Hybrid polarization system underdetermined information reconstruction method and device based on physical constraint

Abstract

The invention provides a hybrid polarization system underdetermined information reconstruction method and device based on physical constraints, and relates to the technical field of radars, and the method comprises the steps: building a system performance model of a hybrid polarization SAR system, considering the non-ideal characteristics and reciprocity hypothesis of the system, and building a real model of hybrid polarization observed quantity; according to a system performance model, under the constraint of reflection symmetry, decomposing the second moment of the mixed polarization observed quantity, estimating a cross polarization component, and reconstructing the second moment of a complete polarization scattering matrix; adopting an unsupervised training set pre-segmentation strategy, selecting a clustering center according to the local density and the relative distance of the sample points, and dividing the training set into a plurality of sub-clusters; based on an improved Wishart hybrid model, performing model training on each sub-cluster by using multiple distance metrics and hyper-parameter optimization strategies; and classifying the polarized SAR image by using the trained model to obtain a classification result. According to the invention, the accuracy and robustness of model training can be improved.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and particularly belongs to the field of polarization classification of polarimetric synthetic aperture radar (Pol-SAR). Specifically, it relates to a method and device for reconstructing underdetermined information of a hybrid polarization system based on physical constraints. Background Art

[0002] Polarimetric synthetic aperture radar (SAR) obtains the ground object scattering matrix information by transmitting and receiving electromagnetic waves of different polarizations, and is used to finely characterize the ground object characteristics. Polarization classification is a key task in polarimetric SAR data processing, aiming to realize automatic recognition and classification of ground objects by using scattering characteristics. In recent years, the hybrid polarization mode has attracted attention due to its wider observation swath and more balanced range ambiguity performance. However, the reduction of its polarization information and the unclear influence mechanism on the target characterization ability limit its application, including: the research on the hybrid polarization mode, especially the research based on real data, is limited, and its potential in practical applications has not been fully explored; the reduction of polarization information in the hybrid polarization mode affects the target characterization ability, but its influence mechanism is not clear, which restricts further application; although existing research has made attempts, the performance of the hybrid polarization mode in polarization image classification still needs to be further improved.

[0003] There are many limitations in existing polarization classification research, including: existing schemes rely on inconsistent feature extraction, introducing risks to the objective comparison of characterization ability. Some research attempts to reconstruct hybrid polarization data into full polarization data, but the statistical model has poor adaptability to artificial ground objects and there is a risk of underfitting.

[0004] There are also many potential risks in existing machine learning frameworks, including: the hyperparameters lack physical meaning, making it difficult to clarify the reasons for the performance differences of classifiers; the public availability of hybrid polarization data is insufficient, making it difficult to apply deep learning methods. Existing research is mostly based on simulated data, and the conclusions are controversial; the statistical model is difficult to effectively fit complex ground object distributions, has a weak relationship with the equivalent number of looks, and the observation results of SAR images do not conform to the intuitive visual perception, resulting in the need for a large amount of expert knowledge and manual input for data annotation. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints. An improved general model is adopted, and by introducing a simple measurement method to evaluate the statistical stability of each pixel point, the statistical characteristics of speckle denoising data can be better fitted. At the same time, a pre-segmentation method for the training set is used to adaptively cluster the training set to effectively manage its inherent diversity. The present invention can perform better training on a training set with a long-tail distribution, and at the same time avoid the complication of the labeling process, thereby improving the accuracy and robustness of model training.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints, comprising the following steps:

[0008] Step 1, construct a system performance model of the hybrid polarization SAR system, consider the non-ideal characteristics and reciprocity assumptions of the hybrid polarization SAR system, and establish a true model of the hybrid polarization observables;

[0009] Step 2, according to the system performance model, under the reflection symmetry constraint, decompose the second moment of the hybrid polarization observables, estimate the cross-polarization components, and reconstruct the second moment of the full polarization scattering matrix;

[0010] Step 3, adopt an unsupervised training set pre-segmentation strategy, select the clustering centers according to the local density and relative distance of the sample points, and divide the training set into multiple sub-clusters;

[0011] Step 4, based on the improved Wishart mixture model, use a variety of distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster;

[0012] Step 5, use the trained improved Wishart mixture model to classify the polarimetric SAR image to obtain the classification result.

[0013] The present invention also provides a device for reconstructing underdetermined information of a hybrid polarization system based on physical constraints, comprising the following modules:

[0014] A model construction module, which constructs a system performance model of the hybrid polarization SAR system, considers the non-ideal characteristics and reciprocity assumptions of the hybrid polarization SA system, and establishes a true model of the hybrid polarization observables;

[0015] A second moment reconstruction module, which decomposes the second moment of the hybrid polarization observables under the reflection symmetry constraint according to the system performance model, estimates the cross-polarization components, and reconstructs the second moment of the full polarization scattering matrix;

[0016] A training set division module, which adopts an unsupervised training set pre-segmentation strategy, selects the clustering centers according to the local density and relative distance of the sample points, and divides the training set into multiple sub-clusters;

[0017] A model training module, which based on the improved Wishart mixture model, uses a variety of distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster;

[0018] A classification module, which uses the trained improved Wishart mixture model to classify the polarimetric SAR image to obtain the classification result.

[0019] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the steps of the above-mentioned method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints are implemented.

[0020] The present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored, wherein when the computer program is executed by a processor, the steps of the above-mentioned method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints are implemented.

[0021] Beneficial effects:

[0022] The present invention significantly improves the classification performance of hybrid polarization synthetic aperture radar (Pol-SAR) data through multiple innovations. First, through reflection symmetry constraints and cross-polarization component estimation, the effective reconstruction of the second-order moment of the full-polarization scattering matrix is realized, making up for the lack of polarization information in the hybrid polarization mode and providing more accurate input data for the classification task. Second, the improved Wishart mixture model (WMM) introduces a new hyperparameter training strategy and multiple distance metrics, which can better fit the statistical characteristics of actual data and show higher classification accuracy and robustness especially when dealing with complex ground objects and denoising data. In addition, the proposed training set pre-segmentation (TSP) method alleviates the problem of model underfitting through unsupervised clustering and reduces the difficulty and cost of training sample annotation. Experimental results show that the classification accuracy of the present invention in the hybrid polarization mode is comparable to that in the full-polarization mode, verifying the effectiveness of the algorithm. Overall, the present invention not only improves the classification accuracy of hybrid polarization data, but also enhances the adaptability, robustness and interpretability of the model, reduces the data annotation cost, and has important application value. Description of the drawings

[0023] Figure 1 is a flowchart of the method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to the present invention;

[0024] Figure 2 is a schematic diagram of the Xinxiang dataset; wherein, (a) is the Pauli color-coded image of the full-polarization data, (b) is the color-coded image of the hybrid polarization data using m-chi decomposition, and (c) is the ground truth map. The red square dots represent the in-situ detection positions;

[0025] Figure 3 is a classification result diagram; wherein, (a) is the full-polarization classification result, and (b) is the hybrid polarization classification result;

[0026] Figure 4Schematic diagram of an underdetermined information reconstruction device for a hybrid polarization system based on physical constraints according to the present invention. Detailed implementation manners

[0027] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0028] As Figure 1 shown, a method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to the present invention includes the following steps:

[0029] Step 1: Construct a system performance model of a hybrid polarization SAR system;

[0030] Step 2: According to the system performance model, reconstruct the second moment of the full polarization scattering matrix: By using the reflection symmetry constraint, reasonably estimate the cross-polarization components to achieve the effective reconstruction of the second moment of the full polarization scattering matrix;

[0031] Step 3: Training set pre-segmentation (TSP): In view of the possible significant differences in scattering characteristics among samples of the same type, an unsupervised TSP strategy is proposed to alleviate the problem of underfitting of the scattering characteristic statistical model and fully explore the classification potential of polarization SAR; Use the second moment of the full polarization scattering matrix as the input for training set pre-segmentation;

[0032] Step 4: Training of an improved Wishart mixture model (IWMM): Propose a training method for the improved Wishart mixture model, and on this basis, propose a new general model to objectively verify the polarization information reconstruction effect;

[0033] Step 5: Classify the polarization SAR image based on the improved Wishart mixture model trained in Step 4.

[0034] Specifically, the said Step 1 includes:

[0035] Considering the non-ideal nature of the system and the reciprocity assumption, the true hybrid polarization observation model is:

[0036] (1)

[0037] Wherein, represents the hybrid polarization observation, represents the full polarization scattering matrix, represents the elements in the polarization scattering matrix, x, y = h, v; h represents horizontal polarization, and v represents vertical polarization. Denotes the absolute amplitude-phase factor introduced by the system, Denotes the equivalent transmit crosstalk, Denotes the hybrid polarization transmit polarization basis, Denotes and The orthogonal polarization basis, which is jointly determined by the amplitude-phase imbalance and isolation of the transmit channels, Corresponds to the cases of the transmit left- and right-hand circularly polarized waves respectively. The superscript T denotes the transpose of a matrix, and j denotes the imaginary unit. And Denotes the receive channel crosstalk factor, Denotes the receive channel imbalance, Denotes the receive distortion matrix:

[0038] (2)

[0039] The isolation of the H / V (H represents horizontal polarization, V represents vertical polarization) polarization channels characterizes the degree of leakage of co-polarization energy into the cross-polarization channels, i.e., the crosstalk coupling effect of the measurement data; the equivalent transmit crosstalk and amplitude-phase consistency characterize the accuracy of the polarization relative information. It can be seen from Equation (1) that low isolation will cause the coupling of co-polarization energy and cross-polarization energy, seriously deteriorating the information effectiveness. In addition, the distortion of the observables caused by the system polarization distortion in characterizing the ground object scattering characteristics leads to the failure of the reflection symmetry constraint, further introducing uncertainty errors into the polarization information reconstruction. Therefore, the hybrid polarization mode requires high system amplitude-phase consistency and isolation, which is the basis for realizing the reconstruction of full polarization scattering information. The internal relationship between system polarization distortion and information reconstruction is that high isolation and high amplitude-phase consistency of the H polarization channel and the V polarization channel make the measurement equation degenerate into a pure physical equation that only characterizes the target scattering characteristics.

[0040] Specifically, step 2 includes:

[0041] First, the second moment of the hybrid polarization observables Can be decomposed into a co-polarization component, a cross-polarization component, and a residual component, i.e.:

[0042] (3)

[0043] Where Denotes the co-polarization component, Denotes the cross-polarization component, Denotes the residual component, Denotes the imaginary unit, Denotes the imaginary part of a complex number, Denotes the spatial average, and the superscript Denotes the transpose conjugate operation.

[0044] When the physical constraints of reflection symmetry are satisfied for the ground objects, the observation matrix satisfies the sparse property. Therefore, the reconstruction of the second moment of the full polarization scattering matrix can be achieved by minimizing the norm of the residual component of .

[0045] The optimization objective function and constraints for reconstructing the second moment of the full polarization scattering matrix are shown as follows:

[0046] (4)

[0047] where represents the value of the variable when the following expression reaches the minimum, represents the reconstructed full polarization scattering matrix of the second moment, represents norm, represents the dimensionality reduction projection matrix:

[0048] (5)

[0049] At this time, the optimization problem based on Equation (4) is still a multi-solution problem, and it is necessary to introduce the volume scattering estimation constraint, that is, the cross-polarization intensity is equal to the volume scattering power. The cross-polarization intensity is estimated through the polarization degree :

[0050] (6)

[0051] where represents the element in the p-th row and q-th column of the covariance matrix of the mixed polarization, and p, q = 1, 2.

[0052] Under the reflection symmetry constraint, the initial value of the second moment of the full polarization scattering matrix

[0053] (7)

[0054] Specifically, the step 3 includes:

[0055] The local density of the class center is greater than the density of other elements within the class, and the class centers of different clusters are far apart. Therefore, a suitable sample center can be selected through the local density and relative distance of the sample points.

[0056] The local density is defined as follows:

[0057] (8)

[0058] where the subscripts i and j represent the pixel numbers, represents the input covariance matrix, The dissimilarity of the covariance matrices corresponding to two pixels denotes the distance threshold denotes the exponential function

[0059] Relative distance is defined as follows

[0060] (9)

[0061] where denotes taking the value with the smallest value in the following formula and with a local density greater than the local density of the current pixel denotes the density variable. Through and the obtained decision value is defined as follows

[0062] (10)

[0063] Since the elements within the clusters after segmentation have more similar scattering characteristics, the Expectation-Maximization (EM) algorithm can achieve better parameter fitting. The pre-segmentation of the training samples in the training set is divided into the following four steps

[0064] The first step: Calculate the decision value of each pixel in the training samples and sort them in descending order. Select the 50 elements with the largest decision value for each type of ground object and include them in the set of candidate clustering centers , and the elements with larger decision values have higher priority as clustering centers

[0065] The second step: Transfer the element with the largest decision value in the set to the set of determined clustering centers . Remove the elements in the set whose dissimilarity from the elements in the set is less than the clustering threshold

[0066] The third step: Repeat the second step until there are no elements in the set

[0067] The fourth step: Within a single category, calculate the dissimilarity between the elements of the training samples and the elements in the determined clustering centers , and divide the elements into the corresponding clusters based on the minimum dissimilarity. The clusters obtained by segmentation independently participate in the training of the improved Wishart mixture model, but all represent the same type of ground object

[0068] Specifically, the said step 4 includes

[0069] ​​The Wishart mixture model uses a combination of multiple distributions to fit the true statistical characteristics of the data. Mathematically, it can be considered that multiple kernel functions are used to approximate the unknown distribution function. The EM algorithm is used to perform maximum likelihood estimation on the statistical model parameters.

[0070] The distance metric derived under the hypothesis testing framework has an exponential mapping relationship with the likelihood function. The general probability density function The expression is as shown in the following formula:

[0071] (11)

[0072] Among them, represents the normalization function, represents a non - negative measurable function, represents the smoothing hyperparameter, represents the class center, represents the model parameter, and exp() represents the exponential function. The process proposed in the present invention uses multiple distance metrics to attempt to obtain higher classification accuracy, and uses the smoothing hyperparameter to replace the number of looks to better fit the statistical characteristics of the actual data, that is:

[0073] (12)

[0074] Among them, represents the estimated ENL (equivalent number of looks), represents the signal - to - noise ratio, is the scale adjustment factor.

[0075] The parameters of the IWMM are re - defined as . Based on the smoothing hyperparameter of each pixel for prediction, its likelihood function is as shown in the following formula:

[0076] (13)

[0077] Among them, represents all unknown parameters, represents the k - th mixing coefficient, and , is the specific realization of the i - th pixel for the k - th latent variable being independently and identically distributed, represents the class center of the k - th distribution, and K represents the total number of sub - classes, represents the probability density function of the distribution of the improved Wishart mixture model.

[0078] The present invention introduces the scale adjustment factor Increase the degrees of freedom of the model. In addition, the equivalent number of looks (ENL) can effectively evaluate the degree of dispersion of the observations of fully developed speckles. However, two points are worth noting: 1) When there are major scatterers within the resolution cell, such as when the number of artificial structures or randomly distributed scatterers within the resolution cell is insufficient, the characterization ability of ENL decreases; 2) Weak scattering cells are more susceptible to noise, clutter, and blurring, resulting in a relatively large deviation from the theoretical scattering centers.

[0079] Finally, the hyperparameters ( , and the scale adjustment factor ) that maximize the classification accuracy of the training samples are selected through iteration. In the expectation (E) step (the E step of the EM algorithm), is denoted as the estimated value, and the superscript (t) represents the number of iterations. Under the condition that the parameter is , the posterior distribution of is estimated through Bayes' theorem, and the posterior probability satisfies:

[0080] (14)

[0081] where the subscript g is a temporary representation to avoid symbol repetition during summation.

[0082] In the maximization (M) step (the M step of the EM algorithm), using the estimated posterior probability, the updated parameter is obtained by maximizing the conditional expectation of the log-likelihood function, and the derivation of the iterative expression is still based on the Wishart distribution.

[0083] The iterative expression for the weight of the subclass is:

[0084] (15)

[0085] where represents the number of samples in a single cluster.

[0086] The iterative expression for the subclass center is:

[0087] (16)

[0088] It can be seen from this that the normalization function and the non-negative measurable function do not affect the estimation of the subclass center and the weight .

[0089] Repeat the E step and the M step until the parameters converge. The mathematical expression for the iteration convergence condition is shown as follows:

[0090] (17)

[0091] (18)

[0092] In equations (17) and (18), and respectively represent the thresholds of the subclass center and weight.

[0093] Specifically, step 5 includes:

[0094] The classification label of the dataset can be obtained by identifying the class with the maximum probability density, that is:

[0095] (19)

[0096] where represents the value of variable l when the following formula reaches the maximum value, represents the probability of belonging to class l, represents the number of classes.

[0097] Example:

[0098] The experimental data involved in the present invention includes fully polarized and hybrid polarized L-band data obtained on December 18, 2023 and January 11, 2024 respectively. The size of the hybrid data is 12000×22300, and the size of the fully polarized data is 12000×21300, that is, about 42 km along the azimuth direction and about 20 km along the slant range direction. This dataset includes 7 identified classes: Chinese cabbage, wheat, tea tree, forest, water body, building, and bare soil. Figure 2 of (a), Figure 2 of (b), Figure 2 of (c) show the corresponding Pauli false color image, m-chi decomposition image, and geographical ground truth. Figure 3 shows the final classification image, Figure 3 of (a) is the fully polarized classification result, Figure 3 of (b) is the hybrid polarized classification result. The corresponding classification accuracies are compared in Table 1.

[0099] Table 1

[0100] The results show that the second moment of the fully polarized scattering matrix reconstructed from the hybrid polarized mode observables in the present invention is similar to the true fully polarized mode, that is, the hybrid polarized mode has a classification ability equivalent to that of the fully polarized mode, verifying the effectiveness of the algorithm.

[0101] Such as Figure 4As shown in the figure, the present invention also provides an underdetermined information reconstruction device based on physical constraints for a hybrid polarization system to implement the steps of the above method, specifically including the following modules:

[0102] A model construction module that constructs a system performance model, considers the non-ideal characteristics and reciprocity assumptions of the system, and establishes a true model of the hybrid polarization observables;

[0103] A second-order moment reconstruction module that decomposes the second-order moment of the hybrid polarization observables under the reflection symmetry constraint according to the system performance model, estimates the cross-polarization components, and reconstructs the second-order moment of the full polarization scattering matrix;

[0104] A training set partitioning module that adopts an unsupervised training set pre-segmentation strategy, selects cluster centers according to the local density and relative distance of sample points, and partitions the training set into multiple sub-clusters;

[0105] A model training module that, based on an improved Wishart mixture model, uses various distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster;

[0106] A classification module that uses the trained model to classify the polarimetric SAR images to obtain classification results.

[0107] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. The feature is that when the processor executes the program, it implements the steps of the above-mentioned underdetermined information reconstruction method based on physical constraints for a hybrid polarization system.

[0108] The present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. The feature is that when the computer program is executed by a processor, it implements the steps of the above-mentioned underdetermined information reconstruction method based on physical constraints for a hybrid polarization system.

[0109] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can be in the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can be in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes. The solutions in the embodiments of the present invention can be implemented in various computer languages, for example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0110] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and combinations of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device generate means for implementing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or one or more of the blocks.

[0111] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including instruction means that implement the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or one or more of the blocks.

[0112] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operational steps are performed on the computer or other programmable device to produce a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or one or more of the blocks.

[0113] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn of the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention.

[0114] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints, characterized in that Including the following steps: Step 1: Construct a system performance model for the hybrid polarimetric SAR system, consider the non-ideal characteristics and reciprocity assumption of the hybrid polarimetric SAR system, and establish a true model of the hybrid polarimetric observables; Step 2: According to the system performance model, under the reflection symmetry constraint, decompose the second moment of the hybrid polarimetric observables, estimate the cross-polarization components, and reconstruct the second moment of the full polarimetric scattering matrix; Step 3: Adopt an unsupervised training set pre-segmentation strategy, select the clustering centers according to the local density and relative distance of the sample points, and divide the training set into multiple sub-clusters; Step 4: Based on the improved Wishart mixture model, use a variety of distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster; Step 5: Use the trained improved Wishart mixture model to classify the polarimetric SAR image and obtain the classification result.

2. The underdetermined information reconstruction method based on physical constraints of a hybrid polarization system according to claim 1, wherein The reflection symmetry constraint in Step 2 is used to ensure the sparse characteristics of the observation matrix, and the second moment of the full polarimetric scattering matrix is reconstructed by minimizing the norm of the residual components.

3. A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to claim 1, characterized in that, The training set pre-segmentation strategy in Step 3 selects the sample centers according to the local density and relative distance of the sample points.

4. A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to claim 1, characterized in that The improved Wishart mixture model in Step 4 is used to fit the statistical characteristics of the actual data.

5. A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to claim 4, characterized in that The model training in step 4 adopts an iterative optimization hyperparameter selection method to maximize the classification accuracy of training samples; the hyperparameters are the distance threshold , the clustering threshold and the scale adjustment factor ; The model parameters of the improved Wishart mixture model are redefined as ; Estimation based on the smoothing hyperparameter of each element, the likelihood function of the improved Wishart mixture model As shown in the following formula: （13） Among them, represents the smoothing hyperparameter, represents the class center, represents the covariance matrix of the i-th pixel, represents all unknown parameters, represents the k-th mixing coefficient, and , is the specific implementation of the i-th element for the k-th latent variable to be independently and identically distributed, represents the class center of the k-th distribution, represents the smoothing hyperparameter of the i-th pixel, K represents the total number of distributions, represents the probability density function of the Wishart distribution of the improved Wishart mixture model.

6. A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to claim 1, characterized in that The classification result in Step 5 is obtained by identifying the class with the maximum probability density, thereby improving the classification accuracy.

7. A method for reconstructing underdetermined information of a hybrid polarization system based on physical constraints according to claim 1, characterized in that The system performance model in Step 1 considers the absolute amplitude-phase factor, equivalent transmit crosstalk, and receive distortion matrix introduced by the system to ensure the accuracy and robustness of the model.

8. An underdetermined information reconstruction device with a hybrid polarization system based on physical constraints, characterized in that Including the following modules: Model construction module: Construct a system performance model for the hybrid polarimetric SAR system, consider the non-ideal characteristics and reciprocity assumption of the hybrid polarimetric SA system, and establish a true model of the hybrid polarimetric observables; Second moment reconstruction module: According to the system performance model, under the reflection symmetry constraint, decompose the second moment of the hybrid polarimetric observables, estimate the cross-polarization components, and reconstruct the second moment of the full polarimetric scattering matrix; Training set division module: Adopt an unsupervised training set pre-segmentation strategy, select the clustering centers according to the local density and relative distance of the sample points, and divide the training set into multiple sub-clusters; Model training module: Based on the improved Wishart mixture model, use a variety of distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster; Classification module: Use the trained improved Wishart mixture model to classify the polarimetric SAR image and obtain the classification result.

9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of a method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints as described in any one of claims 1 to 7.

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