Method and device for reconstructing underdetermined information of hybrid polarization system based on physical constraints

Abstract

The present invention provides a method and device for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints, relating to the field of radar technology. The method comprises: constructing a system performance model of a hybrid polarimetric SAR system, taking into account the non-ideal characteristics of the system and the reciprocity assumption, and establishing a realistic model of the hybrid polarimetric observations; decomposing the second-order moments of the hybrid polarimetric observations based on the system performance model and under the constraint of reflection symmetry, estimating the cross-polarization components, and reconstructing the second-order moments of the full polarimetric scattering matrix; employing an unsupervised training set pre-segmentation strategy to select cluster centers based on the local density and relative distance of sample points, and dividing the training set into multiple subclusters; training each subcluster model based on an improved Wishart hybrid model using multiple distance metrics and hyperparameter optimization strategies; and classifying polarimetric SAR images using the trained model to obtain classification results. The present invention can improve the accuracy and robustness of model training.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, and in particular to the field of polarization classification of Polarimetric Synthetic Aperture Radar (Pol-SAR), and specifically to a method and device for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints. Background Art

[0002] Polarimetric synthetic aperture radar (SAR) acquires ground object scattering matrix information by transmitting and receiving electromagnetic waves of different polarizations, which is used to finely characterize ground object characteristics. Polarimetric classification is a key task in polarimetric SAR data processing, aiming to automatically identify and classify ground objects using scattering characteristics. In recent years, hybrid polarimetric modes have attracted attention due to their wider observation width and more balanced range ambiguity performance. However, the reduced polarimetric information and the mechanism of their impact on target characterization capabilities are still unclear, limiting their application. These factors include: limited research on hybrid polarimetric modes, especially those based on real data, and their potential in practical applications has not been fully explored; the reduced polarimetric information in hybrid polarimetric modes affects target characterization capabilities, but the mechanism of this impact is still unclear, restricting further application; and although existing research has attempted, further improvement of the performance of hybrid polarimetric modes in polarimetric image classification is still needed.

[0003] Existing polarimetric classification research has numerous limitations, including the reliance on inconsistent feature extraction, which poses a risk for objective comparisons of characterization capabilities. Some studies have attempted to reconstruct mixed polarimetric data into fully polarimetric data, but these statistical models are poorly adapted to man-made objects and present the risk of underfitting.

[0004] Existing machine learning frameworks also have many potential risks, including: hyperparameters lack physical meaning, making it difficult to clearly identify the reasons for differences in classifier performance; mixed polarization data are insufficiently public, making deep learning methods difficult to apply, and existing research is mostly based on simulated data, with controversial conclusions; statistical models are difficult to effectively fit the distribution of complex land objects, have a weak relationship with equivalent visual numbers, and the observation results of SAR images do not match intuitive visual perception, resulting in data labeling requiring a large amount of expert knowledge and manual input. Summary of the Invention

[0005] To address the above technical problems, the present invention provides a physically constrained method for reconstructing underdetermined information from a hybrid polarimetric system. This method employs an improved universal model and introduces a simple metric to assess the statistical stability of each pixel, thereby better fitting the statistical characteristics of speckle denoised data. Furthermore, the method utilizes a training set pre-segmentation method to adaptively cluster the training set to effectively manage its inherent diversity. This method enables better training on training sets with long-tailed distributions while avoiding the complexity of the labeling process, thereby improving the accuracy and robustness of model training.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

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

[0008] Step 1: Construct a system performance model of the hybrid polarimetric SAR system, consider the non-ideal characteristics of the hybrid polarimetric SAR system and the reciprocity assumption, and establish a realistic model of the hybrid polarimetric observations;

[0009] Step 2: Based on the system performance model and under the reflection symmetry constraint, the second-order moments of the mixed polarization observations are decomposed, the cross-polarization components are estimated, and the second-order moments of the full polarization scattering matrix are reconstructed.

[0010] Step 3: Use the unsupervised training set pre-segmentation strategy to select cluster centers based on the local density and relative distance of sample points, and divide the training set into multiple subclusters;

[0011] Step 4: Based on the improved Wishart mixture model, a variety of distance metrics and hyperparameter optimization strategies are used 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 results.

[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] Model building module, which builds the 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 realistic model of the hybrid polarization observation quantity;

[0015] The second-order moment reconstruction module decomposes the second-order moment of the mixed polarization observations according to the system performance model and under the reflection symmetry constraint, estimates the cross-polarization components, and reconstructs the second-order moment of the full polarization scattering matrix;

[0016] The training set partitioning module adopts an unsupervised training set pre-segmentation strategy, selects cluster centers based on the local density and relative distance of sample points, and divides the training set into multiple subclusters;

[0017] The model training module is based on the improved Wishart mixture model and uses multiple distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster;

[0018] The classification module uses the trained improved Wishart mixture model to classify the polarimetric SAR images and obtain the classification results.

[0019] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and runnable on the processor, characterized in that 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 having a computer program stored thereon, characterized in that 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] This invention significantly improves the classification performance of mixed-polarimetric synthetic aperture radar (Pol-SAR) data through multiple innovations. First, through reflection symmetry constraints and cross-polarization component estimation, it effectively reconstructs the second-order moments of the fully polarimetric scattering matrix, compensating for the lack of polarization information in mixed-polarimetric patterns and providing more accurate input data for classification tasks. Second, the improved Wishart mixture model (WMM) introduces a new hyperparameter training strategy and multiple distance metrics, which better fit the statistical characteristics of real-world data. It exhibits higher classification accuracy and robustness, particularly when processing complex objects and denoised data. Furthermore, the proposed training set pre-segmentation (TSP) method alleviates model underfitting through unsupervised clustering, reducing the difficulty and cost of training sample annotation. Experimental results demonstrate that the classification accuracy of the proposed method in mixed-polarimetric patterns is comparable to that of the fully polarimetric pattern, validating the effectiveness of the algorithm. Overall, this invention not only improves the classification accuracy of mixed-polarimetric data, but also enhances the model's adaptability, robustness, and interpretability, while reducing data annotation costs, demonstrating significant application value. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0024] Figure 2 Schematic diagram of the Xinxiang dataset; (a) is the Pauli color-coded image of the full polarimetric data, (b) is the color-coded image of the mixed polarimetric data using m-chi decomposition, and (c) is the ground truth map. The red squares indicate the in-situ detection locations.

[0025] Figure 3 is the classification result diagram; (a) is the full polarization classification result, (b) is the mixed polarization classification result;

[0026] Figure 4Schematic diagram of a hybrid polarization system underdetermined information reconstruction device based on physical constraints according to the present invention. DETAILED DESCRIPTION

[0027] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

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

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

[0030] Step 2: Reconstruct the second-order moment of the full polarization scattering matrix based on the system performance model: Leveraging reflection symmetry constraints, a reasonable estimate of the cross-polarization component is made to effectively reconstruct the second-order moment of the full polarization scattering matrix.

[0031] Step 3: Training set pre-segmentation (TSP): To address the significant differences in scattering characteristics between similar samples, an unsupervised TSP strategy is proposed to alleviate the underfitting problem of the scattering characteristic statistical model and fully tap the potential of polarimetric SAR classification. The training set is pre-segmented using the second-order moment of the full polarimetric scattering matrix as input.

[0032] Step 4: Improved Wishart Mixture Model (IWMM) Training: This paper proposes an improved Wishart mixture model training method and, based on this method, a new general model to objectively verify the polarization information reconstruction effect.

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

[0034] Specifically, the step 1 includes:

[0035] Taking into account the non-ideal type of the system and the reciprocity assumption, the real mixed polarization observation model is:

[0036] (1)

[0037] in, represents the mixed 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. represents the absolute amplitude-phase factor introduced by the system, represents the equivalent transmit crosstalk, represents the mixed polarization emission polarization basis, Represents The orthogonal polarization basis is determined by the amplitude and phase imbalance and isolation of the transmission channel. They correspond to the cases of transmitting left-hand and right-hand circularly polarized waves, respectively. The superscript T represents the transpose of the matrix, and j represents the imaginary unit. and represents the receiving channel crosstalk factor, Indicates that the receiving channel is unbalanced. Represents the accepted distortion matrix:

[0038] (2)

[0039] The isolation of the H / V (H represents horizontal polarization, V represents vertical polarization) polarization channels represents the degree of leakage of co-polarized energy into the cross-polarization channel, that is, the crosstalk coupling effect of the measurement data; the equivalent transmission crosstalk and amplitude-phase consistency represent the accuracy of the polarization relative information. As can be seen from Equation (1), low isolation will cause the coupling of co-polarized energy and cross-polarized energy, seriously deteriorating the effectiveness of the information. In addition, the distortion of the observed quantity in representing the scattering characteristics of the ground object caused by the system polarization distortion makes the reflection symmetry constraint invalid, further introducing uncertainty errors in the reconstruction of polarization information. Therefore, the mixed polarization mode requires high system amplitude-phase consistency and isolation, which is the basis for achieving full polarization scattering information reconstruction. The intrinsic relationship between system polarization distortion and information reconstruction is: high isolation and high amplitude-phase consistency of the H-polarization channel and the V-polarization channel cause the measurement equation to degenerate into a pure physical equation that only represents the scattering characteristics of the target.

[0040] Specifically, the step 2 includes:

[0041] First, the second-order moment of the mixed polarization observation It can be decomposed into co-polarization component, cross-polarization component and residual component, namely:

[0042] (3)

[0043] in, represents the co-polarized component, represents the cross-polarization component, represents the residual component, represents the imaginary unit, represents the imaginary part of a complex number, Indicates spatial average, superscript Represents the transpose conjugate operation.

[0044] When the object satisfies the physical constraints of reflection symmetry, the observation matrix satisfies the sparse property. of Norm minimization is used to reconstruct the second-order moment of the full polarization scattering matrix.

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

[0046] (4)

[0047] in, Indicates the value of the variable when the latter formula reaches the minimum value, Represents the reconstructed full polarization scattering matrix The second moment of express norm, Represents the dimension-reduced projection matrix:

[0048] (5)

[0049] At this time, the optimization problem based on formula (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. Estimation of cross-polarization strength :

[0050] (6)

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

[0052] Under the reflection symmetry constraint, the initial value of the second-order moment of the full polarization scattering matrix is Can be set to:

[0053] (7)

[0054] Specifically, the step 3 includes:

[0055] The local density of the cluster center is greater than the density of other elements in the cluster, and the cluster centers of different clusters are far apart. Therefore, the appropriate sample center can be selected based on the local density and relative distance of the sample points.

[0056] Local density The definition is as follows:

[0057] (8)

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

[0059] Relative distance The definition is as follows:

[0060] (9)

[0061] in, It means taking the value with the local density greater than the local density of the current pixel and the minimum value of the latter formula. Denotes the density variable. and Obtained decision value The definition is as follows:

[0062] (10)

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

[0064] Step 1: Calculate the decision value of each pixel in the training sample and sort them in descending order. For each type of ground object, select the 50 elements with the largest decision value and include them in the set of candidate cluster centers. , the element with a larger decision value has a higher priority as the cluster center;

[0065] Step 2: Assemble The element with the largest decision value is transferred to the set that determines the cluster center . Eliminate the collection With collection The element dissimilarity is less than the clustering threshold elements.

[0066] Step 3: Repeat step 2 until the collection There are no elements in .

[0067] Step 4: Within a single category, calculate the elements of the training sample and the determined cluster center The dissimilarity of the elements in the dataset is used to classify the elements into corresponding clusters based on the minimum dissimilarity. The clusters obtained by segmentation participate in the training of the improved Wishart mixture model independently, but all represent the same type of land features.

[0068] Specifically, step 4 includes:

[0069] The Wishart mixture model uses a combination of multiple distributions to fit the true statistical properties of the data. Mathematically, it can be thought of as multiple kernel functions approximating an unknown distribution function. The EM algorithm is used to perform maximum likelihood estimation of the statistical model parameters.

[0070] The distance metric derived in the hypothesis testing framework has an exponential mapping relationship with the likelihood function. The expression is as follows:

[0071] (11)

[0072] in, represents the normalization function, represents a non-negative measurable function, represents the smoothing hyperparameter, represents the class center, Represents model parameters, exp() represents exponential function. The process proposed in this invention uses multiple distance metrics to try to obtain higher classification accuracy, and uses smoothing hyperparameters To replace the visual number to better fit the statistical characteristics of the actual data, namely:

[0073] (12)

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

[0075] The parameters of IWMM are redefined as . The smoothing hyperparameters are based on each pixel To make an estimate, its likelihood function As shown in the following formula:

[0076] (13)

[0077] in, represents all unknown parameters, represents the kth mixing coefficient, and , is the kth latent variable for the i-th pixel The specific implementation of independent and identical distribution, represents the class center of the kth distribution, K represents the total number of subclasses, The probability density function representing the distribution of the modified Wishart mixture model.

[0078] The present invention introduces a scale adjustment factor Increase the degrees of freedom of the model. Furthermore, the equivalent number of views (ENL) can effectively assess the dispersion of observations of fully developed speckle. However, two points are worth noting: 1) When major scatterers exist within the resolution cell, such as when the number of artificial structures or randomly distributed scatterers within the resolution cell is insufficient, the ENL's characterization capability decreases; 2) Weak scatterers are more susceptible to noise, clutter, and blur, resulting in relatively large deviations from the theoretical scattering center.

[0079] Finally, the hyperparameters that maximize the classification accuracy of the training samples are selected iteratively ( , and scale adjustment factor ). In the expectation (E) step (E step of EM algorithm), It is expressed as an estimated value, and the superscript (t) represents the number of iterations. Under the condition of The posterior distribution of satisfy:

[0080] (14)

[0081] The subscript g is a temporary representation to avoid symbol duplication during summation.

[0082] In the maximization (M) step (the M step of the EM algorithm), the estimated posterior probability is used to update the parameters by maximizing the conditional expectation of the log-likelihood function. , the derivation of the iterative expression is still based on the Wishart distribution.

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

[0084] (15)

[0085] in, Indicates the number of samples in a single cluster.

[0086] The iteration expression of the subclass center is:

[0087] (16)

[0088] From this we can see that the normalization function and nonnegative measurable functions Will not affect the sub-category center and weights Estimates.

[0089] Repeat the E and M steps until the parameters converge. The mathematical expression of the iterative convergence condition is shown as follows:

[0090] (17)

[0091] (18)

[0092] In formula (17) and formula (18), and represent the thresholds of subclass centers and weights respectively.

[0093] Specifically, step 5 includes:

[0094] Classification labels of the dataset It can be obtained by identifying the category with the largest probability density, that is:

[0095] (19)

[0096] in, Indicates the value of the variable l when the latter formula reaches its maximum value, represents the probability of belonging to class l, Indicates the number of categories.

[0097] Example:

[0098] The experimental data involved in this paper includes full-polarimetric and mixed-polarimetric L-band data acquired on December 18, 2023, and January 11, 2024, respectively. The mixed-polarimetric data is 12,000 × 22,300 pixels, and the full-polarimetric data is 12,000 × 21,300 pixels, representing approximately 42 km in azimuth and 20 km in slant range. The dataset includes seven defined categories: cabbage, wheat, tea, forest, water, building, and bare soil. Figure 2 (a) Figure 2 (b) Figure 2 (c) shows the corresponding Pauli pseudo-color image, m-chi decomposition image and geographic ground truth. Figure 3 The final classified image is shown. Figure 3 (a) is the full polarization classification result, Figure 3 (b) is the mixed polarization classification result. The corresponding classification accuracy comparison is shown in Table 1.

[0099] Table 1

[0100]

[0101] The results show that the second-order moment of the full polarization scattering matrix reconstructed from the hybrid polarization mode observations is close to the true full polarization mode, that is, the hybrid polarization mode has the same classification ability as the full polarization mode, which verifies the effectiveness of the algorithm.

[0102] like Figure 4As shown, the present invention also provides a hybrid polarization system underdetermined information reconstruction device based on physical constraints to implement the steps of the above method, specifically including the following modules:

[0103] Model building module, which builds the system performance model, considers the non-ideal characteristics of the system and the reciprocity assumption, and establishes a realistic model of the mixed polarization observation quantity;

[0104] The second-order moment reconstruction module decomposes the second-order moment of the mixed polarization observations according to the system performance model and under the reflection symmetry constraint, estimates the cross-polarization components, and reconstructs the second-order moment of the full polarization scattering matrix;

[0105] The training set partitioning module adopts an unsupervised training set pre-segmentation strategy, selects cluster centers based on the local density and relative distance of sample points, and divides the training set into multiple subclusters;

[0106] The model training module is based on the improved Wishart mixture model and uses multiple distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster;

[0107] The classification module uses the trained model to classify the polarimetric SAR images and obtain the classification results.

[0108] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and runnable on the processor, characterized in that 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.

[0109] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that 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.

[0110] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk drives, CD-ROMs, optical storage devices, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention may be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0111] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0112] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0113] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0114] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0115] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints, characterized in that: The following steps are involved: Step 1: Construct a system performance model of the hybrid polarimetric SAR system, consider the non-ideal characteristics of the hybrid polarimetric SAR system and the reciprocity assumption, and establish a realistic model of the hybrid polarimetric observations; Step 2: Based on the system performance model and under the reflection symmetry constraint, the second-order moments of the mixed polarization observations are decomposed, the cross-polarization components are estimated, and the second-order moments of the full polarization scattering matrix are reconstructed. Step 3: Use the unsupervised training set pre-segmentation strategy to select cluster centers based on the local density and relative distance of sample points, and divide the training set into multiple subclusters; Step 4: Based on the improved Wishart hybrid model, a variety of distance metrics and hyperparameter optimization strategies are used to train the model for each sub-cluster; the model training in step 4 adopts an iterative optimization hyperparameter selection method to maximize the classification accuracy of the training samples; the hyperparameter is the distance threshold , clustering threshold and scale adjustment factor ; The model parameters of the modified Wishart mixing model are redefined as ; Improved likelihood function of the Wishart mixture model based on estimating the smooth hyperparameters of each element As shown in the following formula: （13） in, represents the smoothing hyperparameter, represents the class center, represents the covariance matrix of the i-th pixel, represents all unknown parameters, represents the kth mixing coefficient, and , is the relationship between the i-th element and the k-th latent variable The specific implementation of independent and identical distribution, 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; Step 5: Use the trained improved Wishart mixture model to classify the polarimetric SAR image to obtain the classification results.

2. The method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints according to claim 1, characterized in that: The reflection symmetry constraint in step 2 is used to ensure the sparse characteristics of the observation matrix, and to achieve reconstruction of the second-order moment of the full polarization scattering matrix by minimizing the norm of the residual component.

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

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

5. The method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints according to claim 1, characterized in that: The classification result in step 5 is obtained by identifying the category with the largest probability density, thereby improving the classification accuracy.

6. The method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints according to claim 1, characterized in that: The system performance model in step 1 takes into account the absolute amplitude and phase factors, equivalent transmission crosstalk, and reception distortion matrix introduced by the system to ensure the accuracy and robustness of the model.

7. A hybrid polarization system underdetermined information reconstruction device based on physical constraints, characterized by: Includes the following modules: Model building module, which builds the 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 realistic model of the hybrid polarization observation quantity; The second-order moment reconstruction module decomposes the second-order moment of the mixed polarization observations according to the system performance model and under the reflection symmetry constraint, estimates the cross-polarization components, and reconstructs the second-order moment of the full polarization scattering matrix; The training set partitioning module adopts an unsupervised training set pre-segmentation strategy, selects cluster centers based on the local density and relative distance of sample points, and divides the training set into multiple subclusters; The model training module is based on the improved Wishart mixture model and uses multiple distance metrics and hyperparameter optimization strategies to train the model for each sub-cluster; Model training uses an iterative optimization hyperparameter selection method to maximize the classification accuracy of training samples; The hyperparameter is the distance threshold , clustering threshold and scale adjustment factor ; The model parameters of the modified Wishart mixing model are redefined as ; Improved likelihood function of the Wishart mixture model based on estimating the smooth hyperparameters of each element As shown in the following formula: （13） in, represents the smoothing hyperparameter, represents the class center, represents the covariance matrix of the i-th pixel, represents all unknown parameters, represents the kth mixing coefficient, and , is the relationship between the i-th element and the k-th latent variable The specific implementation of independent and identical distribution, 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; The classification module uses the trained improved Wishart mixture model to classify the polarimetric SAR images and obtain the classification results.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints are implemented as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for reconstructing underdetermined information of a hybrid polarimetric system based on physical constraints are implemented as claimed in any one of claims 1 to 6.

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