A three-dimensional space-time phase unwrapping method and system for GB-InSAR

Abstract

The present invention discloses a three-dimensional space-time phase unwrapping method and system for GB-InSAR. The method first combines interference image pairs and interference image groups on multiple radar images, then uses a triangulated network to connect the pixel points in the interference image pairs, establishes a space-dimensional equation group based on any triangle in the triangulated network, and establishes a time-dimensional equation group based on each edge of the triangle in the interference image group. Then, the space-dimensional equation group and the time-dimensional equation group are converted into a simultaneous linear equation group, and the phase ambiguity is solved with the simultaneous linear equation group as a constraint to complete phase unwrapping accurately and efficiently.

Description

Technical Field

[0001] The present invention relates to the technical field of synthetic aperture radar, and in particular to a three-dimensional space-time phase unwrapping method and system for GB-InSAR. Background Art

[0002] In 2020, a total of 7,840 geological disasters occurred across China, including 4,810 landslides, 1,797 collapses, and 899 debris flows. Landslides are the most frequent type of geological disaster, and monitoring and early warning are crucial for disaster prevention and mitigation. GB-InSAR (Ground-Based Interferometric Synthetic Aperture Radar) has been widely used in surface deformation monitoring, offering non-contact, all-weather, high-precision, and near-real-time measurement capabilities.

[0003] Ground-based SAR typically uses differential interferometry, a technique that uses phase information to measure deformation by performing differential interferometry on complex SAR images acquired at the same location but at different times. Due to the periodicity of the complex phase, the interferometric phase pattern is entangled, requiring phase unwrapping—recovering the true phase value—to further measure deformation.

[0004] Typical phase unwrapping algorithms can be summarized into three categories: the first is path integral-based phase unwrapping, such as the branch-cut method and the mass map method; the second is minimum norm-based phase unwrapping, such as the least squares method; and the third is network planning-based phase unwrapping, such as the minimum cost flow algorithm. In the field of GB-InSAR, the minimum cost flow algorithm is widely used. This algorithm is a two-dimensional spatial unwrapping algorithm suitable for unwrapping a large number of non-uniformly distributed pixels in a single interferometric phase image.

[0005] Three-dimensional phase unwrapping is suitable for simultaneously unwrapping multiple interferometric phase patterns, including two-dimensional unwrapping in the spatial dimension and one-dimensional unwrapping in the temporal dimension. Compared to two-dimensional unwrapping algorithms, three-dimensional phase unwrapping algorithms must consider not only spatial constraints but also temporal constraints to improve phase unwrapping accuracy. Summary of the Invention

[0006] In view of this, the present invention provides a three-dimensional space-time phase unwrapping method and system for GB-InSAR, which can achieve accurate unwrapping of multiple GB-InSAR interferometric phase images.

[0007] The specific technical solutions adopted in the present invention are as follows:

[0008] A three-dimensional space-time phase unwrapping method for GB-InSAR, comprising:

[0009] Step 1: Obtaining a GB-InSAR interferometric phase map and an interferometric image group; wherein the interferometric image group includes at least three interferometric phase maps;

[0010] Step 2: Connecting the pixels in the interference phase image using a triangulated network, establishing a spatial dimensional equation group based on the triangles in the triangulated network; and establishing a time dimensional equation group based on each side of the triangle in the interference image group;

[0011] Step 3: Combine the spatial dimension equation group and the time dimension equation group to obtain a simultaneous linear equation group, and solve the phase ambiguity using the simultaneous linear equation group as a constraint to complete phase unwrapping.

[0012] Furthermore, in the step 2, the establishing of the spatial dimensional equation group based on the triangles in the triangulated network is as follows: first establishing a spatial dimensional equation based on the three pixel points P1, P2 and P3 of the triangle in the interference phase image, and then linking multiple spatial dimensional equations to form the spatial dimensional equation group;

[0013] Take any two radar images and record them as Q1 and Q2, perform complex phase interference on Q1 and Q2 to obtain the interference phase map I 1-2 , perform differential operation on Q1 and Q2 to obtain the differential phase diagram D 1-2 ;

[0014] According to the relationship between the second-order differential phases of the three pixel points P1, P2 and P3 The spatial dimension equation is obtained as:

[0015]

[0016] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P2 and P3 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P3 1-2 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P2 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in .

[0017] Furthermore, in the step 2, the step of establishing a time-dimensional equation group based on each side of the triangle in the interference image group is as follows: first establishing a time-dimensional equation based on any two pixel points in the interference phase image, and then combining multiple time-dimensional equations to obtain the time-dimensional equation group;

[0018] According to the relationship between the second-order differential phases of the three differential phase images of any two pixel points P1 and P2 in one interference image group, The time dimension equation is obtained as:

[0019]

[0020] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 2-3 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 1-3 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 2-3 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 1-3 The relationship coefficient in Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in .

[0021] Furthermore, in the step three, the phase ambiguity is solved with the simultaneous linear equations as a constraint as follows: with the simultaneous linear equations as a constraint, the phase ambiguity is solved so that the sum of the absolute values ​​of the phase ambiguity vectors is minimized.

[0022] A three-dimensional space-time phase unwrapping system for GB-InSAR, comprising: an interferometric phase image acquisition module, an equation establishment module, and a phase ambiguity resolution module;

[0023] The interferometric phase image acquisition module is used to acquire the interferometric phase image and the interferometric image group of GB-InSAR; wherein the interferometric image group includes at least three interferometric phase images;

[0024] The equation building module includes a space-dimensional equation unit and a time-dimensional equation unit; the space-dimensional equation unit is used to establish a space-dimensional equation group based on the triangles in the triangulated network; the time-dimensional equation unit is used to establish a time-dimensional equation group based on each side of the triangle; the triangulated network is used to connect the pixel points in the interference phase map;

[0025] The phase ambiguity solving module is used to simultaneously obtain a set of simultaneous linear equations by combining the spatial dimensional equation group and the time dimensional equation group established by the equation establishing module, and solve the phase ambiguity using the set of simultaneous linear equations as a constraint to complete phase unwrapping.

[0026] Furthermore, in the equation establishment module, establishing the spatial dimensional equation group based on the triangles in the triangulated network is as follows: first establishing a spatial dimensional equation based on the three pixel points P1, P2 and P3 of the triangle in the interference phase image, and then linking multiple spatial dimensional equations to form the spatial dimensional equation group;

[0027] Take any two radar images and record them as Q1 and Q2, perform complex phase interference on Q1 and Q2 to obtain the interference phase map I 1-2 , perform differential operation on Q1 and Q2 to obtain the differential phase diagram D 1-2 ;

[0028] According to the relationship between the second-order differential phases of the three pixel points P1, P2 and P3 The spatial dimension equation is obtained as:

[0029]

[0030] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P2 and P3 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P3 1-2 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P2 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in .

[0031] Furthermore, in the equation building module, the time dimension equation group is established according to each side of the triangle in the interference image group by first establishing a time dimension equation according to any two pixel points in the interference phase image, and then combining multiple time dimension equations to obtain the time dimension equation group;

[0032] According to the relationship between the second-order differential phases of the three differential phase images of any two pixel points P1 and P2 in one interference image group, The time dimension equation is obtained as:

[0033]

[0034] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 2-3 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 1-3 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 2-3 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 1-3 The relationship coefficient in Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in .

[0035] Furthermore, in the phase ambiguity solving module, solving the phase ambiguity with the simultaneous linear equations as a constraint is: using the simultaneous linear equations as a constraint, solving the phase ambiguity so that the sum of the absolute values ​​of the phase ambiguity vectors is minimized.

[0036] Beneficial effects:

[0037] (1) A three-dimensional space-time phase unwrapping method for GB-InSAR uses a triangulated network to connect the pixel points in the interferometric phase image, and establishes a space-dimensional equation group based on the triangles in the triangulated network, and establishes a time-dimensional equation group based on each edge of the triangle. The three-dimensional space-time phase unwrapping problem is transformed into an optimization problem under the constraints of a set of simultaneous linear equations. Compared with the conventional two-dimensional phase unwrapping method that does not consider the constraints of the time dimension, the present invention can effectively improve the accuracy of phase unwrapping.

[0038] (2) A time dimension equation group is established based on each edge of the triangle in the interference image group. Compared with the traditional method of establishing time dimension equations based on pixels, establishing time dimension equations based on edges can more comprehensively and fully consider the constraints of the time dimension, further improving the accuracy of the final phase unwrapping of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of a three-dimensional space-time phase unwrapping method for GB-InSAR of the present invention.

[0040] Figure 2 Schematic diagram of pixel points and triangulated network structure according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0041] A three-dimensional space-time phase unwrapping method and system for GB-InSAR first combines multiple radar images into interferometric image pairs and interferometric image groups, then uses a triangulated network to connect the pixels in the interferometric image pairs, establishes a space-dimensional equation group based on any triangle in the triangulated network, and establishes a time-dimensional equation group based on each edge of the triangle in the interferometric image group. Then, the space-dimensional equation group and the time-dimensional equation group are converted into a simultaneous linear equation group, and the phase ambiguity is solved using the simultaneous linear equation group as a constraint to complete phase unwrapping accurately and efficiently.

[0042] The present invention is described in detail below with reference to the accompanying drawings and examples. In this example, the number of phase images, interferometric phase images, differential phase images, and pixels involved are illustrative and are not limited to the numbers shown. During implementation, those skilled in the art can adjust these numbers based on actual circumstances. Similarly, adjustments to these numbers can also alter the number of equations obtained, including the number of spatial and temporal equations, and are not listed here.

[0043] A three-dimensional space-time phase unwrapping method for GB-InSAR, such as Figure 1 As shown, the following steps are included:

[0044] Step 1: Obtain interference image pairs and interference image groups.

[0045] Specifically, the interferometric phase map and interferometric image group of GB-InSAR are obtained; wherein the interferometric image group includes at least three interferometric phase maps. Interferometric image pairs and interferometric image groups are divided according to N radar images, and two radar images are randomly selected from the N radar images to form an interferometric image pair. The total number of interferometric image pairs is N. IP = N(N-1) / 2; randomly select three radar images from N radar images to form an interference image group. The total number of interference image groups is N IG= N(N-1)(N-2) / 6. Each interferometric image pair contains two radar images, and two radar images can generate an interferometric phase map. An interferometric image group includes at least three radar images, and three interferometric phase maps can be obtained by combining two of the three radar images.

[0046] Taking N=4 as an example, we can get 6 interference pairs and 4 interference groups. Each interference pair corresponds to an interference phase diagram, including I 1-2 , I 1-3 , I 1-4 , I 2-3 , I 2-4 and I 3-4 The 4 intervention groups included I 1-2-3 , I 1-2-4 , I 1-3-4 and I 2-3-4 , each interference group includes 3 interference phase images, such as I 1-2-3 Including I 1-2 , I 1-3 and I 2-3 .

[0047] Step 2: Use a triangulated network to connect the pixel points in the interference phase image, and establish a space-dimensional equation group based on any triangle in the triangulated network; establish a time-dimensional equation group based on each edge of the triangle in the interference image group.

[0048] In order to clearly demonstrate the establishment of pixel points, interference phase map, differential phase map, and space dimension equations and time dimension equations, the present invention uses an example to illustrate: take any two radar images and record them as Q1 and Q2, perform complex phase interference on Q1 and Q2 to obtain the interference phase map I 1-2 , perform differential operation on Q1 and Q2 to obtain the differential phase diagram D 1-2 .

[0049] Establish the space-dimensional equation system:

[0050] The spatial dimensional equation group is established based on any triangle in the triangulation network as follows: firstly, a spatial dimensional equation is established based on the three pixel points P1, P2 and P3 of the triangle, and then multiple spatial dimensional equations are combined to form a spatial dimensional equation group.

[0051] According to the relationship between the second-order differential phases of the three pixel points P1, P2 and P3 The spatial dimension equation is obtained as:

[0052]

[0053] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P2 and P3 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P3 1-2 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P2 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in .

[0054] The multiple space-dimensional equations obtained from multiple triangles are connected to form a space-dimensional equation group:

[0055]

[0056] in, It is a T×R-dimensional spatial coefficient matrix, with only three non-zero elements in each row. The pixel point in the interference phase image I 1-2 The R×1-dimensional column vector to be solved, composed of the relationship coefficients in It is a T×1-dimensional column vector, where T represents the number of triangles and R represents the number of non-repeated edges in the T triangles.

[0057] Assume there are two phase images M1 and M2, and the value of each pixel in the image is the true phase. Assume that in M1, the true phase of pixel P1 is The winding phase is in is an integer, and Wrap[] represents the phase wrapping operation. Difference is performed on these two phase images to obtain the differential phase image D 1-2 .use Represents the true phase difference of P1 in images M1 and M2. Perform complex phase interference on these two phase images to obtain the interference phase image I 1-2 .use Indicates that P1 is in I 1-2 The interference phase in

[0058] For pixels P1 and P2, represents the true phase difference between P1 and P2 in image M1, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , In the interference phase diagram I 1-2 In the figure, the interference phase of P1 and P2 is defined as Satisfy the relationship is an integer, indicating that P1 and P2 are in the interference phase diagram I 1-2 The phase ambiguity in .

[0059] The derivation process of the spatial dimensional equation is as follows: For three pixel points P1, P2 and P3, Eq. It is always established, and we can get:

[0060]

[0061]

[0062] in, Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in . Equation (2) is an equation based on a single interferometric phase image and consists of three pixels. It represents the spatial constraint condition and is defined as the spatial constraint equation.

[0063] Assume that there are n pixels distributed in the interference pattern I 1-2 In the above example, we first construct a Delaunay triangulation. For each triangle’s three vertices, we can construct an equation similar to equation (2). The unknown quantity to be solved in the equation is the fuzziness of each edge. Then, we combine all the equations to form a linear system of equations.

[0064]

[0065] Assuming that n pixels can form T triangles, including R non-repeated edges, then It is a T×R dimensional matrix with only three non-zero elements in each row. is the R×1-dimensional column vector to be solved, is a T×1-dimensional column vector. Figure 2 For example, the five pixels P1-P5 in the figure form three triangles T 123 、T 135 and T 345 , 7 edges S 12 、S 13 、S 15 、S 23 、S 34 、S 35 and S 45 The equation group (3) can be expressed as

[0066]

[0067] Establish the time-dimensional equation system:

[0068] The time dimension equation group is established according to each side of the triangle in the interference image group as follows: first, multiple time dimension equations are established according to any two pixel points in the interference phase image, and then the multiple time dimension equations are combined to obtain the time dimension equation group.

[0069] According to the relationship between the second-order differential phases of the three differential phase images of any two pixel points P1 and P2 in an interference image group The time dimension equation is obtained as:

[0070]

[0071] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 2-3 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 1-3 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 2-3 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 1-3 The relationship coefficient in Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in .

[0072] The time dimension equations obtained by combining multiple time dimension equations are:

[0073]

[0074] in, It is an R×3R dimensional matrix, with only three non-zero elements in each row. is the 3R×1 dimensional column vector to be solved, It is an R×1-dimensional column vector, where R represents the number of non-repeated edges in the triangle, that is, the number of time-dimensional equations.

[0075] The derivation process of the time dimension equations is as follows: Assume that there are three phase diagrams M1, M2 and M3, and perform differential analysis on these three phase diagrams to obtain three differential phase diagrams D 1-2 、D 1-3 and D 2-3Perform complex phase interference on these three phase images to obtain three interference phase images I 1-2 , I 2-3 and I 1-3 For pixels P1 and P2, the equation It is always established, and we can further get:

[0076]

[0077]

[0078] in, Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in . Equation (6) is an equation based on three interferometric phase images and consists of two pixels. It represents the time constraint condition and is defined as the time constraint equation.

[0079] For the three interference phase images I 1-2 , I 2-3 and I 1-3 , the Delaunay triangulation constructed by each pixel point is completely consistent. According to the Delaunay triangulation constructed by n pixel points, including T triangles and R non-repeated edges, then referring to formula (6), R equations can be constructed. There are 3R unknown quantities to be solved in the equations, which are the fuzziness on each edge. Then all the equations are combined to form a linear equation system.

[0080]

[0081] in, It is an R×3R dimensional matrix, with only three non-zero elements in each row. is the 3R×1 dimensional column vector to be solved, is an R×1-dimensional column vector.

[0082] by Figure 2 For example, there are 7 edges S in the triangulation network. 12 、S 13 、S 15 、S 23 、S 34 、S 35 and S 45 , the equation group (7) consists of 7 equations, and there are 21 unknown parameters to be solved, which can be expressed as

[0083]

[0084] in, and They are all 7×1 column vectors, representing the phase ambiguity vectors of the 7 edges in the three interferograms, and together they form

[0085] Step 3: Simultaneously obtain a set of simultaneous linear equations by combining the spatial and temporal equations. Solve the phase ambiguity using the set of simultaneous linear equations as constraints to complete phase unwrapping.

[0086] Among them, for the three interference phase images I 1-2 , I 2-3 and I 1-3 According to the spatial constraint equation shown in formula (2) and the time constraint equation shown in formula (6), four linear equations can be established. That is, the simultaneous linear equations obtained by the simultaneous spatial equations and the time equations are:

[0087]

[0088] Among them, the spatial dimension coefficient matrix and are exactly the same, both representing T×R-dimensional spatial coefficient matrices, is the 3R×1-dimensional column vector to be solved; is and constitute, and Represents the pixel points in the interference phase image I 1-2 , I 1-3 and I 2-3 The R×1-dimensional column vector to be solved, consisting of the relationship coefficients in ; and are all T×1-dimensional column vectors, It is an R×1-dimensional column vector, where T represents the number of triangles and R represents the number of non-repeated edges in the T triangles.

[0089] Since the pixels in the three interference images are consistent, they form the same Delaunay triangulation, and the spatial dimension matrix and Exactly the same, expressed as Time dimension vector to be solved is and Therefore, the four equations can be combined:

[0090]

[0091] Among them, 1 R×R Represents an R×R-dimensional identity matrix with only 1s on the diagonal and 0s on the off-diagonal. T×R is a T×R dimensional all-zero matrix.

[0092] The above process is only illustrated by 3 interferometric phase images, but in actual process there will be many interferometric phase images, and the number of corresponding equations will be greater. If there are N radar images, any two of them are selected to form an interferometric image pair, and the total number of interferometric pairs is N. IP = N(N-1) / 2, randomly select three images to form an interference image group, the total number of interference groups is N IG =N(N-1)(N-2) / 6, we can construct the equation system H TS K TS =Φ TS as follows:

[0093]

[0094] Among them, H TS By N IP The spatial constraint equations of the interference pairs and N IG The coefficient matrix of the time constraint equations of the interference groups, K TS is the column vector to be solved, Φ TS is the surround integrated phase vector.

[0095] The system of equations is composed of N IP ×T+N IG ×R equations, the number of unknowns to be solved is N IP ×R, the number of equations is less than the number of unknowns, and there are countless solutions. It can be transformed into an optimization problem under the constraints of a linear equation system for solution.

[0096] That is, solving the phase ambiguity with the simultaneous linear equations as the constraint is: establishing an optimization function with the simultaneous linear equations as the constraint, and then solving the phase ambiguity; the phase ambiguity to be solved is the phase ambiguity that makes the sum of the absolute values ​​of the phase ambiguity vectors reach the minimum value.

[0097] The optimization function is:

[0098] min∑|K TS |

[0099] subject to H TS K TS =Φ TS

[0100] Among them, ∑|K TS | represents the column vector K TS The sum of the absolute values ​​of K TS Indicates phase ambiguity, min indicates minimum value, subject to H TS K TS =ΦTS The system of simultaneous linear equations is in constrained form.

[0101] When solving K TS Finally, the phase integration method is used to untangle all the interference phase patterns.

[0102] In the derivation of the above equations, K TS For example, K TS is the is and constitute, K is used as an example when there are only three interference phase diagrams. TS , that is, n = 3; and are all 7×1 column vectors, representing the phase ambiguity vectors of the 7 edges in the three interference patterns. Similarly, for H TS , Φ TS It also corresponds to formula (11), and is illustrated with three interference phase diagrams, which will not be described in detail here.

[0103] Based on the above-mentioned three-dimensional space-time phase unwrapping method for GB-InSAR, the present invention also provides a three-dimensional space-time phase unwrapping system for GB-InSAR, including: an interference phase image acquisition module, an equation establishment module and a phase ambiguity resolution module.

[0104] The interferometric phase image acquisition module is used to acquire the interferometric phase image and interferometric image group of GB-InSAR; wherein the interferometric image group includes at least three interferometric phase images.

[0105] The equation establishment module includes a space-dimensional equation unit and a time-dimensional equation unit; the space-dimensional equation unit is used to establish a space-dimensional equation group based on the triangles in the triangulated network; the time-dimensional equation unit is used to establish a time-dimensional equation group based on each edge of the triangle; the triangulated network is used to connect the pixel points in the interference phase map.

[0106] The phase ambiguity solving module is used to obtain a set of simultaneous linear equations based on the spatial and time dimensional equations established by the simultaneous equation building module, and solve the phase ambiguity with the set of simultaneous linear equations as constraints to complete phase unwrapping.

[0107] In the equation establishment module, the spatial dimensional equation group is established based on the triangles in the triangulated network: first, a spatial dimensional equation is established based on the three pixel points P1, P2 and P3 of the triangle in the interference phase image, and then multiple spatial dimensional equations are linked to form a spatial dimensional equation group.

[0108] Take any two radar images and record them as Q1 and Q2, perform complex phase interference on Q1 and Q2 to obtain the interference phase map I 1-2 , perform differential operation on Q1 and Q2 to obtain the differential phase diagram D 1-2 ;

[0109] According to the relationship between the second-order differential phases of the three pixel points P1, P2 and P3 The spatial dimension equation is obtained as:

[0110]

[0111] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P2 and P3 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P3 1-2 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P2 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in .

[0112] In the equation building module, a time-dimensional equation group is established based on each side of the triangle in the interference image group: first, a time-dimensional equation is established based on any two pixel points in the interference phase image, and then multiple time-dimensional equations are combined to obtain a time-dimensional equation group.

[0113] According to the relationship between the second-order differential phases of the three differential phase images of any two pixel points P1 and P2 in an interference image group The time dimension equation is obtained as:

[0114]

[0115] in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 2-3 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 1-3 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 2-3 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 1-3 The relationship coefficient in Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in .

[0116] In the phase ambiguity solving module, the phase ambiguity is solved with the simultaneous linear equations as the constraint: with the simultaneous linear equations as the constraint, the phase ambiguity is solved so that the sum of the absolute values ​​of the phase ambiguity vectors is minimized.

[0117] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A three-dimensional space-time phase unwrapping method for GB-InSAR, characterized by: include: Step 1: Obtaining a GB-InSAR interferometric phase image, and further obtaining an interferometric image group; wherein the interferometric image group includes at least three interferometric phase images; Step 2: Connecting the pixels in the interference phase image using a triangulated network, establishing a spatial dimensional equation group based on the triangles in the triangulated network; and establishing a time dimensional equation group based on each side of the triangle in the interference image group; Step 3: Combine the spatial dimension equation group and the time dimension equation group to obtain a simultaneous linear equation group, and solve the phase ambiguity using the simultaneous linear equation group as a constraint to complete phase unwrapping.

2. The three-dimensional space-time phase unwrapping method according to claim 1, characterized in that: In the step 2, the spatial dimensional equation group is established based on the triangles in the triangulated network. The spatial dimensional equation is first established based on the three pixel points P1, P2 and P3 of the triangle in the interference phase image, and then a plurality of the spatial dimensional equations are combined to form the spatial dimensional equation group. Take any two radar images and record them as Q1 and Q2, perform complex phase interference on Q1 and Q2 to obtain the interference phase map I 1-2 , perform differential operation on Q1 and Q2 to obtain the differential phase diagram D 1-2 ; According to the relationship between the second-order differential phases of the three pixel points P1, P2 and P3 The spatial dimension equation is obtained as: in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P2 and P3 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P3 1-2 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P2 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in .

3. The three-dimensional space-time phase unwrapping method according to claim 2, characterized in that: In the step 2, the time-dimensional equation group is established according to each side of the triangle in the interference image group by first establishing a time-dimensional equation according to any two pixel points in the interference phase image, and then combining multiple time-dimensional equations to obtain the time-dimensional equation group; According to the relationship between the second-order differential phases of the three differential phase images of any two pixel points P1 and P2 in one interference image group, The time dimension equation is obtained as: in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 2-3 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 1-3 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 2-3 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 1-3 The relationship coefficient in Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in .

4. The three-dimensional space-time phase unwrapping method according to claim 1, characterized in that: In the step three, solving the phase ambiguity with the simultaneous linear equations as the constraint is: solving the phase ambiguity so that the sum of the absolute values ​​of the phase ambiguity vectors is minimized with the simultaneous linear equations as the constraint.

5. A three-dimensional space-time phase unwrapping system for GB-InSAR, characterized by: include: Interference phase image acquisition module, equation establishment module and phase ambiguity resolution module; The interferometric phase image acquisition module is used to acquire the interferometric phase image of GB-InSAR and further acquire an interferometric image group; wherein the interferometric image group includes at least three interferometric phase images; The equation building module includes a space-dimensional equation unit and a time-dimensional equation unit; the space-dimensional equation unit is used to establish a space-dimensional equation group based on the triangles in the triangulated network; the time-dimensional equation unit is used to establish a time-dimensional equation group based on each side of the triangle; the triangulated network is used to connect the pixel points in the interference phase map; The phase ambiguity solving module is used to simultaneously obtain a set of simultaneous linear equations by combining the spatial dimensional equation group and the time dimensional equation group established by the equation establishing module, and solve the phase ambiguity using the set of simultaneous linear equations as a constraint to complete phase unwrapping.

6. The three-dimensional space-time phase unwrapping system according to claim 5, characterized in that: In the equation building module, the spatial dimensional equation group is established based on the triangles in the triangulated network by first establishing a spatial dimensional equation based on the three pixel points P1, P2 and P3 of the triangle in the interference phase image, and then combining multiple spatial dimensional equations to form the spatial dimensional equation group; Take any two radar images and record them as Q1 and Q2, perform complex phase interference on Q1 and Q2 to obtain the interference phase map I 1-2 , perform differential operation on Q1 and Q2 to obtain the differential phase diagram D 1-2 ; According to the relationship between the second-order differential phases of the three pixel points P1, P2 and P3 The spatial dimension equation is obtained as: in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P2 and P3 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P3 1-2 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P2 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P3 are in the interference phase diagram I 1-2 The relationship coefficient in Represents three pixels P1, P2 and P3 in the interference phase image I 1-2 The surrounding phase integral in .

7. The three-dimensional space-time phase unwrapping system according to claim 6, characterized in that: In the equation building module, the time dimension equation group is established according to each side of the triangle in the interference image group by first establishing a time dimension equation according to any two pixel points in the interference phase image, and then combining multiple time dimension equations to obtain the time dimension equation group; According to the relationship between the second-order differential phases of the three differential phase images of any two pixel points P1 and P2 in one interference image group, The time dimension equation is obtained as: in, Indicates the differential phase diagram D between P1 and P2 1-2 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 2-3 The second-order difference phase in , Indicates the differential phase diagram D between P1 and P2 1-3 The second-order difference phase in , Indicates that P1 and P2 are in the interference phase diagram I 1-2 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 2-3 The relationship coefficient in Indicates that P1 and P2 are in the interference phase diagram I 1-3 The relationship coefficient in Indicates that two pixels P1 and P2 are in the interference phase image I 1-2 , I 2-3 and I 1-3 The surrounding phase integral in .

8. The three-dimensional space-time phase unwrapping system according to claim 5, characterized in that: In the phase ambiguity solving module, solving the phase ambiguity with the simultaneous linear equations as constraints is: using the simultaneous linear equations as constraints, solving the phase ambiguity so that the sum of the absolute values ​​of the phase ambiguity vectors is minimized.

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