An InSAR interference network optimization method based on a multi-factor coherence proxy model

Abstract

This invention discloses an InSAR interferometric network optimization method based on a multi-factor coherence surrogate model. The method includes: constructing a multi-factor feature dataset containing SAR imagery, baseline data, and soil moisture data of the study area; constructing a candidate interferometric pair set, and randomly selecting a subset of sample interferometric pairs from the candidate set; constructing a coherence surrogate prediction model, which uses the multi-factor feature data corresponding to the sample interferometric pair subset and the ground truth values ​​of sample coherence to train the model parameters; inputting the multi-factor feature data corresponding to each interferometric pair in the candidate set into the trained coherence surrogate prediction model and outputting the predicted coherence of each interferometric pair and the optimized interferometric pair network. This invention improves the stability and accuracy of unwrapping and time-series inversion, while also reducing the difficulty of interferometric processing and coherence calculation under large-scale data, and can support the needs of large-scale, long-term, and near-real-time monitoring.

Description

Technical Field

[0001] This invention relates to the field of coherence analysis in synthetic aperture radar interferometry, and more particularly to an InSAR interferometric network optimization method based on a multi-factor coherence surrogate model. Background Technology

[0002] Interferometric Synthetic Aperture Radar (InSAR) and its multi-temporal time-series processing methods can acquire surface deformation information over large areas and have been widely used in applications such as urban subsidence, landslides, volcanic activity, and seismic deformation. In time-series InSAR processing, the appropriate selection of interferometric pairs directly affects the stability and accuracy of subsequent phase unwrapping, error estimation, and time-series inversion. With the rapid increase in the number of SAR satellites and interferograms, the selection of SAR image interferometric pairs has become increasingly complex. SAR image interferometric pairs are affected by time, space, and soil moisture, making it difficult for existing methods to select high-coherence interferometric pairs from massive amounts of SAR imagery. This often leads to the introduction of low-coherence interferograms and the discarding of high-coherence long-baseline interferometric pairs, resulting in the loss of a large number of effective coherence points and unwrapping errors. In big data scenarios, performing phase interferometry and coherence calculations on each of the massive interferometric pairs incurs extremely high computational and storage costs, hindering the construction of interferometric networks for InSAR and limiting the application potential of InSAR technology in large-scale, long-term, and near-real-time monitoring. Therefore, how to adaptively and intelligently select high-quality interferometric pairs from massive amounts of available data (SAR images), and how to perform quality classification and optimization of interferometric pairs, has become one of the core steps in realizing automated and operational time-series InSAR processing, and is also a current technical challenge. Summary of the Invention

[0003] The purpose of this invention is to provide an InSAR interferometric network optimization method based on a multi-factor coherence surrogate model. This method constructs a coherence surrogate prediction model that includes temporal baseline influence factors, spatial baseline influence factors, and soil moisture influence factors to predict coherence, utilizing random sampling... This invention trains model parameters and performs prior evaluation of interference quality for a sample interferometric pair subset on the coherence surrogate prediction model. It effectively quantifies the comprehensive impact of time decay, spatial incoherence, and soil moisture penalty on coherence. Based on the predicted coherence of the interferometric pairs, the optimal set of interferometric pairs is selected and an optimized interferometric pair network is constructed. Furthermore, this invention can use graph theory methods to automatically select an optimized interferometric network with high coherence and high redundancy. This invention not only reduces the risk of erroneous introduction of low-coherence interferograms and erroneous removal of high-coherence interferograms, improving the stability and accuracy of untangling and time series inversion, but also reduces the overhead of interferometric processing and coherence calculation under large-scale data, supporting the needs of large-scale, long-term and near-real-time monitoring.

[0004] The objective of this invention is achieved through the following technical solution: An InSAR interferometric network optimization method based on a multi-factor coherence surrogate model, the method comprising: S1. Construct a multi-factor feature dataset containing SAR images, baseline data, and soil moisture data of the study area. The baseline data includes temporal baselines and vertical baselines.

[0005] S2. Construct a candidate interferometric pair set containing M interferometric pairs by combining the multi-factor feature dataset with SAR images in pairs to form interferometric pairs. Randomly select from the candidate interferometric pair set. As a subset of sample interference pairs, obtain the true value of sample coherence for each sample interference pair in the subset.

[0006] S3. Construct a coherence surrogate prediction model that includes time baseline influence factors, spatial baseline influence factors, and soil moisture influence factors to predict coherence. The coherence surrogate prediction model uses sample interference to train model parameters on the multi-factor feature data corresponding to the subset and the true values ​​of sample coherence.

[0007] S4. Input the multi-factor feature data corresponding to each interference pair in the candidate interference pair set into the trained coherence surrogate prediction model. The coherence surrogate prediction model outputs the predicted coherence of each interference pair. Using the predicted coherence of the interference pairs, select the optimal interference pair set from the candidate interference pair set and construct the interference pair network of the optimal interference pair set.

[0008] To better implement this invention, the coherence surrogate prediction model uses the temporal baseline influence factor, spatial baseline influence factor, and soil moisture influence factor of the interferometric pair as influencing factors to predict the predicted coherence of the interferometric pair. In the coherence surrogate prediction model, the interferometric pair... Predictive coherence The expression is as follows: Interference From SAR images With SAR images Combination and composition, To interfere with Time baseline impact factor, To interfere with Spatial baseline impact factor To interfere with Factors affecting soil moisture.

[0009] Preferably, the coherence surrogate prediction model includes a time baseline fitting unit, which calculates the interferometric pair according to the following formula. Time baseline difference , , SAR image The date, SAR image Date; Interference Time baseline difference Corresponding time baseline impact factor The expression is as follows: ,in This is the lower limit of coherence. , These correspond to the feature time scales under fast and slow time conditions, respectively. , These are the short-term and medium-to-long-term coherence contribution coefficients, respectively. This is the seasonal amplitude coefficient. For seasonal phase shift parameters, The annual cycle length.

[0010] Preferably, the coherence surrogate prediction model includes a spatial baseline fitting unit, which calculates the interferometric pairs according to the following formula. Spatial baseline difference , , To interfere with Corresponding SAR image , The spatial baseline corresponding to the two satellite passes, that is, the straight-line distance between the two satellite orbital positions; This is the radar side-view angle. Baseline tilt angle; interference pair Spatial baseline difference The corresponding spatial baseline impact factor The expression is as follows: ;in For short baseline coherence when the vertical baseline approaches 0, This represents the lower limit of coherence at extremely long baselines. The characteristic baseline length is used to control the coherence rate.

[0011] Preferably, the coherence surrogate prediction model includes a soil moisture influence fitting unit, which will interferometrically adjust the soil moisture influence fitting unit. SAR images , From the perspective of interference Obtain SAR main image from soil moisture data Soil moisture auxiliary images Soil moisture Interference The corresponding expression for the soil moisture influencing factor is as follows: , , These are the weighting coefficients.

[0012] Preferably, the objective function of the coherence surrogate prediction model is to minimize the weighted sum of squared residuals between the predicted coherence of the samples and the true coherence of the samples, as expressed below: ,in The number of sample interference pairs in the sample interference pair subset. The weighting parameters for the sample interference pair k are: To predict the coherence of the samples, The true value of sample coherence; the set of model parameters for the coherence surrogate prediction model is... .

[0013] Preferably, in method S2, the method for obtaining the true value of sample coherence of sample interference pairs in the sample interference pair subset is as follows: first, calculate the coherence of each pixel (a,b) in the sample interference pair, and then calculate the average coherence of all pixels in the sample interference pair and use it as the true value of sample coherence.

[0014] Preferably, the trained coherent surrogate prediction model further includes a model parameter optimization and adjustment module, which utilizes the minimization of the weighted residual sum of squares... The sample interferometry in quantile regression adjusts and optimizes the model parameters of the spatial baseline impact factor in the spatial baseline impact factor, including short baseline coherence. lower limit of coherence Characteristic baseline length .

[0015] Preferably, the method for adjusting and optimizing the parameters of the spatial baseline impact factor model is as follows: From the sample interference pair subset, select sample interference pairs with smaller time baseline differences as the interference pair subset; extract the time baseline influence factor model parameters of the coherence surrogate prediction model. Soil moisture influencing factor model parameters Calculate the time baseline influence factor of sample interferometry pairs. and soil moisture influencing factors The normalized spatial coherence observations are obtained according to the following formula. : ,in Given the true value of sample coherence, the model parameter optimization and adjustment module constructs a function that minimizes the bouncing loss function as the optimization objective, expressed as follows: ; Bouncing ball loss function The expression is as follows: , , The impact factor of the purified spatial baseline is obtained based on the optimization objective of minimizing the bouncing loss function. The corresponding spatial baseline impact factor model parameters The model parameter set of the coherent proxy prediction model is adjusted, optimized and updated.

[0016] Preferably, in method S4, the predicted coherence of each interference pair output by the coherence surrogate prediction model is normalized, as shown in the following expression: ,in To interfere with the normalized weights of k, This indicates the predictive coherence of the coherent surrogate prediction model interfering with k. The maximum value of the predictive coherence for all interference pairs; All candidate interference pairs in the candidate interference pair set are sorted in descending order of normalized weights, and then candidate interference pairs are selected in descending order of normalized weights to be added to the optimal interference pair set and an interference pair network is constructed. The method for evaluating the termination of the selection iteration in the interference network is as follows: Construct a diagonal weight matrix based on normalized weights. Construct the redundancy matrix of the interferometric pair network. , , It is the identity matrix. For designing matrices; redundant matrices The diagonal elements serve as the redundancy of the interference pair k. Determine the redundancy number in the interference pair network. average redundancy Set the average redundancy number The redundancy threshold, when the average redundancy of the interference pair network is... The candidate interference pair selection iteration terminates when the redundancy threshold is reached.

[0017] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) This invention constructs a coherence surrogate prediction model that includes temporal baseline influence factors, spatial baseline influence factors, and soil moisture influence factors to predict coherence, and utilizes random sampling This invention trains model parameters and performs prior evaluation of interference quality for a sample interferometric pair subset on the coherence surrogate prediction model. It effectively quantifies the comprehensive impact of time decay, spatial incoherence, and soil moisture penalty on coherence. Based on the predicted coherence of the interferometric pairs, the optimal set of interferometric pairs is selected and an optimized interferometric pair network is constructed. Furthermore, this invention can use graph theory methods to automatically select an optimized interferometric network with high coherence and high redundancy. This invention not only reduces the risk of introducing low-coherence interferograms and removing high-coherence interferograms, improving the stability and accuracy of untangling and time series inversion, but also reduces the overhead and difficulty of interferometric processing and coherence calculation under large-scale data, supporting the needs of large-scale, long-term and near-real-time monitoring.

[0018] (2) This invention constructs a multi-factor feature dataset containing SAR images, baseline data, and soil moisture data of the study area by analyzing the baseline data and soil moisture data of SAR images. Then, it uses the average coherence of sample interferometric pairs as training samples to establish a coherence surrogate prediction model that integrates the effects of time decay, spatial incoherence, and soil moisture. Next, it uses quantile regression and constrained least squares to estimate the model parameters and obtain a high-precision coherence surrogate prediction model. Based on the predicted coherence, an interferometric pair network is constructed. The interferometric pair network is optimized and screened by the maximum spanning tree, redundant edge addition, phase closed triangle completion, and time bidirectional connection completion. The interferometric pair network that meets the redundancy target and connection constraints is selected.

[0019] (3) In the interferometric pair selection stage, this invention fully considers the comprehensive influence of temporal baseline, spatial baseline and soil moisture changes on coherence. By constructing a coherence surrogate prediction model that integrates double exponential time decay, seasonal cycle, spatial baseline exponential decay and soil moisture penalty term, it realizes the prior prediction of the quality of candidate interferometric pairs and effectively addresses the problem of low coherence or even decoherence caused by changes in surface dielectric properties. Secondly, a more robust two-stage estimation framework is adopted in model training and parameter estimation: first, the global parameters are fitted by bounded constraint nonlinear least squares to ensure the stability of model parameters; quantile regression is introduced for fitting the spatial decoherence term to reduce the influence of low coherence samples and abnormal samples on spatial decay parameters and improve the prediction accuracy of spatial baseline term on coherence. In terms of constructing the interferometric pair network, this invention introduces the reliability theory of geodetic networks into the design of InSAR interferometric networks, normalizes the coherence surrogate value as the edge weight, and uses the redundancy number as an indicator to constrain the interferometric pair network. The interferometric pair network is completed by the maximum spanning tree skeleton, iterative addition of redundant edges, completion of closed triangles and time bidirectional completion. While ensuring network connectivity and a highly coherent framework, this invention further enhances network redundancy and error propagation resistance, significantly improving the stability and reliability of SBAS time-series inversion. By employing a coherence proxy approach, this invention reduces the computational burden on massive candidate interferometry pairs, lowering the computational burden related to coherence. It is more suitable for monitoring surface deformation under large-scale, long-term series and complex land cover conditions, providing a more reliable and efficient technical approach to obtaining high-precision, stable deformation results with good spatial coverage. Attached Figure Description

[0020] Figure 1 This is a flowchart of the InSAR interferometric network optimization method of the present invention; Figure 2 This is a simplified schematic diagram illustrating the principle of the InSAR interferometric network optimization method in the embodiment; Figure 3 This is a schematic diagram illustrating how the coherence proxy prediction model in this embodiment only uses a time baseline to fit coherence. Figure 4 This is a schematic diagram of the coherence surrogate prediction model in the embodiment, which only uses the spatial baseline to fit the coherence. Figure 5 This is a schematic diagram illustrating how the coherence surrogate prediction model in this embodiment fits the coherence using only the sum of soil moisture of the interference pairs. Figure 6 This is a schematic diagram illustrating how the coherence proxy prediction model in this embodiment only uses the soil moisture difference between interference pairs to fit the coherence. Figure 7 The graph shows the prediction performance of the coherent proxy prediction model in the embodiment for consistency verification. Figure 8This is a schematic diagram illustrating the coherence of some interference pairs in the interference pair network of the coherence proxy prediction model in the embodiment; Figure 9 This is a spatial distribution map of deformation in the study area using the coherence surrogate prediction model in the example; Figure 10 for Figure 9 A magnified view of a portion of the image. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to embodiments: Example like Figure 1 As shown, an InSAR interferometric network optimization method based on a multi-factor coherence surrogate model is proposed, the method comprising: S1. Construct a multi-factor feature dataset containing SAR images, baseline data, and soil moisture data of the study area. The baseline data includes temporal and vertical baselines. To ensure the accuracy and consistency of the input features of the coherence surrogate prediction model, this invention prepares and preprocesses the SAR images, baseline data, and soil moisture data before constructing the coherence surrogate prediction model, forming a multi-factor feature dataset that can be used for training and prediction. The method includes: firstly, acquiring N SAR image data of the study area and their corresponding baseline table files, and obtaining the date of each image. With vertical baseline First, a mapping table of "image number - date - vertical baseline" is established for subsequent calculation of candidate interferometric pair features. Second, a set of candidate interferometric pairs is generated based on pairwise combinations of N images. The number of candidate interferometer pairs is M, and the time baseline difference is calculated for any interferometer pair. Spatial baseline difference , , SAR image The date, SAR image The date; , This is the spatial baseline at the time of two satellite transits, i.e., the straight-line distance between the orbital positions of the two satellites. This is the radar side-view angle. The baseline dip angle was used; simultaneously, soil moisture data synchronized with the SAR imagery was acquired, derived from the 0-7 cm depth soil volumetric water content product in the ERA5-Land reanalysis dataset. Through time matching, the precise acquisition date of each SAR image was aligned with the soil moisture time series to obtain the soil moisture value for each image at the corresponding observation time, which was then used for subsequent modeling.

[0022] This embodiment takes Tianjin in northern China as the study area and research object. To implement the InSAR interferometric network optimization method of this invention, the experimental data used mainly include data from the European Space Agency (ESA) Sentinel-1 satellite and the ERA5-Land reanalysis dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF). The SAR data used in this embodiment are C-band ascending orbit images from the Sentinel-1A satellite, totaling 59 scenes, specifically interferometric wide-swath mode data with orbit 69 frames and frame 124, spanning from January 2018 to December 2019. To synchronize with SAR observations and for subsequent coherence modeling, this embodiment extracts soil moisture values ​​at a depth of 0-7 cm at the ground surface corresponding to the transit time of each Sentinel-1A image from the ERA5-Land reanalysis dataset.

[0023] S2. Construct a candidate interferometric pair set containing M interferometric pairs by combining the multi-factor feature dataset with SAR images in pairs (if the multi-factor feature dataset has N SAR images, then the number of interferometric pairs is...). Example: If N is 59, then Randomly selected from the set of candidate interference pairs (This example uses 10%, i.e.) =10) as a subset of sample interference pairs, obtain the true value of sample coherence of each sample interference pair in the subset of sample interference pairs, and use it as an observation for subsequent model training and fitting.

[0024] In some embodiments, the true value of sample coherence of sample interference pairs in a subset of sample interference pairs is obtained as follows: First, the coherence of each pixel (a,b) in the sample interference pair is calculated (this is an important indicator for evaluating the quality of the interference phase and a key factor affecting the quality of the deformation result). The coherence of pixel (a,b) is obtained using a sliding window that includes pixel (a,b). (Example) = The data within the range of 5 is estimated using the following expression: , and The sliding window size (i.e., the data block size) used to calculate coherence. and Let represent the complex values ​​of the main image and the secondary image at (a, b), respectively. For conjugate complex numbers, The absolute value of the complex number is then used to calculate the average coherence of the sample interference over all pixels and to obtain the true value of the sample coherence (as the prior coherence of the sample).

[0025] S3. Construct a coherence surrogate prediction model that includes temporal baseline influence factors, spatial baseline influence factors, and soil moisture influence factors to predict coherence. The coherence surrogate prediction model uses the temporal baseline influence factors, spatial baseline influence factors, and soil moisture influence factors of the interferometric pair as influence factors to predict the predicted coherence of the interferometric pair. Predictive coherence The expression is as follows: Interference From SAR images With SAR images Combination structure, in this invention, SAR imagery With SAR images SAR images sorted chronologically by date Earlier than SAR images Time, early SAR images As the primary image, the later SAR image As a supplementary image; in terms of time scale ; To interfere with Time baseline impact factor, To interfere with Spatial baseline impact factor To interfere with The coherence surrogate prediction model of this invention comprehensively utilizes the temporal baseline influence factor, spatial baseline influence factor, and soil moisture influence factor to perform interferometric pair coherence prediction processing. It describes how the temporal baseline influence factor, spatial baseline influence factor, and soil moisture influence factor jointly affect the coherence of the interferometric pair, and then combines the redundancy index to achieve interferometric network optimization processing.

[0026] In the Tianjin area of ​​northern China, used as a case study, the coherence surrogate prediction model constructs an exponential decay function and fits the coherence using only the time baseline, as shown in the example. Figure 3 As shown, the interference coherence systematically decreases with increasing time baseline value, accompanied by a certain periodicity, effectively capturing and quantifying the attenuation effect of the time baseline on coherence. The coherence surrogate prediction model constructs an exponential decay function, fitting the coherence using only the spatial baseline, as shown... Figure 4 As shown, the interferometric coherence systematically decreases with increasing vertical baseline value, effectively capturing and quantifying the attenuation effect of the vertical baseline on coherence. The coherence surrogate prediction model only utilizes the sum of soil moisture for the interferometric pairs ( Fitting coherence such as Figure 5 As shown, the coherence surrogate prediction model only utilizes the soil moisture difference between interference pairs ( Fitting coherence such as Figure 6 As shown, soil moisture is one of the environmental variables that cannot be ignored in explaining the spatial differentiation and temporal evolution of coherence.

[0027] The coherence surrogate prediction model of this invention includes a time baseline fitting unit, which calculates the interferometric pair according to the following formula. Time baseline difference , , SAR image The date, SAR image Date; Interference Time baseline difference Corresponding time baseline impact factor The expression is as follows: ,in This is the lower limit of coherence. , These correspond to the feature time scales under fast and slow time conditions, respectively. , These are the short-term and medium-to-long-term coherence contribution coefficients, respectively (simultaneously characterizing coherence decay at both rapid and slow time scales). This is the seasonal amplitude coefficient. For seasonal phase shift parameters, The annual cycle length.

[0028] The coherence surrogate prediction model of this invention includes a spatial baseline fitting unit, which calculates the interferometric pairs according to the following formula. Spatial baseline difference , , To interfere with Corresponding SAR image , The spatial baseline corresponding to the two satellite passes, that is, the straight-line distance between the two satellite orbital positions; To interfere with Radar side line of sight angle, To interfere with Baseline tilt angle; interference pair Spatial baseline difference The corresponding spatial baseline impact factor The expression is as follows: ;in For short baseline coherence when the vertical baseline approaches 0, This represents the lower limit of coherence at extremely long baselines. To control the coherence rate, a characteristic baseline length is used. Since the spatial baselines of interferometric pairs have a certain degree of dispersion, for the same vertical baseline value, the coherence may be dispersed over a wide range due to local topography, surface cover, soil moisture differences, and processing noise. To further improve the estimation accuracy of the vertical baseline term, a quantile regression method is used for parameter estimation. The quantile (80% in this embodiment) is used to obtain the upper envelope of spatial attenuation, thereby improving the prediction accuracy of spatial baseline terms for coherence.

[0029] The coherence surrogate prediction model of this invention includes a soil moisture influence fitting unit that interferes with the pair SAR images , Obtaining SAR main image from soil moisture data Soil moisture auxiliary images Soil moisture Interference The corresponding expression for the soil moisture influencing factor is as follows: , , These are the weighting coefficients.

[0030] The coherence surrogate prediction model uses sample interference to train model parameters on multi-factor feature data corresponding to subsets and sample coherence ground values. The model parameter set of the coherence surrogate prediction model is as follows: To achieve accurate predictions using the coherence surrogate model, precise estimation of the 12 parameters in the coherence surrogate prediction model is required, especially accurate capture of the vertical baseline. To address the boundary constraints on coherence, this embodiment employs bounded nonlinear least squares for global parameter optimization and proposes quantile regression for specific fitting of the spatial discoherence term, forming a two-stage parameter estimation framework. The objective function of the coherence surrogate prediction model in this invention is to minimize the weighted sum of squared residuals between the predicted coherence of the samples and the true coherence of the samples, as expressed below: ,in The number of sample interference pairs in the sample interference pair subset. The weighting parameters for the sample interference pair k are: To predict the coherence of the samples, The true value of sample coherence; the set of model parameters for the coherence surrogate prediction model is... .

[0031] In some embodiments, the trained coherent surrogate prediction model further includes a model parameter optimization and tuning module, which utilizes the weighted residual sum of squares to minimize the frontier... The sample interferometry in quantile regression adjusts and optimizes the model parameters of the spatial baseline impact factor in the spatial baseline impact factor, including short baseline coherence. lower limit of coherence Characteristic baseline length This embodiment can be optimized using the Levenberg-Marquardt algorithm. Parameter boundary constraints ensure physical rationality. Because InSAR coherence is affected by non-geometric factors such as atmospheric delay and random vegetation movement, observed values ​​are often lower than the theoretical geometric coherence. To reduce the bias in estimating the vertical baseline attenuation function parameters by low-coherence samples, this embodiment introduces quantile regression. By fitting the "upper envelope" of the data, the parameters of the spatial baseline influence factor model (also known as the spatial attenuation parameters) are refined. Preferably, the method for adjusting and optimizing the parameters of the spatial baseline impact factor model is as follows: From the sample interferometer subset, select sample interferometer pairs with smaller time baseline differences as the interferometer pair subset (selecting the interferometer pair subset with shorter time baselines to reduce the interference of time decoherence on the spatial term estimation); extract the time baseline influence factor model parameters of the coherence surrogate prediction model. Soil moisture influencing factor model parameters Calculate the time baseline influence factor of sample interferometry pairs. and soil moisture influencing factors The normalized spatial coherence observations are obtained according to the following formula. : ,in Given the true value of sample coherence, the model parameter optimization and adjustment module constructs a function that minimizes the bouncing loss function as the optimization objective, expressed as follows: ; Bouncing ball loss function The expression is as follows: , , For quantile parameters, Values (Example uses the 80th percentile). The impact factor of the purified spatial baseline is obtained based on the optimization objective of minimizing the bouncing loss function. The corresponding spatial baseline impact factor model parameters (i.e., the refined spatial decay parameters) and adjust, optimize, and update the model parameter set of the coherence surrogate prediction model. In this invention, the quantile parameter q=0.8 (taking the 80th quantile) is used to fit the upper envelope trend of spatial decay, obtaining a spatial decay curve that more closely resembles the "upper envelope trend," thus improving the prediction accuracy and robustness of the spatial baseline term for coherence. Quantile regression directly estimates the conditional quantile function, which is less sensitive to abnormally low values ​​compared to mean regression, making it suitable for upper envelope extraction. The spatial term parameters obtained from quantile regression are used to replace the spatial term parameters (i.e., the spatial baseline influence factor model parameters) in the global fitting. The final model parameters were obtained by [the process]. In the case study of Tianjin in northern China, the final estimated model parameters are shown in the table below:

[0032] To verify the predictive performance of the coherence surrogate prediction model (hereinafter referred to as the coherence surrogate model), statistical indices between surrogate predictive coherence and true coherence were calculated, and the results are as follows: Figure 7 As shown, the two exhibit a significant consistency trend. The RMSE between the surrogate prediction coherence and the true coherence is 0.03 and the R² is 0.71, indicating that the coherence surrogate prediction model has high prediction accuracy and can reliably approximate the true coherence.

[0033] S4. Input the multi-factor feature data corresponding to each interference pair in the candidate interference pair set into the trained coherence surrogate prediction model. The coherence surrogate prediction model outputs the predicted coherence of each interference pair. Using the predicted coherence of the interference pairs, select the optimal interference pair set from the candidate interference pair set and construct the interference pair network of the optimal interference pair set. That is, screen out the interferogram network that has both high coherence and can ensure stable and reliable time series solution.

[0034] In some embodiments, the predicted coherence of each interference pair output by the coherence surrogate prediction model is normalized, and the edge weights of each interference pair are constructed to ensure that the weights are normalized to the interval [0, 1]. The expression is as follows: ,in The normalized weight of the interference pair k is defined, and its value ranges from [0, 1]. This indicates the predictive coherence of the coherent surrogate prediction model interfering with k. The maximum value of the predictive coherence for all interference pairs; All candidate interference pairs in the candidate interference pair set are sorted in descending order of normalized weights, and candidate interference pairs are selected in descending order of normalized weights to be added to the optimal interference pair set and an interference pair network is constructed. The method for evaluating the termination of the selection iteration in the interference network is as follows: Construct a diagonal weight matrix based on normalized weights. , Construct the redundancy matrix of the interferometric pair network. , , It is the identity matrix. For designing matrices; redundant matrices The diagonal elements serve as the redundancy of the interference pair k. Determine the redundancy number in the interference pair network. average redundancy Set the average redundancy number The redundancy threshold, when the average redundancy of the interference pair network is... The candidate interferometric pair selection iteration terminates when the redundancy threshold is reached. In the Tianjin area of ​​northern China, this embodiment effectively screened out interferometric pairs with high overall coherence using the InSAR interferometric network optimization method, obtaining 290 interferometric pairs. The coherence of some of these pairs is illustrated in the diagram below. Figure 8 As shown in the figure; this embodiment, after constructing and optimizing an interferometric network in a certain study area, reflects the spatial distribution characteristics of the main subsidence areas as follows. Figure 9 , Figure 10 As shown, the monitoring point density and spatial coverage details of a certain study area in this embodiment are both good. In this embodiment, the interferometric pair network selection iteration uses a greedy algorithm to optimize the interferometric pairs within the network. Before the iteration begins, a high-coherence skeleton is first constructed using the maximum spanning tree algorithm, with normalized weights as edge weights. The maximum spanning tree is then searched in the graph composed of candidate interferometric pairs to ensure basic network connectivity. Next, all candidate interferometric pairs are arranged in descending order of normalized weights, and the interferometric pairs with the highest weights are added to the interferometric pair network sequentially. When the average value... The iteration stops when the target redundancy number is reached; for example, the redundancy threshold is set in the range of 0.8 to 0.9, and the average redundancy number... When the value is between 0.8 and 0.9, the network achieves a better balance between reliability and computational burden; finally, triangular closure and time bidirectional connection completion are used to improve the stability of phase solution and time series.

[0035] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An InSAR interferometric network optimization method based on a multi-factor coherence surrogate model, characterized in that: The methods include: S1. Construct a multi-factor feature dataset containing SAR images, baseline data, and soil moisture data of the study area. The baseline data includes temporal baselines and vertical baselines. S2. Construct a candidate interferometric pair set containing M interferometric pairs by combining the multi-factor feature dataset with SAR images in pairs to form interferometric pairs. Randomly select from the candidate interferometric pair set. As a subset of sample interference pairs, obtain the true value of sample coherence for each sample interference pair in the subset of sample interference pairs; S3. Construct a coherent surrogate prediction model that includes time baseline influence factors, spatial baseline influence factors, and soil moisture influence factors to predict coherence. The coherent surrogate prediction model uses sample interference to train model parameters on the multi-factor feature data corresponding to the subset and the true value of sample coherence. S4. Input the multi-factor feature data corresponding to each interference pair in the candidate interference pair set into the trained coherence surrogate prediction model. The coherence surrogate prediction model outputs the predicted coherence of each interference pair. Using the predicted coherence of the interference pairs, select the optimal interference pair set from the candidate interference pair set and construct the interference pair network of the optimal interference pair set.

2. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 1, characterized in that: The coherence surrogate prediction model uses the temporal baseline influence factor, spatial baseline influence factor, and soil moisture influence factor of the interferometric pair as influencing factors to predict the predicted coherence of the interferometric pair. In the coherence surrogate prediction model, the interferometric pair... Predictive coherence The expression is as follows: Interference From SAR images With SAR images Combination and composition, To interfere with Time baseline impact factor, To interfere with Spatial baseline impact factor To interfere with Factors affecting soil moisture.

3. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 2, characterized in that: The coherence surrogate prediction model includes a time baseline fitting unit, which calculates the interferometric pair according to the following formula. Time baseline difference , , SAR image The date, SAR image Date; Interference Time baseline difference Corresponding time baseline impact factor The expression is as follows: ,in This is the lower limit of coherence. , These correspond to the feature time scales under fast and slow time conditions, respectively. , These are the short-term and medium-to-long-term coherence contribution coefficients, respectively. This is the seasonal amplitude coefficient. For seasonal phase shift parameters, The annual cycle length.

4. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 3, characterized in that: The coherence surrogate prediction model includes a spatial baseline fitting unit, which calculates the interferometric pairs according to the following formula. Spatial baseline difference , , To interfere with Corresponding SAR image , The spatial baseline corresponding to the two satellite passes, that is, the straight-line distance between the two satellite orbital positions; This is the radar side-view angle. Baseline tilt angle; interference pair Spatial baseline difference The corresponding spatial baseline impact factor The expression is as follows: ;in For short baseline coherence when the vertical baseline approaches 0, This represents the lower limit of coherence at extremely long baselines. The characteristic baseline length is used to control the coherence rate.

5. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 4, characterized in that: The coherent surrogate prediction model includes a soil moisture influence fitting unit, which will interferometric pair SAR images , Obtaining SAR main image from soil moisture data Soil moisture auxiliary images Soil moisture Interference The corresponding expression for the soil moisture influencing factor is as follows: , , These are the weighting coefficients.

6. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 5, characterized in that: The objective function of the coherence surrogate prediction model is to minimize the weighted sum of squared residuals between the predicted coherence of the samples and the true coherence of the samples, as expressed below: ,in The number of sample interference pairs in the sample interference pair subset. The weighting parameters for the sample interference pair k are: To predict the coherence of the samples, The true value of sample coherence; the set of model parameters for the coherence surrogate prediction model is... .

7. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 1, characterized in that: In method S2, the true value of sample coherence of sample interference pairs in the sample interference pair subset is obtained as follows: first, the coherence of each pixel (a,b) in the sample interference pair is calculated, and then the average coherence of all pixels in the sample interference pair is calculated and used as the true value of sample coherence.

8. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 6, characterized in that: The trained coherent surrogate prediction model also includes a model parameter optimization and tuning module, which minimizes the weighted sum of squared residuals. The sample interferometry in quantile regression adjusts and optimizes the model parameters of the spatial baseline impact factor in the spatial baseline impact factor, including short baseline coherence. lower limit of coherence Characteristic baseline length .

9. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 8, characterized in that: The method for adjusting and optimizing the parameters of the spatial baseline impact factor model is as follows: From the sample interference pair subset, select sample interference pairs with smaller time baseline differences as the interference pair subset; extract the time baseline influence factor model parameters of the coherence surrogate prediction model. Soil moisture influencing factor model parameters Calculate the time baseline influence factor of sample interferometry pairs. and soil moisture influencing factors The normalized spatial coherence observations are obtained according to the following formula. : ,in Given the true value of sample coherence, the model parameter optimization and adjustment module constructs a function that minimizes the bouncing loss function as the optimization objective, expressed as follows: ; Bouncing ball loss function The expression is as follows: ， ， The impact factor of the purified spatial baseline is obtained based on the optimization objective of minimizing the bouncing loss function. The corresponding spatial baseline impact factor model parameters The model parameter set of the coherent proxy prediction model is adjusted, optimized and updated.

10. The InSAR interferometric network optimization method based on a multi-factor coherence surrogate model according to claim 1, characterized in that: In method S4, the predicted coherence of each interference pair output by the coherence surrogate prediction model is normalized, as shown in the following expression: ,in To interfere with the normalized weights of k, This indicates the predictive coherence of the coherent surrogate prediction model interfering with k. The maximum value of the predictive coherence for all interference pairs; All candidate interference pairs in the candidate interference pair set are sorted in descending order of normalized weights, and then candidate interference pairs are selected in descending order of normalized weights to be added to the optimal interference pair set and an interference pair network is constructed. The method for evaluating the termination of the selection iteration in the interference network is as follows: Construct a diagonal weight matrix based on normalized weights. Construct the redundancy matrix of the interferometric pair network. , , It is the identity matrix. For designing matrices; redundant matrices The diagonal elements serve as the redundancy of the interference pair k. Determine the redundancy number in the interference pair network. average redundancy Set the average redundancy number The redundancy threshold, when the average redundancy of the interference pair network is... The candidate interference pair selection iteration terminates when the redundancy threshold is reached.

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