Hyperspectral unmixing method based on learnable implicit variable iterative unfolding network

Abstract

The application discloses a hyperspectral sparse unmixing method of a learnable implicit variable iterative unfolding network, and comprises the following steps: constructing an unmixing model by sparse constraint optimization; constructing an alternating direction iteration by variable splitting and an augmented Lagrangian method; modeling an alternating direction iteration step as an implicit unfolding network module, including a learnable layer of abundance variable and multiplier variable; constructing a learnable smooth convolution layer to improve the smoothness of abundance patches; realizing spectral unmixing and reconstruction by a coding-decoding structure; and realizing model training by adopting an unsupervised loss function. The application uses the optimization mechanism of a classical sparse unmixing model to design a learnable network, the network layer is designed based on algorithm iteration steps, the sparsity and patch smoothness of hyperspectral abundance are fully met, and the explainability and transparency are enhanced; an unsupervised training mechanism is introduced, the network availability is enhanced; the model parameter size and overfitting phenomenon are reduced through model driving and network parameter sharing, and the model is lightened.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing hyperspectral image processing technology, specifically relating to a hyperspectral sparse unmixing method using a learnable implicit variable iterative expansion network. Background Technology

[0002] Hyperspectral remote sensing images are obtained by continuously sensing ground features using a narrow, continuous spectral channel. Their spectral (electromagnetic spectrum) resolution spans the visible, near-infrared, mid-infrared, and thermal infrared bands, with accuracy down to the nanometer (nm) level. They are characterized by multiple bands, continuity between spectral channels, and "image-spectrum integration." Any pixel in a hyperspectral remote sensing image represents an approximately continuous spectral curve, encompassing spatial, radiometric, and spectral information.

[0003] However, due to the large spatial resolution of hyperspectral remote sensing imagers and the complex and diverse distribution of actual ground features, many pixels in hyperspectral images are mixtures of spectra from various substances; these pixels are called mixed pixels. The existence of mixed pixels makes many pixel-based methods for substance classification and area measurement insufficient for practical applications. Hyperspectral image demixing technology is a recognition technique developed to address this problem. It involves quantitative analysis of spectral data, aiming to quickly and accurately obtain the various substances and their proportions (abundance coefficients) in mixed pixels by representing the observation data as a superposition of pure spectra (endmembers), thus acquiring specific information about the mixed pixels, such as... Figure 2 As shown.

[0004] Hyperspectral image unmixing has been widely used in fields such as medical imaging, geological exploration, and precision agriculture due to its role in promoting accurate identification and application in subsequent processes.

[0005] Currently, traditional iterative unmixing algorithms are divided into two main categories, based on whether a spectral library is required during the unmixing process: 1) Algorithms that do not require a spectral library are called blind source unmixing, such as the PPI algorithm researched by Joseph W. Boardman et al., the N-FINDR model proposed by MEWinte, and the VCA method researched by JMP Nascimento et al. 2) Algorithms that require a spectral library as an endmember dictionary are called semi-blind source separation methods, such as the SUnSAL algorithm created by Jos'e M. Bioucas-Dias and M'ario A.T. Figueiredo et al., and the collaborative (also known as "multi-task" or "simultaneous") sparse regression framework (CLSUnSAL) designed by Marian-Daniel Iordache et al. With the advancement of deep neural network technology, many scholars have also developed unmixing models based on autoencoders, such as the Deep Autoencoder (DAE) by Palsson B et al., and the SCNL model invented by Lin Qi.

[0006] Traditional iterative algorithms offer good interpretability and sound mathematical logic, but they often require hundreds or even thousands of iterations. Neural network models, on the other hand, are fast and perform well, but their interpretability is relatively low. Summary of the Invention

[0007] The purpose of this invention is to propose a hyperspectral sparse unmixing method for learnable implicit variable iterative expansion networks.

[0008] The technical solution to achieve the objective of this invention is as follows: Firstly, this invention provides a hyperspectral sparse unmixing method for learnable implicit variable iterative expansion networks, comprising the following steps:

[0009] Step 1: Process the raw hyperspectral data and spectral library to obtain model input; based on the sparsity characteristics of abundance, construct an unmixing model with sparsity constraints;

[0010] Step 2: Using variable splitting and augmented Lagrange methods, construct an alternating direction iterative solution form for the unmixed model;

[0011] Step 3: Model the alternating direction iteration step as a network module containing implicitly learnable parameters, which includes learnable layers for abundance variables and multiplier variables;

[0012] Step 4: Based on the piecewise smoothness of the spatial distribution of endmember abundance, construct a learnable convolutional smoothing layer and insert it into the learnable module to complete the iterative structure of the implicit unfolding network.

[0013] Step 5: Treat the spectral library as an encoder and the spectral demixing process as a decoding process, and re-encode the demixed abundance to achieve spectral reconstruction;

[0014] Step 6: Use unsupervised loss function to train the model: calculate the mean square error between the reconstructed spectrum and the input spectrum, the spectral angular distance, and the spectral information entropy loss function. Train the model through backpropagation to obtain the abundance of each endmember and the reconstructed spectrum under the optimal model parameters.

[0015] In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in the first aspect.

[0016] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0017] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in the first aspect.

[0018] Compared with existing technologies, the main features of this invention are: 1) strong interpretability, achieved by replacing some parameters in the traditional ADMM solution method with learnable parameters to construct the network core; 2) integration of spatial convolution, which involves adding spatial convolutional layers to the backbone network to introduce spatial information constraints; 3) lightweight, with network parameter sharing reducing model parameter size and overfitting, achieving rapid unmixing of lightweight models; and 4) unsupervised, meaning that this invention uses an unsupervised loss function to optimize parameters through backpropagation, thereby constructing a linear unmixing network model for mixed spectra. Experimental verification shows that this invention can achieve rapid and accurate unmixing of hyperspectral images, which is helpful for sub-pixel mineral composition analysis and can be widely applied to hyperspectral unmixing in land resources, mineral exploration, and precision agriculture.

[0019] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention—a hyperspectral sparse unmixing method for learnable implicit variable iterative expansion networks.

[0021] Figure 2 This is a schematic diagram of a hyperspectral linear unmixing model.

[0022] Figure 3 The result is the demixing result on analog data DC1 with a noise level of 40dB.

[0023] Figure 4Statistical graphs of three evaluation metrics for various algorithms on simulated data DC1.

[0024] Figure 5 The result is the demixing result on analog data DC2 with a noise level of 40dB.

[0025] Figure 6 This is a statistical chart showing the performance of various algorithms on the simulated data DC2 using three evaluation metrics.

[0026] Figure 7 This is the demixing result on the analog data DC3.

[0027] Figure 8 Statistical graphs of three evaluation metrics for various algorithms on simulated data DC3.

[0028] Figure 9 These are abundance maps obtained from the Cuprite dataset using different algorithms. Detailed Implementation

[0029] This invention addresses the hyperspectral unsupervised unmixing problem in fields such as land cover analysis, precision agriculture, environmental monitoring, disaster assessment, and mineral surveys. It proposes a hyperspectral sparse unmixing method using a learnable implicit variable iterative expansion network, such as... Figure 1 , Figure 2 As shown, the method includes the following steps:

[0030] Step 1, Sparse constraint optimization to construct unmixing model: Based on the sparsity characteristics of abundance, construct an unmixing model with sparsity constraints;

[0031] Step 2, constructing alternating direction iteration using variable splitting and augmented Lagrange method: Using variable splitting and augmented Lagrange method, construct the alternating direction iterative solution form of the unmixed model;

[0032] Step 3, Model the alternating direction iteration step as an implicitly expanded network module: Model the alternating direction iteration step as a network module containing implicitly learnable parameters, which includes learnable layers of abundance variables (×2) and multiplier variables (×1);

[0033] Step 4, Construct a learnable smooth convolutional layer: Based on the piecewise smoothness of the spatial distribution of endmember abundance, construct a learnable smooth convolutional layer and insert it into the learnable module to complete the iterative structure of the implicit unfolding network.

[0034] Step 5, encoding and decoding structure to realize spectral demixing and reconstruction: if the spectral library is regarded as an encoder, then the spectral demixing process can be regarded as a decoding process. Based on this characteristic, the demixed abundance is re-encoded to realize spectral reconstruction.

[0035] Step 6: Use unsupervised loss functions to train the model: Calculate the mean square error (MSE), spectral angular distance (SAD), and spectral information entropy (SID) loss functions between the reconstructed spectrum and the input spectrum. Train the model through backpropagation to obtain the unmixing abundance and reconstructed spectrum under the optimal model parameters.

[0036] The following is a detailed explanation of each step.

[0037] The first step is to construct a sparse constraint optimization model to resolve the unmixing problem:

[0038] (1) Processing raw hyperspectral data and spectral libraries to obtain model input

[0039] Raw hyperspectral image data Where B represents the number of hyperspectral bands, and L and W represent the width and height of the image spatial dimension, respectively. The original hyperspectral data... Pixel-by-pixel scanning sorts the pixels in the column direction to form a spectral pixel matrix Y = [y1, y2, ..., y]. i ,…,y N ]∈R B×P Where P = L × W represents the number of hyperspectral pixels, y i ∈R L Let represent the i-th spectral pixel, 1≤i≤P. Band matching is performed between the spectral library A and the hyperspectral data Y to ensure that their spectral dimensions are consistent.

[0040] (2) The general form of the linear model for hyperspectral unmixing is as follows:

[0041] Y = AX + N#(1)

[0042] Where Y∈R B×P Represents a hyperspectral data matrix, A∈R B×N Represents an end-member dictionary containing N end-members, X∈R N×P Represents the abundance matrix, N∈R B×P Represents noise.

[0043] By introducing sparsity and nonnegativity constraints, we obtain the optimization solution function for the model described in equation (1):

[0044]

[0045] In equation (2), λ>0 is the regularization parameter. Represents set R + The index function is: if X i,j ∈R + ,

[0046] The second step involves variable splitting and augmented Lagrange multiplication to construct alternating direction iterations:

[0047] To solve for the abundance variable X, we construct the Lagrangian function of equation (2):

[0048]

[0049] In the formula, Z = X is the auxiliary variable, α is the Lagrange multiplier, and ρ > 0 is the penalty factor. Z i，j Let X represent the element in the i-th row and j-th column of matrix Z, if X... i，j ∈S, ι S (X i，j ) = 0; ι S (X i，j ) = ∞.

[0050] Therefore, the alternating direction iteration format of equation (3) is:

[0051]

[0052] Where U = -α / ρ.

[0053] For the first iteration: According to the solution of the convex optimization problem, we can obtain:

[0054] X k+1 =(A T A+ρI) -1 [A T Y+ρ(Z k -U k )]#(5)

[0055] Second iteration: Solving using the soft thresholding algorithm, we have:

[0056] Z k+1 =max{0, soft(X)} k -Z k )}#(6)

[0057] Combining equations (5) and (6), the iterative form of alternating directions is obtained as follows:

[0058]

[0059] The third step involves modeling the alternating direction iteration steps as implicitly unfolded network modules:

[0060] For the first step of iteration X k+1 =(A T A+ρI) -1 [A T Y+ρ(Z k-U k To model this, let H = ρI, and set H and ρ as learnable parameters as the abundance variable layer 1, outputting the unconstrained abundance variable X. k+1 Specifically:

[0061] X k+1 =(A T A+H) -1 [A T Y+ρ(Z k -U k )]#(8)

[0062] Iteration step Z k+1 =max{0, soft(X)} k+1 -Z k Modeling λ / ρ)} as

[0063] Z k+1 =ReLU(X) k+1 -Z k -θ)#(9)

[0064] Here, the parameter θ is a learnable parameter, which serves as the abundance variable layer 2, outputting the non-negative and sparse-constrained abundance variable Z. k +1 .

[0065] The third step of the iteration U k+1 =U k +ρ(X k+1 -Z k+1 In this process, the parameter ρ is set as a learnable parameter (hereinafter referred to as μ for easy distinction from the parameter ρ in the first step of the iteration) and used as a layer of multiplier variables to update the Lagrange multipliers.

[0066] U k+1 =U k +μ(X k+1 -Z k+1 )#(10)

[0067] The sparse model-driven implicit unfolding network module is now as follows:

[0068]

[0069] Step 4: Construct learnable smooth convolutional layers:

[0070] In terms of spatial distribution, the abundance of a single endmember has a one-sided smoothness characteristic. Based on this prior, a learnable convolutional layer is constructed and inserted between two abundance variable layers. First, the result of equation (8) is transformed in dimensionality: Then in three-dimensional data Performing a two-dimensional convolution operation on the endmember dimension yields the smooth constraint abundance tensor C.k+1 .

[0071]

[0072] The convolution kernel is initialized using a two-dimensional Gaussian filter, and the kernel weights are allowed to propagate backward.

[0073] The iterative structure of the sparse model-driven implicit unfolding network is now as follows:

[0074]

[0075] Step 5: The encoding / decoding structure enables spectral demixing and reconstruction.

[0076] The multiplier layer in the last iteration (13) is replaced with a normalization layer to complete the sparse model-driven implicit expansion network. If the process of obtaining the estimated abundance by processing the input spectrum through the sparse model-driven implicit expansion network is analogous to the decoding process, then the reconstructed spectrum can be obtained by recoding the endmember abundance using the spectral library A.

[0077]

[0078] Step 6: Use an unsupervised loss function to train the model.

[0079] Calculate the unsupervised loss function:

[0080] Loss=α1L MSE +α2L SAD +α3L SID #(15)

[0081] The backpropagation mechanism of deep learning is used to train the network parameters, and finally the unmixed abundance and reconstructed spectrum under the optimal model parameters are output.

[0082] in, It calculates the mean square error between the input image and the reconstructed image; It calculates the average spectral angular distance between the input image and the reconstructed image; It calculates the average spectral entropy between the input image and the reconstructed image. Y = [y1, y2, ..., y...] i ,…,y P ], Let α1, α2, and α3 represent the spectrum of a pixel in the input image and the spectrum of a pixel in the reconstructed image, respectively. α1, α2, and α3 are the weights of the three components.

[0083] In summary, this invention fully utilizes the geometric characteristics of the endmember spectral space of hyperspectral images, the sparsity of abundance, and the piecewise smoothness of the abundance of a single endmember in the spatial dimension; it cleverly integrates the abundance unification constraint and the non-negativity constraint into the network; it combines the interpretability of classical iterative algorithms with the backpropagation characteristics of deep neural networks, which greatly reduces the number of iterations and effectively improves the interpretability of the network; and the network parameters are shared for each iterative module, making the network lightweight and simple overall.

[0084] The effects of this invention can be further illustrated by the following simulation experiments:

[0085] Simulation conditions

[0086] This embodiment uses two types of data in the simulation experiment: simulated hyperspectral data and actual datasets.

[0087] (1) The spectral library used in the simulation experiment is the USGS spectral library A∈R released by the National Geological Survey in September 2007. 224×498 This spectral library contains 498 spectral data points, each containing 224 bands of information within the wavelength range of 0.4 μm to 2.5 μm. Due to excessively high correlation among some endmembers in the library, we pruned it, reducing the number of endmembers to 240, i.e., A∈R. 224×240 All experiments used the cropped spectral library A∈R. 224×240 conduct.

[0088] (2) The simulated data DC1 contains 224 bands and the image size is 75×75 pixels. The abundance map contains both pure regions and mixed regions. Each mixed region is the result of mixing 2 to 5 endmembers. The abundance scores of the 5 endmembers in the background pixels are randomly set to 0.1149, 0.0741, 0.2003, 0.2055 and 0.4051, respectively. The 5 endmembers are randomly selected from the spectral library and are: talc, actinolite, serpentine, ammonium feldspar and analcime.

[0089] (3) The simulated data DC2 aims to simulate the mineral distribution in the real environment. First, an abundance map is generated, and then five endmembers are randomly selected from the spectral library for linear mixing (potassium gypsum, microcline, vesuvianite, zinc montmorillonite, and sphericalite). The resulting dataset contains 224 bands, with an image size of 64×64 pixels, and does not contain any pure pixels.

[0090] (4) The simulated data DC3 was used to generate distribution maps of five minerals using the Gaussian Field Method, and these maps were used as the actual abundance distributions. The abundance map size for each mineral was 128×128, and then we randomly selected data from A∈R... 224 ×240Five different endmembers were selected from the spectral library (including: zeolite, hyaluronic acid, bubblyite, tremolite, and chromite), Gaussian noise with a signal-to-noise ratio of 40 was added, and a simulated dataset was generated in a linear mixing mode.

[0091] (5) The actual hyperspectral dataset is the well-known Cuprite dataset captured by the Visible Infrared Imaging Spectrometer (AVIRIS). The data used in the experiment is a portion of the Cuprite dataset, with a size of 250×191 pixels, containing 224 bands between 400 and 2500 nm, and a spectral resolution of 10 nm. Before this experiment, bands 1-2, 105-115, 150-170, and 223-224 were removed due to water vapor absorption and high noise levels, leaving 188 usable bands.

[0092] All simulation experiments were performed using PyCharm and Python 3.9 on a Windows 11 operating system.

[0093] Simulation content

[0094] This invention uses simulated hyperspectral datasets and real hyperspectral datasets to test the unmixing effect of the algorithm. To test the performance of the algorithm, the proposed hyperspectral sparse unmixing method using a learnable implicit variable iterative expansion network is compared with currently popular unmixing algorithms internationally. The comparison methods include: the SUnSAL algorithm, a single-pixel sparse regression algorithm based on the Alternating Direction Multiplier Method (ADMM) created by Jos'e M. Bioucas-Dias and M'ario A.T. Figueiredo et al.; and the l... 1 / 2 The l1 norm in the SUnSAL algorithm is replaced by a new norm, and a collaborative (also known as "multi-task" or "simultaneous") sparse regression framework (CLSUnSAL) is designed. Yong Ma et al. addressed the issue of nonlinear effects ignored by most hyperspectral unmixing models (and nonlinearity being treated only as outliers), and the problem that the l2 norm loss function used in traditional unmixing models is too sensitive to noise and outliers, proposing the RSU algorithm, which is more robust to noise and outliers. Le Sun et al. designed an algorithm using the l2 norm... 1 / 2 Unmixing algorithm for norm constraints (CSUnL) 1 / 2 ).

[0095] The evaluation metrics used in this invention are abundance reconstruction error (ASRE), root mean square error (RMSE), and spectral angle distance (SAD).

[0096] Analysis of Simulation Experiment Results

[0097] (1) Simulated dataset DC1

[0098] From index value table 1 and Figure 4 The comparison revealed that the present invention exhibits lower SAD and RSME, indicating that the method can better fit hyperspectral data; it also shows higher ASRE, indicating that the abundance obtained by the unmixing method is closer to the true value. Figure 3 The abundance plots clearly show that, compared to other algorithms, the boundaries of each color patch in the abundance plot of this invention are clearer and the colors are more uniform. In particular, in the abundance plot of endmember 3 (plate serpentine), it can be seen that the results of the CLSUnSAL method and this invention are closest to the true value overall. However, the CLSUnSAL method shows color patches that are not present in the true value and the results of this invention, indicating that the unmixing results of this invention are more accurate and contain less noise.

[0099] Table 1. Three evaluation metrics for different algorithms on simulated data DC1 with a noise level of 40 dB.

[0100] Algorithm SUnSAL CLSUnSAL RSU <![CDATA[CSUnL 1 / 2 ]]> OURS RMSE 0.1189 0.1139 1.2865 5.5034 0.0923 SAD 0.0111 0.0103 0.0135 0.0209 0.0098 ASRE 10.4186 14.1461 12.4663 5.3809 22.8967

[0101] (2) Simulated dataset DC2

[0102] From index value table 2 and Figure 6 Comparative analysis revealed that this invention yields better index values, significantly outperforming other methods in terms of indicators. This demonstrates that this method can better reconstruct hyperspectral data and yields abundance values ​​closer to the true values. Figure 5 The abundance map clearly shows that, compared to other algorithms, the results of this invention and the CLSUnSAL method are closer to the true abundance map. Further observation of the chromaticity bars on the right side of each endmember abundance map, especially the range of values ​​for endmember 1 (potassium gypsum), reveals that the abundance range of this invention is closer to the true value, indicating that the overall accuracy of this invention is also higher than other algorithms.

[0103] Table 2. Three evaluation metrics for different algorithms on simulated data DC2 with a noise level of 40 dB.

[0104] Algorithm SUnSAL CLSUnSAL RSU <![CDATA[CSUnL 1 / 2 ]]> OURS RMSE 0.1252 0.0922 1.0517 3.7125 0.0815 SAD 0.0120 0.0110 0.0192 0.0242 0.0100 ASRE 6.0101 13.2788 9.6987 8.2194 19.0072

[0105] (3) Simulated dataset DC3

[0106] From index value table 3 and Figure 8 The comparison revealed that this invention exhibits excellent SAD and RSME, indicating that the method can better reconstruct the observed spectrum; it also demonstrates higher ASRE, indicating that the unmixing results of this method are more accurate. Figure 7 The abundance plot clearly shows that some traditional methods are affected by the correlation of endmembers in the spectral library, resulting in excessive deviations in the unmixing results for some endmembers. For example, regarding the unmixing abundance of endmember 5 (chromite), the unmixing results of the SUnSAL and CLSUnSAL algorithms are 0, while the abundance value of this invention is significantly closer to the true value than the other algorithms. Observing the dark background of the abundance plot, it can be seen that the texture of the dark part of the result of this invention is closest to the true value, which also proves that the result of this invention is more accurate.

[0107] Table 3. Three evaluation metrics for different algorithms on simulated data DC3

[0108] Algorithm SUnSAL CLSUnSAL RSU <![CDATA[CSUnL 1 / 2 ]]> OURS RMSE 0.2274 0.2005 0.4517 4.5995 0.2002 SAD 0.0279 0.0274 0.0287 0.0586 0.0277 ASRE 6.0322 6.9087 5.3559 5.3510 11.5792

[0109] (4) Actual dataset

[0110] Figure 9 Displays SUnSAL, CLSUnSAL, RSU, and CSUnL on the Cuprite dataset. 1 / 2 Abundance maps of three minerals—alumite, ammonium hydrate feldspar, and chalcedony—obtained in this invention are shown. To facilitate comparative analysis of the abundance maps, the hyperspectral mineral mapping software Tetracorder, developed by the United States Geological Survey (USGS), was used to identify the mineral information contained in the spectra and generate mineral distribution maps, such as... Figure 9 As shown in the left column of the image. Each pixel in the image indicates whether the point belongs to a certain mineral, but does not show the content of a certain mineral at that point. Therefore, we only use it for qualitative comparative analysis here, and not as a true abundance map. Figure 9 The rightmost column shows the unmixing results of this invention; a warmer hue indicates a higher mineral content. For alunite minerals, SUnSAL, CLSUnSAL, RSU, and CSUnL... 1 / 2 The abundance map obtained by this invention is not significantly different from that obtained by Tetracorder, and is very similar to the results obtained by Tetracorder. However, for the minerals ammonium feldspar and chalcedony, the abundance map obtained by this invention is visually purer and the color distribution is more concentrated, proving that our algorithm is more effective than other algorithms.

[0111] The above four experimental results show that the hyperspectral sparse unmixing method of the present invention, which introduces learning parameters into the traditional ADMM algorithm and adds spatial convolutional layers to obtain a learnable implicit variable iterative unfolding network, can achieve higher unmixing accuracy and better unmixing effect.

Claims

1. A hyperspectral unmixing method of a learnable implicit variable iterative unfolding network, characterized in that, Comprising the following steps: Step 1, processing the original hyperspectral data and the spectral library to obtain model input; according to the sparsity of abundance, a model for unmixing is constructed with sparsity constraint; specifically: (1) processing the original hyperspectral data and the spectral library to obtain model input Original hyperspectral image data Wherein, B represents the band number of hyperspectral, L and W represent the width and height of image space dimension respectively; the original hyperspectral data is divided into a matrix Y = [y1, y2, …, yP] ∈ R Pixel by pixel scanning is sorted in the column direction to form a spectral pixel matrix Y = [y1, y2, …, yP] ∈ R i ,…,y N ] ∈ R B×P , wherein P = L × W represents the number of hyperspectral pixels, y i ∈ R L , represents the i-th spectral pixel, 1 ≤ i ≤ P; the spectral library A is matched with the hyperspectral data Y in the band, so that the spectral dimensions of both are consistent; (2) the linear model of hyperspectral unmixing is as follows: Y = AX + N (1) where Y ∈ R B×P represents a hyperspectral data matrix, A ∈ R B×N represents an endmember dictionary containing N endmembers, X ∈ R N×P represents an abundance matrix, N ∈ R B×P represents noise; Introducing sparsity and non-negative constraints, the optimization function of the model described in equation (2) is obtained: In formula (2), λ > 0 is a regularization parameter, denotes the indicator function of the set R + , i.e. has: if Step 2, using variable splitting and augmented Lagrange method, an alternating direction iterative solution form of the unmixing model is constructed; specifically: To solve the abundance variable X, a Lagrangian function of equation (3) is constructed where Z = X is an auxiliary variable, a is a Lagrange multiplier, and p > 0 is a penalty factor, Z i,j denotes the element of matrix Z in the i-th row and j-th column, if Then, the alternating direction iterative format of equation (3) is: Where U = - alpha / p; For the first step iteration: From the solution of the convex optimization problem we have: X k+1 = (A T A+ρI) -1 [A T Y+ρ(Z k -U k )] (5) Second step iteration: Solving with soft threshold algorithm, we have: Z k+1 = max{0, soft(X k - Z k )} (6) Integrating equations (5) and (6), the alternating direction iterative form is obtained: Step 3, modeling the alternating direction iterative step into a network module containing implicit learnable parameters, which includes learnable layers of abundance variables and multiplier variables; specifically as follows: Modeling the first step of iteration X k+1 = (A T + ρI) -1 [A T + ρI k - U k ] and let H = ρI, set H and ρ as learnable parameters as the abundance variable layer 1, output the unconstrained abundance variable X k+1 ; Specifically: X k+1 = (A T + H) -1 [A T + p(Z k - U k )] (8) Iterate second step Z k+1 = max{0, soft(X k+1 - Z k , λ / ρ)} modeled as Z k+1 = ReLU(X k+1 - Z k - θ) (9) where the parameter θ is a learnable parameter, as the abundance variable layer 2, outputs the abundance variable Z with non-negative and sparsity constraints k+1 ; The third step of iteration U k+1 = U k + p(X k+1 - Z k+1 ) The parameter p is set as a learnable parameter mu as a multiplier variable layer, and the Lagrange multiplier is updated; U k+1 = U k + μ(X k+1 - Z k+1 ) (10) Thus the sparse model driven implicit unfolding network module is: Step 4, according to the piecewise smoothness of endmember abundance in spatial distribution, a learnable convolution smoothing layer is constructed and inserted into the learnable module to complete the iterative structure of the implicit unfolding network; specifically: The abundance of single endmember has the characteristic of one-sided smoothness in spatial distribution. Based on this prior, a learnable convolution layer is constructed and inserted between the two abundance variable layers. First, the result of equation (8) is dimensionally transformed: Then, a two-dimensional convolution operation is performed on the endmember dimension of the three-dimensional data to obtain the smoothness-constrained abundance tensor C k+1 : The initialization of the convolution kernel selects two-dimensional Gaussian filter initialization, and the convolution kernel weight is allowed to be back propagated; Thus the iterative structure of the sparse model driven implicit unfolding network is: Step 5, regarding the spectral library as an encoder and the spectral unmixing process as a decoding process, the unmixing abundance is re-encoded to realize spectral reconstruction; Step 6, unsupervised loss function is adopted to realize model training: the mean square error, spectral angle distance and spectral information entropy loss function of the reconstructed spectrum and the input spectrum are calculated, the model is trained through back propagation, and the unmixing endmember abundance and the reconstructed spectrum under the optimal model parameter are obtained.

2. The hyperspectral unmixing method of claim 1, wherein, Step 5 is specifically: The multiplier layer in the last iteration (13) is replaced by a normalization layer to complete the sparse model driven implicit unfolding network; the process of obtaining the estimated abundance by inputting the spectrum into the sparse model driven implicit unfolding network is analogous to the decoding process, and the endmember abundance is re-encoded using the spectral library A to obtain the reconstructed spectrum 3. The hyperspectral unmixing method of claim 2, wherein, Step 6 adopts unsupervised loss function to realize model training, specifically: Calculate the unsupervised loss function: Loss = a1L MSE + a2L SAD + a3L SID (15) Using the back propagation mechanism of deep learning to train network parameters, finally output the unmixing abundance and reconstructed spectrum under the optimal model parameter; wherein, is the mean square error between the input image and the reconstructed image; is the mean spectral angle distance between the input image and the reconstructed image; is the mean spectral information entropy between the input image and the reconstructed image; Y = [y1, y2,..., y i , P , represent the spectrum of one pixel of the input image and the reconstructed image, respectively; and a1, a2, a3 are the weights of the three components.

4. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to realize the steps of the method of any one of claims 1-3.

5. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to realize the steps of the method of any one of claims 1-3.

6. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the method of any one of claims 1-3.

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