SAR low-coherence interferogram robust phase slope removal method based on least square

Abstract

A robust phase slope removal method for an SAR low-coherence interferogram based on least squares comprises the following steps: step 1, acquiring a single-view complex image of a domestic SAR satellite, selecting a master image and a slave image, performing registration and interference processing, removing a DEM (Digital Elevation Model) and a flat phase, and performing multi-view processing to obtain a preprocessed interferogram; 2, performing frequency domain analysis on the interferogram, and preliminarily estimating the modulation frequency of a linear phase slope; step 3, establishing an azimuth phase slope model, and fitting slope parameters by using least square; and step 4, applying the slope parameter obtained by fitting to the interferogram to realize removal and correction of the azimuth phase slope. According to the method, stable phase slope removal can be realized in a low-coherence environment, the accumulative influence of unwrapping errors is remarkably reduced, and the method has the advantages of being high in robustness and adapting to the characteristics of a domestic SAR (Synthetic Aperture Radar). According to the method, the precision and the reliability of an interference measurement result can be effectively improved, and high-quality technical support is provided for deformation monitoring and geological disaster early warning application.

Description

Technical Field

[0001] This invention relates to a robust phase ramp removal method for low-coherence interferograms of SAR based on least squares, belonging to the field of synthetic aperture radar interferometry and signal processing technology. Background Technology

[0002] Interferometric synthetic aperture radar (InSAR) technology, as an advanced space-based Earth observation method, combines the high-resolution imaging capabilities of synthetic aperture radar with the advantages of interferometry. It can fully utilize the phase information in radar images to obtain surface elevation and deformation information. Due to its all-weather, all-time, wide-area coverage, and high-precision monitoring characteristics, InSAR technology has been widely used in digital elevation model generation, surface subsidence monitoring, observation and early warning of natural disasters such as earthquakes and landslides, as well as monitoring human activities such as urban construction, mining, and water resource utilization. The phase in the interferogram mainly reflects the distance change between the radar satellite and the ground target during two imaging sessions. This change can be decomposed into multiple components, including the reference ellipsoid phase, elevation phase, deformation phase, atmospheric delay phase, orbital phase, and unavoidable noise phase. Differential interferometry can eliminate the reference ellipsoid phase and elevation phase, thereby extracting deformation information more prominently. However, in practical applications, even after removing the flat and elevation phases, abnormal residual phase slopes still commonly exist in differential interferograms. These slopes appear as linear phase distributions in a fringe pattern, primarily along the azimuth direction and parallel in the range direction. Existing research indicates that this type of phase slope is also prevalent in interferograms from domestic satellites, severely impacting the reliability and accuracy of the interferometric results. Currently, the cause of this phenomenon is generally attributed to orbital errors. Due to the limited orbital positioning accuracy of some SAR satellites, including domestic ones, baseline estimation becomes biased, manifesting as a systematic linear phase slope during interferometric processing. The presence of this erroneous phase negatively impacts phase interpretation in low-coherence regions. Therefore, effectively identifying and removing residual phase slopes in interferograms has become a key issue in improving the accuracy of interferometric measurements using domestic SAR data.

[0003] To eliminate the aforementioned phase slope, existing technical solutions mainly address it from two levels. The first is to suppress the residual phase slope in the interferogram by directly calibrating the orbital state vector or baseline parameters. The main advantage of this method is that it can solve the problem of interferometric phase residuals caused by orbital errors at the source, theoretically ensuring the accuracy of subsequent interferometric measurements. However, in practical applications, this type of method often has certain limitations, such as strong dependence on auxiliary data and stringent conditions for obtaining ground control points or external elevation data, making its widespread application in practical engineering difficult. The second approach intervenes at the data processing level, directly processing the signal of the generated interferogram and removing the residual linear phase component through mathematical modeling and estimation. These two technical approaches constitute the main ideas for solving this problem.

[0004] Further research on baseline correction methods is generally categorized into three types: The first type relies entirely on information from the interferogram itself, such as registration offsets or interferogram frequencies, to calculate baseline parameters. Its advantage is that it requires no additional auxiliary data, making it suitable for processing in situations lacking external information. However, due to limited accuracy, this type of method is typically only used for initial baseline estimation. The second type is based on ground control points (GCPs). Its principle is to establish observation equations using the unwrapped interferometric phase and known control point elevations, and then invert baseline parameters using nonlinear least squares. However, obtaining high-precision ground control points is often difficult in real-world scenarios. The third type is based on external DEMs, which indirectly construct control point information by introducing external digital elevation models to improve the accuracy of baseline parameter estimation. In baseline correction methods based on interferogram information, Knedlike et al. in 1999 derived the geometric relationship between pixel offsets and baseline components based on the registration offsets of the interferogram pairs, and combined this with the dynamic estimation characteristics of Kalman filtering to achieve time-varying baseline parameter estimation. This method can progressively correct the baseline components that change over time, thus achieving a relatively stable estimate. However, due to limited estimation accuracy, this method is more suitable for rapid estimation of the initial baseline. Subsequently, He et al. further improved this approach in 2008, proposing a method combining Kalman filtering with registration parameters to address the shortcomings of traditional orbital parameter methods, control point methods, and frequency domain methods in baseline estimation. Singh et al. proposed a method for baseline parameter inversion using the Fourier spectrum characteristics of interference fringes. This method is based on the theoretical framework of the relationship between fringe frequencies and baseline geometry in the interferogram. By performing Fourier analysis on the interference fringes, the parallel and perpendicular components of the baseline can be directly estimated. This method can extract baseline information from the interferogram itself and is particularly suitable for differential interferometry scenarios. Subsequently, Li et al. further developed a baseline estimation algorithm based on the power spectrum of two-dimensional fast Fourier transform. This method estimates the perpendicular component of the baseline and combines it with the parallel component obtained from orbital data for flat-ground phase removal experiments. However, this method is somewhat dependent on the flatness of the selected image region. Regarding baseline estimation methods based on ground control points (GCPs), Small et al. established observation equations using GCPs in 1993 and solved the baseline parameters using an iterative three-parameter nonlinear least squares (NLS) method. This method can significantly improve the accuracy of the baseline model and provide reliable support for generating digital elevation models (DEMs).Furthermore, in 1996, Joughinet et al. used repeating orbit SAR data from the ERS-1 satellite to generate interferograms and eliminated phase fringes caused by ice sheet movement using a double-difference method, thus obtaining an interferogram that only reflected topographic relief, further confirming the effectiveness of combining external high-precision measurement data for baseline estimation. However, in practical applications, it is often difficult to obtain precise ground control points for the target area. In such cases, it is considered to roughly extract ground control points from an external digital elevation model (DEM). Liu et al. and Kohlhaseet et al. used residual phase extracted from an external DEM to invert and correct baseline errors, thereby reducing the impact of orbital uncertainties on interferometric fringes. In this process, the introduction of the DEM shifted baseline error estimation from relying on dense control points to relying on external topographic information. In 2020, Xu et al. addressed the dependence of traditional methods on orbit accuracy, image registration, or the selection of flat areas. They obtained a more realistic expression for flat phase by adding the flat phase calculated from the initial baseline to the residual phase obtained from quadratic polynomial fitting. Then, they combined this with the interferometric observation equation to invert the baseline parameters, thus avoiding dependence on external elevation information.

[0005] Another approach is to directly process the residual phase on the interferometric layer. This method does not attempt to estimate the baseline error itself, but focuses on correcting its impact on the interferogram. Its advantage lies in not relying on external precise orbital information or ground control points. A common method in this category is to remove the orbital error phase by fitting a polynomial function model between the residual orbital phase and spatial coordinates. In 2014, Zhang et al. proposed a multi-master image MTI InSAR joint estimation model for orbital errors in InSAR data. Compared to traditional methods that often rely on plane fitting or network separation, this method utilizes the differences in spatiotemporal characteristics between deformation signals and orbital errors to simultaneously estimate orbital errors and deformation rates without phase unwrapping. Wright et al. used multi-temporal InSAR data from the ERS-1 / 2 satellite from 1992 to 1999 to analyze crustal deformation in the western Tibetan Plateau. During the processing, they introduced SRTM DEM to remove the topographic phase and superimposed multiple interferograms to suppress noise, thereby mitigating the residual phase stripes caused by orbital errors and inaccurate baseline estimation to some extent. In 2021, Du et al. addressed the difficulty of accurately fitting orbital phase slopes using traditional polynomial methods by proposing a polynomial fitting method based on image block segmentation. This method divides SAR images into overlapping small blocks in the azimuth and range directions, estimates the orbital error planes separately within local areas, and stitches them together using iterative least squares. Compared to a unified polynomial model for the entire image, this method can better eliminate long-wavelength phase stripes caused by orbital baseline errors. Building on polynomial fitting, Xu et al. further pointed out that orbital errors not only manifest as long-wavelength phase slopes but also have a certain elevation dependence. Therefore, they introduced elevation-related terms into the traditional polynomial model and used robust regression to estimate parameters, thereby simultaneously compensating for residual orbital errors and local terrain-related phases. In 2018, Tian et al. proposed a residual orbital error modeling method combining spatial and frequency domains. In the spatial domain, polynomial coefficients are automatically determined through K-fold cross-validation, avoiding the subjectivity of manually setting model complexity.

[0006] However, both refining orbital parameters and processing interferograms are fundamentally based on a crucial premise: the ramp phase originates entirely from orbital errors. Orbital error theory indicates that it should manifest as a linear combination of range and azimuth ramps in the interferogram. However, in actual satellite-observed interferograms, the azimuth ramp is absolutely dominant. This suggests that, besides orbital errors, other systematic error sources, such as on-board time synchronization errors, may exist that directly cause azimuth phase ramps. Therefore, attributing all ramp phenomena solely to orbital errors and using this as a basis for correction may not fundamentally solve the problem. Furthermore, most current signal processing methods based on interferograms tend to perform ramp fitting and removal after phase unwrapping, making their effectiveness highly dependent on the accuracy of phase unwrapping. In regions of poor coherence, the propagation and accumulation of unwrapping errors severely distort subsequent ramp estimations, leading to correction failures and greatly limiting the applicability of this method in low-coherence scenarios. Therefore, a new method is needed to extract and remove residual ramp phase directly from the interferogram signal without relying on too many prior assumptions. Summary of the Invention

[0007] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a robust phase ramp removal method for SAR low-coherence interferograms based on least squares. This method does not rely on precise orbits, does not require phase unwrapping, and can robustly estimate and remove phase ramps under low-coherence conditions. The technical solution of this invention is: A robust phase ramp removal method for low-coherence interferograms of SAR based on least squares includes the following steps: Step 1: Acquire single-view complex images from domestic SAR satellites, select master-slave images, perform registration, resampling and interferometry, then remove DEM phase and flat-ground phase, and perform multi-view processing to obtain preprocessed complex interferograms; Step 2: Perform frequency domain analysis on the preprocessed complex interferograms to detect the azimuth energy distribution characteristics of each complex interferogram and preliminarily estimate the modulation frequency of the linear phase ramp; Step 3: Establish a mathematical model of the azimuth phase slope, and under the condition of maintaining the phase winding characteristics, use the least squares method to robustly fit and solve the slope parameters to obtain the inherent azimuth phase slope error frequency corresponding to each single-view complex image. Step 4: Apply the fitted ramp parameters to the preprocessed complex interferogram to remove and correct the azimuth phase ramp; Step 5: Optimize and evaluate the quality of the corrected complex interferogram. If the quality evaluation index does not reach the preset threshold, adjust the preprocessing parameters and iterate again to ensure that high phase accuracy and stability can still be maintained under low coherence conditions.

[0008] Furthermore, step 1 includes the following sub-steps: Step 11: Perform precise registration on P-scene single-view multiple images of the same area acquired by the domestic SAR satellite, and use one scene as the master image and the rest as slave images to generate Q initial interferograms by pairing them up, where Q≥P-1; Step 12: Perform flat-ground phase and DEM phase removal on the initial interferogram to eliminate the system phase components caused by terrain undulation and orbital geometry; Step 13: Perform 20×20 multi-view processing on the interferogram after removing the flat phase and DEM phase to improve coherence, suppress noise and enhance phase stability in low coherence regions, and obtain the preprocessed complex interferogram.

[0009] Furthermore, step 2 involves frequency domain analysis of the preprocessed complex interferograms to detect the azimuth energy distribution characteristics of each complex interferogram and to preliminarily estimate the modulation frequency of the linear phase ramp. This step specifically includes the following sub-steps: Step 21: Perform an azimuth-to-Fourier transform on the preprocessed complex interferogram to convert it from the spatial domain to the frequency domain, and obtain the corresponding amplitude-frequency diagram; Step 22: In the amplitude-frequency diagram, identify the azimuth frequency coordinates of the energy peak point relative to the zero-frequency center. This corresponds to the modulation frequency of the linear phase ramp in the interferogram. This is the frequency offset of the energy peak point in the azimuth direction; Step 23: Extract the frequency offset of the energy peak point in the azimuth direction. ,Will The difference in frequency between the inherent phase ramp error of the master image and the slave image in the interferogram. The initial estimate of the resulting modulation frequency, This is the phase ramp modulation frequency.

[0010] Furthermore, step 3 establishes a mathematical model of the azimuth phase slope, and while preserving the phase entanglement characteristics, robustly fits and solves the slope parameters using the least squares method to obtain the inherent azimuth phase slope error frequency corresponding to each single-view complex image, including the following sub-steps: Step 31: Establish a system of linear equations ,in, It is a Q×1 vector, where each element is the estimated phase ramp modulation frequency for each interferogram. , It is a P×1 unknown vector, representing the inherent azimuth phase slope error frequency of each SLC image. , , It is a Q×P design matrix, where each row corresponds to an interferogram combination. ,exist The column position is 1, in The column position is -1, and the rest of the positions are 0; Step 32: Solve the system of linear equations using the least squares criterion. Calculations yielded The least squares solution, i.e., the parameter vector The optimal estimate ; Step 33: Apply the obtained optimal estimate value Each element in the table represents the azimuth inherent phase ramp error frequency of the corresponding SLC image. The optimal estimate. Furthermore, step 5 optimizes and evaluates the quality of the corrected complex interferogram. If the quality evaluation index does not reach the preset threshold, the preprocessing parameters are adjusted and iterative processing is performed again, including the following sub-steps: Step 51: Calculate the coherence coefficient of each pixel in the corrected interferogram. And assign weights to each pixel based on the coherence coefficient. ; Step 52: Based on the assigned weights Calculate the weighted unit vector complex sum of the pixel phases across the entire interferogram or within a selected evaluation region. With total weights Then calculate the normalized vector magnitude. Compared with circular standard deviation ; in, It is a complex phase.

[0011] Step 53: Calculate the standard deviation If the result is less than the preset threshold, the quality of the corrected interferogram is deemed acceptable, and the final result is output. Otherwise, the process automatically returns to the preprocessing step to adjust the parameters and re-executes the entire process until the quality requirements are met.

[0012] Secondly, the present invention also proposes a processor for running a program, wherein the program executes the method during runtime.

[0013] Thirdly, the present invention also proposes a non-volatile storage medium comprising: a computer program product, wherein the method is executed when the computer program product is executed.

[0014] Fourthly, the present invention also proposes a computer program product, which includes a computer program that, when executed by a processor, implements the method described.

[0015] The beneficial effects of this invention compared to the prior art are: (1) The slope removal method of the present invention is a phase slope removal scheme based on Fourier transform and least squares optimization. It can effectively overcome the untangling dependence of low coherence region while maintaining the simplicity of operation, and has stronger robustness and applicability.

[0016] (2) This invention solves the problem of poor phase slope removal in low coherence regions due to the complex causes of errors and the reliance on phase unwrapping in traditional methods by directly performing frequency domain analysis and least squares estimation on the interferogram in the complex domain. It can achieve high-precision and robust estimation and removal of residual phase slope, especially dominant azimuth slope, without the need for pre-unwrapping of the phase or relying on precise orbit data, which significantly improves the accuracy and reliability of domestic SAR satellite interferometry products in applications such as deformation monitoring.

[0017] (3) Based on an in-depth analysis of the systematic phase error characteristics in SAR interferograms, this invention designs a robust phase ramp removal method that operates directly in the complex domain. The key difference between this invention and traditional methods that correct orbital errors and polynomial fitting methods based on interferograms is that it completely avoids controversial assumptions about the causes of errors and unreliable phase unwrapping steps. This invention uses frequency domain analysis to directly extract the linear modulation frequency from the wrapped phase, obtaining a high-precision initial ramp estimate unaffected by unwrapping errors. Furthermore, by employing a least-squares estimation model, it can comprehensively utilize the observation information from multiple interferograms to accurately calculate the inherent systematic errors of each image. Attached Figure Description

[0018] Figure 1 This is a flowchart of the phase ramp removal method of the present invention; Figure 2 A schematic diagram of the azimuth linear ramp fringes present in the unwrapped SAR interferogram; Figure 3 In response to Figure 2 Aspect-to-Fourier transform of the interferogram; Figure 4 A schematic diagram of the slope fringe features of 15 unwrapped interferograms composed of 8 images from August 11, 2023 to January 3, 2024 after removing the DEM and flat phase. Figure 5 This is a schematic diagram showing the result of removing the phase ramp from the same set of unwrapped interferograms using the method of the present invention. Detailed Implementation

[0019] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0020] This invention provides a robust phase ramp removal method for low-coherence interferograms of SAR based on least squares. Based on an in-depth analysis of the systematic phase error characteristics in domestic SAR interferograms, this invention designs a robust phase ramp removal method that operates directly in the complex domain. The key difference between this invention and traditional methods that correct for orbital errors and polynomial fitting methods based on interferograms lies in the fact that it completely avoids controversial assumptions about the causes of errors and unreliable phase unwrapping steps. This invention uses frequency domain analysis to directly extract the linear modulation frequency from the wrapped phase, obtaining a high-precision initial ramp estimate unaffected by unwrapping errors. Furthermore, by employing a least-squares estimation model, it can comprehensively utilize observation information from multiple interferograms to accurately calculate the inherent systematic errors of each image.

[0021] This invention not only effectively solves the technical bottleneck of slope removal failure caused by the difficulty of phase unwrapping in low-coherence regions, but also enhances the universality of processing phase slopes with complex origins. Furthermore, the proposed method has a clear algorithm flow, high computational efficiency, and is easy to integrate and implement in existing processing systems. This provides convenient technical support for the widespread application of high-quality InSAR technology in fields such as geological disaster emergency response and wide-area infrastructure monitoring, and helps to promote and facilitate the large-scale and operational application of domestically produced SAR satellite data in related industries.

[0022] This invention provides a robust phase ramp removal method for low-coherence interferograms of domestic SAR based on least squares. The method can be applied to InSAR elevation measurement, time-series deformation monitoring and other fields.

[0023] See Figure 1 This is a schematic flowchart illustrating a robust phase ramp removal method for low-coherence interferograms of domestically produced SAR based on least squares. Figure 1 As shown, the method mainly includes the following steps: Step 1: Data preprocessing: Acquire single-view complex images from domestic SAR satellites, perform registration, resampling and interferometry, then remove DEM phase and flat-ground phase, and perform multi-view processing to obtain preprocessed complex interferograms.

[0024] Specifically, the process involves: first, using P-scene SLC images (single-view complex images) of the same observation area as input, and appropriately selecting the master and slave images according to imaging time and baseline conditions, performing registration and resampling to obtain Q-frame complex-form initial InSAR interferograms. Next, the flat-land phase and DEM phase are removed from each initial interferogram. To improve coherence, suppress noise, and enhance phase quality in low-coherence areas, this step further applies 20×20 multi-view processing to the interferograms after removing the flat-land phase and DEM phase. The complex interferograms obtained through the above preprocessing provide input for subsequent steps. Figure 2 As shown, even after removing the DEM and flat phase, there are still obvious azimuth linear phase ramp fringes in the unwrapped interferogram.

[0025] The above content can be abstracted into steps, as shown in steps 11 to 13 below: Step 11: Perform precise registration on P-scene single-view multiple images of the same area acquired by the domestic SAR satellite, and use one scene as the master image and the rest as slave images to generate Q initial interferograms by pairing them up, where Q≥P-1; Step 12: Perform flat-ground phase and DEM phase removal on the initial interferogram to eliminate the system phase components caused by terrain undulation and orbital geometry; Step 13: Perform 20×20 multi-view processing on the interferogram after removing the flat phase and DEM phase to improve coherence, suppress noise and enhance phase stability in low coherence regions, and obtain the preprocessed complex form interferogram.

[0026] Step 2: Perform azimuth frequency domain analysis on the preprocessed interferogram to detect energy distribution characteristics and preliminarily estimate the modulation frequency of the phase slope. This aims to identify the spectral shift caused by azimuth linear phase error, thereby providing initial frequency values ​​for subsequent quantitative phase slope correction.

[0027] Specifically, step 2 includes: Step 21: Process the preprocessed interferogram obtained in Step 1 Along the azimuth direction Perform a Fourier transform to convert it from the azimuth domain to the spatial domain and then to the azimuth domain. For each fixed range gate... Performing this operation yields the azimuth frequency domain representation of the interferogram.

[0028] Step 22: Calculate the amplitude values ​​of the azimuth spectrum and generate an azimuth amplitude-frequency diagram. For example... Figure 2 The interferogram shown exhibits a significant azimuth linear phase ramp. In its azimuth amplitude-frequency plot, a significant energy peak appears outside the zero-frequency main lobe. The azimuth frequency coordinates of this energy peak relative to the zero-frequency center are: This corresponds to the modulation frequency of the linear phase ramp in the interferogram. This is the frequency offset of the energy peak point in the azimuth direction; Step 23: Extract the azimuth frequency offset corresponding to the energy peak point identified in Step 22. According to the signal model established in this invention, the interferogram... It can be represented as:

[0029] In the formula, , .

[0030] in, , This indicates the master-slave SLC images after registration. Indicates distance direction, Indicates direction. , Indicates the amplitude of the SLC image. , This represents the ideal phase after removing the ramp phase. and Corresponding to the model, with modulation frequency and SLC phase, This represents the linear phase ramp term of the interferogram to be estimated. Through azimuth-to-Fourier transform, this term is represented in the frequency domain as a term located at frequency... The peak value. This is the phase ramp modulation frequency.

[0031] Therefore, we will extract from the amplitude frequency diagram The difference in frequency between the inherent phase ramp error of the master image and the slave image in the interferogram. The preliminary estimate of the resulting modulation frequency.

[0032] Figure 3 Visually demonstrates from Figure 2 An example of the azimuth amplitude-frequency diagram obtained by processing the interferogram in this step is shown in the figure, which clearly marks the energy peak and its corresponding frequency estimate.

[0033] Step 3: By constructing a networked mathematical model covering all interferograms, and while maintaining the phase winding characteristics, the azimuth phase ramp error frequency inherent in each single-view complex image is calculated using the least squares method from the multiple interferogram modulation frequency estimates obtained in Step 2.

[0034] Specifically, step 3 includes: Step 31: Based on the modulation frequency observations obtained from the Q interferograms in Step 2, construct a system of linear equations. The phase ramp modulation frequency of a pair of interferograms... Theoretically, it equals the difference in the inherent error frequencies of the two images, i.e. Based on this, a system of linear equations is established. .

[0035] in, It is The observation vector, whose elements are the modulation frequencies of each interferogram obtained from the preliminary estimation in step 23. , It is The unknown parameter vector represents the inherent azimuth phase slope error frequency of each SLC image to be solved. , It is The design matrix, where each row corresponds to a combination of interferograms. In this row vector, the first Column position is , No. Column position is The remaining elements are 0. The matrix is ​​constructed as follows:

[0036] Step 32: For the system of linear equations To solve this problem, due to the large number of interferograms... Typically greater than the number of parameters to be determined. The least squares criterion is used to solve the problem and obtain the parameter vector. The optimal estimate The solution process aims to minimize the difference between the observed values ​​and the model predictions.

[0037] Step 33: Solve the solution vector obtained in Step 32. Each element in the table represents the azimuth inherent phase ramp error frequency of the corresponding SLC image. The optimal estimate.

[0038] Step 4: Apply the slope parameters obtained from step 3 to the preprocessed interferogram to remove and correct the azimuth phase slope.

[0039] Step 5: Optimize and evaluate the quality of the interferogram after correction in Step 4. If the quality evaluation index does not reach the preset threshold, adjust the preprocessing parameters and perform iterative processing again to ensure that high phase accuracy and stability can still be maintained under low coherence conditions.

[0040] Specifically, step 5 includes: Step 51: Calculate the coherence coefficient of each pixel in the corrected interferogram. And assign weights to each pixel based on the coherence coefficient. This ensures that highly coherent pixels contribute more in subsequent evaluations.

[0041] Step 52: Based on the assigned weights Calculate the weighted unit vector complex sum of the pixel phases within the evaluation region. and total weight This leads to the derivation of the normalized vector magnitude. Compared with circular standard deviation This indicator is sensitive to systematic residuals in phase data and can effectively identify phase errors that have not been completely removed. It is a complex phase.

[0042] Step 53: Compare the calculated standard deviation with a preset threshold. If it is less than the threshold, the quality of the corrected interferogram is deemed acceptable, and the final result is output. Otherwise, automatically return to the preprocessing step (i.e., Step 1) to adjust the parameters and re-execute the entire process until the quality requirements are met. Figure 5 The final result shown is the qualified result after passing the quality control in this step, which is consistent with... Figure 4 The comparison of the original interferograms fully verifies the effectiveness of this quality control mechanism.

[0043] In summary, this invention provides a robust phase slope removal method for low-coherence interferograms of domestic SAR based on least squares, effectively addressing the systematic phase slope residual problem in domestic SAR satellite interferograms. This invention avoids controversial discussions about the specific causes of phase slope and directly processes the interferogram based on its signal characteristics: by performing azimuth frequency domain analysis on the interferogram, the linear modulation characteristics of the phase slope are revealed, and a solution based on networked least squares estimation is proposed to effectively estimate and remove the phase slope. Importantly, this method operates directly on the wrapped phase in the complex domain, avoiding the dependence on the phase unwrapping step in traditional methods, thus exhibiting stronger robustness in low-coherence regions; simultaneously, a quality assessment and iterative optimization mechanism based on circular standard deviation is introduced to ensure the quality of the final output is controllable. It can be seen that this method has a clear implementation process, high computational efficiency, and strong adaptability, and is of great value for improving the quality of domestic SAR satellite interferometric data and promoting its large-scale application in deformation monitoring and geological disaster early warning.

[0044] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A robust phase ramp removal method for SAR low-coherence interferograms based on least squares, characterized in that... include: Step 1: Acquire single-view complex images from domestic SAR satellites, select master-slave images, perform registration, resampling and interferometry, then remove DEM phase and flat-ground phase, and perform multi-view processing to obtain preprocessed complex interferograms; Step 2: Perform frequency domain analysis on the preprocessed interferograms to detect the azimuth energy distribution characteristics of each interferogram and preliminarily estimate the modulation frequency of the linear phase ramp; Step 3: Establish a mathematical model of the azimuth phase slope, and under the condition of maintaining the phase winding characteristics, use the least squares method to robustly fit and solve the slope parameters to obtain the inherent azimuth phase slope error frequency corresponding to each single-view complex image. Step 4: Apply the fitted ramp parameters to the preprocessed complex interferogram to remove and correct the azimuth phase ramp; Step 5: Optimize and evaluate the quality of the corrected complex interferogram. If the quality evaluation index does not reach the preset threshold, adjust the preprocessing parameters and iterate again to ensure that high phase accuracy and stability can still be maintained under low coherence conditions.

2. The robust phase ramp removal method for SAR low-coherence interferograms based on least squares as described in claim 1, characterized in that, Step 1 includes the following sub-steps: Step 11: Perform precise registration on P-scene single-view multiple images of the same area acquired by the domestic SAR satellite, and use one scene as the master image and the rest as slave images to generate Q initial interferograms by pairing them up, where Q≥P-1; Step 12: Perform flat-ground phase and DEM phase removal on the initial interferogram to eliminate the system phase components caused by terrain undulation and orbital geometry; Step 13: Perform 20×20 multi-view processing on the interferogram after removing the flat phase and DEM phase to improve coherence, suppress noise and enhance phase stability in low coherence regions, and obtain the preprocessed complex form interferogram.

3. The robust phase ramp removal method for SAR low-coherence interferograms based on least squares as described in claim 1, characterized in that, Step 2 involves frequency domain analysis of the preprocessed interferograms to detect the azimuth energy distribution characteristics of each interferogram and to preliminarily estimate the modulation frequency of the linear phase ramp. This step specifically includes the following sub-steps: Step 21: Perform an azimuth-to-Fourier transform on the preprocessed interferogram to convert it from the spatial domain to the frequency domain, and obtain the corresponding amplitude-frequency diagram; Step 22: In the amplitude-frequency diagram, identify the azimuth frequency coordinates of the energy peak point relative to the zero-frequency center. This corresponds to the modulation frequency of the linear phase ramp in the interferogram. This is the frequency offset of the energy peak point in the azimuth direction; Step 23: Extract the frequency offset of the energy peak point in the azimuth direction. ,Will The difference in frequency between the inherent phase ramp error of the master image and the slave image in the interferogram. The initial estimate of the resulting modulation frequency, This is the phase ramp modulation frequency.

4. The robust phase ramp removal method for SAR low-coherence interferograms based on least squares as described in claim 3, characterized in that, Step 3 establishes a mathematical model of the azimuth phase slope, and, while preserving the phase winding characteristics, robustly fits and solves the slope parameters using the least squares method to obtain the inherent azimuth phase slope error frequency for each single-view complex image. This includes the following sub-steps: Step 31: Establish a system of linear equations ,in, It is a Q×1 vector, where each element is the estimated phase ramp modulation frequency for each interferogram. , It is a P×1 unknown vector, representing the inherent azimuth phase slope error frequency of each SLC image. , , It is a Q×P design matrix, where each row corresponds to an interferogram combination. ,exist The column position is 1, in The column position is -1, and the rest of the positions are 0; Step 32: Solve the system of linear equations using the least squares criterion. Calculations yielded The least squares solution, i.e., the parameter vector The optimal estimate ; Step 33: Apply the obtained optimal estimate value Each element in the table represents the azimuth inherent phase ramp error frequency of the corresponding SLC image. The optimal estimate.

5. A robust phase ramp removal method for SAR low-coherence interferograms based on least squares as described in claim 4, characterized in that, Step 5 optimizes and evaluates the quality of the corrected complex interferogram. If the quality evaluation index does not reach the preset threshold, the preprocessing parameters are adjusted and iterative processing is repeated, including the following sub-steps: Step 51: Calculate the coherence coefficient of each pixel in the corrected interferogram. And assign weights to each pixel based on the coherence coefficient. ; Step 52: Based on the assigned weights Calculate the weighted unit vector complex sum of the pixel phases across the entire interferogram or within a selected evaluation region. With total weights Then calculate the normalized vector magnitude. Compared with circular standard deviation ;in, It is a complex phase; Step 53: Calculate the standard deviation If the result is less than the preset threshold, the quality of the corrected interferogram is deemed acceptable, and the final result is output. Otherwise, the process automatically returns to the preprocessing step to adjust the parameters and re-executes the entire process until the quality requirements are met.

6. A processor, characterized in that, The processor is used to run a program, wherein the program executes the method according to any one of claims 1 to 5 when it runs.

7. A non-volatile storage medium, characterized in that, include: A computer program product that, when executed, performs the method described in any one of claims 1 to 5.

8. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the steps of the method according to any one of claims 1 to 5.

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