InSAR phase optimization method and system based on composite covariance matrix and tensor column decomposition

Abstract

This invention discloses an InSAR phase optimization method and system based on composite covariance matrix and tensor column decomposition. The method includes: S1, acquiring temporal interferometric data and constructing the covariance matrix corresponding to each pixel based on an adaptive window; S2, optimizing the sample covariance matrix using a fusion estimation strategy, and generating a composite covariance matrix based on the fusion of independently estimated phase and amplitude components; S3, dividing the original SAR image domain into multiple subspaces, and stacking the composite covariance matrix corresponding to each pixel along the spatial dimension into a third-order tensor in each subspace; S4, constructing a low-rank sparse tensor joint tensor decomposition model based on the tensor column kernel norm and L1 norm, separating the sparse tensor from the third-order tensor, and obtaining the low-rank tensor; S5, updating the sparse tensor based on a multivariate decoupling optimization solution strategy, and introducing truncated tensor column singular value decomposition to robustly update the low-rank tensor; S6, reconstructing the optimized covariance matrix based on the low-rank tensor, and solving for the final temporally optimized phase.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing and remote sensing monitoring technology, and relates to a synthetic aperture radar interferometric measurement time-series phase optimization technique based on amplitude-phase fusion covariance matrix and tensor column sparse low-rank decomposition. The invention is entitled "InSAR Phase Optimization Method and System Based on Composite Covariance Matrix and Tensor Column Decomposition". Background Technology

[0002] Synthetic Aperture Radar Interferometry (InSAR) technology uses the phase difference between two or more SAR observations to invert surface deformation or topographic information. However, in practical applications, InSAR observation phases often contain significant noise due to factors such as temporal decorrelation, geometric decorrelation, and atmospheric delay. Especially in long baseline or complex terrain environments, the accuracy of the covariance matrix estimation directly determines the quality of the final interferometric phase.

[0003] Existing temporal phase estimation methods mainly include point target analysis-based methods (such as PS-InSAR) and distributed target analysis-based methods. Among these, EMI and PTA address phase consistency issues to some extent, but in low-coherence regions, single-sample covariance matrix estimation is often affected by noise, leading to estimation bias. Furthermore, while traditional methods based on principal component analysis or robust principal component analysis can remove some noise, they typically flatten the data into a two-dimensional matrix, ignoring the neighborhood structure information of the image in high-dimensional space. Additionally, traditional kernel norm optimization has high computational complexity and limited feature extraction capabilities when processing high-dimensional data. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides an InSAR (Integrated Aperture Radar Interferometry) phase optimization method and system based on composite covariance matrix and tensor column decomposition. This invention suppresses outlier interference by constructing a composite covariance matrix and introduces tensor column decomposition technology to mine higher-order spatiotemporal correlations in the data, thereby achieving reliable phase reconstruction.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition includes the following steps:

[0007] S1. Acquire temporal interferometric data and construct the covariance matrix corresponding to each pixel based on the adaptive window;

[0008] S2. Optimize the sample covariance matrix using a fusion estimation strategy, and generate a composite covariance matrix based on the fusion of independently estimated phase and amplitude components.

[0009] S3. Divide the original synthetic aperture radar (SAR) image domain into multiple subspaces, and stack the composite covariance matrix corresponding to each pixel into a third-order tensor along the spatial dimension within each subspace.

[0010] S4. Construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of tensors, and separate sparse tensors from the constructed third-order tensors to obtain low-rank tensors that represent the real phase signals.

[0011] S5. The multivariate decoupling optimization strategy is used to solve the optimization model. The soft threshold operator is applied to update the sparse tensor. Singular value decomposition of truncated tensor columns is introduced to robustly update the low-rank tensor.

[0012] S6. Based on the low-rank tensor output from step S5, the optimized covariance matrix is ​​reconstructed, and the final time-series optimized phase is solved using the principal eigenvector method.

[0013] As a preferred embodiment, step S2 specifically includes:

[0014] S21. Principal component reconstruction extracts the principal component phase. The normalized covariance matrix of the pixel to be processed and its neighborhood is flattened into column vectors and centered. The covariance vector of the center pixel is reconstructed through singular value decomposition, and its phase angle is extracted to obtain the estimated phase component of principal component reconstruction. ;

[0015] S22. Quantities of the amplitudes of off-diagonal elements within the local window are used to determine the noise floor. A second-order moment correction model is used to calculate the squared debiased amplitude based on the observed amplitude and the noise floor, thereby obtaining the debiased amplitude. Based on adaptive weighting coefficients, the debiased amplitude is weighted and fused with the average observed amplitude within the local window to obtain the adaptive neighborhood sample amplitude component. ;

[0016] S23. Based on the decoupled components described above, execute the fusion estimation strategy to construct a composite covariance matrix. Perform a Hadamard product operation on the complex exponential form of the calculated adaptive neighborhood sample amplitude matrix and the principal component reconstruction estimated phase matrix to generate the composite covariance matrix. .

[0017] As a preferred embodiment, in step S21, the principal component reconstruction estimates the phase matrix. for:

[0018]

[0019] in, For pixel covariance vectors, This is the mean vector of the sample matrix within the local window. The largest singular value after centering the sample matrix. For the corresponding left singular vector, For the corresponding right singular vector, the first Conjugate of elements, This indicates the phase angle taking operation. This indicates that the vector is converted back to matrix form.

[0020] As a preferred embodiment, step S22 involves adapting the neighborhood sample amplitude matrix. for:

[0021]

[0022] in, The corrected debiasing amplitude, The observed sample coherence coefficient amplitude, The preset quantile for the amplitude of off-diagonal elements within a local window. This is the mean matrix of the covariance matrix of observations within the local window. The matrix is ​​composed of the debiasing amplitude. These are adaptive weighting coefficients calculated based on a noise basis.

[0023] As a preferred embodiment, in step S23, the composite covariance matrix for:

[0024]

[0025] in, This is the adaptive neighborhood sample magnitude estimation matrix. Covariance estimation of the phase matrix, The imaginary unit, It represents the Hadamardi (or Hadama) stack.

[0026] As a preferred embodiment, in step S3, the original SAR image domain is divided into multiple subspaces, and within each subspace, the composite covariance matrix of the pixels generated in step S2 is stacked along the spatial dimension to form a third-order tensor. .

[0027] As a preferred embodiment, in step S4, a joint decomposition model of low-rank sparse tensors based on the tensor column nuclear norm and L1 norm is constructed. The sparse tensors are separated from the constructed third-order tensors to obtain low-rank tensors representing the true phase signal. The decomposition model is as follows:

[0028] ;

[0029] Where Z is the constructed third-order tensor, It is a low-rank tensor; It is a sparse tensor; Representing sparse tensors norm; For regularization parameters, The nuclear norm of a sequence of tensors representing a low-rank tensor. This is the regularization parameter.

[0030] As a preferred embodiment, in step S5, a multivariate decoupling optimization strategy is used to solve the decomposition model. In each iteration, a soft threshold operator is applied to update the sparse tensor, and a truncated tensor column singular value decomposition is introduced to robustly update the low-rank tensor. This process is repeated until the convergence condition is met or the preset maximum number of iterations is reached, and the final low-rank tensor is output. The specific iterative update formula is as follows:

[0031]

[0032] in, For the first The sparse tensor after the next iteration. For the first The low-rank tensor of the next iteration. For the constructed third-order tensor, For sparse regularization parameters, It represents the Hadamah accumulation. For symbolic functions, This is an operation to determine the maximum value of each element. The residual tensor after removing sparse noise; For the first The low-rank tensor after the next iteration consists of three core tensors. Through tensor modal product Reconstructed from the residual tensor, the core tensor is derived from the residual tensor. Obtained by performing singular value decomposition algorithm on truncated tensor columns.

[0033] The core tensor is derived from the third-order residual tensor. The specific calculation formula is obtained by performing singular value decomposition on a truncated tensor sequence:

[0034]

[0035] in, Let be the matrix formed by expanding the residual tensor along the first dimension; and These are the left singular vector matrix, the diagonal matrix containing the maximum singular value, and the right singular vector conjugate transpose matrix, respectively, after each truncated singular value decomposition. This is an intermediate transition matrix; and The tensor column rank is required to satisfy the truncation error threshold; This indicates that the matrix will be reshaped into a tensor of the specified dimensions.

[0036] As a preferred embodiment, in step S6, the optimized covariance matrix is ​​obtained based on the low-rank tensor reconstruction output in step S5, and the final time-series optimized phase is calculated using the principal eigenvector method. The specific calculation formula is as follows:

[0037]

[0038] in, This is the final low-rank tensor output after the iteration in step S5 converges; The first slicing extracted from low-rank tensors The optimized covariance matrix corresponding to each pixel; For matrix The largest eigenvalue, This is the corresponding normalized principal feature vector; This indicates the operation for extracting the phase angle of a complex number; This is used to obtain the time-optimized phase estimate value corresponding to the pixel.

[0039] This invention also provides an InSAR phase optimization system based on composite covariance matrix and tensor column decomposition for performing the above method, which includes the following modules:

[0040] The data preprocessing module is used to acquire temporal interferometric data and construct the covariance matrix corresponding to each pixel based on an adaptive window;

[0041] The composite covariance matrix construction module is used to optimize the sample covariance matrix using a fusion estimation strategy, generating a composite covariance matrix based on the fusion of independently estimated phase and amplitude components.

[0042] The third-order tensor construction module is used to divide the original SAR image domain into subspaces and stack the composite covariance matrix of pixels along the spatial dimension into a third-order tensor in each subspace.

[0043] The low-rank sparse tensor decomposition module is used to construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of tensor columns. It separates sparse tensors from the constructed third-order tensors to obtain low-rank tensors that represent the true phase signals. It also uses a multivariate decoupling optimization strategy to solve the optimization model, applies a soft threshold operator to update the sparse tensors, and introduces truncated tensor column singular value decomposition to robustly update the low-rank tensors.

[0044] The phase extraction and reconstruction module is used to reconstruct the optimized covariance matrix using the final output low-rank tensor, and to extract the final time-optimized phase using the principal eigenvector method.

[0045] Compared with the prior art, the beneficial effects of this invention are:

[0046] (1) The present invention adopts a composite covariance matrix construction method. By fusing the phase estimation results of the fixed center sample covariance matrix with the amplitude estimation results of adaptive nonlocal sparse contraction, the estimation bias of the single estimator in complex noise environment is effectively corrected, and the robustness of the initial covariance matrix to strong decorrelation interference is improved.

[0047] (2) The present invention optimizes the phase based on the tensor column robust principal component analysis model. It uses tensor column decomposition technology to separate the low-rank phase signal and sparse noise components in the high-dimensional tensor space. While suppressing random noise interference, it maintains the spatial neighborhood structure information of the interference phase and improves the accuracy of time series phase estimation in low coherence region. Attached Figure Description

[0048] Figure 1 This is a flowchart of the InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to Embodiment 1 of the present invention;

[0049] Figure 2 This is a schematic diagram of the InSAR phase optimization system based on composite covariance matrix and tensor column decomposition according to Embodiment 2 of the present invention. Detailed Implementation

[0050] To more clearly illustrate the embodiments of the present invention, specific implementation methods will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0051] The InSAR phase optimization method and system based on composite covariance matrix and tensor column decomposition of the present invention can be summarized as follows: Temporal interferometric data of the pixel to be processed and its spatial neighborhood are acquired, and a composite covariance matrix corresponding to each pixel is constructed. Then, a fusion estimation strategy is adopted to independently estimate the phase component and amplitude component within a local spatial window using principal component reconstruction and adaptive neighborhood sampling methods, respectively, and fuse them into a composite covariance matrix. Next, the original image domain is divided into subspaces, and within each subspace, the composite covariance matrix of the pixels is stacked along the spatial dimension to form a third-order tensor. A low-rank sparse tensor joint decomposition model based on the tensor column kernel norm and L1 norm is constructed, and a multivariate decoupling optimization strategy is used to separate the sparse tensor and output a low-rank tensor. Finally, the optimized covariance matrix is ​​reconstructed using the output low-rank tensor, and the final temporally optimized phase is extracted using the principal eigenvector method.

[0052] Example 1:

[0053] like Figure 1 As shown in the figure, this embodiment presents an InSAR phase optimization method based on composite covariance matrix and tensor column decomposition, which includes the following steps:

[0054] Step 1: Acquire temporal interferometric data and construct the covariance matrix for each pixel based on an adaptive window.

[0055] Step 2: Optimize the sample covariance matrix using a fusion estimation strategy. Generate a composite covariance matrix by fusing the independently estimated phase and amplitude components. The composite covariance matrix synthesized in this way combines the phase information reconstructed from the principal components with the amplitude information after bias correction, which improves the signal-to-noise ratio of the input data and provides a data foundation for subsequent tensor column decomposition.

[0056] Specifically, step one above includes the following steps:

[0057] Obtain coverage of the target research area After scene registration, the complex image sequence of a single view is processed, and the complex observation value of each pixel in the time dimension is extracted to construct a dimensionless complex image. Time series observation vector ;

[0058] For each central pixel to be processed, an initial local spatial neighborhood window is set. Based on statistical homogeneity criteria such as amplitude or distribution similarity, statistically homogeneous pixels with similar scattering characteristics to the central pixel are selected from the local spatial neighborhood window to construct an adaptive window whose shape and size dynamically change with the features of the ground.

[0059] Using the time-series observation vectors of all statistically homogeneous pixels extracted within the adaptive window, the sample covariance matrix of the center pixel is calculated as follows:

[0060]

[0061] in, The dimension to be constructed is The sample covariance matrix, This refers to the total number of statistically homogeneous pixels contained within the adaptive window. For the first in the adaptive window The time-series observation vector of statistically homogeneous pixels It is the conjugate transpose of the time series observation vector.

[0062] Specifically, step two above includes the following steps:

[0063] 1) Principal component reconstruction is used to extract the phase of the principal components. The normalized covariance matrix of the pixel to be processed and its neighborhood is flattened into column vectors and centered. The covariance vector of the center pixel is reconstructed through singular value decomposition, and its phase angle is extracted to obtain the estimated phase component of the principal component reconstruction. The calculation formula is as follows:

[0064]

[0065] in, For pixel covariance vectors, This is the mean vector of the sample matrix within the local window. The largest singular value after centering the sample matrix. For the corresponding left singular vector, For the corresponding right singular vector, the first Conjugate of elements, This indicates the phase angle taking operation. This indicates that the vector is converted back to matrix form.

[0066] 2) Calculate the bias correction for the amplitude of adaptive neighborhood samples. The 5th percentile of the amplitude of off-diagonal elements within the local window is used as the noise base. The observed amplitude was corrected using a second-order moment model. The debiasing amplitude is obtained. Combined with adaptive weights Calculate the final adaptive neighborhood sample magnitude matrix The calculation formula is as follows:

[0067]

[0068] in, The corrected debiasing amplitude, The observed sample coherence coefficient amplitude, This is a preset quantile for the amplitude of off-diagonal elements within a local window. This is the mean matrix of the covariance matrix of observations within the local window. The matrix is ​​composed of the debiasing amplitude. These are adaptive weighting coefficients calculated based on a noise basis.

[0069] 3) Synthesize the composite covariance matrix .

[0070] in, For the adaptive neighborhood sample magnitude matrix, Principal component reconstruction estimates the phase matrix. The imaginary unit, It represents the Hadamardi (or Hadama) stack.

[0071] Step 3: Divide the original SAR image domain into multiple subspaces. Within each subspace, stack the composite covariance matrix G synthesized in Step 2 along the spatial dimension to form a third-order tensor. The third-order tensor constructed in this way preserves the high-dimensional temporal-temporal-spatial structural features of InSAR data, enabling subsequent processing to not only utilize the correlation in the temporal dimension but also fully leverage the nonlocal self-similarity in the spatial dimension, thereby improving denoising performance while maintaining spatial resolution.

[0072] Step 4: Construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of the tensor column. Separate the sparse tensors from the constructed third-order tensors to obtain the low-rank tensors representing the true phase signal. The decomposition model is as follows:

[0073]

[0074] in, It is a low-rank tensor; It is a sparse tensor; Representing sparse tensors norm; For regularization parameters, The tensor column kernel norm represents the low-rank tensor. The model utilizes the expressive power of tensor column decomposition for high-dimensional data to describe the low-rank structure of InSAR data; at the same time, the introduction of L1 norm constraints enables the model to separate out large outlier interference points in the data, enhancing the algorithm's adaptability in complex noise environments.

[0075] Step 5: Solve the decomposition model using a multivariate decoupling optimization strategy, apply a soft threshold operator to update the sparse tensor, and introduce singular value decomposition of truncated tensor columns to robustly update low-rank tensors. The specific iterative formula is as follows:

[0076]

[0077] in, For the first The sparse tensor after the next iteration. For the first The low-rank tensor of the next iteration. For the constructed third-order tensor, For sparse regularization parameters, It represents the Hadamah accumulation. For symbolic functions, This is an operation to determine the maximum value of each element. The residual tensor after removing sparse noise; For the first The low-rank tensor after the next iteration consists of three core tensors. Through tensor modal product Reconstructed from the residual tensor, the core tensor is derived from the residual tensor. The singular value decomposition algorithm of the truncated tensor column is used to obtain it.

[0078] This step, through alternating iterations, utilizes a soft thresholding operator to handle large-amplitude outlier noise and a truncated tensor column singular value decomposition algorithm to preserve the main energy of the data while removing random noise, thus suppressing mixed noise. This process is repeated until the convergence condition is met or the preset maximum number of iterations is reached, outputting the final low-rank tensor. .

[0079] Step 6: Low-rank tensor based on the output of Step 5 Extract the slice matrix corresponding to each pixel. The final timing-optimized phase is calculated using the principal eigenvector method, with the specific calculation formula as follows:

[0080]

[0081] in, This is the final low-rank tensor output after the iteration in step five converges; The first slicing extracted from low-rank tensors The optimized covariance matrix corresponding to each pixel; For matrix The largest eigenvalue, This is the corresponding normalized principal feature vector; This indicates the operation for extracting the phase angle of a complex number; This is used to obtain the time-optimized phase estimate value corresponding to the pixel.

[0082] To quantitatively analyze the differences in the effectiveness of different phase optimization methods in suppressing decoherence, this invention uses the Monte Carlo simulation method to simulate L=90-view temporal InSAR data of N=60 SAR images, with reference to Sentinel-1 SAR satellite parameters. The temporal coherence amplitude matrix is ​​generated by two temporal decoherence models, exponential and seasonal, and the system phase sequence is generated by a temporal linear deformation trend (deformation rate v=5 mm / a).

[0083] The experimental metric used was the root mean square error of deformation rate (RMSE, unit: mm / a). Table 1 shows the statistical results of the deformation rate RMSE for five different phase optimization algorithms under two different time-decoherence models. The algorithms compared included PTA, PCA, EMI, Tucker, and the novel method proposed in this invention.

[0084] Table 1. Comparison of deformation rate RMSE (mm / a) for different phase optimization algorithms

[0085]

[0086] Analysis of the experimental data in Table 1 shows that the proposed method based on hybrid robust covariance and tensor column decomposition achieves the lowest RMSE values ​​under both different time-decoherence models, indicating that its phase recovery accuracy is superior to the other four comparative algorithms. Specifically, the PTA method, due to its incomplete utilization of spatial neighborhood information, has RMSEs of 5.7 mm / a and 5.3 mm / a under the exponential and seasonal models, respectively; the PCA and EMI methods maintain RMSEs between 2.6 mm / a and 3.6 mm / a. The traditional Tucker decomposition method introduces a tensor model, reducing the RMSE to 1.5 mm / a to 1.9 mm / a, but still differs from the method of this invention. Further comparison revealed that in the exponential decay model, the deformation rate RMSE of the method in this invention was 0.7 mm / a, a reduction of approximately 73% compared to the EMI method (2.6 mm / a), and a reduction of approximately 53% compared to the similar Tucker tensor decomposition (1.5 mm / a). This demonstrates that the present invention, by utilizing tensor column decomposition combined with amplitude-phase fusion covariance matrix, can recover the true phase history from noise-inundated signals. Furthermore, in the seasonal decoherence model, the errors of all methods increased, while the RMSE of the method in this invention was 1.0 mm / a, an improvement of approximately 47% in accuracy compared to the Tucker method's 1.9 mm / a. This verifies that the tensor column robust principal component analysis model constructed in this invention can separate non-stationary noise through sparse constraints, exhibiting good adaptability and stability under complex temporal decoherence modes, reducing phase estimation errors, and improving the accuracy of long-term InSAR deformation monitoring.

[0087] Example 2

[0088] like Figure 2 As shown, this embodiment discloses an InSAR phase optimization system based on composite covariance matrix and tensor column decomposition, used to execute the above method. It includes a data preprocessing module, a composite covariance matrix construction module, a third-order tensor construction module, a low-rank sparse tensor decomposition module, and a phase extraction and reconstruction module. Wherein:

[0089] The data preprocessing module in this embodiment is used to acquire temporal interference data and construct the covariance matrix corresponding to each pixel based on an adaptive window.

[0090] The composite covariance matrix construction module in this embodiment is used to optimize the sample covariance matrix using a fusion estimation strategy, and to generate a composite covariance matrix based on the fusion of independently estimated phase components and amplitude components.

[0091] The third-order tensor construction module in this embodiment is used to divide the original SAR image domain into subspaces, and stack the composite covariance matrix corresponding to the pixel into a third-order tensor along the spatial dimension in each subspace.

[0092] The low-rank sparse tensor decomposition module in this embodiment is used to construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of tensor columns, separate sparse tensors from the constructed third-order tensors to obtain low-rank tensors that represent the true phase signals, solve the optimization model using a multivariate decoupling optimization strategy, update the sparse tensors using a soft threshold operator, and introduce truncated tensor column singular value decomposition to robustly update the low-rank tensors.

[0093] The phase extraction and reconstruction module in this embodiment is used to reconstruct the optimized covariance matrix using the final output low-rank tensor, and to extract the final time-optimized phase using the principal eigenvector method.

[0094] The specific process of this embodiment can be referred to in the above embodiment of the InSAR phase optimization method based on composite covariance matrix and tensor column decomposition, which will not be repeated here.

[0095] In summary, this invention effectively solves the problem of severe decorrelation noise in low coherence regions through the synergistic effect of amplitude-phase fusion covariance matrix reconstruction and low-rank sparse decoupling based on tensor column decomposition.

[0096] The above description is merely a detailed explanation of preferred embodiments and principles of the present invention. For those skilled in the art, there may be changes in specific implementation methods based on the ideas provided by the present invention, and these changes should also be considered within the scope of protection of the present invention.

Claims

1. An InSAR phase optimization method based on composite covariance matrix and tensor column decomposition, characterized in that, Includes the following steps: S1. Acquire temporal interferometric data and construct the covariance matrix corresponding to each pixel based on the adaptive window; S2. Optimize the sample covariance matrix using a fusion estimation strategy, and generate a composite covariance matrix based on the fusion of independently estimated phase and amplitude components. S3. Divide the original synthetic aperture radar image domain into multiple subspaces, and stack the composite covariance matrix corresponding to the pixel into a third-order tensor along the spatial dimension in each subspace. S4. Construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of tensors, and separate sparse tensors from the third-order tensors constructed in step S3 to obtain low-rank tensors that represent the real phase signals. S5. The multivariate decoupling optimization strategy is used to solve the optimization model. The soft threshold operator is applied to update the sparse tensor. Singular value decomposition of truncated tensor columns is introduced to robustly update the low-rank tensor. S6. Based on the low-rank tensor output from step S5, the optimized covariance matrix is ​​reconstructed, and the final time-series optimized phase is solved using the principal eigenvector method.

2. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 1, characterized in that, Step S2 specifically includes: S21. Principal component reconstruction extracts the principal component phase. The normalized covariance matrix of the pixel to be processed and its neighborhood is flattened into column vectors and centered. The covariance vector of the center pixel is reconstructed through singular value decomposition, and its phase angle is extracted to obtain the estimated phase component of principal component reconstruction. ; S22. Calculate the quantiles of the amplitudes of off-diagonal elements within the local window to determine the noise floor. Using a second-order moment correction model, calculate the squared debiased amplitude based on the observed amplitude and the noise floor to obtain the debiased amplitude. Based on adaptive weighting coefficients, weight and fuse the debiased amplitude with the average observed amplitude within the local window to obtain the adaptive neighborhood sample amplitude component. ; S23. Based on the above decoupled components, execute the fusion estimation strategy to construct the composite covariance matrix, and calculate the adaptive neighborhood sample amplitude matrix. Phase matrix estimated by principal component reconstruction Perform the Hadamard product operation on the complex exponential form to generate the composite covariance matrix. .

3. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 2, characterized in that, In step S21, the principal components reconstruct and estimate the phase matrix. for: in, The pixel covariance vector This is the mean vector of the sample matrix within the local window. The largest singular value after centering the sample matrix. For the corresponding left singular vector, For the corresponding right singular vector, the first Conjugate of elements, This indicates the phase angle taking operation. This indicates that the vector is converted back to matrix form.

4. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 3, characterized in that, In step S22, the adaptive neighborhood sample amplitude matrix for: in, The corrected bias amplitude. The observed sample coherence coefficient amplitude, The preset quantile for the amplitude of off-diagonal elements within a local window. This is the mean matrix of the covariance matrix of observations within the local window. The matrix is ​​composed of the debiasing amplitude. These are adaptive weighting coefficients calculated based on a noise basis.

5. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 4, characterized in that, In step S23, the composite covariance matrix for: in, This is the adaptive neighborhood sample magnitude estimation matrix. To estimate the phase matrix for covariance, The imaginary unit, It represents the Hadamardi (or Hadama) stack.

6. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 5, characterized in that, Step S3: Divide the original SAR image domain into multiple subspaces, and stack the composite covariance matrices generated in step S2 along the spatial dimension into a third-order tensor within each subspace. .

7. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 6, characterized in that, Step S4 specifically includes: S4. Construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of tensors, and separate sparse tensors from the constructed third-order tensors to obtain low-rank tensors representing the true phase signal. The decomposition model is as follows: Where Z is the constructed third-order tensor. It is a low-rank tensor; It is a sparse tensor; Representing sparse tensors norm; For regularization parameters, The nuclear norm of a sequence of tensors representing a low-rank tensor; This is the regularization parameter.

8. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 7, characterized in that, Step S5 specifically includes: S5. A multivariate decoupling optimization strategy is employed to solve the optimization model. A soft threshold operator is applied to update the sparse tensor, and truncated tensor column singular value decomposition is introduced to robustly update the low-rank tensor. This process is repeated until the convergence condition is met or the preset maximum number of iterations is reached, and the final low-rank tensor is output. The specific iterative update formula is as follows: in, For the first The sparse tensor after the next iteration. For the first The low-rank tensor of the next iteration. For the constructed third-order tensor, For sparse regularization parameters, It represents the Hadamah accumulation. For symbolic functions, This is an operation to determine the maximum value of each element. The residual tensor after removing sparse noise; For the first The low-rank tensor after the next iteration consists of three core tensors. Through tensor modal product Reconstructed from the residual tensor, the core tensor is derived from the residual tensor. Obtained by performing singular value decomposition algorithm on truncated tensor columns.

9. The InSAR phase optimization method based on composite covariance matrix and tensor column decomposition according to claim 8, characterized in that, Step S6 specifically includes: S6. Based on the low-rank tensor output from step S5, the optimized covariance matrix is ​​reconstructed, and the final time-series optimized phase is calculated using the principal eigenvector method. The specific calculation formula is as follows: in, This is the final low-rank tensor output after the iteration in step S5 converges; The first slicing extracted from low-rank tensors The optimized covariance matrix corresponding to each pixel; For matrix The largest eigenvalue, This is the corresponding normalized principal feature vector; This indicates the operation for extracting the phase angle of a complex number; This is used to obtain the time-optimized phase estimate value corresponding to the pixel.

10. An InSAR phase optimization system based on hybrid robust covariance and tensor column decomposition, used to perform the method as described in any one of claims 1-9, characterized in that, Includes the following modules: The data preprocessing module is used to acquire temporal interferometric data and construct the covariance matrix corresponding to each pixel based on an adaptive window; The composite covariance matrix construction module is used to optimize the sample covariance matrix using a fusion estimation strategy, generating a composite covariance matrix based on the fusion of independently estimated phase and amplitude components. The third-order tensor construction module is used to divide the original SAR image domain into subspaces, and stack the composite covariance matrix corresponding to the pixel along the spatial dimension into a third-order tensor in each subspace. The low-rank sparse tensor decomposition module is used to construct a joint decomposition model of low-rank sparse tensors based on the nuclear norm and L1 norm of tensor columns. It separates sparse tensors from the constructed third-order tensors to obtain low-rank tensors that represent the true phase signals. It also uses a multivariate decoupling optimization strategy to solve the optimization model, applies a soft threshold operator to update the sparse tensors, and introduces truncated tensor column singular value decomposition to robustly update the low-rank tensors. The phase extraction and reconstruction module uses the final low-rank tensor to reconstruct the optimized covariance matrix and uses the principal eigenvector method to extract the final time-optimized phase.

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