High-dimensional phase linking method and system based on priori knowledge regularization

Abstract

The invention provides a high-dimensional phase linking method and system based on priori knowledge regularization, and belongs to the technical field of radar remote sensing InSAR, and the method comprises the steps: estimating a regularized coherence matrix based on a priori matrix; a distributed scatterer phase estimator based on secondary loss measurement is obtained, the distributed scatterer phase estimator is solved, a secondary loss solving method based on characteristic decomposition and a secondary loss solving method based on a BFGS algorithm are deduced to find an optimal phase, and low-sample secondary loss measurement phase linkage is achieved. And for low-sample secondary loss measurement phase links, on the basis of a statistical test method, whether the low-sample secondary loss measurement phase links belong to distributed scatterer points or not is judged from probability statistics under a given significance level condition. According to the method, priori knowledge with practical significance is utilized, so that coherence matrix estimation is more accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of radar remote sensing InSAR, and in particular 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-based earth 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 acquired at different times in the same area to achieve high-precision, high-density measurement point extraction and analysis. This technology can detect small deformations of the surface over time, and the measurement accuracy can reach centimeters to millimeters. A key challenge of MT-InSAR technology is to extract meaningful information from the interferometric phase affected by atmospheric conditions, terrain and signal incoherence.

[0003] In order to solve the problem of signal decoherence and improve the quality of interference phase, domestic and foreign researchers have proposed the following technologies:

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

[0005] The typical DSI method includes 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, will seriously affect the accuracy of the phase sequence estimation. The sample coherence matrix (SCM) is a well-known and easy-to-implement coherence matrix (CM) estimation method, which 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-time series of SAR data, on the one hand, accurately estimating the sample coherence matrix requires multiple samples, and on the other hand, under the assumption of a stationary distribution of the image, it means that a larger local window is required 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, a low-sample high-dimensional estimation problem.

[0006] In order to solve this problem, under the premise of considering the matrix structure, the regularization idea provides an effective strategy to deal with the problem of coherence matrix estimation when the sample is insufficient. A large number of scholars have conducted relevant research. In particular, in recent studies, a class of linear shrinkage algorithms have been introduced and integrated into the robust coherence matrix estimator for complex elliptic symmetric (CES) distribution data. These algorithms are essentially completed by shrinking the estimation of the coherence matrix to 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 to the identity matrix. Y. Bai borrowed Ollila's method of regularized cone sample coherence matrix estimation to shrink the matrix to the identity matrix. C. Zhao borrowed the method of Ledoit regularized shrinkage estimator to shrink the coherence matrix with some elements to the same matrix. The above methods use the algorithm of matrix linear shrinkage based on the regularization idea to solve the problem of singular estimation of the coherence matrix caused by insufficient sample number. However, the above methods do not have a clear shrinkage direction during the matrix shrinkage process, but shrink towards the unit matrix; subsequently, Sun et al. proposed shrinking the sample coherence matrix to the prior matrix , as shown in formula (1), its idea is similar to the estimation through diagonal loading regularization, but no prior matrix is ​​given estimation method.

[0007] (1)

[0008] in, represents the optimal coherence matrix estimated by the iterative method, is the regularization weight, is the prior matrix, N is the number of images, K is the number of samples, is any positive definite matrix (the optimal coherence matrix is ​​found by iteration, which requires the input of initial values. The right side of the formula The first input of , which can generally be the identity matrix), is the complex data vector of the i-th image pixel, Refers to the Hermitian transpose, and t represents the number of iterations. In actual MT-InSAR processing, there are currently two ways to determine the prior matrix: :

[0009] (a) The prior matrix of the entire InSAR data stack Assume that the elements of the coherence matrix for:

[0010] (2)

[0011] in, ;

[0012] ;

[0013] ;

[0014] in, is the decorrelation caused by thermal noise and depends on the signal-to-noise ratio SNR, which is usually assumed to be a constant value. is caused by the different angles of incidence between the two radar paths. It is and The vertical baseline between the two images in the image, is the critical baseline. It is the result of physical mechanisms changing over time. It is The time baseline of the interferometer pair, is the decorrelation rate, and exp() represents the exponential function. The advantage of this method of determining the prior matrix is ​​that the calculation speed is fast because all image points use the same T. The disadvantage is that different T will inevitably be generated for different types of objects as the image spatial position changes.

[0015] (b) Classification prior matrix after dividing the image into blocks . First, classify the pixels on the image, such as using a clustering method, and then use the pixels belonging to the same category as samples, and estimate the coherence matrix respectively, which is used as the prior coherence estimate of the pixels belonging to this category. In actual processing, in order to save computer memory and improve processing speed and classification accuracy, the image is divided into blocks with overlapping areas, and the above process is processed according to image blocks. The advantage of this method is that it can take into account the characteristics of coherence characteristics that change with the type of terrain and has a faster calculation speed. The disadvantage is that when the differential phase is not stationary, for example, the most common non-stationarity in the SAR interferogram is the uncompensated rapidly changing interference phase in the spatial sample. Under this condition, the prior matrix The phase estimation accuracy is poor.

[0016] Phase Linking (PL) algorithms are statistical methods that combine multiple interferometric phases into a single equivalent single reference phase. Assuming 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 (PTA) algorithm. These optimized equivalent single reference phases of DS targets can be combined with PS in the traditional PSI processing framework. Accurate estimation of the linked phase is crucial to mitigate the decorrelation effect on SAR data. Therefore, since the introduction of the PL method by Guarnieri and Tebaldini et al., many studies have been conducted 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 coherence weight factors, which provides phase optimization flexibility by introducing coherence information. The CAESAR algorithm proposed by Fornaro et al. is a phase optimization method based on multiple scattering mechanism, which uses the eigenvalue decomposition (EVD) of the coherence matrix and can extract different scattering components. The MLE (EMI) algorithm based on EVD proposed by Ansari et al., which uses coherence information and is efficient in calculation and estimation. Ho Tong Minh and Ngo proposed a compression technique for PL estimation. The method is to divide a large amount of data into small stacks, compress the data and enhance the interference component of the noise-free short-time baseline. In general, the differences between the above PL algorithms can be attributed to the weight criteria adopted in each algorithm, which can be coherence-based, sparse-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 studies, Wang et al. proposed a new likelihood function as the objective function to estimate the phase. The algorithm uses the phase and the true matrix as unknowns at the same time, 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 this objective function form, so this method only provides an evaluation index for phase sequence estimation. Bai et al. implemented DS phase history estimation based on the idea of ​​flat coherence measurement. This method uses the Frobenius norm function as the objective function, but this method has no statistical significance and there is no corresponding statistical test method.

[0017] The following is a brief introduction to the maximum likelihood phase linking method:

[0018] Given N single-look complex (SLC) SAR images registered with repeated orbits, based on the central limit theorem, assuming that the normalized SAR data vector y follows zero mean and discrete matrix The probability density function (PDF) is:

[0019] (3)

[0020] in, represents the probability density function, det(.) represents the determinant operation, and the scattering characteristics of DS can be obtained by the discrete matrix Represents the discrete matrix It can be expressed using real coherence values ​​and real phase values:

[0021] (4)

[0022] Among them, the actual phase value ;

[0023] Where j represents the imaginary unit, T represents the real coherence value, represents the N estimated optimal phases.

[0024] ;

[0025] is the set of N optimal phases estimated from N(N-1) / 2 interference pairs. represents the true coherence amplitude value. The phase of any 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, such as Therefore, PL estimates N-1 optimal interference phases from N(N-1) / 2 phases.

[0026] Defining the coherence matrix ,in Represents the expected operation. Discrete matrix The maximum likelihood estimate of 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 needed to estimate In reality, T is unknown, so it is usually used represents T, surface

[0029] The estimated coherence matrix is ​​shown in Figure 2, so the above formula can be expressed as:

[0030] (6)

[0031] in, 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, there are two problems in the existing low-sample high-dimensional coherence matrix estimation methods: first, there is no clear shrinkage direction during the matrix shrinkage process, but it shrinks towards the unit matrix; second, effective prior knowledge is not 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 is only applicable to the case of sufficient samples. The most recent study 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 phase optimization method of the coherent weight factor proposed by Cao et al., and has no statistical significance and no corresponding statistical test method. Summary of the invention

[0034] In order to solve the above technical problems, the present invention provides a high-dimensional phase linking method and system based on prior knowledge regularization, which uses prior knowledge to calculate the prior matrix, and shrinks the coherence matrix to the prior matrix through a regularized shrinkage method, breaking the limitation of the traditional method of shrinking to the unit matrix. The introduced prior matrix provides a clear direction for shrinkage, which is more reasonable and has practical significance compared with shrinking to the unit matrix. In addition, for high-dimensional problems, the present invention proposes a low-sample-oriented quadratic loss metric phase linking method to supplement the existing phase linking method.

[0035] In order to achieve the above object, the present invention adopts the following technical solution:

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

[0037] Step 1, estimating a regularized coherence matrix based on a priori matrix;

[0038] Step 2: A distributed scatterer phase estimator based on quadratic loss metric is solved, and a quadratic loss solution method based on eigendecomposition and a quadratic loss solution method based on the BFGS algorithm are derived to find the optimal phase, thus realizing 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, under the condition of a given significance level, determine whether it belongs to a distributed scatterer point.

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

[0041] A matrix estimation module estimates the regularized coherence matrix based on the prior matrix;

[0042] Phase linking module, distributed scatterer phase estimator based on quadratic loss metric, and solves the distributed scatterer phase estimator, derives the quadratic loss solution method based on eigendecomposition and the quadratic loss solution method based on BFGS algorithm to find the optimal phase, and realizes low sample quadratic loss metric phase linking;

[0043] The test and discrimination module provides a statistical test method for the low sample quadratic loss metric phase link, and determines whether it belongs to a distributed scatterer point from a probability perspective under a given significance level.

[0044] The present invention also discloses an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the high-dimensional phase linking 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 a processor, the steps of the high-dimensional phase linking method based on prior knowledge regularization are implemented.

[0046] The latest and closest existing technology 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," inIEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-15, 2023,Art no. 5221215, doi: 10.1109 / TGRS.2023.3330971.). This article aims at the low-sample high-dimensional problem, estimates the coherence matrix using a regularized tapered sample coherence matrix estimator (ie, Tabasco), 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-mentioned article, the prior knowledge regularized coherence matrix estimation method proposed in the present invention utilizes the prior knowledge with practical significance, so that the coherence matrix estimation is more accurate;

[0048] 2. Compared with the phase link method based on the F-norm as the objective function, the low-sample quadratic loss metric phase link proposed in the present invention has statistical significance and corresponding statistical test methods. The low-sample quadratic loss metric phase link can be tested by R score, and given the significance level, the possibility of belonging to the DS point can be judged from the probability. The phase link method based on the F-norm as the objective function is essentially similar to the method of phase optimization of the coherent 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 flow chart of the high-dimensional phase linking method based on prior knowledge regularization of the present invention;

[0050] Figure 2 Select a schematic diagram for homogeneous pixels;

[0051] Figure 3a It is a schematic diagram of the comparison of RMSE values ​​of the trace normalized coherence matrix estimation method;

[0052] Figure 3b This is a schematic diagram for comparing the RMSE values ​​of the identity matrix regularization coherence matrix estimation method;

[0053] Figure 3c This is a schematic diagram of comparing RMSE values ​​of coherence matrix estimation of the present invention;

[0054] Figure 3d This is a schematic diagram of the comparison of RMSE values ​​of the Tabasco method;

[0055] Figure 4 Schematic diagram for comparing different phase linking methods. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended 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] like Figure 1 As shown, the high-dimensional phase linking method based on prior knowledge regularization in an embodiment of the present invention includes the following steps:

[0058] Step 1: Estimating the regularized coherence matrix based on the prior matrix, including:

[0059] Step 1.1: For each image pixel P, define an estimation window centered at the image pixel P, where pixels with the same statistical information as the image pixel P are identified. Figure 2 As shown in the figure, the black solid line box indicates the range of the search window. It is recommended to select twice the number of images as the window size; for example, for 50 SAR images, select a 10×10 size range as the search window.

[0060] Step 1.2: Perform a KS test on the amplitude data vector of each image pixel and pixel P in the search window, and select all pixels in the search window that are statistically homogeneous with the image pixel P at a given significance level (generally the significance level is set to 0.05). Figure 2 As shown in the figure, the black dotted box represents the window of the KS test. The size of the KS test window is generally much smaller than the search window. Therefore, four types of pixels can be detected within the search window. The first type is the pixels that pass the KS test and are connected to P ( Figure 2 The second category is pixels that pass the KS test and are not connected to P ( Figure 2 The third category is pixels that are homogeneously clustered within the search window and connected to P ( Figure 2 The fourth category is pixels that are homogeneously clustered within the search window and are not connected to P ( Figure 2 medium-dark grid pixels).

[0061] Step 1.3: Based on the similarity of properties of adjacent homogeneous pixels, the idea of ​​clustering is used to group the above four types of pixels as sufficient samples to calculate the sample coherence matrix. The calculated sample correlation matrix C is used as the prior matrix .

[0062] (7)

[0063] Where H represents the Hermitian transpose, is the set of SHPs (homogeneous pixels) used in 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 pixels with the same statistical information as the image pixel P to estimate the initial coherence matrix To ensure the purity of homogeneous pixels, the search window should be smaller than the estimated window in step 1.1. For example, the number of images can be selected as the new window size.

[0065] Step 1.5: In the new window, by performing a 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 pixels in the search window that are statistically homogeneous with the image pixel P, i.e., homogeneous pixels. To ensure the accuracy of the selection of homogeneous pixels, discard the pixels in the window that pass the KS test but are not connected to the image pixel P (i.e., only keep the pixels in the search window that are statistically homogeneous with the image pixel P). Figure 2 ).

[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: The prior matrix and the initial coherence matrix Substitute into the following formula and obtain the final coherence matrix through iteration: .

[0068] ;

[0069] Step 2: Based on the regularized coherence matrix in step 1, low sample quadratic loss metric phase linking is performed, including:

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

[0071] (8)

[0072] in, It includes phase of is a diagonal matrix of order n, I is the identity matrix of order n, represents the quadratic loss metric minimization operation, represents the final coherence matrix observed in step 1, represents the true coherence value; since is unknown, which is consistent with the MLE (maximum likelihood estimation) method. Estimate the true coherence value ; Therefore, the above formula can be expressed as:

[0073] (9)

[0074] The above problem belongs to a nonlinear optimization problem, and two estimators are proposed to solve it: a quadratic loss estimator based on eigendecomposition and a 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 cost of both solvers is very low.

[0075] First, Expand and get , then take the trace operation Tr and remove the Irrelevant items ,get:

[0076] ;

[0077] Using matrix inequalities Scaling the first term yields:

[0078] ;

[0079] Where A is an arbitrary Hermitian matrix.

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

[0081] (10)

[0082] Among them, the intermediate matrix , 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 eigendecomposition: In order to effectively solve (10), we first introduce the condition: = 1, transforming the unconstrained problem into a constrained problem. In addition, define the intermediate matrix , transforming the above problem into a more concise form:

[0084] (11)

[0085] in, is the intermediate matrix The eigenvector corresponding to the smallest eigenvalue.

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

[0087] (12)

[0088] Where λ represents the Lagrange multiplier, which is set by The gradient of is zero, so:

[0089] (13)

[0090] The above formula is equivalent to the characteristic decomposition problem:

[0091] (14)

[0092] untie is the intermediate matrix The eigenvector corresponding to the minimum eigenvalue is finally obtained from Extracting phase history from .

[0093] 2) BFGS-based quadratic loss estimator: Equation (10) can also be solved using the BFGS algorithm. First, use and Will Rewritten as:

[0094] (15)

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

[0096] Expand to get:

[0097] (16)

[0098] Among them, the subscripts l, k, n, and m represent the row and column positions of the matrix elements respectively. It means to expand and sum by elements. represents the interference phase of the elements in the kth row and the lth column, represents the interference phase of the element in the mth row and nth column, represents the interferometric phase reconstructed by phase optimization.

[0099] Using the symmetric properties of transpose and conjugate matrices: , merge the same type to get:

[0100] (17)

[0101] Finally, we can use the symmetry property again:

[0102] (18)

[0103] Similarly:

[0104] (19)

[0105] The subscripts l and k represent the row and column positions of the matrix elements, respectively. It means to expand and sum by elements. represents the interference phase, represents the interferometric phase reconstructed by phase optimization, represents the final coherence matrix observed in step 1, represents the true coherence value;

[0106] So we get:

[0107] (20)

[0108] in, represents the optimal phase, It is about the optimal phase expression.

[0109] Among them, the intermediate parameters a and b are expressed by the following formula:

[0110] ;

[0111] ;

[0112] gradient / It can be obtained in the following forms:

[0113] (twenty one)

[0114] in, denotes the diagonal elements of the regularized prior coherence matrix, Denote the diagonal elements of the true coherence value matrix, and use Instead, n is the matrix element index;

[0115] in, ;

[0116] The calculated gradients are integrated into the BFGS optimization framework. BFGS requires initialization, uses the eigendecomposition method to obtain the initial solution, and finds the optimal solution as the optimal phase through iteration.

[0117] Through the prior matrix The regularized coherence matrix estimation method and low sample quadratic loss metric phase link are used to complete the phase estimation of distributed scatterer time series.

[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 link in step 2, including:

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

[0120] (twenty two)

[0121] in, represents the real coherence matrix, represents the coherence matrix estimated under the assumption that the hypothesis is true, RST represents the Rao test, represents the n-order identity matrix; represents a sample set consisting of p n-dimensional column vectors, represents the observed interference correlation matrix, E[ ] represents the expected operation, represents the coherence matrix estimated under the assumption that When Tends to obey the freedom of distribution, n is the number of images. Therefore, given a significant level Under these conditions, the threshold Determine the rejection region ,Right now:

[0122] (twenty three)

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

[0124] There are many methods for estimating low-sample high-dimensional matrices, and the purpose is to shrink the estimation of the coherence matrix to a better-conditioned target matrix. For example, Abramovich borrowed the idea of ​​Ledoit diagonal loading and proposed a regularized Taylor estimator that shrinks to the unit matrix. Y. Bai borrowed Ollila's method of regularized conical sample coherence matrix estimation to shrink the matrix to the unit matrix. C. Zhao borrowed the method of Ledoit regularized shrinkage estimator to shrink the coherence matrix with partial elements to the same matrix. E. Ollila et al. proposed the Tabasco method to complete matrix shrinkage.

[0125] Similarly, there are many known phase linking methods. For example, SqueeSAR technology is an example of a PL method using the phase triangulation (PTA) algorithm. Cao et al. proposed a method of equal weight and coherent weight factor phase optimization, which provides phase optimization flexibility by introducing coherence information. The CAESAR algorithm proposed by Fornaro et al. is a phase optimization method based on the multiple scattering mechanism, which uses the eigenvalue decomposition (EVD) of the coherence matrix and can extract different scattering components. The MLE (EMI) algorithm based on EVD proposed by Ansari et al. uses coherence information to be efficient in calculation and estimation. Ho Tong Minh and Ngo proposed a compression technique for PL estimation. The method is to divide a large amount of data into small stacks, compress the data to enhance the interference component of the noise-free short-time baseline.

[0126] For coherence matrix estimation, the prior matrix regularization coherence matrix estimation method of the present invention ( Figure 3c ) and 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 ) were compared; 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] like Figure 4As shown, for the phase linking method: through simulation experiments, the phase linking method of the quadratic loss metric of the present invention is compared with the SqueeSAR method, the LaMLE method, and the coherent weight method; the results show that the phase linking method based on the quadratic loss metric of the eigendecomposition has similar effects to the LaMLE method, while the phase linking method based on the quadratic loss metric of 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 means "Cramér-Rao Lower Bound". 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 link system based on prior knowledge regularization, comprising the following modules:

[0129] A matrix estimation module estimates the regularized coherence matrix based on the prior matrix;

[0130] Phase linking module, distributed scatterer phase estimator based on quadratic loss metric, and solves the distributed scatterer phase estimator, derives the quadratic loss solution method based on eigendecomposition and the quadratic loss solution method based on BFGS algorithm to find the optimal phase, and realizes low sample quadratic loss metric phase linking;

[0131] The test and discrimination module provides a statistical test method for the low sample quadratic loss metric phase link, and determines whether it belongs to a distributed scatterer point from a probability perspective under a given significance level.

[0132] The present invention also discloses an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the 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. When the computer program is executed by a processor, the steps of the high-dimensional phase linking method based on prior knowledge regularization are implemented.

[0134] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The schemes in the embodiments of the present invention may be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0135] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes 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 a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0136] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0137] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0138] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted 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 changes and modifications 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 equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A high-dimensional phase linking method based on prior knowledge regularization, characterized in that: The steps include: Step 1, estimating a regularized coherence matrix based on a priori matrix; Step 2: A distributed scatterer phase estimator based on quadratic loss metric is solved, and a quadratic loss solution method based on eigendecomposition and a quadratic loss solution method based on the BFGS algorithm are derived to find the optimal phase, thus realizing low-sample quadratic loss metric phase linking; Step 3: For the low sample quadratic loss metric phase link, based on the statistical test method, under the condition of a given significance level, determine whether it belongs to a distributed scatterer point.

2. The high-dimensional phase linking method based on prior knowledge regularization according to claim 1, characterized in that: The step 1 comprises: Step 1.1: For each image pixel P, define an estimation window centered at the image pixel P, where pixels with the same statistical information as the image pixel P are identified; Step 1.2: By performing a KS test on the amplitude data vector of each image pixel in the search window and the image pixel P, all pixels in the search window that are statistically homogeneous with the image pixel P are selected at a given significance level; Step 1.3: Using the clustering idea, 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 clustered in the search window and are connected to the image pixel P, and the pixels that are homogeneously clustered in the search window and are not connected to the image pixel P are grouped as samples to calculate the sample coherence matrix. As a priori matrix : (7) Where H represents the Hermitian transpose, is the set of homogeneous pixels used in the estimation of the prior matrix; 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 pixels with the same statistical information as the image pixel P to estimate the initial coherence matrix ; Step 1.5: In the new search window, by performing a KS test on the amplitude data vector of each image pixel, at a given significance level, select all image pixels in 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 formula (7): ; Step 1.7: Using the Prior Matrix and the initial coherence matrix , substitute into the following formula, and obtain the final regularized coherence matrix through iteration: ； in, 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 at the tth iteration; represents the regularized coherence matrix obtained at the t+1th iteration.

3. The high-dimensional phase linking method based on prior knowledge regularization according to claim 2, characterized in that: The step 2 comprises: The optimal phase estimate is obtained by using a distributed scatterer phase estimator based on a quadratic loss metric for: (8) in, It includes phase The diagonal matrix of , I is the identity matrix, represents the quadratic loss metric minimization operation, represents the regularized coherence matrix estimated based on the prior matrix, represents the true coherence value; since T is unknown, use Estimate the true coherence value ; Therefore, the above formula is expressed as: (9) Two estimators are used to solve the problem, namely, a quadratic loss estimator based on eigendecomposition and a quadratic loss estimator based on the BFGS algorithm. First, expand equation (8) and perform trace calculation to remove Irrelevant items , using the matrix inequality The properties of are scaled, and finally the positive definiteness of the Hadamard product is used to obtain: (10) Where A is an arbitrary Hermitian matrix, the intermediate matrix , j represents the imaginary unit, [ ,..., ] represents the phase sequence to be estimated, N is the number of images, represents the Hadamard product.

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 eigendecomposition, we first introduce the condition: =1, transform the unconstrained problem into a constrained problem; define the intermediate matrix , transforming the above problem into a more concise form: (11) in, is the intermediate matrix The eigenvector corresponding to the minimum eigenvalue; By describing the above equation with Lagrangian function and performing derivative operation, the problem is converted into a characteristic 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 Extracting phase history from .

5. The high-dimensional phase linking method based on prior knowledge regularization according to claim 3, characterized in that: For the BFGS-based quadratic loss estimator, the BFGS algorithm is used to solve it. Using the properties of matrix trace operations and the symmetric properties of conjugate matrices, it is rewritten and expanded to obtain: (20) Among them, the intermediate parameter a and the intermediate parameter b are expressed by the following formula: ； Among them, subscript l and subscript k represent the row and column positions of matrix elements respectively. It means to expand and sum by elements. represents the interference phase, represents the interferometric phase reconstructed by phase optimization; The gradient of formula (20) / Obtained through: (21) in, denotes the diagonal elements of the regularized prior coherence matrix, Denote the diagonal elements of the true coherence value matrix, and use Instead, n is the matrix element index; in: ； The calculated gradients are integrated into the BFGS optimization framework. After BFGS initialization, the eigendecomposition method is used to obtain the initial solution, and the optimal solution is found as the optimal phase through iteration; Through the prior matrix The regularized coherence matrix estimation method and low sample quadratic loss metric phase link are used to complete the phase estimation of distributed scatterer time series.

6. The high-dimensional phase linking method based on prior knowledge regularization according to claim 1, characterized in that: The step 3 comprises: In the null hypothesis Under the condition that , the statistic of Rao test is: (22) Where RST stands for Rao test, represents the n-th order identity matrix, represents a sample set consisting of p n-dimensional column vectors, represents the observed interference coherence matrix, E[ ] represents the expected operation, represents the coherence matrix estimated under the assumption that the coherence matrix is ​​established, where T represents the true coherence value matrix. When Tends to obey the freedom of distribution, n is the number of images; at a given significance level Under the condition, through the threshold Determine the rejection region ,Right now: (23)。 7. The high-dimensional phase linking method based on prior knowledge regularization according to claim 6, characterized in that: If RST is greater than , it is determined that the phase triangle model cannot be well fitted, that is, it cannot be determined as a distributed scatterer point.

8. A high-dimensional phase link system based on prior knowledge regularization, characterized in that: Includes the following modules: A matrix estimation module estimates the regularized coherence matrix based on the prior matrix; Phase linking module, distributed scatterer phase estimator based on quadratic loss metric, and solves the distributed scatterer phase estimator, derives the quadratic loss solution method based on eigendecomposition and the quadratic loss solution method based on BFGS algorithm to find the optimal phase, and realizes low sample quadratic loss metric phase linking; The test and discrimination module measures the phase link for low sample quadratic loss and, based on the statistical test method, probabilistically determines whether it belongs to a distributed scatterer point under a given significance level.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the high-dimensional phase linking method based on prior knowledge regularization as described in any one of claims 1 to 7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the high-dimensional phase linking method based on prior knowledge regularization as claimed in any one of claims 1 to 7 are implemented.

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