Bridge deformation monitoring method based on permanent scatterer interferometry

Abstract

The application discloses a bridge deformation monitoring method based on permanent scatterer interference, first uses a traditional PS-InSAR method and only models height phase to solve PS point height information, then uses an improved free combination network combined with threshold screening to obtain more accurate height information, long-term settlement deformation information and periodic thermal expansion deformation information by using the height information obtained in the first step; the PS-InSAR method of the application through step-by-step iteration and combined with a high redundancy network can monitor the deformation of a truss bridge, can obtain more accurate and robust height and deformation parameter estimation results, and therefore the deformation monitoring capability of the application is superior to that of the traditional PS-InSAR method.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a bridge deformation monitoring method based on permanent scatterer interference. BACKGROUND

[0002] The InSAR (Interferometric Synthetic Aperture Radar) is an effective means for monitoring ground deformation. Compared with the means for monitoring on site by using sensors, it has low monitoring cost and large monitoring range; compared with optical satellite image monitoring, it has more comprehensive information, can monitor millimeter-scale micro deformation by using phase information, and has all-weather monitoring capability without being affected by cloud and rain.

[0003] When the interference technology is applied to long-term settlement monitoring of a bridge, the following challenges are mainly faced. In the case of long-time observation, the SAR (Synthetic Aperture Radar) image will have a serious decorrelation phenomenon; in addition, the deformation form of the bridge is complex, and there are long-term settlement deformation, thermal expansion deformation and other deformation forms. These two points increase the difficulty of bridge deformation monitoring. In order to improve the monitoring accuracy, the current mainstream method is to use the PS-InSAR (Permanent Scatterer Interferometry), which first detects the pixels with stable backscattering in the SAR image sequence, called permanent scatterer (PS), and then connects the PS points to form a network, and solves the parameters in the network.

[0004] Regarding the deformation parameter solving, the existing methods are roughly divided into two categories: the first category is the phase unwrapping method, which first unwraps the phase in the network after removing the terrain phase, and then obtains the deformation value according to the unwrapped phase. The phase unwrapping method has the advantages of not needing to make assumptions about the deformation form of the study area, and thus can better adapt to the nonlinear deformation environment, but the phase unwrapping method requires to meet the phase continuity assumption, which is difficult to meet in the PS-InSAR processing process, and thus the application is relatively limited; the second category is the time-domain ambiguity estimation method, which first models the terrain phase, and then searches for the parameter set that maximizes the time-domain coherence coefficient in the pre-set solution space, and takes the parameter value as the final deformation parameter solving result. The method avoids the phase unwrapping step and is easy to implement, and thus is the mainstream method in current engineering implementation, but it needs to model the deformation in advance, and thus has weak monitoring capability for complex nonlinear deformation, and the pre-set solution space also reduces the robustness of the algorithm. SUMMARY

[0005] Therefore, the application provides a bridge deformation monitoring method based on permanent scatterer interference, which can more stably monitor the bridge deformation information of the truss structure.

[0006] A bridge deformation monitoring method based on permanent scatterer interference comprises the following steps:

[0007] Step one, select the SAR image of the bridge to be monitored, select the PS point of each SAR image;

[0008] Step two, solve the preliminary PS point elevation parameter, specifically including:

[0009] S201, model the flat-removed phase

[0010] Model the PS point phase after flat-removed phase as:

[0011]

[0012] Wherein, is the phase after flat-removed, λ is the radar wavelength, B ⊥ is the vertical baseline distance, R is the slant range, θ is the radar downward angle, h is the height difference of the PS point relative to the height of the flat, w is the residual phase;

[0013] S202, connect the PS points in network and solve the parameters:

[0014] Use Delaunay triangle network to connect the PS points in network, and calculate the differential phase on the connecting arc Set the search range of the height difference Δh of the two PS points connected by each arc, and each to-be-searched value in the search range is recorded as Δh m ,

[0015]

[0016] Wherein γ m is the time domain coherence coefficient, N is the number of SAR images, i is the serial number of the selected SAR image, represents the differential phase of the PS point in the i-th SAR image, represents the vertical baseline distance of the PS point in the i-th SAR image, j is the imaginary unit; so that γ m The maximum Δh m is the search result of the differential elevation estimation of the arc;

[0017] S203, least square adjustment and outlier rejection, specifically:

[0018] Set the phase vector composed of all PS points as The differential phase vector on the arc is K, M are the number of PS points and the number of connecting arcs respectively; the connection relationship of the arc is represented by matrix B, that is:

[0019]

[0020] Therefore, according to the search result of the differential elevation estimation between the PS points Δhm , the difference elevation vector Δh = [Δh0, Δh1, …, ΔhN-1]T is obtained, where Δh0, Δh1, …, ΔhN-1 are the difference elevations between the PS points. M ] T The estimated value of the elevation of each PS point is obtained by the weighted least squares method. After obtaining the estimated value of the elevation of the PS point, the residual of the estimated value of the elevation between the PS points is calculated, and the arc with a residual greater than a given threshold is deleted. Thus, the connection relationship B of the arc between the PS points is updated, and then the difference elevation vector Δh is updated. Then, the estimated value of the elevation of each PS point and the residual are calculated again based on the updated difference elevation vector Δh, and it is judged whether the residual is greater than the given threshold. The arc with a residual greater than the given threshold is deleted. In this way, the process is repeated until all residuals are less than or equal to the given threshold.

[0021] Step three, solving the deformation parameters based on the last updated arc connection relationship of step two, obtaining the elevation value of each PS point,

[0022] which is h in formula (1), and calculating the phase of the PS point according to the formula;

[0023] S301, modeling the residual phase

[0024] First, remove the elevation phase obtained based on formula (1), and denote the residual phase as Modeling it:

[0025]

[0026] Where v is the long-term subsidence rate, t is the time difference between the main and auxiliary images, k is the thermal expansion coefficient, ΔT is the temperature difference between the main and auxiliary images, and h' is the difference between the true elevation of the PS point and h obtained in step two.

[0027] S302, connecting the PS points into a high-redundancy network and solving the parameters

[0028] First, connect the PS points using a free connection network, that is, connect all PS point pairs that satisfy a given distance threshold. Then, calculate the difference phase of each connection arc Given the difference elevation search range Δh' m , the difference deformation rate range Δv m , and the difference thermal expansion coefficient range Δk m , combine the search values of the three parameters in their respective search ranges to calculate the time-domain coherence coefficient under each combination of parameters:

[0029] Wherein, represents the difference phase of the PS point in the i-th SAR image calculated in this step.

[0030] After obtaining the time-domain coherence coefficients γ of all parameter combinations corresponding to each connection arc, the network is established in the following way:

[0031] 1) If the maximum value of the time domain coherence coefficient γ is less than the set threshold value, the arc is directly deleted; max

[0032] 2) For each arc remaining after 1) deletion, a coefficient α is set, and all coordinates (Δh', Δv, Δk) satisfying the time domain coherence coefficient γ > αγ max are recorded;

[0033] 3) The recorded coordinates are clustered by DBSCAN, and if the clustering is one class, the arc is retained, and if the clustering is multiple classes, the arc is deleted; the finally retained arc constitutes the high-redundancy network;

[0034] S303, least square adjustment and gross error rejection

[0035] Similar to S203, based on the arc connection relationship of the high-redundancy network finally obtained in S302, the maximum value of the time domain coherence coefficient γ max is determined to search for the differential height vector Δh', the differential deformation rate vector Δv and the differential thermal expansion coefficient vector Δk, and the height vector h' of each PS point, the deformation rate vector v and the thermal expansion coefficient vector k are obtained by weighted least square method;

[0036] The height vector h', the deformation rate vector v and the thermal expansion coefficient vector k residual between two PS points connected by an arc are calculated, the arc with a residual greater than the corresponding set threshold value is deleted, and the high-redundancy network is updated; based on the updated high-redundancy network, the height vector h' of each PS point, the deformation rate vector v and the thermal expansion coefficient vector k are obtained again by weighted least square method according to the differential height vector Δh', the differential deformation rate vector Δv and the differential thermal expansion coefficient vector Δk of the arc; so as to repeat, the height vector h', the deformation rate vector v and the thermal expansion coefficient vector k are subjected to gross error rejection, and finally the three parameters are obtained, and the bridge deformation monitoring is completed.

[0037] Preferably, in the step one, the method for selecting the PS point is:

[0038] The theoretical coherence between images is calculated according to the track baseline information, and the image with the maximum average coherence is taken as the main image; then all the secondary images are sequentially registered to the main image based on the sliding window registration method of the image complex coherence coefficient; after the registration is completed, the flat ground phase of each interferogram is calculated and removed, and then the amplitude deviation value of each pixel in the image is calculated, and the pixel points less than the given threshold value are identified as PS points.

[0039] The present application has the following beneficial effects:

[0040] ​The present application firstly uses the traditional PS-InSAR method and only models the height phase to solve the PS point height information, and then uses the improved free combination network combined with threshold screening in the second step to obtain more accurate height information, long-term subsidence deformation information and periodic thermal expansion deformation information by using the preliminary height information obtained in the first step. The present application has the following comparison with the traditional PS-InSAR method:

[0041] The PS points identified by the truss structure bridge are mainly distributed on the upper and lower ends of the truss, so the height difference is large, and the solution space of the search parameters is large, so it is difficult to obtain robust and correct parameter results using the traditional PS-InSAR method; the step-by-step iterative method proposed by the present application can preferentially search for relatively correct elevation values, thereby reducing the solution space range and obtaining more robust parameter results.

[0042] Due to the characteristics of the bridge shape, the identified PS points are distributed in a long strip shape in the image, the Delaunay triangle network used in the traditional PS-InSAR has low redundancy, and is easily cut off as an island in subsequent processing, and cannot obtain correct results. At the same time, the bridge deformation form is complex, and long-term subsidence deformation and periodic thermal expansion deformation exist at the same time, and the low-redundancy Delaunay triangle network is difficult to provide sufficient phase information; the present application uses the free combination network combined with the threshold screening step based on clustering, which improves the network redundancy, more effectively utilizes the phase information, and removes the wrong arcs, thereby improving the accuracy of the estimation results.

[0043] The PS-InSAR method of the present application can obtain more accurate and robust height and deformation parameter estimation results by monitoring the deformation of the truss bridge through step-by-step iteration and combining a high-redundancy network, so the deformation monitoring capability of the present application is superior to that of the traditional PS-InSAR method. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a flowchart of the present application;

[0045] Fig. 2(a) is the position and optical, radar image of the bridge in the embodiment of the present application, and Fig. 2(b) is the PS point selection result of the bridge in the embodiment of the present application;

[0046] Figure 3 (a) and Figure 3 (b) are the coherence coefficient distribution and clustering results of the arcs that should be retained, Figure 3 (c) and Figure 3 (d) are the coherence coefficient distribution and clustering results of the arcs that should be deleted;

[0047] Fig. 4(a) is the elevation inversion result of the traditional method under the conditions (1)-(4) shown in Table 2; Fig. 4(b) is the elevation inversion result of the present application under the conditions (1)-(4) shown in Table 2

[0048] Figure 5 (a), Figure 5 (b) are respectively the long-term settlement deformation rate and the thermal expansion coefficient obtained by the present application; Figure 5 (c) and (d) are respectively the long-term settlement deformation rate and the thermal expansion coefficient obtained by the traditional PS-InSAR method;

[0049] Fig. 6(a), Fig. 6(b) and Fig. 6(c) are respectively the elevation result, the long-term settlement rate and the thermal expansion coefficient obtained by the present application plotted on Google Earth. DETAILED DESCRIPTION

[0050] The present application will be described in detail below with reference to the accompanying drawings and embodiments.

[0051] The present application discloses a truss bridge deformation monitoring method based on PS-InSAR. In solving the height and deformation parameters, first, only the elevation is modeled, and the traditional PS-InSAR method is used to solve the initial value of the elevation. Then, in the second step, a high-redundancy PS point connection network is established, the long-term settlement deformation and the periodic thermal expansion deformation are modeled, and all parameters are iteratively solved on the basis of the elevation information obtained in the first step.

[0052] As shown in Fig. 1, it is a flowchart of the present application, which specifically comprises the following steps: Figure 1

[0053] Step one, data preprocessing and PS point selection:

[0054] According to the orbital baseline information, the theoretical coherence between images is calculated, and the image with the maximum average coherence is taken as the main image. Then, based on the sliding window registration method of image complex coherence coefficient, all secondary images are sequentially registered to the main image. After registration, the flat phase of each interferogram is calculated and removed. Subsequently, the amplitude deviation value of each pixel in the image is calculated, and the pixel points less than the given threshold value are identified as PS points.

[0055] Step two, solving the initial PS point elevation parameters:

[0056] This step specifically implements sub-steps S201-S203 on the identified PS points.

[0057] S201, modeling the flat phase

[0058] The flat phase of the PS point is modeled as:

[0059] ​

[0060] where, is the post-terrain-correction phase, λ is the radar wavelength, B ⊥ is the vertical baseline, R is the slant range, θ is the radar depression angle, h is the height difference of PS point relative to the height of the terrain, w is the residual phase.

[0061] S202, connect the PS points and solve the parameters:

[0062] Use the Delaunay triangle network to connect the PS points and calculate the differential phase on the connecting arc Set the search range of the height difference Δh of the two PS points connected by each arc, and each to-be-searched value in the search range is denoted as Δh m , and has:

[0063]

[0064] where γ m is the time domain coherence coefficient, N is the number of SAR images, i is the serial number of the selected SAR image, represents the differential phase of the PS point in the i-th SAR image, represents the vertical baseline of the PS point in the i-th SAR image, and j is the imaginary unit. So that γ m is the maximum Δh m is the search result of the differential height estimation of the arc.

[0065] S203, least square adjustment and outlier rejection

[0066] Let the phase vector composed of all PS points be The differential phase vector on the arc is K and M are the number of PS points and the number of connecting arcs respectively. The connecting relationship of the arc can be represented by the matrix B, that is:

[0067]

[0068] Therefore, according to the search result of the differential height estimation Δh m between PS points, the differential height vector Δh = [Δh0, Δh1, …, Δh M ] TThe estimated value of the elevation of each PS point identified can be obtained by weighted least squares (WLS), and after obtaining the estimated value of the elevation of the PS point, the residual of the estimated value of the elevation between the PS points is calculated, and the arc with a residual greater than a given threshold is deleted; thereby updating the connection relationship B of the arcs between the PS points, and then updating the differential elevation vector Ah, and then re-calculating the estimated value of the elevation of each PS point and the residual based on the updated differential elevation vector Ah, and judging whether the residual is greater than the given threshold, and deleting the arc with a residual greater than the given threshold; in this way, the process is repeated until all residuals are less than or equal to the given threshold.

[0069] Step three, solving deformation parameters based on the last updated arc connection relationship in step two, obtaining the elevation value of each PS point,

[0070] That is h in formula (1), and the phase of the PS point is calculated according to the formula.

[0071] S301, modeling the residual phase

[0072] First, remove the elevation phase obtained based on formula (1), and denote the residual phase as Modeling it:

[0073]

[0074] Where v is the long-term subsidence rate, t is the time difference between the main and auxiliary images, k is the thermal expansion coefficient, ΔT is the temperature difference between the main and auxiliary images, h' is the difference between the true elevation of the PS point and the elevation obtained in step two, and the remaining variables have the same meaning as in step S201.

[0075] S302, connecting the PS points into a high-redundancy network and solving parameters

[0076] First, use a free connection network to connect the PS points, that is, connect all PS point pairs that satisfy a given distance threshold. Then, as in step S202, calculate the differential phase of each connection arc Given the differential elevation search range, the differential deformation rate range, and the differential thermal expansion coefficient range, combine the search values of the three parameters in their respective search ranges to calculate the time-domain coherence coefficient under each combination of parameters.

[0077] The time-domain coherence coefficient calculation formula at this time is as follows:

[0078] After obtaining the time-domain coherence coefficient γ of each connection arc corresponding to all parameter combinations, the network is established in the following way:

[0079] 1) If the maximum value γ of the time-domain coherence coefficient γ is max less than a set threshold, the arc is directly deleted;

[0080] 2) For each arc left after 1), set a coefficient a, and record all coordinates (Δh', Δv, Δk) that satisfy the time-domain coherence coefficient γ > aγ max , where a is usually 0.85.

[0081] 3) For the recorded coordinates, perform DBSCAN clustering, if the clustering is one class, the arc is retained, if the clustering is multiple classes, the arc is deleted.

[0082] The network composed of the finally retained arcs is the high-redundancy network.

[0083] Since the γ max of each arc has been obtained, the following method can be directly used for adjustment.

[0084] S303, least square adjustment and gross error elimination

[0085] Similar to S203, based on the arc connection relationship of the high-redundancy network finally obtained in S302, the difference height vector Δh', the difference deformation rate vector Δv and the difference thermal expansion coefficient vector Δk are determined according to the maximum value γ max of the time-domain coherence coefficient, and the height vector h', the deformation rate vector v and the thermal expansion coefficient vector k of each PS point can be obtained respectively by using the weighted least square method (WLS).

[0086] The height vector h', the deformation rate vector v and the thermal expansion coefficient vector k residual between two PS points connected by an arc are calculated, the arc whose residual is greater than the corresponding set threshold value is deleted, and the high-redundancy network is updated; based on the updated high-redundancy network, the height vector h', the deformation rate vector v and the thermal expansion coefficient vector k of each PS point are obtained respectively by using the weighted least square method (WLS) according to the difference height vector Δh', the difference deformation rate vector Δv and the difference thermal expansion coefficient vector Δk of the arc; so as to repeat the above steps, the height vector h', the deformation rate vector v and the thermal expansion coefficient vector k are subjected to gross error elimination, and finally the three parameters are obtained, and the bridge deformation monitoring is completed.

[0087] Embodiment example:

[0088] The satellite-borne SAR data is processed by using the application, so as to further verify the feasibility and effectiveness of the technology.

[0089] As shown in FIG. 2, the position, optical image, SAR image and PS point selection result of the truss bridge to be monitored are given, and it can be seen that the selected PS points are uniformly distributed on the bridge.

[0090] Table 1 gives the detailed information of the four test cases, as shown in Figure 4, the elevation estimation results of the traditional PS-InSAR method and the method proposed in the application under the four test cases shown in Table 1 are given, it can be seen that in the case of retaining different PS point numbers and search ranges, the estimation results of the traditional PS-InSAR method are not robust and are easily disturbed by the artificially set hyperparameters; while in the case of modeling only the elevation information in the first step iteration, the method proposed in the application can obtain more accurate and robust estimation results.

[0091] Table 1: Test case information

[0092]

[0093] Figure 3 The schematic diagram of threshold screening using a clustering method in the construction process of a high-redundancy network is given. Figure 5 The long-term settlement rate and the thermal expansion coefficient inverted by the traditional PS-InSAR method and the method proposed in the application are given. It can be seen that once the low-redundancy network constructed by the traditional method is cut off, the inverted results will jump and cause errors. Table 2 gives the residual phase standard deviation after the relevant parameters are inverted by the method proposed in the application and the traditional PS-InSAR method, and the smaller the standard deviation, the more accurate the inverted parameters. Both of them jointly illustrate the advantages of the two-step parameter solving combined with the high-redundancy network in the deformation monitoring of truss bridges proposed in the application.

[0094] Table 2: Residual phase evaluation results

[0095]

[0096] Figure 5 The deformation monitoring results of the truss bridge to be monitored by the method proposed in the application are given, and the results show that the thermal expansion deformation of the steel structure bridge with seasonal changes in temperature accounts for the main part, the long-term deformation rate is related to the height of the bridge structure and is within the normal range.

[0097] In conclusion, the above is only a preferred embodiment of the application, and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A method for bridge deformation monitoring based on permanent scatterer interferometry, characterized in that, Comprise the following steps: Step one, select the SAR image of the bridge to be monitored, select the PS point of each SAR image; Step two, solve the initial PS point elevation parameter, specifically including: S201, modeling the flat earth phase The PS point phase after the flat earth phase is modeled as: (1) wherein, is the post-terrain-cleared phase, is the radar wavelength, is the vertical baseline distance, is the slant range, is the radar depression angle, is the height difference of the PS point height relative to the height of the flat ground, is the residual phase; S202, connect the PS point network and solve the parameters: The PS points are connected to form a network using a Delaunay triangle network, and the differential phase on the connecting arc is calculated The height difference of the two PS points connected by each arc is set The search range is set to the height difference of the two PS points connected by each arc , and each value to be searched in the search range is recorded as （2） wherein is the time domain coherence coefficient, is the number of SAR images, is the serial number of the selected SAR image, denotes the differential phase of the PS point in the i-th SAR image, denotes the vertical baseline distance of the PS point in the i-th SAR image, is the imaginary unit; such that is the maximum is the differential height estimate of the arc found by the search; S203, least squares adjustment, gross error rejection, specifically: Let the phase vector composed of phases of all PS points be , and the differential phase vector on the arc be , respectively be the number of PS points and the number of connecting arcs; the connecting relationship of the arcs is represented by matrix , that is: （3） Thus, the difference height estimation result between the PS points obtained by searching , the difference height vector is constituted , the estimation value of the height of each PS point is obtained by the weighted least square method, after the estimation value of the height of the PS point is obtained, the residual of the estimation value of the height between the PS points is calculated, and the arc whose residual is greater than the given threshold is deleted; thus, the connection relationship of the arc between the PS points is updated , then the difference height vector is updated , and then the estimation value of the height of each PS point and the residual are recalculated based on the updated difference height vector , and it is judged whether the residual is greater than the given threshold, and the arc whose residual is greater than the given threshold is deleted; in this way, until all the residuals are less than or equal to the given threshold; Step three, solving deformation parameters: based on the last updated arc connection relationship in step two, the elevation value of each PS point is obtained, that is, the in formula (1) , and the phase of the PS point is calculated according to the formula; S301, modeling the residual phase First, the height phase based on formula (1) is removed, and the remaining phase is recorded as Modeling it: wherein, is the long-term settling rate, is the time difference between the primary and secondary images, is the thermal expansion coefficient, is the temperature difference between the primary and secondary images, is the difference between the true elevation of the PS point and the elevation obtained in step two, is the difference between the true elevation of the PS point and the elevation obtained in step two. S302, connect the PS point to a high redundancy network and solve the parameters Firstly, the PS points are connected by free connection network, i.e. all the PS point pairs satisfying a given distance threshold are connected; then the differential phase of each connection arc is calculated ; given the differential height search range , the differential deformation rate range , and the differential thermal expansion coefficient range , the time-domain coherence coefficients under each combination of parameters are calculated by combining the search values of the three parameters in their respective search ranges: （5） wherein, denotes the differential phase of the PS point in the i-th SAR image calculated in this step; obtain the time-domain coherence coefficients of all parameter combinations corresponding to each connection arc After that, the network is established in the following way: 1) If the time-domain coherence coefficient maximum value If the value is less than the set threshold, the arc will be deleted directly. 2) Set a coefficient for each arc left after 1) , record all coordinates satisfying the time domain coherence coefficient ;​ 3) DBSCAN clustering is performed on the recorded coordinates. If the clustering is one class, the arc is retained. If the clustering is multiple classes, the arc is deleted. The network composed of the finally retained arcs is the high redundancy network; S303, least squares adjustment, gross error rejection Similar to S203, based on the arc connection relationship of the high-redundancy network finally obtained in S302, the elevation vector of each PS point is obtained by weighted least square method according to the maximum value of the time domain coherence coefficient The difference elevation vector obtained by searching is determined The difference deformation rate vector is determined The difference thermal expansion coefficient vector is determined The elevation vector of each PS point is obtained by weighted least square method The deformation rate vector of each PS point is obtained by weighted least square method The thermal expansion coefficient vector of each PS point is obtained by weighted least square method ; Calculate the elevation vector between two PS points connected by an arc , the deformation rate vector and the thermal expansion coefficient vector Residual, delete the arc with residual greater than the corresponding set threshold, update the high redundancy network; based on the updated high redundancy network, according to the difference elevation vector , the difference deformation rate vector and the difference thermal expansion coefficient vector , the elevation vector , the deformation rate vector and the thermal expansion coefficient vector of each PS point are obtained by weighted least squares method respectively; repeat the above steps to eliminate gross errors in the elevation vector , the deformation rate vector and the thermal expansion coefficient vector , and finally obtain the three parameters to complete the bridge deformation monitoring.

2. A method for monitoring deformation of a bridge based on permanent scatterer interferometry as claimed in claim 1, wherein, In the step one, the method for selecting the PS point is: According to the track baseline information, the theoretical coherence between images is calculated, and the image with the maximum average coherence is taken as the main image. Then, based on the sliding window registration method of image complex coherence coefficient, all the secondary images are sequentially registered to the main image; After registration, the flat earth phase of each interferogram is calculated and removed. Subsequently, the amplitude deviation value of each pixel in the image is calculated, and the pixel points less than the given threshold value are identified as PS points.

Images