the analysis data into the trained accurate prediction model, and predicting the corresponding accuracy; the training process of the accurate prediction model is consistent with the training process of the anomaly detection model, and both are deep neural network models;

[0031] In step 5, the method for calculating the clone size includes:

[0032]

[0033] Φ i =min(exp(||X i -X j ||));

[0034] In the formula, R i is the clone size of the i-th antibody, Int is the upward rounding function, q is the initial antibody population size, Φ i is the affinity of the ith antibody, f i is the fitness of the ith antibody, min is the minimum function, exp is the natural exponential function, ||X i -Xj || is the Euclidean distance between the i-th antibody and the j-th antibody, i≠j, j∈[1,q].

[0035] Furthermore, in step 4, the method of antibody screening is: selecting h antibodies with the largest fitness from the initial antibody group, q>h>1;

[0036] In step 6, the method for generating the selected antibody group comprises:

[0037] Calculate the fitness of each antibody in the cloned antibody group, and add them up in sequence to obtain the total antibody fitness, divide the fitness of each antibody by the total antibody fitness, and obtain the selection probability of each antibody; sort the selection probability of each antibody from large to small, and replace each selection probability in order according to the positive order with the sum of each selection probability and all selection probabilities before the corresponding selection probability; obtain all selection probabilities after replacement and mark them as replacement probabilities; the antibody corresponding to the replacement probability is consistent with the antibody corresponding to the selection probability before replacement; regard every two adjacent replacement probabilities as an analysis set according to the positive order; mark the replacement probability with the largest value in each analysis set as the first probability , mark the replacement probability with a smaller value as the second probability; construct the probability screening range corresponding to each analysis set according to the first probability and the second probability of each analysis set, wherein the first probability is the maximum value of the probability screening range, the second probability is the minimum value of the probability screening range, and the minimum value is an open interval, and the maximum value is a closed interval; each analysis set corresponds to the antibody corresponding to the second probability; wherein the minimum value of the probability screening range corresponding to the first antibody is 0, and the maximum value is the corresponding selection probability; randomly generate h random numbers between (0, 1], select the antibody corresponding to the probability screening range where the h random numbers are located, and generate a selected antibody group.

[0038] Furthermore, the fitness of each antibody is calculated and sorted from large to small to generate a sorting table; half of the antibodies in the variant antibody group are screened out according to the positive order of the sorting table and marked as screening antibodies; new antibodies are generated by interpolation method for every two adjacent screening antibodies; the fitness corresponding to each new antibody is calculated and added to the sorting table, and the antibodies corresponding to the first y fitness in the sorting table are retained to generate an interpolated antibody group, where y is the number of antibodies in the variant antibody group;

[0039] The expression of the new antibody is: X X =(1-α′)X′+α′X″; where X X is a new antibody, X′ and X″ are two adjacent screening antibodies, α′ is an interpolation coefficient, and α′ is a random number between [0, 1];

[0040] In step 9, the method for antibody recombination comprises:

[0041] Randomly select Y antibodies from the mutant antibody group as parent antibodies for antibody recombination to generate progeny antibodies S c , until the number of unselected antibodies in the variant antibody group is less than Y, the antibody recombination is completed; the recombinant antibody group includes multiple progeny antibodies S c ;

[0042] Progeny antibody S c The calculation methods include:

[0043]

[0044] In the formula, X′ Y is the Yth parent antibody, S Y is the Yth scale factor, the scale factor is a randomly generated real number and not all Y scale factors are 0;

[0045] In step 11, the method for determining whether the iteration is completed includes:

[0046] Preset an iteration threshold, and compare the number of iterations t with the iteration threshold;

[0047] If the number of iterations t is greater than or equal to the iteration threshold, the iteration ends;

[0048] If the number of iterations t is less than the iteration threshold, the iteration continues.

[0049] Furthermore, the method for dividing the n target sub-regions is as follows: dividing the target region into grids according to a preset grid size, and the divided grids correspond to the target sub-regions one by one;

[0050] The hyperspectral data includes spectral information and spatial information; the spectral information is the reflectance of each pixel point in the target sub-region at each wavelength; the spatial information is the geographical location coordinates of each pixel in the hyperspectral data corresponding to the target sub-region;

[0051] The spectral data cube is a three-dimensional data structure, which corresponds to the hyperspectral data one by one; the spectral data cube includes width, height and depth; the width is the number of pixels in the horizontal direction of the corresponding hyperspectral data; the height is the number of pixels in the vertical direction of the corresponding hyperspectral data; the depth is the spectral information in the corresponding hyperspectral data; the spatial spectral feature data includes gray level co-occurrence matrix and spectral similarity; the gray level co-occurrence matrix is ​​the frequency of occurrence of the reflectivity combination of every two adjacent pixels in each spectral data cube; the spectral similarity is the similarity of the reflectivity between every two pixels in each spectral data cube.

[0052] Furthermore, the method for extracting spatial spectral feature data includes:

[0053] Input each spectral data cube into the trained feature extraction model in turn to extract the corresponding spatial spectral feature data; wherein the feature extraction model includes a spatial extraction model and a spectral extraction model, the spatial extraction model is used to extract the gray-level co-occurrence matrix from the spectral data cube, and the spectral extraction model is used to extract the spectral similarity from the spectral data cube;

[0054] The training process of the spectral extraction model includes:

[0055] Collect b groups of spectral data cubes in advance, set corresponding spectral similarities for all b groups of spectral data cubes, b is an integer greater than 1, and convert the spectral data cubes and the corresponding spectral similarities into a corresponding set of feature vectors; use each set of feature vectors as input to a spectral extraction model, the spectral extraction model uses a set of predicted spectral similarities corresponding to each group of spectral data cubes as output, and uses the actual spectral similarities corresponding to each group of spectral data cubes as a prediction target, the actual spectral similarity is the pre-set spectral similarity corresponding to the spectral data cube; minimize the sum of prediction errors of all spectral data cubes as a training target; train the spectral extraction model until the sum of prediction errors converges and stops training; the spectral extraction model is a deep neural network model; the training process of the spatial extraction model is consistent with the training process of the spectral extraction model, and both are deep neural network models.

[0056] Furthermore, the method for extracting difference data from each hyperspectral data includes:

[0057] An autoencoder is introduced to compress the spectral information of hyperspectral data, compress the redundant spectral information in the hyperspectral data, and obtain spectral compressed data;

[0058] Obtain the reflectance corresponding to each wavelength in the spectral compression data, calculate the reflectance variance corresponding to each wavelength and the reflectance covariance between every two wavelengths;

[0059] The calculated reflectance variance and reflectance covariance are integrated into a variance matrix; the expression of the variance matrix Σ is: In the formula, is the reflectivity variance of the mth wavelength, Cov(a m ,a2) is the reflectivity covariance between the mth wavelength and the second wavelength;

[0060] The variance matrix is ​​transformed nonlinearly using a nonlinear function to obtain difference data.

[0061] Furthermore, the method for calculating the reflectivity variance corresponding to each wavelength includes:

[0062] Count the number of reflectances corresponding to a wavelength, add the reflectances corresponding to each wavelength in turn, and then divide by the number of reflectances to obtain the mean reflectance corresponding to each wavelength; subtract the corresponding mean reflectance from each reflectance, and square it to obtain the reflectance difference corresponding to each reflectance; subtract one from the number of reflectances to obtain the calculated number; add the reflectance differences corresponding to each wavelength in turn, and then divide by the calculated number to obtain the reflectance variance corresponding to each wavelength;

[0063] The method for calculating the reflectivity covariance between each two wavelengths includes:

[0064] Mark one of the wavelengths as the first wavelength, and mark the other wavelength as the second wavelength; mark the reflectivity corresponding to the first wavelength as the first reflectivity, and mark the reflectivity corresponding to the second wavelength as the second reflectivity; number each first reflectivity incrementally, and number each second reflectivity incrementally, wherein the starting number corresponding to the first reflectivity is consistent with the starting number corresponding to the second reflectivity, and the starting number is the first number when the incremental numbering is performed; subtract the corresponding reflectivity mean from each first reflectivity to obtain the first difference; subtract the corresponding reflectivity mean from each second reflectivity to obtain the second difference; multiply the first difference and the second difference with the same corresponding number to obtain the difference product; add each difference product in turn, and then divide it by the calculated number to obtain the reflectivity covariance between the first wavelength and the second wavelength.

[0065] Technical effects and advantages of the hyperspectral remote sensing abnormal small target detection method based on multi-aperture spectral information fusion of the present invention:

[0066] The target area is subdivided, and the hyperspectral data of each target sub-area is collected. The hyperspectral data is converted into a spectral data cube. Combined with the extracted spatial spectral features and difference data, the variational autoencoder and LSTM neural network are used for model training, and the model parameters are adjusted to achieve small target anomaly detection; the robustness of anomaly detection under spectral aliasing interference is enhanced through block processing of hyperspectral data and multi-aperture information fusion; and deep learning technology is introduced to enhance the system's anomaly detection capability, especially adaptive feature learning and redundant compression of complex spectral data, to achieve higher detection accuracy and lower false alarm rate; at the same time, the LSTM neural network is integrated to improve the processing capability of dynamic targets; in addition, the clonal selection algorithm is used to adjust the model parameters to simulate the adaptive sensitivity adjustment of biological neurons, which further ensures the accuracy and robustness of the anomaly detection results. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is a flow chart of a method for detecting abnormal small targets in hyperspectral remote sensing using multi-aperture spectral information fusion according to Example 1 of the present invention;

[0068] Figure 2 This is a flow chart of the model parameter adjustment steps of Example 1 of the present invention;

[0069] Figure 3 Flow chart of the method for calculating reflectivity variance in Embodiment 1 of the present invention;

[0070] Figure 4 This is a flow chart of a method for calculating reflectivity covariance according to Embodiment 1 of the present invention. DETAILED DESCRIPTION

[0071] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0072] Example 1

[0073] See also Figure 1 As shown, the hyperspectral remote sensing abnormal small target detection method using multi-aperture spectral information fusion described in this embodiment includes:

[0074] S1: Divide the target area into n target sub-areas.

[0075] The method for dividing the n target sub-regions is as follows: the target region is divided into grids according to a preset grid size, and the divided grids correspond to the target sub-regions one by one; the grid size is preset by a technician in this field according to the actual situation of the target region.

[0076] S2: Collect hyperspectral data for each target sub-area.

[0077] Hyperspectral data includes spectral information and spatial information; spectral information is the reflectance of each pixel in the target sub-area at each wavelength, and hyperspectral data usually covers multiple bands from visible light to near infrared, short-wave infrared and even mid-infrared; spatial information is the geographic location coordinates of the target sub-area corresponding to each pixel in the hyperspectral data; hyperspectral data is acquired by the hyperspectral remote sensing data acquisition chip in the hyperspectral sensing equipment; hyperspectral sensing equipment includes spacecraft, satellites, drones, etc.

[0078] It should be understood that collecting hyperspectral data of each target sub-region can effectively simulate the multi-aperture information acquisition mode of the fly visual system and provide an accurate characterization of the properties of the target sub-region.

[0079] S3: Convert each hyperspectral data into a spectral data cube and extract spatial spectral feature data.

[0080] The spectral data cube is a three-dimensional data structure, which corresponds to the hyperspectral data one by one. The spectral data cube includes width, height and depth. The width corresponds to the number of pixels in the horizontal direction in the hyperspectral data. The height corresponds to the number of pixels in the vertical direction in the hyperspectral data. The depth corresponds to the spectral information in the hyperspectral data. The spatial spectral feature data includes gray-level co-occurrence matrix and spectral similarity. The gray-level co-occurrence matrix is ​​the frequency of occurrence of the reflectance combination of each two adjacent pixels in each spectral data cube. The spectral similarity is the similarity of the reflectance between each two pixels in each spectral data cube.

[0081] Methods for extracting spatial spectral feature data include:

[0082] Each spectral data cube is input into the trained feature extraction model in turn to extract the corresponding spatial spectral feature data; wherein the feature extraction model includes a spatial extraction model and a spectral extraction model, the spatial extraction model is used to extract the gray-level co-occurrence matrix from the spectral data cube, and the spectral extraction model is used to extract the spectral similarity from the spectral data cube.

[0083] The training process of the spectral extraction model includes:

[0084] Collect b groups of spectral data cubes in advance, set corresponding spectral similarities for the b groups of spectral data cubes, b is an integer greater than 1, and convert the spectral data cubes and the corresponding spectral similarities into a corresponding set of feature vectors; the spectral similarities corresponding to the spectral data cubes are collected by those skilled in the art in the process of extracting historical spatial spectral feature data, and the corresponding spectral similarities are extracted from each group of spectral data cubes in turn according to actual experience; and the corresponding spectral similarities are set for the b groups of spectral data cubes in turn;

[0085] Each group of feature vectors is used as the input of the spectral extraction model. The spectral extraction model uses a group of predicted spectral similarities corresponding to each group of spectral data cubes as output, and uses the actual spectral similarity corresponding to each group of spectral data cubes as the prediction target. The actual spectral similarity is the pre-set spectral similarity corresponding to the spectral data cube; minimizing the sum of the prediction errors of all spectral data cubes is used as the training target; wherein the calculation formula of the prediction error is η K =(β K -ε K ) 2 , where η K is the prediction error, K is the group number of the eigenvector corresponding to the spectral data cube, β K is the predicted spectral similarity corresponding to the Kth group of spectral data cubes, ε Kis the actual spectral similarity corresponding to the Kth group of spectral data cubes; the spectral extraction model is trained until the sum of the prediction errors reaches convergence and the training is stopped.

[0086] The above-mentioned spectral extraction model is specifically a deep neural network model; it includes an input layer, a hidden layer and an output layer; each hidden layer includes multiple neurons, each neuron is connected to the neurons in the next layer, and the connection contains weights, which determine the importance and influence of data transmission in the neural network; an activation function is applied to each neuron between the hidden layer and the output layer, and the activation function introduces nonlinearity, allowing the network to learn more complex patterns and features.

[0087] The training process of the spatial extraction model is consistent with that of the spectral extraction model, and both are deep neural network models.

[0088] It should be noted that the purpose of extracting spatial spectral feature data is to: enhance target recognition capability: spatial spectral features can effectively capture the shape, texture and other features of the target; help to more accurately identify and locate small targets in complex backgrounds; reduce background interference: by extracting spatial features, the impact of background noise can be reduced and the robustness of target anomaly detection can be improved; improve classification performance: the gray level co-occurrence matrix (GLCM) can provide texture features of target sub-regions, which vary significantly in different types of ground objects, and spectral similarity can measure spectral differences to help more accurate classification; realize multi-scale analysis: the extraction of spatial features can be analyzed at different scales, thereby capturing different features of small targets and improving the detection capability of small targets.

[0089] S4: Extract difference data from each hyperspectral data.

[0090] Methods for extracting difference data from each hyperspectral data include:

[0091] An autoencoder is introduced to compress the spectral information of hyperspectral data, compress the redundant spectral information in the hyperspectral data, and obtain spectral compressed data; the autoencoder can learn the important features in high-dimensional spectral data under unsupervised conditions, improve the accuracy and efficiency of difference data extraction, and suppress spectral aliasing interference; the autoencoder is an existing technology and will not be described in detail here.

[0092] Obtain the reflectance corresponding to each wavelength in the spectral compression data, calculate the reflectance variance corresponding to each wavelength and the reflectance covariance between every two wavelengths.

[0093] See also Figure 3 As shown, the method for calculating the reflectance variance corresponding to each wavelength includes:

[0094] Count the number of reflectances corresponding to a wavelength, add the reflectances corresponding to each wavelength in turn, and then divide by the number of reflectances to obtain the mean reflectance corresponding to each wavelength; subtract the corresponding mean reflectance from each reflectance and square it to obtain the reflectance difference corresponding to each reflectance; subtract one from the number of reflectances to obtain the calculated number; add the reflectance differences corresponding to each wavelength in turn, and then divide by the calculated number to obtain the reflectance variance corresponding to each wavelength.

[0095] See also Figure 4 As shown, the method for calculating the reflectivity covariance between each two wavelengths includes:

[0096] Mark one of the wavelengths as the first wavelength, and mark the other wavelength as the second wavelength; mark the reflectivity corresponding to the first wavelength as the first reflectivity, and mark the reflectivity corresponding to the second wavelength as the second reflectivity; number each first reflectivity incrementally, and number each second reflectivity incrementally, wherein the starting number corresponding to the first reflectivity is consistent with the starting number corresponding to the second reflectivity, and the starting number is the first number when the incremental numbering is performed; subtract the corresponding reflectivity mean from each first reflectivity to obtain the first difference; subtract the corresponding reflectivity mean from each second reflectivity to obtain the second difference; multiply the first difference and the second difference with the same corresponding number to obtain the difference product; add each difference product in turn, and then divide it by the calculated number to obtain the reflectivity covariance between the first wavelength and the second wavelength.

[0097] The calculated reflectance variance and reflectance covariance are integrated into a variance matrix; the expression of the variance matrix Σ is: In the formula, is the reflectivity variance of the mth wavelength, Cov(a m ,a2) is the reflectivity covariance between the mth wavelength and the second wavelength;

[0098] Nonlinear functions (such as Sigmoid, ReLU (Rectified Linear Unit), Tanh, etc.) are used to perform nonlinear transformation on the variance matrix to obtain difference data.

[0099] S5: Perform anomaly detection based on the spatial spectral feature data and the difference data.

[0100] Methods for performing anomaly detection include:

[0101] The spatial spectral feature data and difference data of historical calculations are obtained and marked as historical data. Based on the historical data, the model parameters are adjusted and the anomaly detection model is trained. The anomaly detection model is based on a variational autoencoder and integrated with an LSTM. Both the variational autoencoder and the LSTM are existing technologies, so the training process of the anomaly detection model is also existing technology and will not be described in detail here. The model parameters include a learning rate, a forget gate weight, a weight matrix, a bias term and a time step. The weight matrix includes an input gate weight matrix and an output gate weight matrix, and the bias term includes an input gate bias term and an output gate bias term.

[0102] It should be noted that adjusting the model parameters can simulate the fast charging and slow discharging mechanism of biological neurons, improve the response speed to abnormal signals, and delay forgetting of weak signals. By adjusting the model parameters, the model can quickly capture anomalies when the signal strength changes, and gradually fade weaker or noisy signals, which is similar to the adaptive adjustment process of biological neurons in response to signals of different intensities and durations.

[0103] The spatial spectral feature data and difference data corresponding to each target sub-region are respectively input into the trained anomaly detection model, and a detection label is output. The detection label is a digital label corresponding to the detection result. The detection result includes normal detection and abnormal detection, which is used for anomaly detection.

[0104] like Figure 2 As shown, the steps of adjusting the model parameters include:

[0105] Step 1: Construct M parameter sets, set different numerical labels for different parameter sets, and mark them as parameter labels, where M is an integer greater than 1;

[0106] Step 2: Randomly generate an initial antibody group, where the antibodies in the initial antibody group correspond one to one with the parameter labels;

[0107] Step 3: Determine the fitness function;

[0108] Step 4: Calculate the fitness of each antibody in the initial antibody group, and perform antibody screening to generate a memory antibody group;

[0109] Step 5: Calculate the corresponding clone size for each antibody in the memory antibody group, and clone it to generate a clone antibody group;

[0110] Step 6: Calculate the selection probability of each antibody in the cloned antibody group, and determine whether to select the antibody based on the selection probability to generate a selected antibody group;

[0111] Step 7: Perform cloud adaptive mutation on each antibody in the selected antibody group using a cloud adaptive mutation operator to generate a mutant antibody group; cloud adaptive mutation is an existing technology and will not be described in detail here;

[0112] Step 8: Using an interpolation method to generate new antibodies for the antibodies in the variant antibody group to generate an interpolated antibody group;

[0113] Step 9: Recombining the antibodies in the variant antibody group to generate a recombinant antibody group;

[0114] Step 10: merging the interpolated antibody group and the recombinant antibody group to generate a merged antibody group;

[0115] Step 11: Determine whether the iteration is finished; if so, calculate the fitness of each antibody in the combined antibody group, and obtain the parameter set corresponding to the parameter label of the antibody with the largest fitness; if not, perform antibody screening on the combined antibody group, regenerate the memory antibody group, and return to step 5.

[0116] In the above step 1, the parameter range corresponding to each parameter in the model parameters is obtained, a value is randomly selected from each parameter range, a parameter set is constructed, and a total of M parameter sets are constructed, and the M parameter sets are all different; the parameter range is obtained by technical personnel in this field according to actual conditions.

[0117] In the above step 2, the initial antibody group X(0) = {X1, X2, X3, ... X q}, X q is the qth antibody, that is, the size of the initial antibody population is q; the range of antibodies is M parameter sets; the number of iterations t of the initial antibody population is 0.

[0118] In the above step 3, the expression of the fitness function is: f=zq; where f is the fitness and zq is the accuracy; the method for obtaining the accuracy is: taking the parameter set corresponding to the antibody and the historical data as analysis data, inputting the analysis data into the trained accurate prediction model, and predicting the corresponding accuracy; the training process of the accurate prediction model is consistent with the training process of the anomaly detection model, and both are deep neural network models.

[0119] In the above step 4, the method of antibody screening is: h antibodies with the largest fitness are screened out from the initial antibody group, q>h>1.

[0120] In the above step 5, the method for calculating the clone size includes:

[0121]

[0122] Φ i =min(exp(||X i -Xj ||));

[0123] In the formula, R i is the clone size of the i-th antibody, Int is the upward rounding function, q is the initial antibody population size, Φ i is the affinity of the ith antibody, f i is the fitness of the ith antibody, min is the minimum function, exp is the natural exponential function, ||X i -X j || is the Euclidean distance between the i-th antibody and the j-th antibody, i≠j, j∈[1,q].

[0124] It should be noted that when calculating the Euclidean distance between the ith antibody and the jth antibody, normalization is performed so that 0≤||X i -X j ||≤1.

[0125] In the above step 6, the method for generating the selected antibody group comprises:

[0126] Calculate the fitness of each antibody in the cloned antibody group, and add them up in sequence to obtain the total antibody fitness, divide the fitness of each antibody by the total antibody fitness, and obtain the selection probability of each antibody; sort the selection probability of each antibody from large to small, and replace each selection probability in order according to the positive order with the sum of each selection probability and all selection probabilities before the corresponding selection probability; obtain all selection probabilities after replacement and mark them as replacement probabilities; the antibody corresponding to the replacement probability is consistent with the antibody corresponding to the selection probability before replacement; regard every two adjacent replacement probabilities as an analysis set according to the positive order; mark the replacement probability with the largest value in each analysis set as the first probability , mark the replacement probability with a smaller value as the second probability; construct the probability screening range corresponding to each analysis set according to the first probability and the second probability of each analysis set, wherein the first probability is the maximum value of the probability screening range, the second probability is the minimum value of the probability screening range, and the minimum value is an open interval, and the maximum value is a closed interval; each analysis set corresponds to the antibody corresponding to the second probability; wherein the minimum value of the probability screening range corresponding to the first antibody is 0, and the maximum value is the corresponding selection probability; randomly generate h random numbers between (0, 1], select the antibody corresponding to the probability screening range where the h random numbers are located, and generate a selected antibody group.

[0127] Exemplarily, the selection probabilities of the three antibodies are 0.5, 0.3, and 0.2, respectively; since there is no value before 0.5, 0.5 is still 0.5 after replacement; since 0.3 is preceded by 0.5, 0.3 is replaced by 0.3+0.5=0.8, and since 0.2 is preceded by 0.3 and 0.5, 0.2 is replaced by 0.2+0.3+0.5=1; therefore, the replacement probabilities are 0.5, 0.8, and 1, respectively; 0.5 and 0.8 are an analysis set, and the probability screening range corresponding to the second antibody is (0.5,0.8]; 0.8 and 1 are also an analysis set, and the probability screening range corresponding to the third antibody is (0.8,1]; the probability screening range corresponding to the first antibody is (0,0.5]; if the randomly generated random number is 0.7, since 0.7 is within (0.5,0.8], the second antibody is selected.

[0128] In the above step 8, the method for generating the interpolated antibody group includes:

[0129] Calculate the fitness of each antibody in the variant antibody group, and sort them from large to small to generate a sorting table; select half of the antibodies in the variant antibody group in positive order according to the sorting table, and mark them as screening antibodies; use the interpolation method to generate new antibodies for every two adjacent screening antibodies; calculate the fitness corresponding to each new antibody, and add it to the sorting table, retain the antibodies corresponding to the first y fitnesses in the sorting table, and generate an interpolated antibody group, where y is the number of antibodies in the variant antibody group.

[0130] The expression of the new antibody is: X X =(1-α′)X′+α′X″; where X X is a new antibody, X′ and X″ are two adjacent screened antibodies, α′ is the interpolation coefficient, and α′ is a random number between [0, 1].

[0131] In the above step 9, the method for antibody recombination comprises:

[0132] Randomly select Y antibodies from the mutant antibody group as parent antibodies for antibody recombination to generate progeny antibodies S c , until the number of unselected antibodies in the variant antibody group is less than Y, the antibody recombination is completed; in this embodiment, Y is preferably 3; the recombinant antibody group includes multiple progeny antibodies S c .

[0133] Progeny antibody S c The calculation methods include:

[0134]

[0135] In the formula, X′ Y is the Yth parent antibody, S Yis the Yth scaling factor, which is a randomly generated real number and not all Y scaling factors are 0.

[0136] In the above step 11, the method for determining whether the iteration is finished includes:

[0137] Preset the iteration threshold, which is preset by those skilled in the art according to the algorithm accuracy;

[0138] Compare the number of iterations t with the iteration threshold;

[0139] If the number of iterations t is greater than or equal to the iteration threshold, the iteration ends;

[0140] If the number of iterations t is less than the iteration threshold, the iteration continues.

[0141] It should be understood that adjusting the model parameters can make the model parameters quickly approach the optimal state, improve the response speed to abnormal signals, and realize the fast polarization mechanism; at the same time, the use of LSTM neural network can selectively forget the input signal, and the response of weak signals will be delayed and eliminated, realizing the slow depolarization mechanism, avoiding long-term response to weak abnormal signals; that is, by simulating the fast charging and slow discharging mechanism of biological neurons, the response speed to abnormal signals is improved, and weak signals are delayed and forgotten.

[0142] This embodiment subdivides the target area, collects hyperspectral data of each target sub-area, and converts the hyperspectral data into a spectral data cube. Combined with the extracted spatial spectral features and difference data, a variational autoencoder and an LSTM neural network are used for model training, and the model parameters are adjusted to achieve small target anomaly detection; the robustness of anomaly detection under spectral aliasing interference is enhanced through block processing of hyperspectral data and multi-aperture information fusion; and deep learning technology is introduced to enhance the anomaly detection capability of the system, especially adaptive feature learning and redundant compression of complex spectral data, to achieve higher detection accuracy and lower false alarm rate; at the same time, an LSTM neural network is integrated to improve the processing capability of dynamic targets; in addition, a clonal selection algorithm is used to adjust the model parameters to simulate the adaptive sensitivity adjustment of biological neurons, which further ensures the accuracy and robustness of the anomaly detection results.

[0143] Example 2

[0144] The present application also provides an electronic device. The electronic device may include one or more processors and one or more memories. The memories store computer-readable codes, and when the computer-readable codes are executed by the one or more processors, the hyperspectral remote sensing abnormal small target detection method using multi-aperture spectral information fusion as described above may be executed.

[0145] The method or system according to the implementation manner of the present application can also be implemented with the aid of the architecture of an electronic device. The electronic device may include a bus, one or more CPUs, ROM, RAM, a communication port connected to a network, input / output, a hard disk, etc. A storage device in the electronic device, such as a ROM or a hard disk, can store the hyperspectral remote sensing abnormal small target detection method with multi-aperture spectral information fusion provided in the present application. Furthermore, the electronic device may also include a user interface. Of course, the architecture shown is only exemplary. When implementing different devices, one or more components in the electronic device shown may be omitted according to actual needs.

[0146] Example 3

[0147] One embodiment of the present application discloses a computer-readable storage medium. Computer-readable instructions are stored on the computer-readable storage medium. When the computer-readable instructions are executed by a processor, the hyperspectral remote sensing abnormal small target detection method based on multi-aperture spectral information fusion according to the embodiment of the present application described with reference to the above figures can be executed. The storage medium includes, but is not limited to, for example, volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and cache memory (cache), etc. Non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.

[0148] In addition, according to the implementation of the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the present application provides a non-transitory machine-readable storage medium, which stores machine-readable instructions, and the machine-readable instructions can be executed by a processor to execute instructions corresponding to the method steps provided in the present application, for example: a hyperspectral remote sensing abnormal small target detection method with multi-aperture spectral information fusion. When the computer program is executed by a central processing unit (CPU), the above functions defined in the method of the present application are executed.

[0149] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

[0150] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information, characterized in that: include: S1: Divide the target area into n target sub-areas; S2: Collect hyperspectral data of each target sub-area; S3: Convert each hyperspectral data into a spectral data cube and extract spatial spectral feature data; S4: extracting difference data from each hyperspectral data; S5: Perform anomaly detection based on the spatial spectral feature data and the difference data.

2. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 1 is characterized in that: The method for performing anomaly detection comprises: Obtain historically calculated spatial spectral feature data and difference data and mark them as historical data; based on historical data, adjust model parameters and train anomaly detection model; the anomaly detection model is based on variational autoencoder and integrates LSTM; model parameters include learning rate, forget gate weight, weight matrix, bias term and time step; weight matrix includes input gate weight matrix and output gate weight matrix, and bias term includes input gate bias term and output gate bias term; The spatial spectral feature data and difference data corresponding to each target sub-region are respectively input into the trained anomaly detection model, and the detection label is output. The detection label is a digital label corresponding to the detection result, and the detection result includes normal detection and abnormal detection.

3. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 2 is characterized in that: The step of adjusting the model parameters comprises: Step 1: Construct M parameter sets, set different numerical labels for different parameter sets, and mark them as parameter labels, where M is an integer greater than 1; Step 2: Randomly generate an initial antibody group, where the antibodies in the initial antibody group correspond one to one with the parameter labels; Step 3: Determine the fitness function; Step 4: Calculate the fitness of each antibody in the initial antibody group, and perform antibody screening to generate a memory antibody group; Step 5: Calculate the corresponding clone size for each antibody in the memory antibody group, and clone it to generate a clone antibody group; Step 6: Calculate the selection probability of each antibody in the cloned antibody group, and determine whether to select the antibody based on the selection probability to generate a selected antibody group; Step 7: Perform cloud adaptive mutation on each antibody in the selected antibody group using a cloud adaptive mutation operator to generate a mutant antibody group; Step 8: Using an interpolation method to generate new antibodies for the antibodies in the variant antibody group to generate an interpolated antibody group; Step 9: Recombining the antibodies in the variant antibody group to generate a recombinant antibody group; Step 10: merging the interpolated antibody group and the recombinant antibody group to generate a merged antibody group; Step 11: Determine whether the iteration is finished; if so, calculate the fitness of each antibody in the combined antibody group, and obtain the parameter set corresponding to the parameter label of the antibody with the largest fitness; if not, perform antibody screening on the combined antibody group, regenerate the memory antibody group, and return to step 5.

4. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 3 is characterized in that: In the step 1, a parameter range corresponding to each parameter in the model parameters is obtained, a value is randomly selected from each parameter range, a parameter set is constructed, and a total of M parameter sets are constructed, and the M parameter sets are all different; In step 2, the initial antibody group X ( 0 ) ={X1,X2,X3,…Xq}, X q is the qth antibody, that is, the size of the initial antibody population is q; the range of antibodies is M parameter sets; the number of iterations t of the initial antibody population is 0; In step 3, the fitness function is expressed as: f=zq; wherein f is the fitness and zq is the accuracy; the accuracy is obtained by using the parameter set and historical data corresponding to the antibody as analysis data, inputting the analysis data into the trained accurate prediction model, and predicting the corresponding accuracy; the training process of the accurate prediction model is consistent with the training process of the anomaly detection model, and both are deep neural network models; In step 5, the method for calculating the clone size includes: F i =min(exp(X i -X j )); In the formula, R i is the clone size of the i-th antibody, Int is the upward rounding function, q is the initial antibody population size, Φ i is the affinity of the ith antibody, f i is the fitness of the ith antibody, min is the minimum function, exp is the natural exponential function, X i -X j is the Euclidean distance between the i-th antibody and the j-th antibody, i≠j, j∈[1,q].

5. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 4 is characterized in that: In step 4, the method of antibody screening is: screening out h antibodies with the largest fitness from the initial antibody group, q>h>1; In step 6, the method for generating the selected antibody group comprises: Calculate the fitness of each antibody in the cloned antibody group, and add them up in sequence to obtain the total antibody fitness, divide the fitness of each antibody by the total antibody fitness, and obtain the selection probability of each antibody; sort the selection probability of each antibody from large to small, and replace each selection probability in order according to the positive order with the sum of each selection probability and all selection probabilities before the corresponding selection probability; obtain all selection probabilities after replacement and mark them as replacement probabilities; the antibody corresponding to the replacement probability is consistent with the antibody corresponding to the selection probability before replacement; regard every two adjacent replacement probabilities as an analysis set according to the positive order; mark the replacement probability with the largest value in each analysis set as the first probability , mark the replacement probability with a smaller value as the second probability; construct the probability screening range corresponding to each analysis set according to the first probability and the second probability of each analysis set, wherein the first probability is the maximum value of the probability screening range, the second probability is the minimum value of the probability screening range, and the minimum value is an open interval, and the maximum value is a closed interval; each analysis set corresponds to the antibody corresponding to the second probability; wherein the minimum value of the probability screening range corresponding to the first antibody is 0, and the maximum value is the corresponding selection probability; randomly generate h random numbers between (0, 1], select the antibody corresponding to the probability screening range where the h random numbers are located, and generate a selected antibody group.

6. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 5, characterized in that: In step 8, the method for generating the interpolated antibody group includes: Calculate the fitness of each antibody in the variant antibody group, and sort them from large to small to generate a sorting table; select half of the antibodies in the variant antibody group in positive order according to the sorting table, and mark them as screening antibodies; use the interpolation method to generate new antibodies for every two adjacent screening antibodies; calculate the fitness corresponding to each new antibody, and add it to the sorting table, retain the antibodies corresponding to the first y fitness in the sorting table, and generate an interpolated antibody group, where y is the number of antibodies in the variant antibody group; The expression of the new antibody is: X X =(1-α′)X′+α′X″; where X X is a new antibody, X′ and X″ are two adjacent screening antibodies, α′ is an interpolation coefficient, and α′ is a random number between [0, 1]; In step 9, the method for antibody recombination comprises: Randomly select Y antibodies from the mutant antibody group as parent antibodies for antibody recombination to generate progeny antibodies S c , until the number of unselected antibodies in the variant antibody group is less than Y, the antibody recombination is completed; the recombinant antibody group includes multiple progeny antibodies S c ; Progeny antibody S c The calculation methods include: In the formula, X′ Y is the Yth parent antibody, S Y is the Yth scale factor, the scale factor is a randomly generated real number and not all Y scale factors are 0; In step 11, the method for determining whether the iteration is completed includes: Preset an iteration threshold, and compare the number of iterations t with the iteration threshold; If the number of iterations t is greater than or equal to the iteration threshold, the iteration ends; If the number of iterations t is less than the iteration threshold, the iteration continues.

7. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 6 is characterized in that: The method for dividing the n target sub-regions is as follows: dividing the target region into grids according to a preset grid size, and the divided grids correspond to the target sub-regions one by one; The hyperspectral data includes spectral information and spatial information; The spectral information is the reflectivity of each pixel in the target sub-area at each wavelength; The spatial information is the geographical location coordinates of the target sub-region corresponding to each pixel in the hyperspectral data; The spectral data cube is a three-dimensional data structure, corresponding to the hyperspectral data one by one; the spectral data cube includes width, height and depth; the width is the number of pixels in the horizontal direction in the corresponding hyperspectral data; The height is the number of pixels in the vertical direction of the corresponding hyperspectral data; the depth is the spectral information in the corresponding hyperspectral data; the spatial spectral feature data includes the gray level co-occurrence matrix and the spectral similarity; the gray level co-occurrence matrix is ​​the frequency of the reflectance combination of each two adjacent pixels in each spectral data cube; Spectral similarity is the similarity of the reflectance between every two pixels in each spectral data cube.

8. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 7, characterized in that: The method for extracting spatial spectrum feature data comprises: Input each spectral data cube into the trained feature extraction model in turn to extract the corresponding spatial spectral feature data; wherein the feature extraction model includes a spatial extraction model and a spectral extraction model, the spatial extraction model is used to extract the gray-level co-occurrence matrix from the spectral data cube, and the spectral extraction model is used to extract the spectral similarity from the spectral data cube; The training process of the spectral extraction model includes: Collect b groups of spectral data cubes in advance, set corresponding spectral similarities for all b groups of spectral data cubes, b is an integer greater than 1, and convert the spectral data cubes and the corresponding spectral similarities into a corresponding set of feature vectors; use each set of feature vectors as input to a spectral extraction model, the spectral extraction model uses a set of predicted spectral similarities corresponding to each group of spectral data cubes as output, and uses the actual spectral similarities corresponding to each group of spectral data cubes as a prediction target, the actual spectral similarity is the pre-set spectral similarity corresponding to the spectral data cube; minimize the sum of prediction errors of all spectral data cubes as a training target; train the spectral extraction model until the sum of prediction errors converges and stops training; the spectral extraction model is a deep neural network model; the training process of the spatial extraction model is consistent with the training process of the spectral extraction model, and both are deep neural network models.

9. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 8, characterized in that: The method for extracting difference data from each hyperspectral data comprises: An autoencoder is introduced to compress the spectral information of hyperspectral data, compress the redundant spectral information in the hyperspectral data, and obtain spectral compressed data; Obtain the reflectance corresponding to each wavelength in the spectral compression data, calculate the reflectance variance corresponding to each wavelength and the reflectance covariance between every two wavelengths; The calculated reflectance variance and reflectance covariance are integrated into a variance matrix; the expression of the variance matrix Σ is: In the formula, is the reflectivity variance of the mth wavelength, Cov(a m ,a2) is the reflectivity covariance between the mth wavelength and the second wavelength; The variance matrix is ​​transformed nonlinearly using a nonlinear function to obtain difference data.

10. The method for detecting abnormal small targets in hyperspectral remote sensing by fusion of multi-aperture spectral information according to claim 9, characterized in that: The method for calculating the reflectivity variance corresponding to each wavelength includes: Count the number of reflectances corresponding to a wavelength, add the reflectances corresponding to each wavelength in turn, and then divide by the number of reflectances to obtain the mean reflectance corresponding to each wavelength; subtract the corresponding mean reflectance from each reflectance, and square it to obtain the reflectance difference corresponding to each reflectance; subtract one from the number of reflectances to obtain the calculated number; add the reflectance differences corresponding to each wavelength in turn, and then divide by the calculated number to obtain the reflectance variance corresponding to each wavelength; The method for calculating the reflectivity covariance between each two wavelengths includes: Mark one of the wavelengths as the first wavelength, and mark the other wavelength as the second wavelength; mark the reflectivity corresponding to the first wavelength as the first reflectivity, and mark the reflectivity corresponding to the second wavelength as the second reflectivity; number each first reflectivity incrementally, and number each second reflectivity incrementally, wherein the starting number corresponding to the first reflectivity is consistent with the starting number corresponding to the second reflectivity, and the starting number is the first number when the incremental numbering is performed; subtract the corresponding reflectivity mean from each first reflectivity to obtain the first difference; subtract the corresponding reflectivity mean from each second reflectivity to obtain the second difference; multiply the first difference and the second difference with the same corresponding number to obtain the difference product; add each difference product in turn, and then divide it by the calculated number to obtain the reflectivity covariance between the first wavelength and the second wavelength.

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