Distributed Target InSAR Phase Estimation Method Based on Tensor Decomposition

Abstract

The present invention discloses a distributed target InSAR phase estimation method based on tensor decomposition, comprising the following steps: first, registering the full stack SAR image and extracting homogeneous pixels; then, dividing the registered image into multiple small subspaces; finally, stacking the pixel covariance matrix within each subspace into a third-order tensor form, and constructing an optimal phase estimation tensor decomposition model to obtain the optimal phase estimation value of each pixel. The present invention utilizes the advantages of tensors in data description and storage, constructs a third-order tensor model using the covariance matrices of multiple pixels, replaces existing matrix operations with tensor operations, replaces matrix eigendecomposition with corresponding tensor decomposition, constructs an optimal phase estimation tensor decomposition model, realizes distributed target phase optimization, and converts the "pixel-by-pixel" calculation mode in the existing optimal phase estimation method into a "multi-pixel" calculation mode, so as to improve the calculation efficiency and accuracy of phase estimation.

Description

Technical Field

[0001] The present invention belongs to the field of synthetic aperture radar interferometry (InSAR) data, and in particular relates to a distributed target InSAR phase estimation method based on tensor decomposition. Background Art

[0002] Optimal phase estimation is a key technical step in distributed target InSAR, proposed to establish the principle of phase consistency. Simply put, per-pixel phase consistency means that for each of the three interferometric phases obtained from three SLC images, each interferometric phase can be reconstructed from the other two interferometric phases. However, for distributed target InSAR, this phase consistency principle is broken after multi-look filtering. To restore the original phase consistency principle and improve the signal-to-noise ratio (SNR), the phase must be re-estimated. Different phase estimation methods have varying computational efficiency and accuracy. Effective phase estimation methods can reduce the impact of noise and improve the signal-to-noise ratio (SNR), which is crucial for improving the quality of interferograms and the accuracy of temporal deformation model solutions.

[0003] As early as 2002, researchers proposed a phase estimation scheme known as the phase triangulation algorithm (PTA). Under optimal phase estimation conditions, PTA seeks the maximum likelihood estimate (MLE) of the system phase. In 2011, researchers applied the maximum likelihood estimation method to the SqueeSAR framework. While the covariance estimation in MLE is asymptotically unbiased and efficient, its performance degrades significantly under low coherence conditions. Many improved covariance matrix estimation methods have attempted to reduce the coherence estimation bias, and robust M-estimators have been proposed as an alternative to MLE. In 2012, researchers proposed an InSAR interferometric phase estimation method based on generalized correlation steering vectors. First, a generalized correlation steering vector with a large registration error is determined from the joint data vector. The generalized correlation steering vector is then used to estimate the synthetic aperture radar interferometric phase. This method achieves automatic image registration while effectively reducing interferometric phase noise. Theoretical analysis and computer simulation results demonstrate that this method can accurately estimate the terrain interferometric phase even with a registration error of one pixel. In 2014, researchers proposed a phase estimation method based on eigendecomposition (EVD) and applied it to the CAESAR framework. Experiments showed that this method can effectively improve computational efficiency. In 2016, researchers proposed an eigendecomposition method (EVC) that uses the coherence matrix instead of the covariance matrix. The main advantage of this method is that it compensates for amplitude imbalances between SAR images. In 2016, researchers proposed a phase estimation method based on integer least squares (ILS). Studies have shown that this method has high estimation accuracy. In 2016, Bai Shengxiang et al. proposed an optimal phase estimation method based on weighted joint covariance matrix fitting. This method fully utilizes the coherence information in the covariance matrix and uses weighted joint covariance matrix fitting instead of eigendecomposition for interferometric phase estimation, avoiding the influence of signal subspace diffusion during the phase estimation process. In 2018, researchers proposed a maximum likelihood phase estimation method (EMI) based on eigendecomposition. This method combines eigendecomposition and maximum likelihood estimation to achieve phase optimization. The process is simple and computationally efficient. In 2022, some scholars proposed a phase estimation algorithm based on Fisher information. Based on EMI, this algorithm uses Fisher information instead of coherence matrix as the weight matrix, which can effectively suppress the impact of coherence matrix estimation error.

[0004] In summary, phase estimation is crucial for deformation monitoring and analysis using distributed target InSAR technology, and its results directly impact the accuracy of subsequent time-series deformation information extraction. However, existing optimal phase estimation methods all use a single pixel as the computational unit, resulting in low computational efficiency. They also only consider correlations in the temporal dimension while ignoring those in the spatial dimension, which in turn affects their accuracy. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology, utilize tensor decomposition theory, and take advantage of the advantages of tensors in data description and storage to propose an optimal phase estimation method based on tensor decomposition. This method uses the covariance matrix of multiple pixels to construct a third-order tensor model, replaces matrix operations with tensor operations, and replaces matrix eigendecomposition with corresponding tensor decomposition to achieve distributed target phase optimization, and converts the "pixel-by-pixel" calculation mode in the existing optimal phase estimation method into a "multi-pixel" calculation mode, so as to improve the computational efficiency and accuracy of phase estimation.

[0006] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0007] A distributed target InSAR phase estimation method based on tensor decomposition is used to optimize the phase value in distributed target InSAR to improve the accuracy of InSAR deformation information extraction. The phase estimation method includes the following steps:

[0008] 1) Register the original full-stack images. Specifically, the acquired time-series SAR images are precisely registered using the enhanced spectral diversity registration method, and homogeneous pixels are identified within a certain window size around the pixel center based on amplitude information.

[0009] 2) Subspace division: Divide the registered original SAR image into multiple small subspaces, and obtain the pixel covariance matrix within each small subspace.

[0010] 3) Establish a third-order tensor model: Based on the similar statistical characteristics between pixels in a smaller subspace, the pixel covariance matrices within each small subspace are stacked to construct a third-order tensor model of the covariance matrix.

[0011] 4) Optimal phase estimation tensor decomposition model: The Tucker decomposition algorithm in tensor decomposition is used to decompose the third-order tensor model of the covariance matrix constructed above, and the original tensor is decomposed into the product of a low-rank core tensor and the factor matrix under the corresponding mode. After tensor decomposition, the eigenvalues ​​of each factor matrix are arranged according to the size of the eigenvalue. By constructing the relationship between the coherence matrix and the eigenvector, it can be seen that the eigenvector corresponding to the largest eigenvalue in the factor matrix represents the weight of the image. When the main factor of image decoherence is the time baseline, the image close to the time center of each group of images usually has the largest weight, and the weights of other images vary with the image time. When there is periodic interference in the image, its eigenvector represents the weight difference between the images, so it can be understood as the weighting of multi-view in the time dimension; finally, the factor matrix is ​​brought into the general phase estimation model as a weight matrix to obtain the optimal phase estimate, as follows:

[0012] According to step 3), the pixel covariance matrix within a given subspace size is expressed as a third-order tensor According to tensor decomposition theory, we can Decompose into a core tensor And the modular multiplication of the corresponding factor matrix, that is:

[0013]

[0014] in, (m1≤m,n1≤n), factor matrix

[0015] According to the principle of optimal phase estimation of distributed targets, when performing tensor decomposition, only the third-order tensor Decompose in the time dimension, while the spatial dimension remains unchanged, that is, the factor matrix W of the spatial dimension P Assumed to be the unit matrix, its third-order tensor It can be expressed as

[0016]

[0017] After tensor decomposition, the eigenvalues ​​of each factor matrix are arranged according to the size of the eigenvalue:

[0018]

[0019]

[0020] Since the covariance matrix of each pixel is a symmetric matrix, and the dimensions under mode-1 and mode-2 are the same, u i =v i , that is U P =U P , in the actual calculation process, you only need to select one of them.

[0021] The difference between the phase estimation model and the time-space dimension reduction and compression model of time-series InSAR images is that phase estimation only needs to be decomposed in the time dimension, while the time-series InSAR image time-space dimension reduction and compression model decomposes in both the time and space dimensions. After decomposition, phase estimation does not require linear transformation, while image compression requires linear transformation.

[0022] 5) Optimal phase estimation:

[0023] The optimal phase estimation value is calculated using the phase estimation model constructed in step 4).

[0024] After adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art.

[0025] 1) The present invention uses tensor decomposition theory to achieve distributed target InAR phase estimation. Based on the similar statistical characteristics between pixels in a small subspace, the pixel covariance matrix in the subspace can be stacked into a third-order tensor form. Then, an optimal phase estimation tensor decomposition model is constructed. At the same time, the correlation between the temporal and spatial dimensions between adjacent pixels is considered, which is conducive to improving its estimation accuracy.

[0026] 2) The present invention utilizes the advantages of tensors in data description and storage, replaces matrix operations with tensor operations, and replaces matrix eigendecomposition with corresponding tensor decomposition to achieve distributed target phase optimization, and converts the "pixel-by-pixel" calculation mode in the existing optimal phase estimation method into a "multi-pixel" calculation mode. Compared with the phase estimation method based on matrix eigendecomposition, the present invention has the advantages of high precision and high computational efficiency.

[0027] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings are part of this application and are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but do not constitute an undue limitation of the present invention. Obviously, the drawings described below are only some embodiments. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without inventive effort. In the accompanying drawings:

[0029] Figure 1 This is the flow chart of the distributed InSAR phase estimation method;

[0030] Figure 2 This is a comparison diagram of interference phase information before and after phase optimization;

[0031] Figure 3 This is a comparison diagram of coherence before and after phase optimization;

[0032] Figure 4 Comparison of the coherence matrix before and after phase optimization for a single pixel;

[0033] Figure 5 Phase information before and after optimization for a single pixel.

[0034] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but rather to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0036] Example 1

[0037] A distributed target InSAR phase estimation method based on tensor decomposition is used to optimize the phase value in distributed target InSAR to improve the accuracy of InSAR deformation information extraction. The phase estimation method includes the following steps:

[0038] 1) Register the original full-stack images. Specifically, the acquired time-series SAR images are precisely registered using the enhanced spectral diversity registration method, and homogeneous pixels are identified within a certain window size around the pixel center based on amplitude information.

[0039] 2) Subspace division: Divide the registered original SAR image into multiple small subspaces, and obtain the pixel covariance matrix within each small subspace.

[0040] 3) Establish a third-order tensor model: Based on the similar statistical characteristics between pixels in a smaller subspace, the pixel covariance matrices within each small subspace are stacked to construct a third-order tensor model of the covariance matrix.

[0041] 4) Optimal phase estimation tensor decomposition model: The Tucker decomposition algorithm in tensor decomposition is used to decompose the third-order tensor model of the covariance matrix constructed above, and the original tensor is decomposed into the product of a low-rank core tensor and the factor matrix under the corresponding mode. After tensor decomposition, the eigenvalues ​​of each factor matrix are arranged according to the size of the eigenvalue. By constructing the relationship between the coherence matrix and the eigenvector, it can be seen that the eigenvector corresponding to the largest eigenvalue in the factor matrix represents the weight of the image. When the main factor of image decoherence is the time baseline, the image close to the time center of each group of images usually has the largest weight, and the weights of other images vary with the image time. When there is periodic interference in the image, its eigenvector represents the weight difference between the images, so it can be understood as the weighting of multi-view in the time dimension; finally, the factor matrix is ​​brought into the general phase estimation model as a weight matrix to obtain the optimal phase estimate, as follows:

[0042] According to step 3), the pixel covariance matrix within a given subspace size is expressed as a third-order tensor According to tensor decomposition theory, we can Decompose into a core tensor And the modular multiplication of the corresponding factor matrix, that is:

[0043]

[0044] in, (m1≤m,n1≤n), factor matrix

[0045] According to the principle of optimal phase estimation of distributed targets, when performing tensor decomposition, only the third-order tensor Decompose in the time dimension, while the spatial dimension remains unchanged, that is, the factor matrix W of the spatial dimension P Assumed to be the unit matrix, its third-order tensor It can be expressed as:

[0046]

[0047] After tensor decomposition, the eigenvalues ​​of each factor matrix are arranged according to the size of the eigenvalue:

[0048]

[0049]

[0050] Since the covariance matrix of each pixel is a symmetric matrix, and the dimensions under mode-1 and mode-2 are the same, u i =v i , that is U P =V P , in the actual calculation process, you only need to select one of them.

[0051] The difference between the phase estimation model and the time-space dimension reduction and compression model of time-series InSAR images is that phase estimation only needs to be decomposed in the time dimension, while the time-series InSAR image time-space dimension reduction and compression model decomposes in both the time and space dimensions. After decomposition, phase estimation does not require linear transformation, while image compression requires linear transformation.

[0052] 5) Optimal phase estimation:

[0053] The optimal phase estimation value is calculated using the phase estimation model constructed in step 4).

[0054] To verify the feasibility and reliability of this method, Sentinel-1A data (orbit number 26) covering the Kunming Basin was selected as the SAR data source. Both eigendecomposition (EVD)-based and tensor decomposition-based methods were used to perform optimal phase estimation experiments for the fourth burst in the second strip of ascending data from orbit number 26. Furthermore, SRTM-1 elevation data, with a resolution of 30 meters and obtained jointly by NASA and the National Institute of Surveying, Mapping and Geoinformation (NIMA), were used as a reference. Precision Orbit Data (POD) was used to eliminate systematic errors caused by the orbit.

[0055] The distributed target InSAR phase estimation method based on tensor decomposition, the technical solution implementation process is as shown in the attached Figure 1 As shown, the steps are as follows

[0056] 1) Figure 2 The original differential interferogram, EVD decomposition, and optimized interferogram obtained by tensor decomposition of the fourth burst covering the study area are shown. As can be seen from the figure, the interferogram quality after phase optimization is significantly better than the original interferogram, while the interferogram obtained by tensor decomposition is better than the interferogram obtained by EVD decomposition, especially in non-urban areas.

[0057] 2) Figure 3 The changes in coherence ratio before and after phase optimization for the distributed targets in the study area, with interferometry pairs from 20180107 to 20180531, are shown. Figure 3(a) shows the coherence diagram before phase estimation, 3(b) shows the coherence diagram after optimization using the eigendecomposition method, and 3(c) shows the coherence diagram after optimization using the tensor decomposition method. The figures clearly show that the coherence of the interferogram is significantly improved after phase optimization, especially in areas with low coherence. Coherence statistics show that the average coherence before phase estimation is 0.17, the average coherence after optimization using the eigendecomposition method is 0.44, and the average coherence after optimization using the tensor decomposition method is 0.48. Although it is difficult to visually distinguish the phase estimation quality of the eigendecomposition method from that of the tensor decomposition method, coherence statistics show that the phase estimation method based on tensor decomposition is superior to the phase estimation method based on eigendecomposition.

[0058] 3) Select Figure 3 Single pixel analysis is performed on point P shown in (a), and the coherence matrix information before and after phase estimation and the phase optimization values ​​obtained by different phase estimation methods are plotted respectively, as shown in Figure 4 As shown. Figure 4It can be seen that when the time baseline is short (i.e., the coherence is high), the coherence before and after phase estimation is not much different, but when the time baseline is long (i.e., the coherence is low), the coherence after phase optimization is significantly improved.

[0059] 4) Figure 5 is the phase value before and after phase estimation at point P. It can be seen from the figure that the phase estimation values ​​obtained by the two phase estimation methods are highly consistent, which shows that the phase optimization result obtained by the phase estimation method based on tensor decomposition has higher reliability.

[0060] The implementation case of the present invention uses low-resolution Sentinel-1A image data for experimental analysis. Since many SAR satellites with different bands and resolutions have been successfully launched at home and abroad, such as RADARSAT-2, COSMO-SkyMed, TerraSAR, SAOCOM, L-SAR, etc., the application fields and application effects of each satellite are different. The distributed target InSAR phase estimation method based on tensor decomposition described in the present invention can also be applied to the processing of the above-mentioned different SAR satellite image data.

[0061] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as above in terms of a preferred embodiment, it is not intended to limit the present invention. Any technician familiar with this patent can make slight changes or modifications to equivalent embodiments using the above technical content without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the solution of the present invention.

Claims

1. A distributed target InSAR phase estimation method based on tensor decomposition, characterized in that: The following steps are involved: 1) Register the original full-stack images: The acquired time-series SAR images are precisely registered using the enhanced spectral diversity registration method, and homogeneous point pixels are identified within a certain window size range at the center of the pixel based on the amplitude information; 2) Subspace division: Divide the registered original SAR image into multiple small subspaces and obtain the pixel covariance matrix within each small subspace; 3) Establish a third-order tensor model: Based on the similar statistical characteristics between pixels in a smaller subspace, the pixel covariance matrices within each small subspace are stacked to construct a third-order tensor model of the covariance matrix, that is, converting the matrix into a tensor; 4) Optimal phase estimation tensor decomposition model: For a time series InSAR image dataset Z m×n , where m represents the number of images and n represents the number of pixels, then n covariance matrices Q can be obtained m×m , using n covariance matrices, a third-order tensor model can be constructed According to tensor decomposition theory, we can Decompose into a core tensor And the modular multiplication of the corresponding factor matrix, that is: in, Factor Matrix According to the principle of optimal phase estimation for distributed targets, when performing tensor decomposition, only the third-order tensor Decompose in the time dimension, while the spatial dimension remains unchanged, that is, the factor matrix W of the spatial dimension P Assuming it to be the unit matrix, its third-order tensor It can be expressed as: After tensor decomposition, the eigenvalues ​​of each factor matrix are arranged according to the size of the eigenvalue: 5) Optimal phase estimate: The optimal phase estimate can be obtained by substituting the factor matrix as a weight matrix into the general phase estimation model.

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