CN112859077A - Multistage synthetic aperture radar interference phase unwrapping method - Google Patents

Multistage synthetic aperture radar interference phase unwrapping method Download PDF

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CN112859077A
CN112859077A CN202110111087.XA CN202110111087A CN112859077A CN 112859077 A CN112859077 A CN 112859077A CN 202110111087 A CN202110111087 A CN 202110111087A CN 112859077 A CN112859077 A CN 112859077A
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synthetic aperture
aperture radar
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CN112859077B (en
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卢丽君
王萌萌
程春泉
杨书成
赵争
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Chinese Academy of Surveying and Mapping
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Abstract

The invention relates to a multistage synthetic aperture radar interference phase unwrapping method, which comprises the following steps: (1) generating a synthetic aperture radar interference image; (2) generating a synthetic aperture radar differential interference pattern by applying an external digital elevation model; (3) carrying out phase unwrapping on the synthetic aperture radar differential interference pattern by using a minimum cost flow method to obtain an initial synthetic aperture radar unwrapping differential interference pattern; (4) according to different coherence thresholds, performing iterative unwrapping on the initial synthetic aperture radar unwrapped differential interferogram by using a branch-cut method to obtain a final synthetic aperture radar unwrapped differential interferogram; (5) and compensating the terrain phase to obtain a final synthetic aperture radar unwrapping interferogram. The method can improve the success rate of the interference phase unwrapping of the existing single synthetic aperture radar, can play an important role in the three-dimensional reconstruction of the earth surface and the height extraction of the earth objects in the satellite-borne and airborne interference synthetic aperture radar system, and has better technical effects.

Description

Multistage synthetic aperture radar interference phase unwrapping method
Technical Field
The invention relates to a digital photogrammetry processing method of remote sensing images, in particular to a synthetic aperture radar interference phase unwrapping method.
Background
Interferometric Synthetic Aperture Radar (InSAR) has shown increasing advantages as an active microwave remote sensing technology in topographic mapping. The interferometric phase information of Synthetic Aperture Radar (SAR) images is key information for extracting terrain and height. In the interferometric measurement of the synthetic aperture radar, the unwrapping of the interferometric phase of the synthetic aperture radar (abbreviated as unwrapping) is to restore the wrapped interferometric phase to the true interferometric phase, and is a key and important step in the whole processing chain. In areas with complex terrain and ground feature conditions, interference phase decoherence is easily caused due to the influence of terrain change and vegetation, and certain areas in interference images show low coherence. These low coherence (coherence factor less than 0.2) regions are subject to unwrapping errors in a single unwrapping process, resulting in a failure to unwrapp the entire synthetic aperture radar interference image. In order to guarantee successful unwrapping in a medium-high coherence (coherence coefficient is greater than 0.3) region, a multistage synthetic aperture radar interference phase unwrapping method needs to be developed.
Generally, the interferometric phase unwrapping method of the synthetic aperture radar mainly comprises the following steps: (1) one type of method is a classical path tracking algorithm, namely a branch cutting method, in the method, all residue points in two-dimensional phase data are detected by using minimum closed path integral formed by a pixel set, and all integral paths do not contain unbalanced residue points by using branch cutting. The method has fast calculation speed, the unwrapping phase and the wrapping phase only have integral phase period difference, and the main value of the real phase cannot be damaged; the biggest defect of the method is that in areas with low coherence and dense residue points, the branch cut is difficult to be correctly set, an accurate solution cannot be obtained frequently, and even the branch cut forms isolated areas, and the solution cannot be obtained in the isolated areas. (2) Another type of method is called network flow method, which is typically a minimum cost flow method, and its main idea is to minimize the difference between the derivative of the unwrapping phase and the derivative of the wrapping phase, and it can also limit the whole error within a small range, prevent the retransmission of the error, and make the unwrapping result more accurate and the calculation efficiency relatively higher. Although the minimum cost flow method has a high success rate of unwrapping, it is also easy to have unwrapping errors in areas with complex terrain and features, thereby causing a global unwrapping failure.
Disclosure of Invention
The invention provides a multistage synthetic aperture radar interference phase unwrapping method, which combines two synthetic aperture radar interference phase unwrapping methods (a minimum cost stream method and a branch cutting method) to carry out repeated iteration unwrapping treatment according to respective characteristics of the two synthetic aperture radar interference phase unwrapping methods by controlling a coherence coefficient threshold, and can realize high-precision synthetic aperture radar interference phase unwrapping in a terrain and ground object complex area.
A multistage synthetic aperture radar interference phase unwrapping method comprises the following steps:
s1: generating a synthetic aperture radar interference image comprising an interference pattern and a coherence coefficient pattern;
s2: generating a synthetic aperture radar differential interference pattern by utilizing an external DEM;
s3: unwrapping the synthetic aperture radar differential interference pattern by using a minimum cost flow method to obtain an initial synthetic aperture radar unwrapped differential interference pattern;
s4: according to different coherence coefficient thresholds, carrying out iterative unwrapping on the initial synthetic aperture radar unwrapping differential interferogram by using a branch cutting method to obtain a final synthetic aperture radar unwrapping differential interferogram;
s5: and compensating the terrain phase according to the synthetic aperture radar unwrapping differential interference pattern to obtain the synthetic aperture radar unwrapping interference pattern.
Further, in step S1, performing conjugate multiplication and coherence coefficient calculation according to the obtained synthetic aperture radar image pair, so as to generate a synthetic aperture radar interference image, where the synthetic aperture radar image pair is:
Figure BDA0002919369380000021
m and S areA plurality of complex numbers representing the master image and the slave image of the synthetic aperture radar image pair, respectively, | M | and | S | representing the modes of the master image and the slave image, respectively,
Figure BDA0002919369380000031
and
Figure BDA0002919369380000032
respectively representing the phases of the master image and the slave image, j representing an imaginary number;
the generation of the interferogram by conjugate multiplication of the master image and the slave image is as follows:
Figure BDA0002919369380000033
Figure BDA0002919369380000034
synthetic aperture radar interference phase;
wherein, the coherence coefficient graph obtained by coherence calculation is as follows:
Figure BDA0002919369380000035
γ denotes a coherence coefficient, and E denotes a mean value calculation.
Further, in step S2, an elevation phase is generated by using the external DEM, and a difference operation is performed on the elevation phase and the generated interferogram to obtain a synthetic aperture radar differential interference phase, so as to generate a synthetic aperture radar differential interferogram, where the elevation phase of the external DEM:
Figure BDA0002919369380000036
Figure BDA0002919369380000037
indicating the elevation phase of an external DEM, B⊥Being the vertical baseline of the synthetic aperture radar system,lambda represents the wavelength of the synthetic aperture radar system, R represents the slant distance of the synthetic aperture radar system, theta represents the incident angle of the synthetic aperture radar system, and deltaz represents the height difference of adjacent pixels in the external DEM;
the elevation phase of the external DEM of the interferogram generated by the differential operation is as follows:
Figure BDA0002919369380000038
in the formula (5), the first and second groups,
Figure BDA0002919369380000039
is the synthetic aperture radar differential interference phase.
Further, in step S3, selecting a set coherence coefficient threshold, and unwrapping the synthetic aperture radar differential interference pattern by using a phase unwrapping algorithm of a least cost stream method to obtain an initial synthetic aperture radar unwrapped differential interference phase, thereby forming an initial synthetic aperture radar unwrapped differential interference pattern; the initial synthetic aperture radar unwrapping differential interference phase is as follows:
Figure BDA00029193693800000310
ψMCFrepresenting the initial synthetic aperture radar unwrapping differential interference phase after unwrapping by using a minimum cost flow method, W { } represents an unwrapping operator, n represents the whole period number after unwrapping, gamma represents a coherence coefficient, and gamma representshRepresenting a set coherence factor threshold, the SAR unwrapping differential interference phase psiMCFFor a coherence coefficient greater than gammahIn the Synthetic Aperture Radar (SAR)
Figure BDA0002919369380000041
The result of the unwrapping operation.
Further, in step S4, using γ as the number of steps of the coherence coefficient, decreasing the threshold of the coherence coefficient step by step, and applying a branch-cut method to solve the initial synthetic aperture radar solutionThe wrapping differential interference phase is subjected to iterative unwrapping until the iteration reaches a set coherence coefficient threshold value gammalEnding iteration to obtain a synthetic aperture radar unwrapping differential interference phase after iterative unwrapping, thereby forming a final synthetic aperture radar unwrapping differential interference pattern;
the synthetic aperture radar unwrapping differential interference phase is as follows:
Figure BDA0002919369380000042
Figure BDA0002919369380000043
representing the synthetic aperture radar unwrapping differential interference phase after each iteration unwrapping by applying a branch-cut method, m representing the iteration number, gammaTRepresenting different threshold values of the coherence coefficient used for each iterative unwrapping, gamma representing the number of steps of the coherence coefficient, gammalRepresenting a set threshold value of a coherence factor, the SAR unwrapping differential interference phase
Figure BDA0002919369380000044
For a coherence coefficient greater than gammaTIn the Synthetic Aperture Radar (SAR)
Figure BDA0002919369380000045
The result of the unwrapping operation, psiBRAnd (4) unwrapping the set of differential interference phases for the synthetic aperture radar after each iteration unwrapping.
Further, in step S5, the synthetic aperture radar under different coherence factor threshold conditions is unwrapped by the method having the differential phase ψMCFAnd psiBRThe phase compensation of the terrain is carried out,
Figure BDA0002919369380000046
Figure BDA0002919369380000047
obtaining synthetic aperture radar unwrapping interference phase psiunw。
After the multistage synthetic aperture radar interference phase unwrapping method provided by the invention, high-precision synthetic aperture radar interference phase unwrapping in complex terrain and ground object areas is realized, and success of unwrapping in medium and high-coherence areas is guaranteed. The method for unwrapping the interference phase of the multi-stage synthetic aperture radar plays an important role in three-dimensional reconstruction of the earth surface and height extraction of earth objects based on the synthetic aperture radar interference measurement technology, and has a good technical effect.
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The present invention will be described in further detail below with reference to the accompanying drawings so that the above advantages of the present invention will be more apparent.
FIG. 1 is a flow chart of a multi-stage SAR interferometric phase unwrapping method according to the present invention;
FIG. 2 is a synthetic aperture radar unwrapped differential interferogram unwrapped using a single least cost stream method;
FIG. 3 is an initial synthetic aperture radar unwrapped differential interferogram unwrapped using a least-cost-stream method;
fig. 4 is a synthetic aperture radar unwrapped differential interferogram after iterative unwrapping using a branch-and-cut method.
Detailed Description
As shown in fig. 1, the multi-stage synthetic aperture radar interferometric phase unwrapping method provided by the invention combines two synthetic aperture radar interferometric phase unwrapping methods (a minimum cost stream method and a branch cutting method) for multiple iterative unwrapping by controlling a coherence coefficient threshold, is suitable for satellite-borne and airborne synthetic aperture radar interferometric images, and can realize high-precision synthetic aperture radar interferometric phase unwrapping in a terrain and ground object complex area. The invention comprises the following steps:
s1: firstly, according to the obtained synthetic aperture radar image pair, conjugate multiplication and coherence coefficient calculation are carried out, so that a synthetic aperture radar interference image is generated, wherein the synthetic aperture radar interference image comprises an interference image and a coherence coefficient image. Wherein, the synthetic aperture radar image pair can be expressed as:
Figure BDA0002919369380000051
in formula (1), M and S are complex numbers, which respectively represent the master image and the slave image in the synthetic aperture radar image pair, | M | and | S | respectively represent the modes of the master image and the slave image,
Figure BDA0002919369380000052
and
Figure BDA0002919369380000053
the phases of the master and slave images are represented, respectively, and j represents an imaginary number.
Generating an interferogram by conjugate multiplication of the master image and the slave image by formula (2):
Figure BDA0002919369380000061
wherein
Figure BDA0002919369380000062
Synthetic aperture radar interferometric phase.
By the formula (3), a coherence coefficient map is obtained by coherence calculation.
Figure BDA0002919369380000063
γ denotes a coherence coefficient, and E denotes a mean value calculation.
S2: and generating an Elevation phase according to an external DEM (Digital Elevation Model), carrying out differential operation on the Elevation phase and the generated interferogram to obtain a synthetic aperture radar differential interference phase, and further generating a synthetic aperture radar differential interferogram.
By equation (4), the elevation phase of the external DEM is obtained:
Figure BDA0002919369380000064
in the formula (4), the first and second groups,
Figure BDA0002919369380000065
indicating the elevation phase of an external DEM, B⊥And the vertical baseline of the synthetic aperture radar system is shown, lambda represents the wavelength of the synthetic aperture radar system, R represents the slant range of the synthetic aperture radar system, theta represents the incident angle of the synthetic aperture radar system, and deltaz represents the height difference of adjacent pixels in the external DEM.
Generating the elevation phase of the external DEM of the interferogram by equation (5):
Figure BDA0002919369380000066
in the formula (5), the first and second groups,
Figure BDA0002919369380000067
is the synthetic aperture radar differential interference phase.
And generating a synthetic aperture radar differential interference image through the synthetic aperture radar differential interference phase.
S3: selecting a higher coherence coefficient threshold value, wherein The coherence coefficient threshold value is more than 0.8, and unwrapping The synthetic aperture radar differential interference pattern by using a phase unwrapping algorithm of a Minimum Cost Flow (MCF) method to obtain an initial synthetic aperture radar unwrapping differential interference phase, as shown in a formula (6), thereby forming an initial synthetic aperture radar unwrapping differential interference pattern.
Figure BDA0002919369380000068
In the formula (6), psiMCFRepresenting the synthetic aperture radar unwrapping differential interference phase after unwrapping by using a minimum cost flow method, W { } represents an unwrapping operator, n represents the whole period number after unwrapping, gamma represents a coherence coefficient, and gamma representshIndicating a higher phaseDry coefficient threshold, synthetic aperture radar unwrapped differential interference phase psi calculated in equation (6)MCFFor a coherence coefficient greater than gammahIn the Synthetic Aperture Radar (SAR)
Figure BDA0002919369380000071
The result of the unwrapping operation.
S4: using gamma as the step number of the coherence coefficient, gradually reducing the threshold value of the coherence coefficient, and applying a Branch cutting method (BR, Branch Cut) to perform iterative unwrapping on the initial unwrapped differential interference phase of the synthetic aperture radar until iterating to a lower threshold value gamma of the coherence coefficient as shown in formula (7)l(0.2<γl<0.4), finishing the iteration to obtain the synthetic aperture radar unwrapped differential interference phase psi after the iteration unwrappingBR。ψMCFAnd psiBRThe synthetic aperture radar unwrapping differential interference phases under different coherence coefficient threshold values are formed together, and therefore a final synthetic aperture radar unwrapping differential interference pattern is formed.
Figure BDA0002919369380000072
In the formula (7), the first and second groups,
Figure BDA0002919369380000073
representing the synthetic aperture radar unwrapping differential interference phase after each iteration unwrapping by applying a branch-cut method, m representing the iteration number, gammaTRepresenting different threshold values of the coherence coefficient used for each iterative unwrapping, gamma representing the number of steps of the coherence coefficient, gammalRepresenting lower threshold value of coherence coefficient, and (7) calculating unwrapped differential interference phase of synthetic aperture radar
Figure BDA0002919369380000074
For a coherence coefficient greater than gammaTIn the Synthetic Aperture Radar (SAR)
Figure BDA0002919369380000075
The result of the unwrapping operation, psiBRAnd (4) unwrapping the set of differential interference phases for the synthetic aperture radar after each iteration unwrapping.
S5: and compensating the terrain phase aiming at the synthetic aperture radar unwrapping differential interference pattern to obtain a synthetic aperture radar unwrapping interference phase and form a synthetic aperture radar unwrapping interference pattern.
Through the formula (8), the synthetic aperture radar unwrapping differential phase psi of the synthetic aperture radar under the conditions of different coherence coefficient threshold values calculated by the formulas (6) and (7) is obtainedMCFAnd psiBRAnd performing terrain phase compensation, thereby forming a synthetic aperture radar unwrapping interference phase.
Figure BDA0002919369380000076
Figure BDA0002919369380000081
In the formula (8), psiunwRepresenting the synthetic aperture radar unwrapping interference phase.
The phase unwrapping experiment is performed by using the satellite-borne synthetic aperture radar interference image, and fig. 2 is a synthetic aperture radar unwrapping differential interference map (with a coherence coefficient threshold of 0.3) unwrapped by using a single minimum cost stream method in the embodiment.
Fig. 3 is an initial synthetic aperture radar unwrapping differential interferogram (coherence coefficient threshold of 0.85) using a minimum cost flow method, and fig. 4 is a synthetic aperture radar unwrapping differential interferogram (coherence coefficient step number of 0.05, coherence coefficient threshold of 0.3) after iterative unwrapping of an initial synthetic aperture radar unwrapping differential interference phase using a branch-and-cut method.
It can be seen that after the multi-stage synthetic aperture radar interference phase unwrapping method is implemented, no global unwrapping error exists, a correct synthetic aperture radar unwrapping interference phase value is reserved in a medium-high coherence region, and the accuracy of the synthetic aperture radar interference measurement technology in terrain and height measurement can be improved.
The particular embodiments disclosed above are illustrative only, as numerous modifications and variations could be made thereto by those skilled in the art in light of the above teachings and are within the scope of the invention. It will be appreciated by persons skilled in the art that the foregoing detailed description is provided for the purpose of illustrating the invention and is not to be construed as limiting the invention. The scope of the invention is defined by the claims and their equivalents.

Claims (6)

1. A multistage synthetic aperture radar interference phase unwrapping method comprises the following steps:
s1: generating a synthetic aperture radar interference image comprising an interference pattern and a coherence coefficient pattern;
s2: generating a synthetic aperture radar differential interference pattern by utilizing an external DEM;
s3: unwrapping the synthetic aperture radar differential interference pattern by using a minimum cost flow method to obtain an initial synthetic aperture radar unwrapped differential interference pattern;
s4: according to different coherence coefficient thresholds, carrying out iterative unwrapping on the initial synthetic aperture radar unwrapping differential interferogram by using a branch cutting method to obtain a final synthetic aperture radar unwrapping differential interferogram;
s5: and compensating the terrain phase according to the synthetic aperture radar unwrapping differential interference pattern to obtain the synthetic aperture radar unwrapping interference pattern.
2. The multi-stage synthetic aperture radar interferometric phase unwrapping method of claim 1, further comprising: in step S1, performing conjugate multiplication and coherence coefficient calculation according to the obtained synthetic aperture radar image pair, thereby generating a synthetic aperture radar interference image, where the synthetic aperture radar image pair is:
Figure FDA0002919369370000011
m and S are complex numbers respectively representing synthetic aperture radar imagesA master image and a slave image in the pair, | M | and | S | represent the modulus of the master image and the slave image, respectively,
Figure FDA0002919369370000012
and
Figure FDA0002919369370000013
respectively representing the phases of the master image and the slave image, j representing an imaginary number;
the generation of the interferogram by conjugate multiplication of the master image and the slave image is as follows:
Figure FDA0002919369370000014
Figure FDA0002919369370000015
synthetic aperture radar interference phase;
wherein, the coherence coefficient graph obtained by coherence calculation is as follows:
Figure FDA0002919369370000021
γ denotes a coherence coefficient, and E denotes a mean value calculation.
3. The multi-stage synthetic aperture radar interferometric phase unwrapping method of claim 2, further comprising: in step S2, an elevation phase is generated by using an external DEM, and a difference operation is performed on the elevation phase and the generated interferogram to obtain a synthetic aperture radar differential interference phase, thereby generating a synthetic aperture radar differential interferogram, wherein the elevation phase of the external DEM:
Figure FDA0002919369370000022
Figure FDA0002919369370000023
indicating the elevation phase of an external DEM, B⊥The vertical baseline of the synthetic aperture radar system is shown, lambda represents the wavelength of the synthetic aperture radar system, R represents the slant range of the synthetic aperture radar system, theta represents the incident angle of the synthetic aperture radar system, and delta z represents the height difference of adjacent pixels in the external DEM;
the elevation phase of the external DEM of the interferogram generated by the differential operation is as follows:
Figure FDA0002919369370000024
in the formula (5), the first and second groups,
Figure FDA0002919369370000025
is the synthetic aperture radar differential interference phase.
4. The multi-stage synthetic aperture radar interferometric phase unwrapping method of claim 3, wherein: in step S3, selecting a set coherence coefficient threshold, and unwrapping the synthetic aperture radar differential interference pattern by using a phase unwrapping algorithm of a least cost stream method to obtain an initial synthetic aperture radar unwrapped differential interference phase, thereby forming an initial synthetic aperture radar unwrapped differential interference pattern; the initial synthetic aperture radar unwrapping differential interference phase is as follows:
Figure FDA0002919369370000026
ψMCFrepresenting the initial synthetic aperture radar unwrapping differential interference phase after unwrapping by using a minimum cost flow method, W { } represents an unwrapping operator, n represents the whole period number after unwrapping, gamma represents a coherence coefficient, and gamma representshRepresenting a set coherence factor threshold, the SAR unwrapping differential interference phase psiMCFFor a coherence coefficient greater than gammahSynthetic aperture radar difference ofFractional interference phase
Figure FDA0002919369370000027
The result of the unwrapping operation.
5. The multi-stage synthetic aperture radar interferometric phase unwrapping method of claim 4, wherein: in step S4, using γ as the step number of the coherence coefficient, decreasing the threshold of the coherence coefficient step by step, and applying a branch-cut method to perform iterative unwrapping on the initial unwrapped differential interference phase of the synthetic aperture radar until the initial unwrapped differential interference phase is iterated to a set threshold γ of the coherence coefficientlEnding iteration to obtain a synthetic aperture radar unwrapping differential interference phase after iterative unwrapping, thereby forming a final synthetic aperture radar unwrapping differential interference pattern;
the synthetic aperture radar unwrapping differential interference phase is as follows:
Figure FDA0002919369370000031
Figure FDA0002919369370000032
Figure FDA0002919369370000033
representing the synthetic aperture radar unwrapping differential interference phase after each iteration unwrapping by applying a branch-cut method, m representing the iteration number, gammaTRepresenting different threshold values of the coherence coefficient used for each iterative unwrapping, gamma representing the number of steps of the coherence coefficient, gammalRepresenting a set threshold value of a coherence factor, the SAR unwrapping differential interference phase
Figure FDA0002919369370000034
For a coherence coefficient greater than gammaTIn the Synthetic Aperture Radar (SAR)
Figure FDA0002919369370000035
The result of the unwrapping operation, psiBRAnd (4) unwrapping the set of differential interference phases for the synthetic aperture radar after each iteration unwrapping.
6. The multi-stage synthetic aperture radar interferometric phase unwrapping method of claim 5, wherein: in step S5, the synthetic aperture radar under different coherence factor threshold conditions is unwrapped by the differential phase ψMCFAnd psiBRThe phase compensation of the terrain is carried out,
Figure FDA0002919369370000036
Figure FDA0002919369370000037
obtaining synthetic aperture radar unwrapping interference phase psiunw。
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