CN113670410A - Wetland water level measuring method, device and equipment and readable storage medium - Google Patents

Wetland water level measuring method, device and equipment and readable storage medium Download PDF

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CN113670410A
CN113670410A CN202110898439.0A CN202110898439A CN113670410A CN 113670410 A CN113670410 A CN 113670410A CN 202110898439 A CN202110898439 A CN 202110898439A CN 113670410 A CN113670410 A CN 113670410A
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water level
interference
image
wetland
composite data
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谢酬
田帮森
郭亦鸿
朱玉
唐文家
张紫萍
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Qinghai Ecological Environment Monitoring Center
Aerospace Information Research Institute of CAS
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Aerospace Information Research Institute of CAS
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01FMEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F23/00Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm
    • G01F23/22Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water
    • G01F23/28Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water by measuring the variations of parameters of electromagnetic or acoustic waves applied directly to the liquid or fluent solid material
    • G01F23/284Electromagnetic waves
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021SAR image post-processing techniques
    • G01S13/9023SAR image post-processing techniques combined with interferometric techniques
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9094Theoretical aspects

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  • Fluid Mechanics (AREA)
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  • Investigating Or Analysing Materials By Optical Means (AREA)

Abstract

The invention provides a wetland water level measuring method, a device, equipment and a readable storage medium, which relate to the technical field of synthetic aperture radar interferometry, and the method also comprises the following steps: determining homogeneous pixels of the differential interference fringe pattern, and extracting the distributed scatterers based on the homogeneous pixels; the method can determine accurate scatterer points and extract water level information more accurately, further measure the water level of the wetland more accurately, obtain more accurate wetland water level change and ensure the accuracy of extracting the wetland hydrological information.

Description

Wetland water level measuring method, device and equipment and readable storage medium
Technical Field
The invention relates to the technical field of synthetic aperture radar interferometry, in particular to a wetland water level measuring method, device and equipment and a readable storage medium.
Background
The particularity and the importance of the wetland have been paid attention all over the world, the remote sensing technology has been widely applied to wetland investigation due to the advantages of high spatial resolution, wide coverage and low artificial economic cost, and the related applications mainly focus on the aspects of wetland identification and classification, wetland resource investigation, wetland resource dynamic change investigation, wetland vegetation biomass estimation and the like. However, of greater concern to geodesic ecologists are water level, water area, vegetation height and vegetation coverage, which directly affect the environment of choice for the habitat of the migratory birds. In a wetland ecosystem, changes of wetland hydrological conditions such as water level, water quantity, flooding frequency, flooding time and the like are always the focus of attention in wetland protection, play a leading role in wetland organism distribution and wetland soil properties, and influence the habitat environment of wetland animals together with the growth condition of wetland vegetation. The problem of wetland water level and vegetation height measurement cannot be directly solved by optical remote sensing, and meanwhile, vegetation coverage can have great influence on the water body identification precision of the optical remote sensing wetland. Radar altimeters have been used for monitoring the water level of large inland water bodies such as large lakes and amazon forests, but for small lakes or marshes, the echo of the radar altimeter is deformed due to the small water body area, and a large amount of data is lost due to the influence of the surrounding terrain. Due to the problems, the requirements of wetland ecologists on the wetland water level and the vegetation height cannot be met by remote sensing means such as optical remote sensing, radar altimeters and the like.
The backscatter signal of Synthetic Aperture Radar (SAR) is very sensitive to terrain slope, surface roughness, dielectric constant and the like, and can penetrate through vegetation to further solve the problem of underestimation of water area by optical data, and has been widely applied to the feature definition of wetland type, wetland condition and overflow. The SAR has unique advantages in the aspect of height inversion because the SAR not only measures the amplitude of the echo reflected by a ground target, but also records the phase information of the echo. The interferometry technology is widely applied to surface deformation monitoring and surface height measurement, and great progress is made in wetland water level monitoring. The launching lift-off of the novel sensor expands the application capability of the SAR, and particularly, the influence of time decoherence is greatly reduced by an X-frequency-band land radar additional digital elevation model (TanDEM-X) double-base system, so that the wetland vegetation height inversion becomes possible. Therefore, the unique advantages of SAR make it have great potential in wetland hydrology and vegetation parameter inversion.
For the evaluation of the health level of the wetland system, the continuous acquisition of hydrological monitoring data for a long time is necessary. The development of the Permanent Scatterer (PS) technology and the Small Baseline set (SBAS) technology has promoted the obvious progress of the application capability of the SAR technology. However, due to the serious incoherent property of the ground object target in the wetland area, the ground surface coverage is greatly different from the urban area, a large number of artificial buildings do not exist, the main ground objects are vegetation, water surfaces and the like, the main problem is how to determine accurate scatterer points, and meanwhile, the traditional method is insufficient in water level information extraction precision.
Therefore, a method for measuring a moisture level, which can determine an accurate scatterer point and extract water level information more accurately, is an important issue to be solved in the art.
Disclosure of Invention
The invention provides a wetland water level measurement method, a wetland water level measurement device, wetland water level measurement equipment and a readable storage medium, which are used for solving the defects that a teacher and a brother region in the prior art cannot determine accurate scatterer points and the water level information extraction precision is not enough, realizing more accurate wetland water level measurement and acquiring more accurate wetland water level change.
The invention provides a wetland water level measuring method, which comprises the following steps:
registering and calibrating a synthetic aperture radar image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time sequence synthetic aperture radar image, and the synthetic aperture radar image to be processed is an image of a wetland area;
based on the coherence of interference image pairs, carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs;
carrying out phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
based on a small baseline set technology, acquiring the water level change of the unwrapped differential interference pattern, and before phase unwrapping is performed on the differential interference pattern to obtain the unwrapped differential interference pattern, the method further comprises the following steps:
determining homogeneous pixels of the differential interference fringe pattern, and extracting a distributed scatterer based on the homogeneous pixels;
and carrying out self-adaptive shape filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
According to the wetland water level measuring method provided by the invention, the homogeneous pixels of the differential interference fringe pattern are determined, and the distributed scatterers are extracted based on the homogeneous pixels, and the method specifically comprises the following steps:
acquiring the connection number of all pixels of each pixel of the differential interference fringe pattern in a corresponding preset window, and taking the pixel higher than the preset connection number as the homogeneous pixel in the preset window; the pixel is the central point of a corresponding preset window, and the probability distribution of the multi-temporal backscattering coefficient values of the homogeneous pixel between two adjacent pixels on the statistical test is the same;
removing the homogeneous pixels which are not communicated with the central point, and determining a distributed scatterer block corresponding to the central point;
and acquiring the coherence of the distributed scatterer blocks, and extracting the distributed scatterers of the distributed scatterer blocks with higher first coherence.
According to the wetland water level measuring method provided by the invention, after the coherence of the distributed scatterer block is obtained and the distributed scatterers of the distributed scatterer block higher than the first coherence are extracted, the method further comprises the following steps:
and removing the flat ground phase and the terrain phase from the distributed scatterers.
According to the wetland water level measurement method provided by the invention, the water level change of the unwrapped differential interference pattern is obtained based on a small baseline set technology, and the method specifically comprises the following steps:
constructing a linear model through the distributed scatterers;
acquiring the relative water level change of the linear model based on an L1 norm minimization algorithm, an L2 norm minimization algorithm and an optimal interference network;
integrating the relative water level change based on an L1 norm minimization algorithm to obtain a relative water level sequence;
comparing the relative water level sequence with reference water level observation data to obtain the linear offset of the absolute value of the water level;
and removing the linear offset in the relative water level sequence to obtain an absolute water level sequence.
According to the wetland water level measuring method provided by the invention, the relative water level change is integrated based on an L1 norm minimization algorithm to obtain a relative water level sequence, and a terrain error, an atmospheric noise and an orbit error are removed; wherein the atmospheric noise is obtained by numerical weather prediction.
According to the wetland water level measurement method provided by the invention, the composite data are paired and combined based on the coherence of interference image pairs to obtain a plurality of interference image pairs of the composite data, and a differential interference fringe pattern is generated according to the interference image pairs, and the method specifically comprises the following steps:
selecting the interference image pair higher than the second coherence as the interference image pair of the composite data, and carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data;
constructing a basic interference network based on a minimum spanning tree method;
adding a plurality of interference image pairs of the composite data into the basic interference network to obtain the optimal interference network;
and generating a differential interference fringe pattern according to a plurality of interference image pairs of the composite data.
According to the wetland water level measurement method provided by the invention, the synthetic aperture radar image to be processed is registered and calibrated to obtain the registered composite data, and the method specifically comprises the following steps:
taking one of the synthetic aperture radar images to be processed as a main image, and registering other synthetic aperture radar images to be processed to the main image; wherein the main image has stable scattering characteristics.
The invention also provides a wetland water level measuring device, which comprises:
the registration module is used for registering and scaling the synthetic aperture radar image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time series synthetic aperture radar image, and the synthetic aperture radar image to be processed is a wetland image;
the matching combination module is used for matching and combining the composite data based on the coherence of interference image pairs to obtain a plurality of interference image pairs of the composite data and generating a differential interference fringe pattern according to the interference image pairs;
the phase unwrapping module is used for carrying out phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
a water level measuring module for obtaining the water level variation of the unwrapped differential interference pattern based on a small baseline set technique, wherein before the phase unwrapping module, the apparatus further comprises:
the scatterer extraction module is used for determining homogeneous pixels of the differential interference fringe pattern and extracting distributed scatterers based on the homogeneous pixels;
and the self-adaptive filtering module is used for carrying out self-adaptive terrain filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
The invention also provides electronic equipment which comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor executes the program to realize the steps of any one of the wetland water level measuring methods.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of any of the above-described methods of measuring moisture level.
According to the wetland water level measurement method, the device, the equipment and the readable storage medium, homogeneous pixels of a differential interference pattern are determined, a scatterer with high coherence is further determined by extracting a distributed scatterer based on the homogeneous pixels, so that a stable scatterer is determined, the influence of external errors is eliminated by performing self-adaptive terrain filtering on the differential interference pattern after the distributed scatterer is extracted, so that the coherence of the scatterer is improved, the two points are combined with the prior art, accurate scatterer points can be determined, water level information can be extracted more accurately, more accurate wetland water level measurement is carried out, more accurate wetland water level change is obtained, and the accuracy of wetland hydrologic information extraction is ensured.
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In order to more clearly illustrate the technical solutions of the present invention or the prior art, the following briefly introduces the drawings needed for the embodiments or the prior art descriptions, and obviously, the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a first schematic flow chart of the wetland water level measurement method provided by the invention;
fig. 2 is a first flow diagram illustrating a specific process of step S300 in the wetland water level measurement method provided by the present invention;
fig. 3 is a detailed flow diagram of step S300 in the wetland water level measurement method provided by the invention;
fig. 4 is a specific flowchart of step S600 in the wetland water level measurement method provided by the present invention;
fig. 5 is a specific flow diagram of step S200 in the wetland water level measurement method provided by the present invention;
FIG. 6 is a schematic structural view of the wetland water level measuring device provided by the invention;
fig. 7 is a first structural schematic diagram of a scatterer extraction module in the wetland water level measurement device provided by the invention;
fig. 8 is a second specific structural diagram of a scatterer extraction module in the wetland water level measurement device provided by the invention;
FIG. 9 is a schematic structural view of a water level measuring module in the wetland water level measuring device provided by the invention;
FIG. 10 is a schematic structural diagram of a pair of combined modules in the wetland water level measuring device provided by the invention;
fig. 11 is a schematic structural diagram of an electronic device provided in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The wetland water level measuring method of the invention is described below with reference to fig. 1, and is applied to data monitoring and evaluation of wetland areas, and the method comprises the following steps:
s100, registering and calibrating the SAR image to be processed to obtain registered composite data, wherein the composite data is amplitude image and phase information corresponding to the amplitude image.
In this embodiment, in step S100, the polarization mode of the SAR image to be processed is horizontal emission horizontal reception (HH), and Single-view complex (SLC) data is obtained, so that the composite data is a continuous L-band HH polarized (time series) SAR image, and the SAR image to be processed is an image of a wetland area.
Since the coastal wetland is located at the land-sea boundary, the low coherence surface targets such as the sea and the mudflat occupy a large area on the SAR image, and in this embodiment, in order to ensure the registration accuracy, the registration method is improved, specifically, step S100 specifically includes the following steps:
supposing that SAR images to be processed have M +1 scene SAR influence, taking one SAR image to be processed as a main image, registering other SAR images (auxiliary images) to be processed to the main image according to information such as orbit parameters, pulse repetition frequency, time information and an external Digital Elevation Model (DEM), registering pixels between the main image and the auxiliary image, ensuring the registration precision by a gross error removal method, and realizing sub-pixel-level registration; wherein the main image has stable scattering properties as a basis for registration.
It will be appreciated that the specific registration accuracy may be set as a practical matter.
S200, based on the coherence of the interference image pairs, carrying out pairing combination on the composite data, namely carrying out complex conjugate operation to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs.
S300, determining a homogeneous Pixel (SHP) of the differential interference fringe image, and extracting a Distributed Scatterer (DS) based on the SHP.
S400, carrying out self-adaptive terrain filtering on the differential interference fringe image after the DS is extracted.
S500, performing phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
s600, acquiring the water level change of the unwrapped differential interference pattern based on the SBAS technology.
The wetland water level measurement method is different from the traditional SAR technology, the step S300 and the step S400 are added, the scatterer with higher coherence is further determined through the step S300, the stable scatterer is determined, the influence of external errors is eliminated through the step S400, the coherence of the scatterer is improved, the step S300 and the step S400 are combined into the traditional SAR technology, the accurate scatterer point can be determined, the water level information can be accurately extracted, the wetland water level measurement can be accurately carried out, more accurate wetland water level change is obtained, and the accuracy of wetland hydrological information extraction is ensured.
Taking reed wetland as an example, which is a typical DS, the echo signal of each resolution unit on the SAR image is the vector sum of backscattering of all independent scattering targets in the resolution unit, and exhibits a characteristic of obvious gaussian distribution. DS backscatter energy is relatively low to PS and usually occupies several neighboring pixels on the SAR image, whose scattering properties have the same probability distribution. Statistical Homogeneous Pixels (HP) with probability distribution were confirmed by statistical tests (statistical test) on the differential fringe pattern. The SHP can be identified around each pixel by performing statistical analysis on the registered L-band HH polarization composite data and checking whether the multi-temporal backscattering coefficient values of two adjacent pixels belong to the same distribution on the statistical test.
The wetland water level measuring method of the invention is described below with reference to fig. 2, and the step S300 specifically includes the following steps:
s310, acquiring the connected number of all pixels of each pixel of the differential interference fringe pattern in a corresponding preset window, specifically, checking by adopting an Anderson-Darling (AD) test method, and taking the pixel higher than the preset connected number as an SHP in the preset window and keeping the SHP; the pixels are the central points of the corresponding preset windows, and the probability distribution of the multi-temporal backscattering coefficient values of the SHP between two adjacent pixels on the statistical test is the same.
In the present embodiment, the preset window is an 11 × 11 window, and the DS is determined by traversing all pixels through the preset window.
S320, removing the SHP which is not communicated with the central point, and determining the DS block corresponding to the central point so as to ensure the spatial connectivity of the DS block corresponding to the central point of the preset window.
S330, acquiring the coherence of the DS blocks, and extracting the distributed scatterers of the distributed scatterer blocks with the first coherence.
Preferably, the first coherence is 0.3, i.e. if the coherence of the entire DS block is less than 0.3, the decoherence block will be regarded as a decoherence block rather than a DS block, and the decoherence block will not participate in the subsequent steps.
The wetland water level measuring method of the invention is described below with reference to fig. 3, and after step S330, the method further comprises the following steps:
and S340, removing the flat ground phase and the terrain phase from the DS to eliminate the influence of DEM errors and improve the coherence of the DS.
In step S300, a preset window centered on each pixel is defined, then a two-sample Four-person (GoF) test with a given significance level is applied between each pixel in each preset window, all pixels that can be considered as SHPs are selected, pixels that are not directly connected to the central point through other SHPs are discarded, and finally, all SHPs connected to the central point are used for subsequent steps. Step S300 determines, pixel by pixel, SHPs having the same scatter statistical distribution based on the significance level and connectivity principle, and determines DS using the number of connected pixels as a threshold.
The wetland water level measuring method of the invention is described below with reference to fig. 4, and the step S600 specifically includes the following steps:
s610, constructing a linear model through the DS.
And S620, acquiring the relative water level change of the linear model based on an L1 norm minimization algorithm, an L2 norm minimization algorithm and an optimal interference network.
On each unwrapped differential fringe pattern, each coherent pixel (x, y) is from time tiTo time tjCan be estimated by equation (1), where equation (1) is:
Figure BDA0003198891600000101
wherein, thetaincIs the angle of incidence of the SAR, λ is the wavelength of the SAR,
Figure BDA0003198891600000103
representing the coherent pixel (x, y) and the reference point (x, y) on the unwrapped differential fringe pattern0,y0) N is the noise phase, and a water level survey point is selected as a reference point (x)0,y0) Corresponding water level change can be generated by using water level survey point data
Figure BDA0003198891600000102
Deformation parameter estimation is always a hot spot and a difficulty in long-time sequence interferometry, an existing algorithm usually adopts an L2 norm minimization algorithm, and a large amount of deformation estimation errors often occur in non-cities. In step S620, based on the SBAS technique, the full-resolution differential interference fringe phase map subjected to the adaptive terrain filtering is unwrapped, the full-resolution interference phase estimation is performed, the interference phase quality of the DS is improved on the basis of maintaining the interference phase of the point scatterer, and the DS with a high coherence coefficient is selected based on the full-resolution differential interference fringe phase map, specifically, the low-pass part of the deformation phase and the residual terrain error (residual phase) are estimated by a least square algorithm (L2 norm minimization algorithm); for the differential interference fringe phase diagram with the residual terrain error (residual phase) removed, an improved simplex method is adopted to carry out L1 norm minimization calculation to form parameter error diagram detection and coarse difference elimination, and on the basis, an L2 norm minimization algorithm is adopted to solve the deformation phase, so that the precision and stability of deformation phase estimation are improved; the nonlinear deformation part with high resolution is solved by Singular Value Decomposition (SVD) algorithm.
And S630, integrating the relative water level change based on an L1 norm minimization algorithm to obtain a relative water level sequence.
In the method, based on an L1 norm minimization algorithm, relative water level changes are extracted from the adaptive terrain filtered differential interference fringe patterns, specifically, on each differential interference fringe pattern, all coherent pixels (x, y) are unwrapped by taking a pixel with a known water level as a reference. For each coherent pixel (x, y), the optimal interference network forms equation (2), where equation (2) is:
BΔh=CΔφ+Δh0+n (2)
wherein,
Figure BDA0003198891600000111
delta phi is the unwrapping value of the phase change value of the differential interference fringe pattern after the adaptive terrain filtering, B is a matrix defined by the formed optimal interference network, delta h is a relative water level change vector on adjacent acquisition time on a coherent pixel (x, y), and delta h is a relative water level change vector on the coherent pixel (x, y)0And (3) representing a noise phase for a relative water level change vector on the water level check point, wherein the noise phase comprises removing terrain errors, atmospheric noise and orbit errors. Because wetland areas are generally flat (with different altitudes of 0-5 meters), the influence of terrain errors of DEM can be ignored, orbit errors (translated into linear phase fringes on a differential interference fringe pattern) can be removed by removing linear trends from an un-unwound differential interference fringe pattern, in the SBAS technology, the atmospheric effect is generally assumed to be completely unrelated to the change of deformation information in time, and can be estimated and eliminated by space-dimensional low-pass and time-dimensional high-pass filtering, however, because the water level change and the atmospheric disturbance are high-frequency signals in a time dimension, the atmospheric phase removal method cannot be adopted in wetland application. Therefore, the final water level time series may contain a certain degree of atmospheric noise. In this embodiment, Numerical Weather Prediction (NWP) is used to mitigate atmospheric effects during processing. Preferably, the atmospheric noise estimated by using the NWP is 1.2-4.3cm in the wetland area, namely the range of the SAR image to be processed.
The SVD algorithm can obtain the L2 norm solution of the L2 norm minimization algorithm, however, in coastal wetlands, some irrelevant areas, such as open water areas, are often present, and areas with high coherence are divided. This often introduces phase unwrapping errors, i.e., phase jumps between different regions, and the L2 norm minimization algorithm often performs poorly in detecting these phase jumps in the unwrapped data. In contrast, for the problem that non-urban area phase unwrapping errors occur frequently and are difficult to detect, the L1 norm minimization algorithm can provide a more robust phase inversion solution, and the L1 norm solution with respect to water level changes is shown in formula (3), where formula (3) is:
Figure BDA0003198891600000121
wherein,
Figure BDA0003198891600000122
the L1 norm minimization algorithm, which is an L1 norm solution, can give a solution to the water level change by integration
And S640, comparing the relative water level sequence with the reference water level observation data to obtain the linear offset of the absolute value of the water level.
And S650, removing the linear offset in the relative water level sequence to obtain an absolute water level sequence.
It should be noted that only the change of the relative water level can be obtained from the phase unwrapping, so the Inter-metric Synthetic Aperture Radar (SAR) observation needs to be calibrated by the ground hydrological observation to obtain the absolute water level estimation. To estimate the absolute water level, the relative water level changes collected at adjacent times are integrated to obtain a relative water level sequence. And then, the relative sequence is associated with the reference water level observation data to obtain an absolute water level sequence. There is always a linear offset between the relative water level sequence generated by InSAR and the reference water level observation data. By comparing the water level sequence observed by InSAR with the water level observation data, the linear offset can be estimated. After the linear offset is removed, an absolute water level sequence of InSAR inversion is generated.
When imaging pairs are paired, the traditional method only uses maximum time base line and space base line constraints, for example, sets appropriate time base line and vertical base line, but does not judge coherence of interference image pairs, so that after all interference image pairs are subjected to differential interference fringe pattern generation, some interference image pairs with low coherence are necessary, the differential interference fringe patterns and unwrapping results generated by the interference image pairs are not ideal, and therefore the interference image pairs need to be removed for subsequent processing.
The wetland water level measuring method of the invention is described below with reference to fig. 5, and the step S200 specifically includes the following steps:
s210, selecting an interference image pair higher than the second coherence as an interference image pair of the composite data, and performing pairing combination on the composite data, namely performing complex conjugate operation to obtain a plurality of interference image pairs of the composite data.
S220, constructing a basic interference network based on a Minimum Spanning Tree (MST) method, and generating an interference image pair connection image of all SAR images to be processed.
And S230, adding the plurality of interference image pairs of the composite data into the basic interference network to obtain an optimal interference network, and generating an optimal interference image pair connection image with balanced calculation precision and calculation efficiency.
And S240, generating a differential interference fringe pattern according to the plurality of interference image pairs of the composite data.
In step S210, by analyzing the coherence of the typical interference image pair, determining the overall coherence of the to-be-processed SAR image and the change rule of the coherence of the sea pond over time, and evaluating the coherence of all interference image pairs by combining the spatial baseline decorrelation evaluation function, and using this as the connection weight, in step S230, adding the interference image pair with high coherence obtained in step S210 into the basic interference network to form a final optimal interference network, which can reduce redundant computation and ensure the accuracy of wetland hydrological information extraction.
In step S200, an interference image pair selection method is established to identify the optimal interference network formed on the spatio-temporal baseline plane, and the optimal interference network is constructed based on the MST algorithm and the second coherence (coherence coefficient threshold). In the present embodiment, the theoretical coherence coefficient is estimated by formula (4), where formula (4) is:
Figure BDA0003198891600000131
wherein, γspatialRepresenting a spatial component, γtemporalRepresenting a time component, gammadopplerRepresenting the Doppler component, gammanoiseRepresenting a thermal noise component, BperpRepresents a spatial centroid baseline, Δ t represents a temporal centroid baseline, Δ fdc represents a Doppler centroid baseline, Bperp_cIs the critical baseline corresponding to when the coherence is zero. Fdc in FBD mode for ALOS PALSAR (PALSAR is an L-band SAR sensor carried by ALOS micro)cIs 1521Hz, TcThe time decay constant was 2500 days for the wetland area. The ALOS PALSAR has a SNR (signal to noise ratio) of 6.95dB in FBD mode.
Preferably, the second coherence is 0.6, i.e. the interference correlation with a calculated theoretical coherence coefficient greater than 0.6 is added to the underlying interference network constructed in the spatio-temporal plane according to equation (4).
The wetland water level measuring device provided by the invention is described below, and the wetland water level measuring device described below and the wetland water level measuring method described above can be referred to correspondingly.
The wetland water level measuring device of the invention is described below with reference to fig. 6, and is applied to data monitoring and evaluation of a wetland area, and the device comprises:
the registration module 100 is configured to perform registration and calibration on the SAR image to be processed to obtain registered composite data, where the composite data is an amplitude image and phase information corresponding to the amplitude image.
In this embodiment, in the registration module 100, HH is adopted as the polarization mode of the SAR image to be processed, and SLC data is obtained, so that the composite data is a continuous L-band HH polarized (time series) SAR image, and the SAR image to be processed is an image of a wetland area.
Since the coastal wetland is located at the land-sea boundary, the low coherence surface targets such as the sea and the mudflat occupy a large area on the SAR image, in this embodiment, in order to ensure the registration accuracy, the registration method is improved, specifically, the registration module 100 specifically includes the following steps:
supposing that SAR images to be processed have M +1 scene SAR influence, taking one of the SAR images to be processed as a main image, registering other SAR images (auxiliary images) to be processed to the main image according to information such as track parameters, pulse repetition frequency, time information, external DEM and the like, carrying out pixel registration between the main image and the auxiliary image, ensuring the registration precision by a gross error removal method, and realizing sub-pixel level registration; wherein the main image has stable scattering properties as a basis for registration.
It will be appreciated that the specific registration accuracy may be set as a practical matter.
And the pairing combination module 200 is used for carrying out pairing combination on the composite data based on the coherence of the interference image pairs, namely carrying out complex conjugate operation to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs.
And the scatterer extraction module 300 is configured to determine an SHP of the differential interference fringe pattern, and extract a DS based on the SHP.
And the adaptive filtering module 400 is configured to perform adaptive terrain filtering on the differential interference fringe pattern after the DS is extracted.
The phase unwrapping module 500 is configured to perform phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
and the water level measuring module 600 is configured to obtain the water level change of the unwrapped differential interference fringe pattern based on the SBAS technology.
The wetland water level measuring device is different from the traditional SAR technology, the scatterer extraction module 300 and the adaptive filtering module 400 are added, the scatterer which keeps higher coherence is further determined through the scatterer extraction module 300 so as to determine a stable scatterer, the influence of external errors is eliminated through the adaptive filtering module 400 so as to improve the coherence of the scatterer, and the scatterer extraction module 300 and the adaptive filtering module 400 are combined into the traditional SAR technology so as to determine accurate scatterer points and extract water level information more accurately, further perform more accurate wetland water level measurement, obtain more accurate wetland water level change and ensure the accuracy of wetland hydrological information extraction.
Taking reed wetland as an example, which is a typical DS, the echo signal of each resolution unit on the SAR image is the vector sum of backscattering of all independent scattering targets in the resolution unit, and exhibits a characteristic of obvious gaussian distribution. DS backscatter energy is relatively low to PS and usually occupies several neighboring pixels on the SAR image, whose scattering properties have the same probability distribution. The statistical HP with probability distribution is confirmed by statistical tests (statistical test) on the differential interference fringe pattern. By performing statistical analysis on the registered L-band HH polarization composite data, whether the multi-temporal backscattering coefficient values of two adjacent pixels belong to the same distribution on the statistical test can be verified, and the SHP around each pixel can be identified.
In the wetland water level measuring device of the present invention described below with reference to fig. 7, the scatterer extraction module 300 specifically includes:
the homogeneous pixel determining unit 310 is configured to obtain a connected number of all pixels of each pixel of the differential interference fringe pattern in a corresponding preset window, specifically, perform inspection by using an Anderson-darling (ad) test method, and use a pixel higher than the preset connected number as an SHP in the preset window and retain the SHP; the pixels are the center points of the corresponding preset windows, and the probability distribution of the multi-temporal backscattering coefficient values of the SHP between two adjacent pixels on the statistical test is the same.
In the present embodiment, the preset window is an 11 × 11 window, and the DS is determined by traversing all pixels through the preset window.
The removing unit 320 is configured to remove the SHP not communicated with the central point, and determine the DS block corresponding to the central point, so as to ensure spatial connectivity of the DS block corresponding to the central point of the preset window.
And a coherence determining unit 330, configured to obtain coherence of the DS blocks, and extract a distributed scatterer higher than the distributed scatterer block with the first coherence.
Preferably, the first coherence is 0.3, i.e. if the coherence of the entire DS block is less than 0.3, the decoherence block will be regarded as a decoherence block rather than a DS block, and the decoherence block will not participate in the subsequent steps.
The wetland water level measuring device of the present invention is described below with reference to fig. 8, and after the coherence determining unit 330, the device further comprises:
and the error removing unit 340 is configured to remove the flat ground phase and the terrain phase from the DS, so as to eliminate the influence of the DEM error and improve the coherence of the DS.
In the scatterer extraction module 300, a preset window centered on each pixel is defined, then a double sample GoF test at a given significance level is applied between each pixel in each preset window, all pixels that can be considered as SHPs are selected, pixels that are not directly connected to the center point through other SHPs are discarded, and finally, all SHPs connected to the center point are used for subsequent steps. The scatterer extraction module 300 determines the SHP with the same scatter statistical distribution pixel by pixel with the significance level and the connectivity principle, and determines the DS with the connectivity number as a threshold.
In the following, the wetland water level measuring device of the invention is described with reference to fig. 9, and the water level measuring module 600 specifically includes:
a model construction unit 610 for constructing a linear model by DS.
And a relative water level variation obtaining unit 620, configured to obtain a relative water level variation of the linear model based on the L1 norm minimization algorithm, the L2 norm minimization algorithm, and the optimal interference network.
Deformation parameter estimation is always a hot spot and a difficulty in long-time sequence interferometry, an existing algorithm usually adopts an L2 norm minimization algorithm, and a large amount of deformation estimation errors often occur in non-cities. In the relative water level change obtaining unit 620, based on the SBAS technique, the full-resolution differential interference fringe phase diagram after the adaptive terrain filtering process is unwrapped, the interference phase estimation of the full resolution is performed, the interference phase quality of the DS is improved on the basis of maintaining the interference phase of the point scatterer, and the DS with a high coherence coefficient is selected based on the full-resolution differential interference fringe phase diagram, specifically, the low-pass part of the deformation phase and the residual terrain error (residual phase) are estimated by a least square algorithm (L2 norm minimization algorithm); for the differential interference fringe phase diagram with the residual terrain error (residual phase) removed, an improved simplex method is adopted to carry out L1 norm minimization calculation to form parameter error diagram detection and coarse difference elimination, and on the basis, an L2 norm minimization algorithm is adopted to solve the deformation phase, so that the precision and the stability of deformation phase estimation are improved; and solving the high-resolution nonlinear deformation part by using an SVD algorithm.
A relative water level sequence obtaining unit 630, configured to integrate the relative water level change based on an L1 norm minimization algorithm to obtain a relative water level sequence.
The SVD algorithm can obtain the L2 norm solution of the L2 norm minimization algorithm, however, in coastal wetlands, some irrelevant areas, such as open water areas, are often present, and areas with high coherence are divided. This often introduces phase unwrapping errors, i.e., phase jumps between different regions, and the L2 norm minimization algorithm often performs poorly in detecting these phase jumps in the unwrapped data. In contrast, for the problem that non-urban area phase unwrapping errors occur frequently and are difficult to detect, the L1 norm minimization algorithm may provide a more robust phase inversion solution.
And a linear offset obtaining unit 640, configured to compare the relative water level sequence with the reference water level observation data, and obtain a linear offset of the absolute value of the water level.
And an absolute water level sequence obtaining unit 650 for removing the linear offset amount in the relative water level sequence to obtain an absolute water level sequence.
It should be noted that only the changes in relative water level can be obtained from the phase unwrapping, and therefore the InSAR observations need to be calibrated by surface hydrological observations to obtain an absolute water level estimate. To estimate the absolute water level, first, the relative water level changes collected at adjacent times are integrated to obtain a relative water level sequence. And then, the relative sequence is linked with the reference water level observation data to obtain an absolute water level sequence. There is always a linear offset between the relative water level sequence generated by InSAR and the reference water level observation data. By comparing the water level sequence observed by InSAR with the water level observation data, the linear offset can be estimated. After the linear offset is removed, an absolute water level sequence of InSAR inversion is generated.
When imaging pairs are paired, the traditional method only uses maximum time base line and space base line constraints, for example, sets appropriate time base line and vertical base line, but does not judge coherence of interference image pairs, so that after all interference image pairs are subjected to differential interference fringe pattern generation, some interference image pairs with low coherence are necessary, the differential interference fringe patterns and unwrapping results generated by the interference image pairs are not ideal, and therefore the interference image pairs need to be removed for subsequent processing.
The wetland water level measuring device of the present invention will be described below with reference to fig. 10, and the combination module 200 specifically includes:
and the pairing and combining unit 210 is configured to select an interference image pair higher than the second coherence as an interference image pair of the composite data, and perform pairing and combining, that is, complex conjugate operation, on the composite data to obtain a plurality of interference image pairs of the composite data.
The first constructing unit 220 is configured to construct a basic interference network based on the MST method, and generate an interference image pair connection map of all the SAR images to be processed.
And a second constructing unit 230, configured to add the plurality of interference image pairs of the composite data into the basic interference network to obtain an optimal interference network, and generate a best interference image pair connection diagram with balanced calculation accuracy and calculation efficiency.
And an interference pattern generating unit 240, configured to generate a differential interference fringe pattern according to the plurality of interference image pairs of the composite data.
In the pairing combination unit 210, the coherence analysis of a typical interference image pair is used to determine the overall coherence of the to-be-processed SAR image and the change rule of the coherence of the sea pond along with time, the coherence of all interference image pairs is evaluated by combining with the spatial baseline decorrelation evaluation function, and the interference image pairs with high coherence obtained by the pairing combination unit 210 are added to the basic interference network in the second construction unit 230 to form a final optimal interference network, so that the redundant computation can be reduced, and the accuracy of wetland hydrological information extraction can be ensured.
In the matching combination module 200, an interference image pair selection method is established to identify the optimal interference network formed on the spatio-temporal baseline plane, and the basis of the construction of the optimal interference network is the MST algorithm and the second coherence (coherence coefficient threshold).
Preferably, the second coherence is 0.6, and the interference coherence with a calculated theoretical coherence coefficient greater than 0.6 is added to the underlying interference network constructed in the spatio-temporal plane.
Fig. 11 illustrates a physical structure diagram of an electronic device, and as shown in fig. 11, the electronic device may include: a processor (processor)810, a communication interface 820, a memory 830 and a communication bus 840, wherein the processor 810, the communication interface 820 and the memory 830 communicate with each other via the communication bus 840. The processor 810 may call the logic instructions in the memory 830 to perform the wetland water level measurement method, which includes the following steps:
s100, registering and calibrating the SAR image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time sequence SAR image, and the SAR image to be processed is an image of a wetland area;
s200, based on the coherence of the interference image pairs, carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs;
s300, determining homogeneous pixels of the differential interference fringe pattern, and extracting the distributed scatterers based on the homogeneous pixels;
s400, carrying out self-adaptive terrain filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
S500, performing phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
s600, acquiring the water level change of the unwrapped differential interference pattern based on a small baseline set technology.
Furthermore, the logic instructions in the memory 830 may be implemented in software functional units and stored in a computer readable storage medium when sold or used as a stand-alone product. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-only memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
In another aspect, the present invention also provides a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the wetland water level measurement method provided by the above methods, the method comprising the steps of:
s100, registering and calibrating the SAR image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time sequence SAR image, and the SAR image to be processed is an image of a wetland area;
s200, based on the coherence of the interference image pairs, carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs;
s300, determining homogeneous pixels of the differential interference fringe pattern, and extracting the distributed scatterers based on the homogeneous pixels;
s400, carrying out self-adaptive terrain filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
S500, performing phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
s600, acquiring the water level change of the unwrapped differential interference pattern based on a small baseline set technology.
In still another aspect, the present invention also provides a non-transitory computer-readable storage medium having stored thereon a computer program, which when executed by a processor, is implemented to perform the above-provided wetland water level measurement method, the method comprising the steps of:
s100, registering and calibrating the SAR image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time sequence SAR image, and the SAR image to be processed is an image of a wetland area;
s200, based on the coherence of the interference image pairs, carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs;
s300, determining homogeneous pixels of the differential interference fringe pattern, and extracting the distributed scatterers based on the homogeneous pixels;
s400, carrying out self-adaptive terrain filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
S500, performing phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
s600, acquiring the water level change of the unwrapped differential interference pattern based on a small baseline set technology.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate components may or may not be physically separate, and components displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the embodiment. One of ordinary skill in the art can understand and implement the present invention without any inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may be modified or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions.

Claims (10)

1. A wetland water level measuring method comprises the following steps:
registering and calibrating the synthetic aperture radar image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time sequence synthetic aperture radar image, and the synthetic aperture radar image to be processed is an image of a wetland area;
based on the coherence of interference image pairs, carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs;
carrying out phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
based on a small baseline set technology, acquiring the water level change of the unwrapped differential interference pattern, wherein before the differential interference pattern is phase unwrapped to obtain the unwrapped differential interference pattern, the method further comprises the following steps:
determining homogeneous pixels of the differential interference fringe pattern, and extracting distributed scatterers based on the homogeneous pixels;
and performing self-adaptive terrain filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
2. The wetland water level measurement method according to claim 1, wherein the step of determining homogeneous pixels of the differential interference fringe pattern and extracting the distributed scatterers based on the homogeneous pixels comprises the following steps:
acquiring the connected number of all pixels of each pixel of the differential interference fringe pattern in a corresponding preset window, and taking the pixel higher than the preset connected number as the homogeneous pixel in the preset window; the pixel is the central point of a corresponding preset window, and the probability distribution of the multi-temporal backscattering coefficient values of the homogeneous pixel between two adjacent pixels on the statistical test is the same;
removing the homogeneous pixels which are not communicated with the central point, and determining a distributed scatterer block corresponding to the central point;
and acquiring the coherence of the distributed scatterer blocks, and extracting the distributed scatterers of the distributed scatterer blocks with higher first coherence.
3. The wetland water level measurement method according to claim 2, wherein after the coherence of the distributed scatterer blocks is obtained and the distributed scatterers of the distributed scatterer blocks having higher first coherence are extracted, the method further comprises the steps of:
and removing the flat ground phase and the terrain phase from the distributed scatterers.
4. The wetland water level measurement method according to claim 1, wherein the acquiring of the water level variation of the unwrapped differential interference pattern based on the small baseline set technique specifically comprises the following steps:
constructing a linear model through the distributed scatterers;
acquiring the relative water level change of the linear model based on an L1 norm minimization algorithm, an L2 norm minimization algorithm and an optimal interference network;
integrating the relative water level change based on an L1 norm minimization algorithm to obtain a relative water level sequence;
comparing the relative water level sequence with reference water level observation data to obtain the linear offset of the absolute value of the water level;
and removing the linear offset in the relative water level sequence to obtain an absolute water level sequence.
5. The wetland water level measurement method according to claim 4, wherein the relative water level variation is integrated based on an L1 norm minimization algorithm to obtain a relative water level sequence step, wherein terrain errors, atmospheric noise and orbit errors are removed; wherein the atmospheric noise is obtained using a numerical weather forecast.
6. The wetland water level measurement method according to claim 4, wherein the composite data is paired and combined based on the coherence of the interference image pairs to obtain a plurality of interference image pairs of the composite data, and a differential interference fringe pattern is generated according to the interference image pairs, specifically comprising the following steps:
selecting the interference image pair higher than the second coherence as the interference image pair of the composite data, and carrying out pairing combination on the composite data to obtain a plurality of interference image pairs of the composite data;
constructing a basic interference network based on a minimum spanning tree method;
adding a plurality of interference image pairs of the composite data into the basic interference network to obtain the optimal interference network;
and generating a differential interference fringe pattern according to a plurality of interference image pairs of the composite data.
7. The wetland water level measurement method according to claim 1, wherein the registering and calibrating of the synthetic aperture radar image to be processed to obtain the registered composite data specifically comprises the following steps:
taking one of the synthetic aperture radar images to be processed as a main image, and registering other synthetic aperture radar images to be processed to the main image; wherein the main image has stable scattering characteristics.
8. A wetland water level measuring device comprises:
the registration module (100) is used for registering and calibrating the synthetic aperture radar image to be processed to obtain registered composite data; the composite data is an amplitude image and phase information corresponding to the amplitude image, the composite data is a time sequence synthetic aperture radar image, and the synthetic aperture radar image to be processed is an image of a wetland area;
the pairing combination module (200) is used for carrying out pairing combination on the composite data based on the coherence of interference image pairs to obtain a plurality of interference image pairs of the composite data, and generating a differential interference fringe pattern according to the interference image pairs;
the phase unwrapping module (500) is used for performing phase unwrapping on the differential interference pattern to obtain an unwrapped differential interference pattern;
a water level measurement module (600) for obtaining water level variations of the unwrapped differential fringe pattern based on a small baseline set technique, characterized in that, before the phase unwrapping module (500), the apparatus further comprises:
a scatterer extraction module (300) for determining homogeneous pixels of the differential fringe pattern, and extracting distributed scatterers based on the homogeneous pixels;
and the self-adaptive filtering module (400) is used for carrying out self-adaptive terrain filtering on the differential interference fringe pattern after the distributed scatterers are extracted.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and operable on the processor, wherein the processor implements the steps of the wetland water level measurement method according to any one of claims 1 to 7 when executing the program.
10. A non-transitory computer-readable storage medium, on which a computer program is stored, wherein the computer program, when executed by a processor, implements the steps of the wetland water level measurement method according to any one of claims 1 to 7.
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* Cited by examiner, † Cited by third party
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