CN115113202A - Interference phase iteration unwrapping method based on two-dimensional Gaussian model - Google Patents
Interference phase iteration unwrapping method based on two-dimensional Gaussian model Download PDFInfo
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Abstract
The invention provides an interference phase iterative unwrapping method based on a two-dimensional Gaussian model, which is applied to large gradient deformation InSAR monitoring of a mining area and comprises the following steps: the method is applied to large gradient deformation InSAR monitoring of a mining area and comprises the following steps: step 1, collecting SAR images to perform data preprocessing, acquiring single-view complex SLC images, forming an interference combination to obtain a winding interference pattern, and calculating the phase of the interference pattern; step 2, conducting adaptive quadtree downsampling processing on the phase of the interference pattern, and calculating the edge unwrapping phase of the mining area by adopting a traditional phase unwrapping method; step 3, establishing a two-dimensional Gaussian function model of the edge unwrapping phase of the mining area, calculating model parameters and inverting the model parameters; step 4, obtaining a winding residual interference phase by estimating a full basin deformation phase of the mining area, and unwrapping the residual interference phase; step 5, acquiring a disentanglement phase of the coal mine area; and 6, obtaining a refined mining area unwrapping phase through iteration of the steps 3-5.
Description
Technical Field
The invention relates to the technical field of monitoring of surface deformation of mining areas, in particular to an interference phase iteration unwrapping method based on a two-dimensional Gaussian model.
Background
Mineral resources are important material conditions indispensable for human survival and are also basic industries related to national civilization, and with continuous mining of mineral resources in recent years, ground surface deformation can cause a series of potential disasters such as ground surface collapse, house inclination, road damage, environmental pollution and the like. The InSAR (interferometric synthetic aperture radar) technology is a ground monitoring technology with large range and high space-time resolution developed in recent years, and can monitor the surface deformation caused by mining of a mining area. One key step in InSAR deformation monitoring is phase unwrapping, with the aim of recovering the true deformation phase from the wrapped phase. The traditional phase unwrapping method comprises a path tracking method, an optimization-based method and a combined denoising and unwrapping method, which solve the problem of ill-conditioned inversion according to the assumption of phase continuity, and the rapid mining of a mining area can cause overlarge deformation gradient and discontinuous phase. Therefore, the traditional phase unwrapping method is very prone to errors when resolving the wrapping interferogram of the mining area, especially in the large deformation gradient area.
In order to solve the application problem of the traditional phase unwrapping method in the monitoring of the InSAR deformation of the mining area, the currently used methods can be roughly divided into three types: phase unwrapping aided by external data such as ground GPS monitoring data, level data, etc.; secondly, a phase unwrapping method based on deep learning; and thirdly, a phase unwrapping method assisted by a probability integration method model. The first method is limited by the availability of external data and is difficult to popularize and apply in a large range, and the second method depends on a large number of training samples and sample reliability and is difficult to ensure the accuracy of a calculation result. The third category of methods requires the collection of underground goaf geometry in the field.
Therefore, the InSAR phase unwrapping of large gradient deformation in the current mining area (such as an underground mining area) is still very difficult, and the application prospect of the InSAR technology in the mine field is severely restricted.
Disclosure of Invention
The invention provides an interference phase iteration unwrapping method based on a two-dimensional Gaussian model, and aims to overcome the limitations that interference patterns are dense in stripes and aliasing is difficult to unwrapp due to rapid mining of a mining area, and accurate phase unwrapping results of the mining area can be obtained without underground mining parameters; and the accuracy of phase unwrapping in a mining area is improved.
In order to achieve the above object, the present invention provides an interference phase iterative unwrapping method based on a two-dimensional gaussian model, which is applied to large gradient deformation InSAR monitoring in a mining area, and comprises:
step 3, establishing a two-dimensional Gaussian function model of the edge unwrapping phase of the mining area, calculating model parameters and inverting the model parameters;
and 6, obtaining a refined mining area unwrapping phase through iteration of the steps 3-5.
Wherein, step 1 includes:
data registration is carried out by taking the SLC image in the first stage as a reference, and interference combination is formed by images of each adjacent time after registration;
the interferogram phase is represented as:
where φ (i) is the wrapping phase of the ith pixel,
k is the number of cycles for the unwrapped phase of the ith pixel.
Wherein, step 3 includes:
the two-dimensional gaussian function model is represented as:
f(i,j,m)＝Sexp(-a(i-x) 2 -2b(i-x)(j-y)-c(j-y) 2 )
where S is amplitude, x, y are coordinates of the center point, R x ，R y Is standard deviation, theta is clockwise rotation angle, and the initial value m of the model parameter is determined according to the position of the deformation area 0 ＝S 0 ,R x0 ，R y0 ,x 0 ，y 0 ,θ 0 ] T Inverting a two-dimensional Gaussian function model by a Levenberg-Marquardt algorithm to obtain an inversion parameter m, wherein [ S, R ═ m x ，R y ,x，y,θ] T 。
Wherein, step 4 includes:
estimating a full basin deformation phase of the mining area according to the inverted model parameters;
subtracting the phase of the interference pattern from the phase of the full basin deformation to obtain a winding residual interference phase;
the wrapped residual interference phase is phase unwrapped using a conventional phase unwrapping algorithm.
Wherein, step 5 includes:
and adding the residual interference phase subjected to phase unwrapping and the full basin deformation phase to obtain the mining area surface unwrapping phase.
Wherein, step 6 includes: refining the unwrapping phase result by iterating the steps 3-5 until the difference between the last unwrapping phase and the last unwrapping phase is less than a threshold value, wherein the threshold value is 0.05; and stopping iteration to obtain the unwrapping phase of the mining area.
For any pixel (i, j), the relationship between the mining area edge unwrapping phase and the two-dimensional Gaussian function model is as follows:
wherein epsilon (i, j) is the residual error of any pixel, and the weighted residual phase obtained by weighting is:
where σ (i, j) represents the variance determined by the image coherence.
The scheme of the invention has the following beneficial effects:
compared with the existing large deformation gradient InSAR phase unwrapping method, the method does not need underground mining parameters, field observation data of a mining area and training samples, only carries out iterative modeling and parameter inversion on the interference phase to carry out phase unwrapping, greatly reduces the limitation in the using process of the method, effectively overcomes the problem that the traditional phase unwrapping method is difficult to unwrapp mining area density and aliasing interference fringes, has important influence on the subsequent LOS surface deformation resolving precision of the mining area, and widens the application prospect of InSAR phase unwrapping of the mining area.
Other advantages of the present invention will be described in detail in the detailed description that follows.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIGS. 2(a) - (c) are graphs showing the simulation results of probability integration for modeling interferograms with a deformation phase of 20rad and noise phases of 0.5rad, 1rad, and 1.5rad, respectively, according to the embodiment of the invention; FIGS. 2 (d) - (f) are graphs showing the simulation results of probability integration to simulate the winding interferograms with a deformation phase of 60rad and a noise phase of 0.5rad, 1rad and 1.5rad, respectively, in the embodiment of the present invention; FIGS. 2 (g) - (i) show the simulation results of the probability integration method for simulating the winding interferograms with deformation phase of 100rad, noise phase of 0.5rad, 1rad and 1.5rad according to the embodiment of the invention;
fig. 3 (a) - (i) are simulation results of two-dimensional gaussian function models with different deformation gradients and different noise phases, which correspond to the simulated winding interferograms of fig. 2(a) - (i);
fig. 4(a) - (i) are the calculated mining area phase unwrapping results of different deformation gradients and different noise phases of the present invention, which correspond to the simulated mining area wrapped interferograms of fig. 2(a) - (i);
fig. 5(a) - (i) are statistical histogram plots of the difference values of different deformation gradients and different noise levels calculated by the embodiment of the present invention, which correspond to the mine phase unwrapping results of fig. 4(a) - (i).
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it is to be noted that, unless otherwise explicitly specified or limited, the terms "mounted", "connected" and "connected" are to be understood broadly, for example, as being either a locked connection, a detachable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In addition, the technical features involved in the different embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Aiming at the existing problems, the invention provides an interference phase iterative unwrapping method based on a two-dimensional Gaussian model, which comprises the steps of firstly carrying out data processing on an SAR image to obtain an wrapped interferogram, secondly carrying out adaptive quadtree downsampling processing on the wrapped interferogram, and obtaining a relatively accurate mining area edge unwrapping phase by adopting a traditional phase unwrapping method; thirdly, establishing a two-dimensional Gaussian function model for describing the deformation of the ground surface of the mining area, and inverting the model parameters of the two-dimensional Gaussian function model by adopting a nonlinear method LM (Levenberg-Marquardt); fourthly, calculating a full basin deformation phase of the mining area by using a two-dimensional Gaussian function model, obtaining a winding residual interference phase by subtracting the phase of the interference pattern, and unwrapping the residual interference phase by using a traditional phase unwrapping method; and fifthly, adding the unwrapped residual interference phase and the full basin deformation phase to obtain a mining area surface unwrapping phase. And finally, iterating the third, fourth and fifth processes until the difference between the last unwrapping phase and the last unwrapping phase is smaller than a certain threshold value, and stopping iteration so as to obtain the final unwrapping phase of the mining area.
As shown in fig. 1, an embodiment of the present invention provides an interferometric phase iterative unwrapping method based on a two-dimensional gaussian model, which is applied to large gradient deformation InSAR monitoring in a mining area, and includes:
preprocessing collected SAR images to obtain single-view complex SLC images, performing data registration by taking the first-stage SLC image as a reference, and forming an interference combination by images of each adjacent time after registration; the wrapped interferogram is obtained by composing the interference combination and calculating the phase of the interferogram.
The interferogram phase is represented as:
where φ (i) is the wrapping phase of the ith pixel,
for the unwrapped phase of the ith pixel, ik is the number of cycles.
Specifically, in the embodiment, a probability integration method is used for simulating three-dimensional large-magnitude time sequence deformation phases (unit is rad) of the ground surface of an underground mining area at four time points, wherein the phases are caused by mining of one underground working face, and the three-dimensional deformation is projected to the LOS direction according to the incident angle and the course angle of TerraSAR-X SAR satellite data to obtain the LOS direction time sequence deformation phases. 3 interferograms with different deformation gradients are obtained by subtracting LOS deformation phases at adjacent time and performing winding calculation. To make the simulation closer to the real situation of the mine exploitation, the atmospheric phase (maximum phase change is 2rad) and different noise phases (0.5rad, 1rad and 1.5rad) are added, and 9 mine interferogram results are simulated by common mode, as shown in fig. 2.
And (3) performing self-adaptive quadtree downsampling processing on the phase of the interference pattern, and calculating the edge unwrapping phase of the mining area by adopting a traditional phase unwrapping method.
Specifically, the embodiment of the invention performs adaptive quadtree downsampling processing on the simulated mining area interferogram result, so that more points are reserved in the deformation area and fewer points are reserved in the non-deformation area, and then the mining area edge unwrapping phase result of the high coherence area is calculated according to the traditional MCF phase unwrapping method.
The adaptive quadtree downsampling processing is an image segmentation algorithm based on uniformity detection, and aims to obtain the mean value of each pixel with the minimum data volume so as to obtain the optimal approximation of an original image. The basic flow of the quadtree downsampling processing on the image is as follows: firstly, the dimension of an image is expanded to be the power of 2 by adding a zero value, then the image is divided into 4 quadrants with the same size, the variance of an unwrapping value in each quadrant is respectively calculated and compared with a preset variance threshold, if the variance of a certain quadrant exceeds the threshold, the quadrant is further decomposed into 4 new quadrants, the process is repeated until the variance of each quadrant is smaller than the given threshold, finally, the mean value or the median value of each decomposed quadrant is assigned to the central coordinate of the quadrant, and only the central coordinate point of the modified quadrant is reserved.
And establishing a two-dimensional Gaussian function model for the unwrapping phase, calculating model parameters and inverting the model parameters.
Specifically, the two-dimensional gaussian function model is represented as:
f(i,j,m)＝Sexp(-a(i-x) 2 -2b(i-x)(j-y)-c(j-y) 2 )
wherein S is amplitude, x, y are center point coordinates, R x ，R y Is standard deviation, theta is clockwise rotation angle, and the initial value m of the model parameter is determined according to the position of the deformation area 0 ＝S 0 ,R x0 ，R y0 ,x 0 ，y 0 ,θ 0 ] T And inverting the two-dimensional Gaussian function model by a Levenberg-Marquardt algorithm to obtain an inversion parameter m, wherein m is [ S, R ═ R x ，R y ,x，y,θ] T 。
For any pixel (i, j), the relationship between the mining area edge unwrapping phase and the two-dimensional Gaussian function model is as follows:
wherein epsilon (i, j) is a residual error of any pixel, and a weighted residual phase obtained by weighting is as follows:
where σ (i, j) represents the variance determined by the image coherence.
And calculating the whole basin deformation phase of the mining area by using a two-dimensional Gaussian function model, calculating the winding residual phase, and performing phase unwrapping on the winding residual phase to obtain the mining area earth surface unwrapping phase.
Specifically, the phase of the full basin deformation is subtracted from the phase of the interference pattern to obtain a winding residual interference phase; phase unwrapping is carried out by using a traditional phase unwrapping algorithm; the method and the device adopt a minimum cost flow method to perform phase unwrapping on the wrapped residual interference phase, and add the phase unwrapped residual interference phase and the full basin deformation phase to obtain the mining area earth surface unwrapping phase.
And refining the calculated unwrapping phase result through iteration to obtain an unwrapping phase of the mining area, setting the threshold value to be 0.05 by taking whether the root mean square of the difference between two adjacent unwrapping phases is smaller than a certain threshold value as a condition for stopping iteration, wherein the simulation result of the two-dimensional Gaussian function model calculated through the last iteration is shown in fig. 3, wherein (a) - (i) in fig. 3 are the simulation results of the two-dimensional Gaussian function models with different deformation gradients and different noise phases, and correspond to the simulated wrapping interferograms (a) - (i) in fig. 2.
And adding the two-dimensional Gaussian model result of the last iteration calculation and the residual unwrapping phase to obtain a phase unwrapping result of the mining area, as shown in FIG. 4. In fig. 4, (a) - (i) are calculated mine phase unwrapping results of different deformation gradients and different noise phases according to the present invention, which correspond to the simulated mine wrapped interferograms of fig. 2(a) - (i); as can be seen from FIG. 4, when the noise level is small, even if the deformation gradient of the mining area is large, the invention can also obtain the high-precision mining area interferogram phase unwrapping result; when the noise level is large, even if the deformation gradient is small, the obtained mine unwrapping phase has certain error, but the error is within an acceptable range. The results show that: within a certain noise error level, the embodiment of the invention can solve the problem that the interference pattern is dense and difficult to be unwrapped due to large gradient deformation of a mining area, and obtain an accurate phase unwrapping result.
In order to evaluate the unwrapping effect of the embodiment of the present invention on the dense interferogram fringes of the mining area, a statistical histogram curve of the difference between the phase unwrapping result and the simulation value is calculated, as shown in fig. 5. FIGS. 5(a) - (i) are statistical histogram plots of differences for different deformation gradients and different noise levels calculated by an embodiment of the present invention corresponding to the mine phase unwrapping results of FIGS. 4(a) - (i); the simulated large-gradient LOS deformation phase is compared with the calculated LOS unwrapping phase of the mining area in the embodiment of the invention, and the two phases are well matched, wherein under the condition that 0.5rad of random noise is added, the 95% probability of the difference between the deformation gradients of 20rad, 60rad and 100rad and the simulated value is 0.16rad, 0.18rad and 0.18rad respectively. Under the condition of adding random noise of 1.0rad, the deformation gradient of 20rad, 60rad and 100rad has 95% probability of difference with the analog value of 0.21rad, 0.28rad and 0.3rad respectively. Under the condition of adding random noise of 2.0rad, the deformation gradient of 20rad, 60rad and 100rad has 95% probability of difference with the analog value of 1.6rad, 1.8rad and 3.0rad respectively. Even if the large-gradient deformation is 100rad, under different noise conditions (0.5rad, 1.0rad and 1.5rad), the difference values respectively account for 1.6 percent, 1.8 percent and 3 percent of the total deformation gradient, and the reliability of the phase unwrapping result of the mining area calculated by the embodiment of the invention is shown, and the accuracy requirement of phase unwrapping of a large-scale deformation interference pattern in the mining area is met.
The embodiment of the invention is as follows: compared with the existing large deformation gradient InSAR phase unwrapping method, the method does not need underground mining parameters, field observation data of a mining area and training samples, and only carries out iterative modeling and parameter inversion on the interference phase to carry out phase unwrapping, so that the method greatly reduces the limitation in the using process, effectively solves the problem that the traditional phase unwrapping method is difficult to unwrappe mining area density and aliasing interference fringes, has important influence on the subsequent LOS deformation resolving precision of the mining area, and widens the application prospect of InSAR phase unwrapping of the mining area.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (8)
1. An interference phase iterative unwrapping method based on a two-dimensional Gaussian model is applied to large gradient deformation InSAR monitoring of a mining area and is characterized by comprising the following steps:
step 1, collecting SAR images to perform data preprocessing, acquiring single-view complex SLC images, forming an interference combination to obtain a winding interference pattern, and calculating the phase of the interference pattern;
step 2, performing adaptive quad-tree downsampling processing on the phase of the interference pattern, and calculating the edge unwrapping phase of the mining area by adopting a traditional phase unwrapping method;
step 3, establishing a two-dimensional Gaussian function model of the mining area edge unwrapping phase, calculating model parameters and inverting the model parameters;
step 4, obtaining a winding residual interference phase by estimating a full basin deformation phase of the mining area, and unwrapping the residual interference phase;
step 5, acquiring a disentanglement phase of the coal mine area;
and 6, obtaining a refined mining area unwrapping phase through iteration of the steps 3-5.
2. The iterative phase unwrapping method according to claim 1, wherein the step 1 includes:
data registration is carried out by taking the SLC image in the first stage as a reference, and the interference combination consists of images of each adjacent time after registration;
the interferogram phase is represented as:
where φ (i) is the wrapping phase of the ith pixel,
k is the number of cycles for the unwrapped phase of the ith pixel.
3. The iterative phase unwrapping method according to claim 1, wherein said step 3 includes:
the two-dimensional gaussian function model is represented as:
f(i,j,m)＝Sexp(-a(i-x) 2 -2b(i-x)(j-y)-c(j-y) 2 )
where S is amplitude, x, y are coordinates of the center point, R x ，R y Is standard deviation, theta is clockwise rotation angle, and the initial value m of the model parameter is determined according to the position of the deformation area 0 ＝[S 0 ,R x0 ，R y0 ,x 0 ，y 0 ,θ 0 ] T And inverting the two-dimensional Gaussian function model by a Levenberg-Marquardt algorithm to obtain an inversion parameter m, wherein m is [ S, R ═ R x ，R y ,x，y,θ] T 。
4. The iterative phase unwrapping method according to claim 1, wherein said step 4 includes:
estimating a full basin deformation phase of the mining area according to the inverted model parameters;
subtracting the phase of the interference pattern from the phase of the full basin deformation to obtain a winding residual interference phase;
the wrapped residual interference phase is phase unwrapped using a conventional phase unwrapping algorithm.
5. The iterative phase unwrapping method according to claim 1, wherein said step 5 includes: and adding the residual interference phase subjected to phase unwrapping and the full basin deformation phase to obtain the mining area surface unwrapping phase.
6. The iterative phase unwrapping method according to claim 1, wherein said step 6 includes: and (4) refining the unwrapping phase result by iterating the steps 3-5 until the difference between the last unwrapping phase and the last unwrapping phase is less than a threshold value, and stopping iteration to obtain the unwrapping phase of the mining area.
7. The iterative phase unwrapping method according to claim 3,
for any pixel (i, j), the relationship between the unwrapping phase of the mine edge and the two-dimensional Gaussian function model is as follows:
wherein epsilon (i, j) is a residual error of any pixel, and a weighted residual phase obtained by weighting is as follows:
where σ (i, j) represents the variance determined by the image coherence.
8. The iterative interferometric phase unwrapping method according to claim 6, wherein the threshold is 0.05.
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