Landslide mass detection method based on improved distributed scatterer InSAR

Abstract

The invention discloses a landslide mass detection method based on an improved distributed scatterer InSAR, and aims to accurately evaluate the movement speed of a landslide. According to the method, a regularization means is integrated in a covariance matrix estimation link, so that the phase error is effectively reduced, and the signal-to-noise ratio of a displacement time sequence is enhanced. Whether a synthetic data test or actual application data verification is passed, the technology shows that the precision and efficiency of landslide speed detection are remarkably improved while the coverage range of reliable monitoring points is expanded. The method is of great significance to accurate monitoring of landslide activities around the power line, and can effectively prevent potential threats of landslide to power transmission facilities.

Description

Technical Field

[0001] The present invention relates to the field of landslide detection, and in particular to a landslide detection method based on improved distributed scatterer InSAR. Background Art

[0002] Geological fragility, rainfall, weathering and human activities lead to stress imbalance in rock formations, which can easily cause collapse and landslides, especially in karst mountainous areas. This seriously threatens the safety of power transmission lines and the losses are difficult to estimate.

[0003] InSAR technology, with its wide coverage and high resolution, has become an important tool for landslide monitoring. In the past two decades, multi-temporal InSAR methods based on permanent scatterers (PS) and distributed scatterers (DS) have been developed to identify risks and track landslide deformation. Permanent scatterer interferometry (PSI) technology removes noise by selecting stable reference points to ensure monitoring accuracy. Technologies such as IPTA, StaMPS, and quasi-permanent scatterers have promoted the application of InSAR. The small baseline set (SBAS) method alleviates the decorrelation problem by using short-time and space baseline interferometric images. Improved methods such as multi-scale InSAR time series, intermittent SBAS (ISBAS), and MintPy have further improved monitoring performance. SqueeSAR uses maximum likelihood estimation and redundant interferometric network strategies to deal with decorrelation.

[0004] However, densely vegetated mountainous areas face challenges such as spatiotemporal decorrelation, complex terrain, and atmospheric interference, which severely impair InSAR accuracy. Karst landslides are particularly frequent along power transmission lines and are often covered by vegetation, resulting in a scarcity of PS targets and limited acquisition of deformation data. Furthermore, the computational complexity of the DS method makes it difficult to establish a link between deformation and failure mechanisms, hindering the understanding and prediction of landslide dynamics.

[0005] To address this challenge, researchers are exploring new methods to improve phase estimation accuracy in vegetation areas. For example, they are using eigenvalue decomposition (EVD) of the covariance matrix to optimize interferogram phase estimation and increase the number and quality of coherent targets. Regularization strategies such as M-estimation, Hadamard–spectral regularization, and shrinkage techniques also show promise, especially in scenarios with long-term coherence.

[0006] However, it is important to note that these strategies remain limited in rapidly decorrelated environments. Low-coherence interferometry works well in PSI but not in DSI. Rapid decorrelation caused by vegetation and topography weakens the reliability of phase measurements and the accuracy of deformation time series, presenting new challenges for landslide monitoring. Summary of the Invention

[0007] To address the shortcomings of existing methods, this paper proposes a landslide detection method based on improved distributed scatterer InSAR. By introducing regularization technology in covariance matrix estimation, it reduces phase estimation bias and improves the signal-to-noise ratio of displacement time series, overcoming the limitations brought by dense vegetation and complex terrain. This method is used to accurately detect landslide movement in power line areas.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A landslide detection method based on improved distributed scatterer InSAR includes the following steps:

[0010] Step 1: Obtain satellite images of the landslide area to form m single-view complex image sets to detect the slow movement of potential landslides;

[0011] Step 2: Extract eigenvalues ​​from the satellite imagery and then use the eigenvalue maximization interferometry method to obtain the maximum likelihood estimate of the phase solution by minimizing the minimum eigenvector of the complete covariance matrix. For long time series, a sequential estimator method is used to reduce the frequency of singularities.

[0012] Step 3: Optimize the phase using the method of homogeneous point detection and new coherence matrix regularization estimation.

[0013] In step 2, the mathematical formula for a single pixel of the EMI method is:

[0014]

[0015] here, represents the estimated phase sequence, ξ represents the Hadamard product The smallest eigenvector of is the key factor used to weight the noise level, and the superscript H represents the Hermitian transpose. is the estimated complete covariance matrix, consisting of m single-view complex images and n pixels in the homogeneous region, is the coherence matrix, given by where each element represents the coherence between two time nodes i and j.

[0016]

[0017] Where p is a set of pixels, x is a complex number, and x* is the complex conjugate;

[0018] Covariance matrix The theoretical probability density function of is composed of the following formula:

[0019]

[0020] Among them, Tr represents the trace of the matrix, Γ represents the hypergeometric function. When the number of samples n < m, the covariance matrix is approximately singular because its determinant is close to zero; in this case, formula (3) is considered a degenerate distribution. Therefore, the coherence matrix is not a full-rank matrix, and its inverse matrix will amplify the estimation error of, and further transmit this error to the estimation of.

[0021] The described Seq method divides the complete covariance matrix into multiple block diagonal matrices, and sequentially compresses them into a subspace cluster with rank 1. Through subspace clustering, these block diagonal matrices are connected to a unique phase reference, thereby obtaining an estimated phase with a higher signal-to-noise ratio than the original EMI method.

[0022] [[ID=1⑧]]In step 3, a non-threshold regularization method is applied in the Seq + EMI method. This new regularization method performs conditional control by adding a scaled identity matrix I to the coherence matrix.

[0023] [[ID=③]]

[0024] Here, the eigenvalues λ of the symmetric positive definite coherence matrix are defined as and the maximum condition number M , <00000⑧0>,

[0028] , ,

[0026] , , ,

[0027] The threshold of is set between 1 ≤ M max ≤ M; the condition number M under the L2 norm is expressed as 1 ≤ M max ≤ M. In this context, the re-adjusted coherence matrix is composed of the following formula

[0025]

[0026] Formula (5) represents a regularization technique for the least squares problem. However, in the context of EMI, ridge regression is only used to re-adjust the coherence matrix. The regularized matrix is then inverted and used as the weighted matrix in the phase optimization process.

[0027] The positive and beneficial effects of the present invention: The present invention proposes a landslide detection method based on improved distributed scatterer InSAR. This method is superior to other advanced technologies in phase recovery, improves the effect and performance of landslide speed detection on the basis of increasing the number of reliable measurement points, helps to accurately detect the landslide movement in the power line area, and avoids damage to the transmission line caused by landslides. Description of the Drawings

[0028] Figure 1 is a flow chart of the present invention;

[0029] Figure 2 Satellite images of the landslide area and the coverage of the Sentinel-1SAR imagery used;

[0030] Figure 3 The theoretical accuracy (phase root mean square error) of the four methods, (a) the number of samples is 49, (b) the number of samples is 121;

[0031] Figure 4 The first row shows the velocity maps estimated using four different time baselines. The second row shows their errors compared to the true values. The third and fourth rows show the same sequence but with different numbers of samples used. The first two rows are based on a sample size of 49, while the last two are based on a sample size of 121.

[0032] Figure 5 Interferograms estimated using three different time baselines, each row represents a different time baseline, and each column represents the results of different methods;

[0033] Figure 6 is the phase signal-to-noise ratio comparison;

[0034] Figure 7 Estimated velocity images from different methods: (a) original phase, (b) multi-view method, (c) EMI, (d) EMI+Seq, and (e) the method proposed in this invention. DETAILED DESCRIPTION

[0035] In order to facilitate ordinary technicians in this field to understand the purpose, technical solutions and advantages of the present invention, the present invention is further described in detail below in conjunction with specific embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0036] like Figure 1 As shown in FIG, a landslide detection method based on improved distributed scatterer InSAR includes the following steps:

[0037] Step 1: Obtain satellite images of the landslide area to form m single-view complex image sets to detect the slow movement of potential landslides, such as Figure 2 As shown;

[0038] Step 2: Extract eigenvalues ​​from the satellite imagery and then use the eigenvalue maximization interferometry (EMI) method to obtain the maximum likelihood estimate (MLE) of the phase solution by minimizing the minimum eigenvector of the complete covariance matrix. For long time series (i.e., large m), the sequential estimator (Seq) method is used to reduce the frequency of singularities.

[0039] Step 3: Optimize the phase by using the method of homogeneous point detection and new coherence matrix regularization estimation.

[0040] In the above-mentioned step 2, in the EMI method, the mathematical formula for a single pixel is:

[0041]

[0042] Here, represents the estimated phase sequence, ξ represents the minimum eigenvector of the Hadamard product where is the key factor for weighting the noise level. The superscript H represents the Hermitian transpose. is the estimated complete covariance matrix, which is composed of m single-look complex images and n pixels within the homogeneous region. is the coherence matrix, which is composed of the modulus of, where each element represents the coherence between two time nodes i and j,

[0043]

[0044] where p is the set of pixel points, x is a complex number, and x* is the complex conjugate.

[0045] The covariance matrix has a theoretical probability density function composed of the following formula:

[0046]

[0047] where Tr represents the trace of the matrix, and Γ represents the hypergeometric function. When the number of samples n < m, the covariance matrix is approximately singular because its determinant is close to zero. In this case, formula (3) is considered a degenerate distribution. Therefore, the coherence matrix is not a full-rank matrix, and its inverse matrix will amplify the estimation error and further transmit this error to the estimation.

[0048] Preferably, the Seq method divides the complete covariance matrix into multiple block diagonal matrices and sequentially compresses them into a subspace cluster with a rank of 1. Through subspace clustering, these block diagonal matrices are connected to a unique phase reference, thereby obtaining an estimated phase with a higher signal-to-noise ratio (SNR) than the original EMI method.

[0049] The block diagonal matrix size of Seq is manually selected by the user. For example, selecting a diagonal matrix size of 20 corresponds to a time baseline of 120 days. In this case, the number of sample pixels only needs to be greater than 20 to reduce the occurrence of singularity issues.

[0050] In step 3, a non-threshold regularization method is applied to the Seq+EMI method to improve the accuracy of InSAR phase estimation. The new regularization method performs conditional control by adding a scaled identity matrix I to the coherence matrix.

[0051]

[0052] Here, the symmetric positive definite coherence matrix The eigenvalue λ is defined as And the maximum condition number M max The threshold is set at 1≤M max ≤M. The condition number M under the L2 norm is expressed as 1≤M max ≤M. In this context, the rescaled coherence matrix It is composed of the following formula.

[0053]

[0054] Equation (5) represents a regularization technique for least squares problems, similar to Tikhonov regularization. However, in the context of EMI, ridge regression is only used to rescale the coherence matrix. The regularized matrix is ​​then inverted and used as the weighting matrix used in the phase optimization process.

[0055] Preferably, the phase superposition method weights the interferogram according to the time baseline, effectively suppressing atmospheric delay and random noise in the time domain. Although the average deformation rate only represents the linear deformation component during the observation period, it can be used as an indicator to identify locations with significant surface deformation and potential unstable areas.

[0056] Example 1

[0057] A landslide detection method based on improved distributed scatterer InSAR, see Figure 1 , including the following steps:

[0058] Obtain satellite imagery of landslide areas to detect slow movement of potential landslides, e.g. Figure 2 As shown;

[0059] The phase estimation performance is evaluated using EMI, Seq+EMI and the new integrated regularization method (Seq+EMI+reg), as shown in Figure 3The test was conducted in two scenarios: both with a time baseline of 600 days (100 single-view complex images), using 49 and 121 samples for phase estimation, respectively. The number of homogeneous pixels per pixel was randomly set to 49 or 121.

[0060] The above method is applied to restore all interferograms, and the original phase is compared with the phase after multi-viewing, EMI, Seq+EMI, and Seq+EMI+reg. The first and second rows show the estimated phase time series with a time baseline of 600 days after applying each method, but with different numbers of samples. Seq+EMI using the regularized coherence matrix has higher estimation accuracy than the original EMI and Seq+EMI. In particular, Figure 3 In b, the performance of Seq+EMI and Seq+EMI+reg are close, while Figure 3 a shows the improvement of the new estimator. This performance improvement can be attributed to the improved estimation of the precision matrix through regularization. Figure 3 In b, 121 samples are used, which is significantly larger than the stacking size, ensuring that the coherence matrix remains positive definite in Seq, so no regularization is required. However, in the case of only 49 samples ( Figure 3 In case a), regularization becomes necessary, which improves the performance, as shown by the higher phase SNR. This improvement shows that regularization improves the accuracy of the precision matrix, bringing it closer to the true value.

[0061] The deformation was simulated using the “peaks” function in MATLAB to further evaluate the velocity estimation performance of these methods. The simulated velocity graph is shown in Figure 2. Figure 4 As shown. Using the synthetic coherence matrix, 100 SAR images of size 200×800 (azimuth×range) are generated. The time-dependent deformation phase is simulated by the "peaks" function, and the noise component comes from the coherence matrix. The terrain and flat ground phases are simulated by precise orbits and external DEM. After stacking all the recovered interferometric images, the velocity estimation results are obtained. Visual inspection of the velocity map shows that the SNR gradually increases from left to right (the stripes are smoother). Overall, the new method shows the most significant improvement, especially after the introduction of regularization, which can recover more points. The velocity estimation accuracy of the new estimator is better than that of other methods, and its deviation is the smallest. These comparison results confirm that SNR is a key factor affecting the accuracy of velocity estimation.

[0062] We visually evaluate the performance of different phase estimation algorithms in recovering the wrapped phase time series, comparing the original phase with multi-visualized phase, EMI, Seq+EMI, and the proposed method. All phase estimation algorithms are applied to the full spatial resolution without preprocessing to allow for direct comparison of their effectiveness.

[0063] Figure 5 Two reconstructed sample interferograms are shown, with different time baselines. The noise level in the original phase is relatively high, even in the interferogram with the shortest time baseline (12 days). In contrast, all phase estimation methods show significant improvements in the recovered signal, such as Figure 3 Although all methods reduce noise, all but EMI show more significant improvements. This is because the latter method excludes weakly coherent pairs during the temporal phase filtering process, while EMI uses a full stack approach.

[0064] The results were further verified by using interferograms of a longer time baseline (84 days and 168 days), as shown in Figure 5 As shown in Figure 3, severe decorrelation noise almost completely obscures the useful signal. Although existing phase estimation methods recover some interferogram phase, they still perform poorly in other regions. In contrast, our method consistently demonstrates satisfactory performance across the entire interferogram, demonstrating high effectiveness in both short-term and long-term interferogram phase recovery.

[0065] The phase quality of different phase estimators is evaluated by calculating the change in SNR before and after phase estimation, thereby quantifying the performance. The SNR indicator is defined as:

[0066]

[0067] here as well as represent the original and optimized phases, respectively.

[0068] The phase variance of each pixel is calculated using a symmetric window of size 10 × 40 (azimuth × range). To ensure a robust velocity estimate, the normalized median absolute deviation and a posterior coherence threshold greater than 0.35 are used to reduce the interference of outliers. Figure 6 The average signal-to-noise ratio (SNR) of the interferogram is shown as the time baseline increases. A higher SNR value reflects better phase estimation performance.

[0069] The SNR improvements of EMI and Seq+EMI are mainly concentrated in the shorter time baseline. The multi-look processed phase shows a negative effect on some interferograms with longer time baselines, such as Figure 6 As shown in Figure 2. In comparison, Seq+EMI shows less performance degradation, followed by EMI. Figure 6 Our proposed method shows significant improvements on all temporal baselines, significantly outperforming other state-of-the-art phase estimation techniques.

[0070] Figure 7The line-of-sight velocity maps estimated using multi-look phase, EMI, Seq+EMI, and the proposed method were compared. For velocity estimation, points with a temporal coherence greater than 0.5 were selected. Across the entire landslide area, multi-look phase retained 3,049 points, the EMI method retained 17,359 points, the Seq+EMI method identified 66,399 points, and the proposed method observed 87,114 points.

[0071] Compared to previous methods, this method increases the number of measurement points by approximately 15 times compared to multi-view phase and by nearly one-third compared to EMI and Seq+EMI methods. While traditional methods struggle to achieve sufficient measurement point coverage in mountainous areas, this method provides a relatively dense distribution of points even in vegetated areas. This significantly increases the number of observation points and allows for clearer delineation of the slow motion of multiple landslide bodies.

[0072] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Other modifications or equivalent substitutions made to the technical solutions of the present invention by ordinary technicians in this field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solutions of the present invention.

Claims

1. A landslide detection method based on improved distributed scatterer InSAR, characterized by: The steps include: Step 1: Obtain satellite images of the landslide area to form m single-view complex image sets to detect the slow movement of potential landslides; Step 2: Extract eigenvalues ​​from the satellite imagery and then use the eigenvalue maximization interferometry method to obtain the maximum likelihood estimate of the phase solution by minimizing the minimum eigenvector of the complete covariance matrix. For long time series, a sequential estimator method is used to reduce the frequency of singularities. Step 3: Optimize the phase using the method of homogeneous point detection and new coherence matrix regularization estimation.

2. The landslide detection method based on improved distributed scatterer InSAR according to claim 1 is characterized by: In step 2, the mathematical formula for a single pixel of the EMI method is: here, represents the estimated phase sequence, ξ represents the Hadamard product The smallest eigenvector of is the key factor used to weight the noise level, and the superscript H represents the Hermitian transpose. is the estimated complete covariance matrix, consisting of m single-view complex images and n pixels in the homogeneous region, is the coherence matrix, given by where each element represents the coherence between two time nodes i and j. Where p is a set of pixels, x is a complex number, and x* is the complex conjugate; Covariance matrix The theoretical probability density function of is composed of the following formula: where Tr represents the trace of a matrix, Γ represents the hypergeometric function, and when the number of samples n < m, the covariance matrix is approximately singular because its determinant is close to zero; in this case, formula (3) is considered a degenerate distribution, and thus, the coherence matrix is not a full-rank matrix, and its inverse matrix will amplify the estimation error and further transmit this error to the estimation of 3. The landslide detection method based on improved distributed scatterer InSAR according to claim 1 is characterized by: The Seq method partitions the complete covariance matrix into multiple block diagonal matrices and compresses them into subspace clusters of rank 1 in sequence. Through subspace clustering, these block diagonal matrices are connected with a unique phase reference, thereby obtaining an estimated phase with a higher signal-to-noise ratio than the original EMI method.

4. The landslide detection method based on improved distributed scatterer InSAR according to claim 1 is characterized by: In step 3, a non-threshold regularization method is applied in the Seq+EMI method. The new regularization method performs conditional control by adding a scaled identity matrix I to the coherence matrix. Here, the symmetric positive definite coherence matrix The eigenvalue λ is defined as And the maximum condition number M max The threshold is set at 1≤M max ≤M; the condition number M under the L2 norm is expressed as 1≤M max ≤M, in this context, the rescaled coherence matrix It is composed of the following formula, Equation (5) represents a regularization technique for least squares problems. However, in the context of EMI, ridge regression is only used to rescale the coherence matrix. The regularized matrix is ​​then inverted and used as the weighting matrix during the phase optimization process.

Images