High-Dimensional Phase Linking Method and System Based on Prior Knowledge Regularization

Abstract

The present invention provides a high-dimensional phase linking method and system based on prior knowledge regularization, belonging to the field of radar remote sensing InSAR technology, including: estimating a regularized coherence matrix based on a prior matrix; a distributed scatterer phase estimator based on a quadratic loss metric, solving the distributed scatterer phase estimator, and deriving a quadratic loss solution method based on eigenvalue decomposition and a quadratic loss solution method based on the BFGS algorithm to find the optimal phase, so as to achieve low-sample quadratic loss metric phase linking; for the low-sample quadratic loss metric phase linking, based on a statistical test method, under the condition of a given significance level, judging statistically whether it belongs to a distributed scatterer point. The present invention utilizes prior knowledge with practical significance to make the estimation of the coherence matrix more accurate.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar remote sensing InSAR, and particularly relates to a high-dimensional phase linking method and system based on prior knowledge regularization. Background Art

[0002] Spaceborne synthetic aperture radar interferometry (InSAR) technology is a space-to-ground observation technology that has developed rapidly in recent years. Multi-temporal InSAR (MT-InSAR) technology is a technology developed on the basis of InSAR that uses multiple synthetic aperture radar (SAR) images obtained at different times in the same area to achieve high-precision and high-density measurement point extraction and analysis. This technology can detect the minute deformations that occur on the earth's surface over time, and the measurement accuracy can reach the centimeter to millimeter level. A key challenge of MT-InSAR technology is to extract meaningful information from the interferometric phase affected by atmospheric conditions, terrain, and signal decorrelation.

[0003] To solve the problem of signal decorrelation and improve the quality of the interferometric phase, domestic and foreign research scholars have proposed the following several technologies:

[0004] The first type of technology is based on persistent scatterer (PS) InSAR, which uses individual scatterers with stable scattering characteristics in the image to calculate deformation information that changes over time. Persistent Scatterer Interferometry (PSI) technology provides deformation information of high-quality point positions in the study area and is widely used in the estimation of surface deformation in urban areas. However, in natural scenes, due to the low density of PS points, it is not sufficient to obtain accurate monitoring results. To solve the problem of limited measurement points in PSI technology, Ferretti et al. proposed distributed scatterer (DS) InSAR technology. DS targets are usually found in natural environments such as grasslands, fields, and bare soil, where multiple scatterers with similar brightness jointly contribute to the information in the resolution cell. Distributed Scatterer Interferometry (DSI) uses distributed scatterers to establish a random signal model in the low-coherence region to invert the phase history and thus calculate the deformation information of the earth's surface.

[0005] Typical DSI methods include two steps: 1) calculating the coherence matrix through selected homogeneous pixels (SHPs); 2) estimating the phase history according to the phase linking (PL) algorithm. The estimation of the coherence matrix, as a crucial step, seriously affects the accuracy of the phase sequence estimation. The sample coherence matrix (SCM) is a well-known and easy-to-implement method for estimating the coherence matrix (CM). It requires a large number of samples to achieve satisfactory accuracy, such as positive definiteness. However, with the shortening of the revisit period of synthetic aperture radar satellites, when processing long-term SAR data, on the one hand, accurate estimation of the sample coherence matrix requires a large number of samples. On the other hand, under the assumption of stationary image distribution, it means that a larger local window needs to be used to obtain samples, that is, the image resolution is reduced. Therefore, in practice, in order to keep the processing result with a sufficiently high resolution, a small number of samples must be used to estimate the coherence matrix, that is, the problem of low-sample high-dimensional estimation.

[0006] To solve this problem, on the premise of considering the matrix structure, the regularization idea provides an effective strategy to deal with the coherence matrix estimation problem when the samples are insufficient. A large number of scholars have carried out relevant research. In particular, in recent research, a class of linear shrinkage algorithms has been introduced and integrated into the robust coherence matrix estimator for complex elliptically symmetric (CES) distributed data. These algorithms essentially complete the estimation of the coherence matrix by shrinking it towards a better-conditioned target matrix, which can be a diagonal matrix or an identity matrix. Abramovich borrowed the idea of Ledoit diagonal loading and proposed a regularized Taylor estimator that shrinks towards the identity matrix. Y. Bai borrowed the method of Ollila's regularized conical sample coherence matrix estimation and shrank the matrix to the identity matrix. C. Zhao borrowed the method of Ledoit's regularized shrinkage estimator and shrank the coherence matrix with some elements towards the same matrix. The above methods utilize the matrix linear shrinkage algorithm based on the regularization idea and solve the problem of singular estimation of the coherence matrix caused by insufficient sample quantity. However, in the process of matrix shrinkage, the above methods do not have a clear shrinkage direction but shrink towards the identity matrix. Subsequently, Sun et al. proposed to shrink the sample coherence matrix to a prior matrix , as shown in Equation (1). Its idea is similar to the estimation regularized by diagonal loading, but the estimation method of the prior matrix is not given.

[0007] (1)

[0008] where represents the optimal coherence matrix estimated by the iterative method, is the regularization weight, is the prior matrix, N is the number of images, and K is the number of samples. is an arbitrary positive definite matrix (to find the optimal coherence matrix by iteration, an initial value needs to be input, refers to the right side of the formula for the first input, usually the identity matrix can be taken), is the complex data vector of the i-th image pixel, denotes the Hermitian transpose, and t represents the number of iterations. In actual MT-InSAR processing, there are currently the following two methods to determine the prior matrix :

[0009] (a) Set the prior matrix of the entire InSAR data stack to a constant value. Assume the elements of the coherence matrix are:

[0010] (2)

[0011] where, ;

[0012] ;

[0013] ;

[0014] where, is the decorrelation caused by thermal noise, which depends on the signal-to-noise ratio SNR and is usually assumed to be a constant value. is caused by the different incident angles between two radar paths. is the th and the th vertical baseline between two images in the th and is the critical baseline.

[0015] (b) Classify the prior matrix First, classify the pixels on the image, such as using the clustering method. Then, take the pixels belonging to the same category as samples, estimate the coherence matrix respectively, and use it as the prior coherence estimate for the pixels belonging to this category. In actual processing, to save computer memory and improve processing speed and classification accuracy, the image is divided into blocks with overlapping regions, and the above process is processed according to the image blocks. The advantage of this method is that it can consider the characteristics of coherence variation with ground object types and has a relatively fast calculation speed. The disadvantage is that when the differential phase is not stationary, for example, the most common non-stationarity in SAR interferograms is the uncompensated rapidly varying interferometric phase in spatial samples. Under such conditions, the phase estimation accuracy of the prior matrix is relatively poor.

[0016] The Phase Linking (PL) algorithm is a statistical method for combining multiple interferometric phases into a single equivalent single-reference phase. Suppose there are N single-look complex (SLC) images. The PL algorithm uses maximum likelihood estimation (MLE) to obtain (N - 1) equivalent single-reference phases from N(N - 1) / 2 all possible interferometric combinations. For example, the SqueeSAR technique is an example of a PL method that uses the Phase Triangulation Algorithm (PTA). The equivalent single-reference phases of these optimized DS targets can be combined with PS and used in the traditional PSI processing framework. Accurately estimating the linking phase is crucial for mitigating the decorrelation effect on SAR data. Therefore, since the PL method was introduced by Guarnieri and Tebaldini et al., many studies have been carried out to improve the accuracy and computational efficiency of PL estimation. Ferretti et al. proposed a quasi-Newton method for unconstrained nonlinear optimization based on the maximum likelihood estimation objective function, namely the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. This optimization technique is efficient in minimizing the nonlinear cost function of the PL problem. Cao et al. proposed a method for phase optimization with equal weight and coherent weight factors, providing phase optimization flexibility by introducing coherence information. The CAESAR algorithm proposed by Fornaro et al. is a method for phase optimization based on the multiple scattering mechanism, using the eigenvalue decomposition (EVD) of the coherence matrix and can extract different scattering components. The EVD-based MLE (EMI) algorithm proposed by Ansari et al. is efficient in calculation and estimation by using coherence information. Ho Tong Minh and Ngo proposed a compression technique for PL estimation. This method divides a large amount of data into small stacks, compressing the data to enhance the interferometric components of short temporal baselines without noise. Generally speaking, the differences between the above PL algorithms can be attributed to the weight criteria adopted in each algorithm, which can be coherence-based, sparsity-based, or other forms of regularization. In addition, the above PL algorithms all use the maximum likelihood function as the objective function, approximate the true matrix by using the sample coherence matrix, and solve the phase as the only variable. In recent research, Wang et al. proposed a new likelihood function as the objective function for estimating the phase. This algorithm takes both the phase and the true matrix as unknowns to participate in the calculation, strictly follows the statistical model, and is not affected by the accuracy of the sample coherence matrix. However, it is difficult to obtain an analytical solution for the form of this objective function. Therefore, this method only provides an evaluation index for phase sequence estimation. Bai et al. realized DS phase history estimation based on the idea of flat coherence measurement. This method uses the Frobenius norm function as the objective function. However, this method has no statistical meaning and no corresponding statistical test method.

[0017] The maximum likelihood phase linking method is briefly introduced as follows:

[0018] Given N repeat orbit-registered single look complex (SLC) SAR images, based on the central limit theorem, it is assumed that the normalized SAR data vector y follows a multivariate normal distribution with zero mean and covariance matrix Its probability density function (PDF) is expressed as:

[0019] (3)

[0020] where, denotes the probability density function, det(.) denotes the determinant operation, and the scattering characteristics of DS can be represented by the covariance matrix The covariance matrix can be represented using the true coherence value and the true phase value:

[0021] (4)

[0022] where, the true phase value ;

[0023] where, j represents the imaginary unit, T represents the true coherence value, denotes N estimated optimal phases.

[0024] ;

[0025] is the set of N optimal phases estimated from N(N - 1) / 2 interferometric pairs. All the in the above formula represent the true coherence amplitude value. The phase of any one image in the time series is set to zero, and the remaining values are measured relative to this arbitrary reference. Without loss of generality, the first value can be set to zero, e.g., . Therefore, PL estimates N - 1 optimal interferometric phases from N(N - 1) / 2 phases.

[0026] Define the coherence matrix , where represents the expectation operation. The maximum likelihood estimate of the covariance matrix can be obtained by maximizing the absolute value of the logarithm of the probability density function:

[0027] (5)

[0028] The true coherence value T is required to estimate , but in reality T is unknown. Generally, is used to represent T, Table

[0029] The estimated coherence matrix is shown, so the above formula can be expressed as:

[0030] (6)

[0031] Among them, represents the matrix trace operation, represents the maximum likelihood estimation operation after transformation, represents the Hadamard product, represents the phase sequence to be estimated.

[0032] Therefore, in the existing low-sample high-dimensional coherence matrix estimation methods, there are two problems: one is that there is no clear contraction direction during the matrix contraction process, but it contracts towards the identity matrix; the other is that no effective prior knowledge is utilized, resulting in inaccurate coherence matrix estimation.

[0033] In addition, most of the existing phase linking methods use the maximum likelihood function and its variants as the objective function for phase estimation, which are only applicable to the case of sufficient samples. The recent research is that Bai et al. proposed a phase linking method with the Frobenius norm as the objective function for low-sample high-dimensional data. This method is essentially similar to the method of optimizing the coherence weight factor phase proposed by Cao et al., and it has no statistical significance and no corresponding statistical test method. Summary of the Invention

[0034] To solve the above technical problems, the present invention provides a high-dimensional phase linking method and system based on prior knowledge regularization. The prior matrix is calculated using prior knowledge, and the coherence matrix is contracted towards the prior matrix through a regularization contraction method, breaking the limitation of the traditional method of contracting towards the identity matrix. The introduced prior matrix provides a clear direction for contraction, which is more reasonable and has practical significance compared to contracting to the identity matrix. In addition, for the high-dimensional problem, the present invention proposes a quadratic loss metric phase linking method for low samples to supplement the existing phase linking methods.

[0035] To achieve the above object, the present invention adopts the following technical solutions:

[0036] The high-dimensional phase linking method based on prior knowledge regularization includes the following steps:

[0037] Step 1, estimate the regularized coherence matrix based on the prior matrix;

[0038] Step 2, a distributed scatterer phase estimator based on quadratic loss metric, and solve the distributed scatterer phase estimator, derive a quadratic loss solution method based on eigenvalue decomposition and a quadratic loss solution method based on the BFGS algorithm to find the optimal phase, and realize low-sample quadratic loss metric phase linking;

[0039] Step 3: For the low-sample quadratic loss metric phase link, based on the statistical test method, determine whether it belongs to the distributed scatterer points under the given significance level condition.

[0040] The present invention also discloses a high-dimensional phase link system based on prior knowledge regularization, including the following modules:

[0041] Matrix estimation module, estimating the regularization coherence matrix based on the prior matrix.

[0042] Phase link module, a distributed scatterer phase estimator based on the quadratic loss metric, solving the distributed scatterer phase estimator, deriving the quadratic loss solution method based on eigenvalue decomposition and the quadratic loss solution method based on the BFGS algorithm to find the optimal phase, and realizing the low-sample quadratic loss metric phase link.

[0043] Test discrimination module, for the low-sample quadratic loss metric phase link, giving a statistical test method to probabilistically determine whether it belongs to the distributed scatterer points under the given significance level condition.

[0044] The present invention also discloses an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned high-dimensional phase link method based on prior knowledge regularization are implemented.

[0045] The present invention also discloses a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by the processor, the steps of the above-mentioned high-dimensional phase link method based on prior knowledge regularization are implemented.

[0046] The most recent and closest prior art is the article published by Bai et al. in 2023 titled "LaMIE: Large-Dimensional Multipass InSAR Phase Estimation for Distributed Scatterers" (Y. Bai, J. Kang, X. Ding, A. Zhang, Z. Zhang and N. Yokoya, "LaMIE: Large-Dimensional Multipass InSAR Phase Estimation for Distributed Scatterers," in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-15, 2023, Art no. 5221215, doi: 10.1109 / TGRS.2023.3330971.). This article addresses the low-sample high-dimensional problem, uses a regularized tapered sample coherence matrix estimator (i.e., Tabasco) to estimate the coherence matrix, and then proposes a phase linking method with the Frobenius norm as the objective function. Therefore, the present invention has the following beneficial effects compared with the prior art:

[0047] 1. Compared with the Tabasco method in the above article, the regularized coherence matrix estimation method of prior knowledge proposed by the present invention utilizes prior knowledge with practical significance, making the coherence matrix estimation more accurate;

[0048] 2. Compared with the phase linking method with the F-norm as the objective function, the low-sample quadratic loss metric phase linking proposed by the present invention has statistical significance and corresponding statistical test methods. The low-sample quadratic loss metric phase linking can be tested by the R score. Given a significance level, the probability of belonging to DS points can be judged. The phase linking method with the F-norm as the objective function is essentially similar to the method of optimizing the coherence weight factor proposed by Cao et al., and does not have statistical significance and corresponding statistical test methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flowchart of the high-dimensional phase linking method based on prior knowledge regularization of the present invention;

[0050] Figure 2 It is a schematic diagram of homogeneous pixel selection;

[0051] Figure 3a Schematic diagram for comparing RMSE values of the trace normalization coherent matrix estimation method

[0052] Figure 3b Schematic diagram for comparing RMSE values of the unit matrix regularization coherent matrix estimation method

[0053] Figure 3c Schematic diagram for comparing RMSE values of the coherent matrix estimation of the present invention

[0054] Figure 3d Schematic diagram for comparing RMSE values of the Tabasco method

[0055] Figure 4 Schematic diagram for comparing different phase linking methods Detailed implementation manners

[0056] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0057] As Figure 1 shown, the high-dimensional phase linking method based on prior knowledge regularization in the embodiment of the present invention includes the following steps:

[0058] Step 1. Estimate the regularization coherent matrix based on the prior matrix, including:

[0059] Step 1.1: For each image pixel P, define an estimation window centered on the image pixel P, and the pixels having the same statistical information as the image pixel P are identified. As Figure 2 shown, the black solid line frame represents the range of the search window. It is recommended to select twice the number of images as the window size; for example, for 50 scenes of SAR images, a 10×10 size range is selected as the search window.

[0060] Step 1.2: By performing a KS test on the amplitude data vectors of each image pixel in the search window and the pixel P, all pixels in the search window that are statistically homogeneous with the image pixel P are selected at a given significance level (generally, the significance level is set to 0.05). As Figure 2 shown, the black dashed line frame represents the window of the KS test. The size of the KS test window is generally much smaller than the search window. Therefore, within the search window, four types of pixels can be monitored. The first type is the pixels that pass the KS test and are connected to P ( Figure 2 the light grid pixels in), the second type is the pixels that pass the KS test and are not connected to P (Figure 2 the pixels of the middle brick stripe (), the third type are the pixels that are homogeneously aggregated within the search window and connected to P ( Figure 2 the pixels of the middle diagonal stripe), the fourth type are the pixels that are homogeneously clustered within the search window and not connected to P ( Figure 2 the pixels of the dark grid (in the figure).

[0061] Step 1.3: Based on the characteristic that neighboring homogeneous pixels have similarity in attributes, use the idea of clustering to gather the above four types of pixel sets as sufficient samples to calculate the sample coherence matrix. Take the calculated sample correlation matrix C as the prior matrix .

[0062] (7)

[0063] where H represents the Hermitian transpose, is the set of SHPs (homogeneous pixels) used in the prior matrix estimation. is the complex data vector of the i-th image pixel.

[0064] Step 1.4: For each image pixel P, define an estimation window centered on the image pixel P, and identify the pixels with the same statistical information as the image pixel P to estimate the initial coherence matrix . To ensure the purity of the homogeneous pixels, the search window should be smaller than the estimation window in Step 1.1 at this time. For example, the number of images can be selected as the new window size;

[0065] Step 1.5: In the new window, through the KS test on the amplitude data vector of each image pixel, at a given significance level (generally, the significance level is set to 0.05), select all the pixels in the search window that are statistically homogeneous with the image pixel P, that is, the homogeneous pixels. To ensure the accuracy of the selection of homogeneous pixels, discard the pixels that pass the KS test but are not connected to the image pixel P in the window (that is, only retain Figure 2 the light grid identification part in the figure).

[0066] Step 1.6: Based on the homogeneous pixels selected in the previous step, calculate the initial coherence matrix using formula (7) .

[0067] Step 1.7: Substitute the prior matrix and the initial coherence matrix into the following formula, and obtain the final coherence matrix through an iterative method .

[0068] ;

[0069] Step 2: Based on the regularized coherence matrix obtained in Step 1, perform low-sample quadratic loss metric phase linking, including:

[0070] The present invention proposes a DS (distributed scatterer) phase estimator based on quadratic loss metric for optimal phase estimation which can be expressed by the following formula:

[0071] (8)

[0072] where, is a -order diagonal matrix containing the phase , I is an -order identity matrix, represents the minimization operation of quadratic loss metric, represents the final coherence matrix obtained by observation in Step 1, represents the true coherence value; since is unknown, similar to the MLE (maximum likelihood estimation) method, is used to estimate the true coherence value

[0073] (9)

[0074] The above problem belongs to a non-linear optimization problem, and accordingly two estimators are proposed to solve it: the quadratic loss estimator based on eigenvalue decomposition and the quadratic loss estimator based on BFGS (Broyden-Fletcher-Goldfarb-Shanno). The former is an efficient estimator that guarantees phase accuracy; the latter is a phase estimator based on iterative optimization. The computational costs of both solvers are very low.

[0075] First, expand to obtain , then take the trace operation Tr and remove the terms irrelevant to to obtain:

[0076] ;

[0077] Use the matrix inequality to scale the first term to obtain:

[0078] ;

[0079] where A is an arbitrary Hermitian matrix.

[0080] Finally, using the positive definiteness of the Hadamard product, we can obtain:

[0081] (10)

[0082] Among them, the intermediate matrix , where j represents the imaginary unit, ,..., represents the phase sequence to be estimated, N is the number of images, represents the Hadamard product.

[0083] 1) Quadratic loss estimator based on eigen - decomposition: To effectively solve (10), first, by introducing the condition: = 1, the unconstrained problem is transformed into a constrained problem. In addition, define the intermediate matrix , and transform the above - mentioned problem into a more concise form:

[0084] (11)

[0085] Among them, is the eigen - vector corresponding to the minimum eigenvalue of the intermediate matrix .

[0086] Then its Lagrangian function can be described as:

[0087] (12)

[0088] Among them, λ represents the Lagrange multiplier. By setting the gradient with respect to to zero, we get:

[0089] (13)

[0090] The above equation is equivalent to the eigen - decomposition problem:

[0091] (14)

[0092] Solve is the eigen - vector corresponding to the minimum eigenvalue of the intermediate matrix . Finally, extract the phase history from .

[0093] 2) Quadratic loss estimator based on BFGS: Equation (10) can also be solved using the BFGS algorithm. First, use and to rewrite as:

[0094] (15)

[0095] Among them, A, B, C, and D respectively represent arbitrary matrices, vec represents the vectorization operation, represents the Kronecker product operation.

[0096] Expanding it gives:

[0097] (16)

[0098] Among them, the subscripts l, k, n, and m respectively represent the row and column positions of the matrix elements, represents the sum by element-wise expansion, represents the interference phase of the element in the k-th row and the l-th column, represents the interference phase of the element in the m-th row and the n-th column, represents the interference phase reconstructed by phase optimization.

[0099] Using the symmetry properties of the transpose and conjugate matrices: , combining the same types gives:

[0100] (17)

[0101] Finally, using the symmetry property again:

[0102] (18)

[0103] Similarly:

[0104] (19)

[0105] The subscripts l and k respectively represent the row and column positions of the matrix elements, represents the sum by element-wise expansion, represents the interference phase, represents the interference phase reconstructed by phase optimization, represents the final coherence matrix observed in step 1, represents the true coherence value;

[0106] Therefore, we get:

[0107] (20)

[0108] Among them, represents the optimal phase, is the expression about the optimal phase of.

[0109] Among them, the intermediate parameters a and b are expressed as follows:

[0110] ;

[0111] ;

[0112] Gradient / can be obtained in the following form:

[0113] (21)

[0114] where represents the diagonal elements of the regularized prior coherence matrix, represents the diagonal elements of the true coherence value matrix, replaced by , and n is the matrix element index;

[0115] where ;

[0116] The calculated gradient is integrated into the BFGS optimization framework. BFGS needs to be initialized, and the initial solution is obtained by using the eigen - decomposition method. The optimal solution is found through iteration as the optimal phase.

[0117] Estimate the time - series phase of distributed scatterers through the regularized coherence matrix estimation method of the prior matrix and the low - sample quadratic loss metric phase linking.

[0118] Step 3: Design a statistical test method to perform an R - score test on the results of the low - sample quadratic loss metric phase linking in Step 2, including:

[0119] Under the condition that the null hypothesis holds, the statistic of the Rao test is:

[0120] (22)

[0121] where represents the true coherence matrix, represents the coherence matrix estimated under the condition that the hypothesis holds, RST represents the Rao test, represents the n - order identity matrix; represents a sample set composed of p n - dimensional column vectors, represents the observed interference correlation matrix, E[ ] represents the expectation operation, represents the coherence matrix estimated under the condition that the hypothesis holds. When the number of samples is large, the statistic tends to follow a distribution with degrees of freedom n is the number of images. Therefore, given a significance level condition, the rejection region can be determined by the threshold ​ , namely:

[0122] (23)

[0123] If RST is greater than , it is determined that the phase triangle model cannot fit well, that is, it cannot be determined as a DS point.

[0124] There are many methods for low-sample high-dimensional matrix estimation, aiming to complete the estimation of the coherence matrix by shrinking it towards a target matrix with better conditions. For example, Abramovich borrowed the idea of Ledoit diagonal loading and proposed a regularized Taylor estimator that shrinks towards the identity matrix. Y. Bai borrowed the method of regularized conical sample coherence matrix estimation by Ollila and shrank the matrix to the identity matrix. C. Zhao borrowed the method of Ledoit regularized shrinkage estimator and shrank the coherence matrix with some elements towards the same matrix. The Tabasco method proposed by E. Ollila et al. completes matrix shrinkage.

[0125] Similarly, there are also many known phase-linking methods. For example, the SqueeSAR technology is an example of a PL method that uses the phase triangulation (PTA) algorithm. Cao et al. proposed a method for optimizing the equal weight and coherent weight factors, providing flexibility in phase optimization by introducing coherent information. The CAESAR algorithm proposed by Fornaro et al. is a method for phase optimization based on the multiple scattering mechanism, using the eigenvalue decomposition (EVD) of the coherence matrix and capable of extracting different scattering components. The MLE (EMI) algorithm based on EVD proposed by Ansari et al. is efficient in calculation and estimation by using coherent information. Ho Tong Minh and Ngo proposed a compression technique for PL estimation. This method divides a large amount of data into small stacks and compresses the data to enhance the interference components of short-time baselines without noise.

[0126] For the estimation of the coherence matrix, through simulation experiments, the prior matrix regularized coherence matrix estimation method of the present invention ( Figure 3c ) is compared with the trace-normalized coherence matrix estimation method ( Figure 3a ), the identity matrix regularized coherence matrix estimation method ( Figure 3b ), and the Tabasco method ( Figure 3d ); the results show that the method of the present invention has the highest RMSE (Root - Mean - Square Error) value near the diagonal, proving that the estimated coherence matrix is the most accurate.

[0127] Such as Figure 4As shown in the figure, for the phase linking method: through simulation experiments, the quadratic loss metric-based phase linking method of the present invention is compared with the SqueeSAR method, the LaMLE method, and the coherent weight method; the results show that the quadratic loss metric-based phase linking method based on eigenvalue decomposition has a similar effect to the LaMLE method, while the quadratic loss metric-based phase linking method based on the BFGS method has a lower RMSE value than other methods as the number of images increases, showing the best effect. In the figure, CRLB is the abbreviation of Cramér-Rao Lower Bound, which represents the "Cramér-Rao lower bound", and the RMSE value of any estimation method will not be lower than the Cramér-Rao lower bound.

[0128] The present invention also discloses a high-dimensional phase linking system based on prior knowledge regularization, including the following modules:

[0129] A matrix estimation module for estimating a regularized coherence matrix based on a prior matrix.

[0130] A phase linking module, a distributed scatterer phase estimator based on a quadratic loss metric, and solving the distributed scatterer phase estimator, deriving a quadratic loss solution method based on eigenvalue decomposition and a quadratic loss solution method based on the BFGS algorithm to find the optimal phase, and realizing low-sample quadratic loss metric phase linking.

[0131] A test discrimination module, for low-sample quadratic loss metric phase linking, gives a statistical test method, and probabilistically determines whether it belongs to a distributed scatterer point under a given significance level.

[0132] The present invention also discloses an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the steps of the above-mentioned high-dimensional phase linking method based on prior knowledge regularization are implemented.

[0133] The present invention also discloses a non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned high-dimensional phase linking method based on prior knowledge regularization are implemented.

[0134] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code. The solutions in the embodiments of the present invention can be implemented in various computer languages. For example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript can be used.

[0135] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0136] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0137] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0138] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0139] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations.

Claims

1. A high-dimensional phase linking method based on prior knowledge regularization, characterized in that It includes the following steps: Step 1: Estimate the regularized coherence matrix based on the prior matrix, including: Step 1.1: For each image pixel P, define an estimation window centered on the image pixel P, where pixels having the same statistical information as the image pixel P are identified; Step 1.2: By performing the KS test on the amplitude data vectors of each image pixel within the search window and the image pixel P, at a given significance level, select all pixels within the search window that are statistically homogeneous with the image pixel P; Step 1.3: Using the idea of clustering, gather the pixels that pass the KS test and are connected to the image pixel P, the pixels that pass the KS test and are not connected to the image pixel P, the pixels that are homogeneously aggregated within the search window and are connected to the image pixel P, and the pixels that are homogeneously clustered within the search window and are not connected to the image pixel P as samples, so as to calculate the sample coherence matrix, and use the calculated sample correlation matrix as the prior matrix : （7） where H represents the Hermitian transpose, is the set of homogeneous pixels used in the prior matrix estimation; is the complex data vector of the i-th image pixel; Step 1.4: For each image pixel P, define an estimation window centered on the image pixel P, and identify the pixels having the same statistical information as the image pixel P for estimating the initial coherence matrix ; Step 1.5: In the new search window, by performing the KS test on the amplitude data vector of each image pixel, at a given significance level, select all image pixels within the search window that pass the KS test and are connected to P, i.e., homogeneous pixels; Step 1.6: Based on the homogeneous pixels selected in Step 1.5, calculate the initial coherence matrix using Equation (7) ; Step 1.7: Utilize the prior matrix and the initial coherence matrix , substitute them into the following formula, and obtain the final regularized coherence matrix through an iterative method: ； Among them, is the regularization weight, N is the number of images, K is the number of samples, is the complex data vector of the i-th image pixel, refers to the Hermitian transpose, t represents the number of iterations, and the initial coherence matrix used in the above formula is ; represents the sample correlation matrix obtained in the t-th iteration; represents the regularized coherence matrix obtained in the (t + 1)-th iteration; Step 2: A distributed scatterer phase estimator based on the quadratic loss metric, and solve the distributed scatterer phase estimator, derive a quadratic loss solution method based on eigenvalue decomposition and a quadratic loss solution method based on the BFGS algorithm to find the optimal phase, and realize low-sample quadratic loss metric phase linking; Step 3: For the low-sample quadratic loss metric phase linking, based on the statistical test method, at a given significance level condition, determine whether it belongs to the distributed scatterer points.

2. The high-dimensional phase linking method based on prior knowledge regularization according to claim 1, wherein The said Step 2 includes: The optimal phase estimation is obtained by using a distributed scatterer phase estimator based on the quadratic loss metric as follows: (8) wherein, is a diagonal matrix containing the phase , I is the identity matrix, represents the operation of minimizing the quadratic loss metric, represents the regularized coherence matrix based on the prior matrix estimation, represents the true coherence value; since T is unknown, use to estimate the true coherence value ; therefore, the above formula is expressed as: (9) Solve using two estimators, and the two estimators are a quadratic loss estimator based on eigenvalue decomposition and a quadratic loss estimator based on the BFGS algorithm; First, expand Equation (8), perform the trace operation, and remove the terms that are irrelevant . Then, use the properties of the matrix inequality for scaling. Finally, utilize the positive definiteness of the Hadamard product to obtain: (10) where A is an arbitrary Hermitian matrix, the middle matrix , j represents the imaginary unit, ,..., represents the phase sequence to be estimated, N is the number of images, denotes the Hadamard product, and Tr represents the trace operation.

3. The high-dimensional phase link method based on prior knowledge regularization according to claim 2, wherein For the quadratic loss estimator based on eigen - decomposition, first, by introducing the condition: = 1, the unconstrained problem is transformed into a constrained problem; define the intermediate matrix , and transform the above - mentioned problem into a more concise form: (11) Among them, is the eigenvector corresponding to the minimum eigenvalue of the intermediate matrix ​ By performing Lagrangian function description and derivative operation on the above formula, convert the problem into an eigenvalue decomposition problem: (14) Among them, λ represents the Lagrange multiplier, and the solution of the above formula is the intermediate matrix The eigenvector corresponding to the minimum eigenvalue , and finally from the intermediate matrix The eigenvector corresponding to the minimum eigenvalue Extract the phase history .

4. The high-dimensional phase linking method based on prior knowledge regularization according to claim 3, characterized in that For the quadratic loss estimator based on BFGS, solve using the BFGS algorithm, and utilize the properties of matrix trace operation and the conjugate matrix symmetry property to rewrite and expand to obtain: (20) where the intermediate parameter a and the intermediate parameter b are represented by the following formula: ； where the subscript \(l\) and the subscript \(k\) respectively represent the row and column positions of the matrix elements, denotes the sum by element expansion, represents the interference phase, represents the interference phase reconstructed by phase optimization; Gradient of formula (20) / obtained in the following form: (21) Among them, represents the diagonal element of the regularized prior coherence matrix, represents the diagonal element of the true coherence value matrix, replaced by where n is the matrix element index; where: ； The calculated gradient is integrated into the BFGS optimization framework. After BFGS initialization, use the eigenvalue decomposition method to obtain the initial solution, and find the optimal solution as the optimal phase through an iterative manner; By means of a priori matrix The estimation of the time series phase of distributed scatterers is completed by a regularization coherent matrix estimation method and a low-sample quadratic loss metric phase link 5. The high-dimensional phase linking method based on prior knowledge regularization according to claim 1, wherein The said Step 3 includes: Under the null hypothesis the statistic of the Rao test is as follows: (22) where RST represents the Rao test, represents the n - order identity matrix, represents a sample set composed of p n - dimensional column vectors, represents the observed interference coherence matrix, E[ ] represents the expectation operation, and Tr represents the trace operation, represents the coherence matrix estimated under the condition that the hypothesis holds, where T represents the true coherence value matrix. When the number of samples is large, the statistic tends to follow a distribution with degrees of freedom of ; n is the number of images. Under the given significance level , the rejection region is determined through the threshold , that is: (23) Among them, represents the null hypothesis.

6. The high-dimensional phase linking method based on prior knowledge regularization according to claim 5, characterized in that If RST is greater than , it is determined that the phase triangle model cannot fit well, that is, it cannot be determined as a distributed scatterer point.

7. A high-dimensional phase link system based on prior knowledge regularization, characterized in that It includes the following modules: A matrix estimation module, which estimates the regularized coherence matrix based on the prior matrix, including: For each image pixel P, define an estimation window centered on the image pixel P, where pixels having the same statistical information as the image pixel P are identified; By performing the KS test on the amplitude data vectors of each image pixel within the search window and the image pixel P, at a given significance level, select all pixels within the search window that are statistically homogeneous with the image pixel P; Using the idea of clustering, pixels that pass the KS test and are connected to the image pixel P, pixels that pass the KS test and are not connected to the image pixel P, pixels that are homogeneously aggregated within the search window and are connected to the image pixel P, and pixels that are homogeneously clustered within the search window and are not connected to the image pixel P are grouped as samples, thereby calculating the sample coherence matrix, and the calculated sample correlation matrix is used as the prior matrix : （7） where H represents the Hermitian transpose, is the set of homogeneous pixels used in the prior matrix estimation; is the complex data vector of the i-th image pixel; For each image pixel P, an estimation window centered on the image pixel P is defined, and pixels having the same statistical information as the image pixel P are identified to estimate the initial coherence matrix ; In the new search window, by performing the KS test on the amplitude data vector of each image pixel, at a given significance level, select all image pixels within the search window that pass the KS test and are connected to P, i.e., homogeneous pixels; Based on the selected homogeneous pixels, calculate the initial coherence matrix using Equation (7). ; Using the prior matrix and the initial coherence matrix , substitute them into the following formula and obtain the final regularized coherence matrix through an iterative method: ； Among them, is the regularization weight, N is the number of images, K is the number of samples, is the complex data vector of the i-th image pixel, refers to the Hermitian transpose, t represents the number of iterations, and the initial coherence matrix used in the above formula is ; represents the sample correlation matrix obtained in the t-th iteration; represents the regularized coherence matrix obtained in the (t + 1)-th iteration; A phase linking module, which is a distributed scatterer phase estimator based on the quadratic loss metric, and solve the distributed scatterer phase estimator, derive a quadratic loss solution method based on eigenvalue decomposition and a quadratic loss solution method based on the BFGS algorithm to find the optimal phase, and realize low-sample quadratic loss metric phase linking; The inspection and discrimination module, aiming at the low-sample quadratic loss metric phase link, based on the statistical test method, probabilistically determines whether it belongs to the distributed scatterer points under the given significance level condition.

8. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the high-dimensional phase link method based on prior knowledge regularization according to any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the high-dimensional phase link method based on prior knowledge regularization according to any one of claims 1 to 6.

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