A phase unwrapping method and system for large gradient deformation areas in a mining area

Abstract

This invention discloses a phase unwrapping method and system for large-gradient deformation regions in mining areas, achieving high-precision unwrapping results in areas where unwrapping is difficult. Specifically, it includes: converting an image (interferometric phase map) to the frequency domain based on a two-dimensional fast Fourier transform (FFT2); obtaining a pre-unwrapped image by solving the Poisson equation and performing an inverse two-dimensional Fourier transform (iFFT2) on the second-order difference result of the image; diluting the interference fringes by performing a complex conjugate multiplication of the original image and the pre-unwrapped result to obtain a noise phase map; and performing an L-type phase unwrapping on the noise phase map. 1 Norm-based phase unwrapping yields the remaining effective phase information within the noisy phase. Finally, the pre-unwrapped result is multiplied conjugately with the remaining phase to obtain the final unwrapped result. This invention solves the problem of low unwrapping accuracy in regions with large gradient changes, effectively improving unwrapping accuracy.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar interferometric data processing, specifically relating to a phase unwrapping method and system for large gradient deformation regions in mining areas. Background Technology

[0002] Interferometric Synthetic Aperture Radar (InSAR) is a key technology for acquiring high-precision Digital Elevation Models (DEMs), monitoring surface deformation, and providing early warning of landslides. Phase unwrapping is a crucial step in InSAR data processing. The accuracy of phase unwrapping results in regions with large gradient changes directly affects the final accuracy of surface deformation monitoring. However, in reality, the absolute phase jump between adjacent pixels in regions with large gradient changes is likely to be greater than π. Commonly used single-baseline phase unwrapping methods are limited by the assumption of phase continuity, resulting in less than ideal accuracy and thus affecting the accuracy of the final InSAR product. Phase unwrapping has always been a research hotspot in the InSAR data processing workflow. Commonly used phase unwrapping methods can be mainly divided into two categories: path-based phase unwrapping and minimum norm-based phase unwrapping methods. The former is represented by methods such as branch cutting, quality map methods, and minimum discontinuity methods. These methods reduce error propagation by calculating residual points and optimizing integration paths. However, in low-quality regions of the interferogram, this type of method exhibits error propagation, leading to accumulated errors and even islanding phenomena, severely impacting the accuracy of phase unwrapping results. The latter method utilizes Minimum-Cost Flow (MCF), Statistical Cost Network Flow (SNAPHU), and L... p Represented by the norm method, this type of method obtains the final unwrapping result by minimizing the difference between the true phase gradient and the estimated phase gradient. However, this type of method is prone to global error propagation and has poor robustness. In large gradient regions of mining areas, due to the limitation of the phase continuity assumption, traditional phase unwrapping methods often fail to obtain good unwrapping results, greatly affecting the accuracy of deformation monitoring in mining areas. To address these issues, the multi-baseline phase unwrapping method has been proposed. This method utilizes the baseline diversity of the interferometric phase map to achieve phase unwrapping. This type of method can break free from the constraints of the phase continuity assumption and can obtain good unwrapping results even in large gradient deformation regions of mining areas. However, the multi-baseline phase unwrapping method requires more data and suffers from poor noise robustness. Therefore, it is particularly important to find a way to obtain more accurate phase unwrapping results in large gradient change regions using the single-baseline phase unwrapping method. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a phase unwrapping method and system for large gradient deformation regions in mining areas, which can solve the problem of low unwrapping accuracy in large gradient change regions and effectively improve the phase unwrapping accuracy.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A phase unwrapping method for large gradient deformation regions in mining areas includes the following steps:

[0006] S1: Perform first-order phase difference on the original interferometric phase map of the large gradient deformation region of the mining area to obtain the phase gradient, perform phase difference on the phase gradient to obtain the second-order difference result, and perform FFT2 transformation on the second-order difference result.

[0007] S2: By adjusting the original interference phase Figure 2 The FFT2 transform result of the first difference is used to solve the Poisson equation, and the solution is then subjected to a two-dimensional inverse Fourier transform iFFT2 to obtain the pre-unwrapped result of the original interference phase diagram.

[0008] S3: By multiplying the original interference phase map with the pre-unwrapped result by complex conjugate to dilute the interference fringes, a noise phase map is obtained;

[0009] S4: By performing L on the noise phase map 1 Norm-phase unwrapping yields the effective phase information remaining in the noise phase;

[0010] S5: Multiply the pre-unwrapped result by the effective phase information using the conjugate multiplication to obtain the final unwrapped phase value.

[0011] Preferably, in S1,

[0012] The method for obtaining the phase gradient by performing a first-order phase difference on the original interferometric phase map of the large-gradient deformation region of the mining area is as follows:

[0013]

[0014]

[0015] In the formula, and Let be the estimated phase gradient values ​​of pixel (i,j) in the range and azimuth directions, respectively. The winding phase values ​​ψ are the same for pixels (i+1,j), (i,j), and (i,j+1). i+1,j ψ i,j ψ i,j+1 These are the absolute phase values ​​of pixels (i+1,j), (i,j), and (i,j+1), respectively.

[0016] The method for obtaining a second-order difference result by performing phase difference on the phase gradient is as follows:

[0017]

[0018]

[0019]

[0020] In the formula, and These are the second-order difference values ​​in the range and azimuth directions of the interferometric phase diagram, respectively. Let (i,j) be the second-order difference gradient of the interferogram pixels (i,j).

[0021] The method for performing FFT2 transformation on the second-order difference result is as follows:

[0022]

[0023] In the formula, l represents interference. Figure 2 The result of the FFT2 transform with difference gradient, where FFT2(·) is a two-dimensional Fast Fourier Transform operation. For interference Figure 2 Difference gradient plot.

[0024] Preferably, in S2,

[0025] For the original interference phase Figure 2 The method for solving the Poisson equation using the FFT2 transformation results of the order difference is as follows:

[0026]

[0027] In the formula, m and n are the number of rows and columns of the interferogram, respectively, and l i,j Let δ be the result of the FFT2 transformation of pixel (i,j). i,j The unwrapped phase in the frequency domain after solving the Poisson equation for pixel (i,j);

[0028] The method for obtaining the pre-unwrapped result of the original interferometric phase map by performing iFFT2 transformation on the solution result is as follows:

[0029]

[0030] In the formula, The result is the pre-unwrapping result, iFFT2(·) is the two-dimensional inverse fast Fourier transform, and δ is the frequency domain pre-unwrapping result.

[0031] Preferably, in step S3, the method for obtaining the noise phase map by multiplying the original interference phase map with the pre-unwrapped result using complex conjugate multiplication to dilute the interference fringes is as follows:

[0032]

[0033] In the formula, This is the original interferometric phase diagram. To pre-detach the results, Represents the multiplication operation, and conj(·) represents taking the conjugate complex number. This is a noise phase diagram.

[0034] Preferably, in S4, L 1 The expression for the norm is:

[0035]

[0036] In the formula, ψ noise The absolute phase is the remaining effective information in the noise. and These are the winding phase gradients in the range and azimuth directions, respectively, representing the residual effective information.

[0037] Preferably, in step S5, the method for obtaining the final unwrapped phase value by performing a conjugate multiplication of the pre-unwrapping result and the effective phase information is as follows:

[0038]

[0039] In the formula, ψ PU This is the final untangling phase.

[0040] The present invention also provides a phase unwrapping system for large gradient deformation regions in mining areas, comprising: a difference module, a pre-unwrapping module, a complex conjugate module, a phase unwrapping module, and a conjugate multiplication module;

[0041] The differential module is used to perform first-order phase difference on the original interferometric phase map of the large gradient deformation region of the mining area to obtain the phase gradient, perform phase difference on the phase gradient to obtain the second-order difference result, and perform FFT2 transformation on the second-order difference result.

[0042] The pre-unwrapping module is used to adjust the original interference phase. Figure 2 The FFT2 transform result of the first difference is used to solve the Poisson equation, and the solution is then subjected to a two-dimensional inverse Fourier transform iFFT2 to obtain the pre-unwrapped result of the original interference phase diagram.

[0043] The complex conjugate module is used to dilute the interference fringes by performing a complex conjugate multiplication of the original interference phase map and the pre-unwrapped result to obtain a noise phase map;

[0044] The phase unwrapping module is used to perform L-processing on the noise phase map. 1Norm-phase unwrapping yields the effective phase information remaining in the noise phase;

[0045] The conjugate multiplication module is used to perform conjugate multiplication between the pre-unwrapping result and the effective phase information to obtain the final unwrapped phase value.

[0046] Preferably, in the differential module,

[0047] The process of performing a first-order phase difference on the original interferometric phase map of the large-gradient deformation region of the mining area to obtain the phase gradient is as follows:

[0048]

[0049]

[0050] In the formula, and Let be the estimated phase gradient values ​​of pixel (i,j) in the range and azimuth directions, respectively. The winding phase values ​​ψ are the same for pixels (i+1,j), (i,j), and (i,j+1). i+1,j ψ i,j ψ i,j+1 These are the absolute phase values ​​of pixels (i+1,j), (i,j), and (i,j+1), respectively.

[0051] The process of performing phase difference on the phase gradient to obtain the second-order difference result is as follows:

[0052]

[0053]

[0054]

[0055] In the formula, and These are the second-order difference values ​​in the range and azimuth directions of the interferometric phase diagram, respectively. Let (i,j) be the second-order difference gradient of the interferogram pixels (i,j).

[0056] The process of performing FFT2 transformation on the second-order difference result is as follows:

[0057]

[0058] In the formula, l represents interference. Figure 2 The result of the FFT2 transform with difference gradient, where FFT2(·) is a two-dimensional Fast Fourier Transform operation. For interference Figure 2 Difference gradient plot.

[0059] Preferably, in the pre-unwrapping module,

[0060] For the original interference phase Figure 2 The process of solving the Poisson equation using the FFT2 transformation result of the order difference is as follows:

[0061]

[0062] In the formula, m and n are the number of rows and columns of the interferogram, respectively, and l i,j Let δ be the result of the FFT2 transformation of pixel (i,j). i,j The unwrapped phase in the frequency domain after solving the Poisson equation for pixel (i,j);

[0063] The process of performing iFFT2 transformation on the solution results to obtain the pre-unwrapped result of the original interference phase map is as follows:

[0064]

[0065] In the formula, The result is the pre-unwrapping result, iFFT2(·) is the two-dimensional inverse fast Fourier transform, and δ is the frequency domain pre-unwrapping result.

[0066] Preferably, in the complex conjugate module, the process of obtaining the noise phase map by multiplying the original interference phase map and the pre-unwrapped result by complex conjugate to dilute the interference fringes is as follows:

[0067]

[0068] In the formula, This is the original interferometric phase diagram. To pre-detach the results, Represents the multiplication operation, and conj(·) represents taking the conjugate complex number. This is a noise phase diagram.

[0069] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0070] This invention employs a phase unwrapping method and system for large gradient deformation regions in mining areas. It involves performing a second-order difference on the original interferogram, then applying an FFT2 transform to the second-order difference result, solving the transform result using the Poisson equation, and finally performing an inverse transform to obtain a pre-unwrapped result. The pre-unwrapped result is then multiplied with the original interferogram using complex conjugate multiplication, resulting in a noise phase map while diluting the fringes. Finally, the noise phase map is subjected to L... 1Norm-based unwrapping is used to obtain the remaining effective phase information in the noisy phase map. Finally, the extracted effective phase information is multiplied conjugately with the pre-unwrapping result to obtain the final unwrapped result. Compared with other existing conventional phase unwrapping methods, this invention can obtain a larger area of ​​effective unwrapping results even in regions with large gradient changes, and this method has better robustness of the unwrapping model, effectively improving the accuracy of the final InSAR product. Attached Figure Description

[0071] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 This is a flowchart of a phase unwrapping method for a large gradient deformation region in a mining area according to an embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of the reference unwrapping phase for the two simulated interference phases used in the embodiments of the present invention;

[0074] Figure 3 This is a schematic diagram of two simulated interference phase data used in an embodiment of the present invention;

[0075] Figure 4 This is a schematic diagram of two simulated interference phase noise-added data used in an embodiment of the present invention;

[0076] Figure 5 This is a schematic diagram showing the phase unwrapping results of two simulated interferometric phase noise-added data branch cutting method and their corresponding unwrapping result errors in an embodiment of the present invention;

[0077] Figure 6 This is a schematic diagram showing the MCF phase unwrapping results of two simulated interferometric phase noise-added data and their corresponding unwrapping result errors in an embodiment of the present invention;

[0078] Figure 7 This is a schematic diagram showing the SNAPHU phase unwrapping results of two simulated interferometric phase noise-added data and their corresponding unwrapping result errors in an embodiment of the present invention;

[0079] Figure 8 For an embodiment of the present invention, two simulated interferometric phase noise-added data are based on FFT2 L 1 A schematic diagram of the phase unwrapping results and corresponding unwrapping result errors of the norm phase unwrapping method;

[0080] Figure 9 This is a schematic diagram of the Google Maps area of ​​the experimental data mining area in an embodiment of the present invention;

[0081] Figure 10 This is a schematic diagram of GF-3 experimental data from an embodiment of the present invention.

[0082] Figure 11 This is a schematic diagram of the interference phase of three experimental data sets in an embodiment of the present invention;

[0083] Figure 12 These are the phase untangling results of the branch cutting method in three experimental data embodiments of the present invention;

[0084] Figure 13 The following are the MCF phase unwrapping results from three experimental data sets in this embodiment of the invention;

[0085] Figure 14 The following are the SNAPHU phase unwrapping results from three experimental data sets in this embodiment of the invention;

[0086] Figure 15 The three experimental data from this invention are the phase unwrapping results based on the L1 norm phase unwrapping method of FFT2. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0089] Example 1

[0090] like Figure 1 As shown, this invention proposes a phase unwrapping method for large gradient deformation regions in mining areas, specifically including the following steps:

[0091] S1: Perform a first-order phase difference on the original interferometric phase map of the large-gradient deformation region of the mining area to obtain the phase gradient. Then, perform a second-order difference on the phase gradient to obtain the second-order difference result. Perform an FFT2 transform on the second-order difference result. The specific formula for the second-order difference is as follows:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] In the formula, and Let be the estimated phase gradient values ​​of pixel (i,j) in the range and azimuth directions, respectively. The winding phase values ​​ψ are the same for pixels (i+1,j), (i,j), and (i,j+1). i+1,j ψ i,j ψ i,j+1 These are the absolute phase values ​​of pixels (i+1,j), (i,j), and (i,j+1), respectively. and These are the second-order difference values ​​in the range and azimuth directions of the interferometric phase diagram, respectively. Let be the sum of the second-order difference gradients of pixels (i,j) in the interferogram. The FFT2 transform expression is:

[0098]

[0099] In the formula, l represents interference. Figure 2 The result of the FFT2 transform with difference gradient, where FFT2(·) is a two-dimensional Fast Fourier Transform operation. For interference Figure 2 Difference gradient plot.

[0100] S2. The pre-unwrapping result of the image is obtained by solving the Poisson equation and performing a two-dimensional inverse Fourier transform (iFFT2) on the second-order difference FFT2 transform result of the interference. The expression for solving the Poisson equation is as follows:

[0101]

[0102] In the formula, m and n are the number of rows and columns of the interferogram, respectively, and l i,j The result of the second-order difference gradient FFT2 transformation of pixel (i,j) is given by δ. i,j The unwrapped phase in the frequency domain after solving the Poisson equation for pixel (i,j). The specific expression for the iFFT2 transform is:

[0103]

[0104] In the formula, The result is the pre-unwrapping result, iFFT2(·) is the two-dimensional inverse fast Fourier transform, and δ is the frequency domain pre-unwrapping result.

[0105] S3. The interference fringes are diluted by performing a complex conjugate multiplication between the original image and the pre-unwrapped result of S2, and a noise phase map is obtained. The specific expression is as follows:

[0106]

[0107] In the formula, This is the original interferometric phase diagram. This is the pre-untangling result for S2. Represents the multiplication operation, and conj(·) represents taking the conjugate complex number. This is a noise phase diagram.

[0108] S4. By performing L on the noise phase map 1 Norm-based phase unwrapping yields the remaining effective phase information within the noisy phase. Theoretically, the wrapped phase difference between adjacent pixels should be equal to the absolute phase difference; however, due to factors such as noise, the wrapped phase difference and the absolute phase difference are often not equal. 1 Minimum norm phase unwrapping achieves phase unwrapping by minimizing the difference between the wrapped phase difference and the absolute phase difference between adjacent pixels. The specific expression is as follows:

[0109]

[0110] In the formula, ψ noise The absolute phase is the remaining effective information in the noise. and These are the winding phase gradients of the residual effective information in the range and azimuth directions, respectively;

[0111] S5. Multiply the pre-unwrapping result of S2 with the residual effective phase obtained in S4 by conjugate to obtain the final unwrapped phase value, as shown in the following expression:

[0112]

[0113] In the formula, ψ PU This is the final untangling phase.

[0114] To verify the technical effect of this invention, unwrapping experiments were conducted on the same interferogram using the branch cutting method, MCF, SNAPHU, and the phase unwrapping method of this invention, respectively. The simulated reference unwrapped phase used in the experiments is as follows: Figure 2 As shown, the simulated interferometric phase data are as follows: Figure 3 As shown, the simulated interferometric phase noise-added data is as follows: Figure 4 As shown. The unwrapping results of the simulated interferometric phase branching method and the corresponding unwrapping result errors are as follows. Figure 5 As shown, the MCF unwrapping results and their corresponding unwrapping error are as follows: Figure 6 As shown, the SNAPHU unwrapping results and their corresponding unwrapping error are as follows: Figure 7 As shown, the untangling result and its error in this invention are as follows: Figure 8As shown. To quantitatively describe the quality of phase unwrapping, we calculated the root mean square error (RMSE) of the error maps obtained by various phase unwrapping methods. For simulated data A, the RMSE of the unwrapping result using the branch cutting method is 0.6918 rad; the RMSE of the unwrapping result using the MCF method is 0.4340 rad; the RMSE of the unwrapping result using the SNAPHU method is 0.3379 rad; and the RMSE of the unwrapping result using the FFT2-based L... 1 The root mean square error (RMSE) of the unwrapping result obtained by the norm phase unwrapping method is 0.3215 rad. For simulated data B, the RMSE of the unwrapping result obtained by the branch cutting method is 0.7662 rad; the RMSE of the unwrapping result obtained by the MCF method is 0.4029 rad; the RMSE of the unwrapping result obtained by the SNAPHU method is 0.4308 rad; while the RMSE of the unwrapping result obtained by the L based on FFT2 of this invention is... 1 The root mean square error (RMSE) of the unwrapping result obtained by the norm-based phase unwrapping method is 0.1010 rad. The results show that the unwrapping result of this invention is significantly superior to the branch-cutting method, MCF, and SNAPHU phase unwrapping methods. Simultaneously, experiments were conducted using the branch-cutting method, MCF, SNAPHU, and the phase unwrapping method of this invention to unwrap real GF-3 data from the Datong mining area in Shanxi Province. The Google Maps map coverage of the experimental data is shown below. Figure 9 As shown; the GF-3 data used in the experiment from the Datong mining area of ​​Shanxi Province are as follows. Figure 10 As shown in the figure, there are many regions with large gradient deformation, and phase discontinuities exist at the deformation center. The interferometric phase diagrams of the three real data used in the experiment are shown below. Figure 11 As shown in the figure, the real data contains high noise and large gradient deformation; the branch-cut phase unwrapping results of the experimental data are as follows: Figure 12 As shown; the experimental data and MCF phase unwrapping results are as follows. Figure 13 As shown; the experimental data and SNAPHU phase unwrapping results are as follows. Figure 14 As shown; the experimental data and the phase unwrapping results of the phase unwrapping method of this invention are as follows. Figure 15As shown in the diagram, Region 1 exhibits a significant phase discontinuity. The unwrapping results from the branching method, MCF, and SNAPHU method in Region 1 show obvious unwrapping errors, while MCF exhibits significant error propagation. The unwrapping result from this invention is more ideal. In Region 2, the unwrapping results from the branching method, MCF, and SNAPHU method show significant unwrapping errors at the subsidence center. Furthermore, MCF exhibits significant error propagation at the lower part of the subsidence deformation. However, the method proposed in this invention not only obtains unwrapping results at the deformation center but also avoids the propagation of unwrapping errors. In Region 3, the unwrapping results from the branching method, MCF, and SNAPHU method show significant unwrapping errors at the deformation center. However, the phase unwrapping method of this invention still achieves relatively ideal unwrapping results. In summary, the results demonstrate that the phase unwrapping method of this invention can obtain more accurate phase unwrapping results.

[0115] In summary, this invention proposes a phase unwrapping method for large-gradient deformation regions in mining areas. Unlike existing unwrapping methods for large-gradient changes in settlement centers, this method does not rely on external prior data, deformation models, or other techniques. Instead, it algorithmically improves the phase unwrapping problem for high noise and large-gradient deformation. First, the original interferometric phase map is subjected to second-order difference, and the difference result is transformed to the frequency domain using FFT2 transformation to remove noise present in the image. Second, the Poisson equation is solved on the transformation result to obtain the pre-unwrapped result of the original interferogram in the frequency domain, and then iFFT2 transformation is performed on the result to obtain the pre-unwrapped result in the spatial domain. At this point, by multiplying the original interferogram with the complex conjugate of the pre-unwrapped result, this step obtains the noise phase map of the original interferogram while simultaneously obtaining the coefficient interference fringes. Then, by performing L... 1 Phase unwrapping based on the norm yields the remaining effective phase information in the noisy phase map. Finally, the extracted effective phase information is multiplied conjugately with the pre-unwrapped result to obtain the final phase unwrapping result. Experiments using simulated and real data demonstrate that this invention, based on FFT2, effectively unwrappes the phase information. 1 The norm-based phase unwrapping method can effectively solve the phase unwrapping problem in the context of high noise and large gradient deformation.

[0116] Example 2

[0117] The present invention also provides a phase unwrapping system for large gradient deformation regions in mining areas, comprising: a difference module, a pre-unwrapping module, a complex conjugate module, a phase unwrapping module, and a conjugate multiplication module;

[0118] The differential module is used to perform first-order phase difference on the original interferometric phase map of the large gradient deformation region of the mining area to obtain the phase gradient, perform phase difference on the phase gradient to obtain the second-order difference result, and perform FFT2 transformation on the second-order difference result.

[0119] The pre-unwrapping module is used to adjust the original interference phase. Figure 2 The FFT2 transform result of the first difference is used to solve the Poisson equation, and the solution is then subjected to a two-dimensional inverse Fourier transform iFFT2 to obtain the pre-unwrapped result of the original interference phase diagram.

[0120] The complex conjugate module is used to dilute the interference fringes by performing a complex conjugate multiplication of the original interference phase map and the pre-unwrapped result to obtain a noise phase map;

[0121] The phase unwrapping module is used to perform L-processing on the noise phase map. 1 Norm-phase unwrapping yields the effective phase information remaining in the noise phase;

[0122] The conjugate multiplication module is used to perform conjugate multiplication between the pre-unwrapping result and the effective phase information to obtain the final unwrapped phase value.

[0123] In this embodiment, in the differential module,

[0124] The process of performing a first-order phase difference on the original interferometric phase pattern to obtain the phase gradient is as follows:

[0125]

[0126]

[0127] In the formula, and Let be the estimated phase gradient values ​​of pixel (i,j) in the range and azimuth directions, respectively. The winding phase values ​​ψ are the same for pixels (i+1,j), (i,j), and (i,j+1). i+1,j ψ i,j ψ i,j+1 These are the absolute phase values ​​of pixels (i+1,j), (i,j), and (i,j+1), respectively.

[0128] The process of performing phase difference on the phase gradient to obtain the second-order difference result is as follows:

[0129]

[0130]

[0131]

[0132] In the formula, and These are the second-order difference values ​​in the range and azimuth directions of the interferometric phase diagram, respectively. Let (i,j) be the second-order difference gradient of the interferogram pixels (i,j).

[0133] The process of performing FFT2 transformation on the second-order difference result is as follows:

[0134]

[0135] In the formula, l represents interference. Figure 2 The result of the FFT2 transform with difference gradient, where FFT2(·) is a two-dimensional Fast Fourier Transform operation. For interference Figure 2 Difference gradient plot.

[0136] In this embodiment, in the pre-unwrapping module,

[0137] For the original interference phase Figure 2 The process of solving the Poisson equation using the FFT2 transformation result of the order difference is as follows:

[0138]

[0139] In the formula, m and n are the number of rows and columns of the interferogram, respectively, and l i,j Let δ be the result of the FFT2 transformation of pixel (i,j). i,j The unwrapped phase in the frequency domain after solving the Poisson equation for pixel (i,j);

[0140] The process of performing iFFT2 transformation on the solution results to obtain the pre-unwrapped result of the original interference phase map is as follows:

[0141]

[0142] In the formula, The result is the pre-unwrapping result, iFFT2(·) is the two-dimensional inverse fast Fourier transform, and δ is the frequency domain pre-unwrapping result.

[0143] In this embodiment, the process of obtaining the noise phase map by performing a complex conjugate multiplication of the original interference phase map and the pre-unwrapping result to dilute the interference fringes in the complex conjugate module is as follows:

[0144]

[0145] In the formula, This is the original interferometric phase diagram. To pre-detach the results, Represents the multiplication operation, and conj(·) represents taking the conjugate complex number. This is a noise phase diagram.

[0146] In this embodiment, in the phase unwrapping module, L 1 The expression for the norm is:

[0147]

[0148] In the formula, ψ noise The absolute phase is the remaining effective information in the noise. and These are the winding phase gradients in the range and azimuth directions, respectively, representing the residual effective information.

[0149] In this embodiment, the process of performing a conjugate multiplication of the pre-unwrapping result and the effective phase information to obtain the final unwrapped phase value in the conjugate multiplication module is as follows:

[0150]

[0151] In the formula, ψ PU This is the final untangling phase.

[0152] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A phase unwrapping method for large gradient deformation regions in mining areas, characterized in that, Includes the following steps: S1: Perform first-order phase difference on the original interferometric phase map of the large gradient deformation region of the mining area to obtain the phase gradient, perform phase difference on the phase gradient to obtain the second-order difference result, and perform FFT2 transformation on the second-order difference result. S2: By solving the Poisson equation for the FFT2 transformation result of the second-order difference of the original interference phase diagram, and performing a two-dimensional inverse Fourier transform iFFT2 on the solution result, the pre-unwrapping result of the original interference phase diagram is obtained. S3: By multiplying the original interference phase map with the pre-unwrapped result by complex conjugate to dilute the interference fringes, a noise phase map is obtained; S4: By performing L on the noise phase map 1 Norm-phase unwrapping yields the effective phase information remaining in the noise phase; S5: Multiply the pre-unwrapped result by the effective phase information using the conjugate multiplication to obtain the final unwrapped phase value.

2. The phase unwrapping method for large gradient deformation regions in mining areas according to claim 1, characterized in that, In S1, The method for obtaining the phase gradient by performing a first-order phase difference on the original interferometric phase map of the large-gradient deformation region of the mining area is as follows: In the formula, and Let be the estimated phase gradient values ​​of pixel (i,j) in the range and azimuth directions, respectively. The winding phase values ​​ψ are the same for pixels (i+1,j), (i,j), and (i,j+1). i+1,j ψ i,j ψ i,j+1 These are the absolute phase values ​​of pixels (i+1,j), (i,j), and (i,j+1), respectively. The method for obtaining a second-order difference result by performing phase difference on the phase gradient is as follows: In the formula, and These are the second-order difference values ​​in the range and azimuth directions of the interferometric phase diagram, respectively. Let (i,j) be the second-order difference gradient of the interferogram pixels (i,j). The method for performing FFT2 transformation on the second-order difference result is as follows: In the formula, l represents the result of the second-order difference gradient FFT2 transformation of the interferogram, and FFT2(·) is the two-dimensional fast Fourier transform operation. This is the second-order difference gradient plot of the interferogram.

3. The phase unwrapping method for large gradient deformation regions in mining areas according to claim 1, characterized in that, In S2, The method for solving the Poisson equation from the FFT2 transformation of the second-order difference of the original interferometric phase diagram is as follows: In the formula, m and n are the number of rows and columns of the interferogram, respectively, and l i,j Let δ be the result of the FFT2 transformation of pixel (i,j). i,j The unwrapped phase in the frequency domain after solving the Poisson equation for pixel (i,j); The method for obtaining the pre-unwrapped result of the original interferometric phase map by performing iFFT2 transformation on the solution result is as follows: In the formula, The result is the pre-unwrapping result, iFFT2(·) is the two-dimensional inverse fast Fourier transform, and δ is the frequency domain pre-unwrapping result.

4. The phase unwrapping method for large gradient deformation regions in mining areas according to claim 1, characterized in that, In step S3, the method for obtaining the noise phase map by multiplying the original interference phase map with the pre-unwrapped result using complex conjugate multiplication to dilute the interference fringes is as follows: In the formula, This is the original interferometric phase diagram. To pre-detach the results, Represents the multiplication operation, and conj(·) represents taking the conjugate complex number. This is a noise phase diagram.

5. The phase unwrapping method for large gradient deformation regions in mining areas according to claim 1, characterized in that, In S4, L 1 The expression for the norm is: In the formula, ψ noise The absolute phase is the remaining effective information in the noise. and These are the winding phase gradients in the range and azimuth directions, respectively, representing the residual effective information.

6. The phase unwrapping method for large gradient deformation regions in mining areas according to claim 5, characterized in that, In step S5, the method for obtaining the final unwrapped phase value by performing a conjugate multiplication of the pre-unwrapping result and the effective phase information is as follows: In the formula, ψ PU This is the final untangling phase.

7. A phase unwrapping system for large gradient deformation regions in mining areas, characterized in that, include: Differential module, pre-unwrapping module, complex conjugate module, phase unwrapping module, and conjugate multiplication module; The differential module is used to perform first-order phase difference on the original interferometric phase map of the large gradient deformation region of the mining area to obtain the phase gradient, perform phase difference on the phase gradient to obtain the second-order difference result, and perform FFT2 transformation on the second-order difference result. The pre-unwrapping module is used to solve the Poisson equation by performing a two-dimensional inverse Fourier transform (iFFT2) on the FFT2 result of the second-order difference of the original interference phase map, and to obtain the pre-unwrapping result of the original interference phase map by performing a two-dimensional inverse Fourier transform (iFFT2) on the solution result. The complex conjugate module is used to dilute the interference fringes by performing a complex conjugate multiplication of the original interference phase map and the pre-unwrapped result to obtain a noise phase map; The phase unwrapping module is used to perform L-processing on the noise phase map. 1 Norm-phase unwrapping yields the effective phase information remaining in the noise phase; The conjugate multiplication module is used to perform conjugate multiplication between the pre-unwrapping result and the effective phase information to obtain the final unwrapped phase value.

8. The phase unwrapping system for large gradient deformation regions in mining areas according to claim 7, characterized in that, In the differential module The process of performing a first-order phase difference on the original interferometric phase map of the large-gradient deformation region of the mining area to obtain the phase gradient is as follows: In the formula, and Let be the estimated phase gradient values ​​of pixel (i,j) in the range and azimuth directions, respectively. The winding phase values ​​ψ are the same for pixels (i+1,j), (i,j), and (i,j+1). i+1,j ψ i,j ψ i,j+1 These are the absolute phase values ​​of pixels (i+1,j), (i,j), and (i,j+1), respectively. The process of performing phase difference on the phase gradient to obtain the second-order difference result is as follows: In the formula, and These are the second-order difference values ​​in the range and azimuth directions of the interferometric phase diagram, respectively. Let (i,j) be the second-order difference gradient of the interferogram pixels (i,j). The process of performing FFT2 transformation on the second-order difference result is as follows: In the formula, l represents the result of the second-order difference gradient FFT2 transformation of the interferogram, and FFT2(·) is the two-dimensional fast Fourier transform operation. This is the second-order difference gradient plot of the interferogram.

9. The phase unwrapping system for large gradient deformation regions in mining areas according to claim 7, characterized in that, In the pre-unwrapping module The process of solving the Poisson equation for the FFT2 transformation result of the second-order difference of the original interferometric phase diagram is as follows: In the formula, m and n are the number of rows and columns of the interferogram, respectively, and l i,j Let δ be the result of the FFT2 transformation of pixel (i,j). i,j The unwrapped phase in the frequency domain after solving the Poisson equation for pixel (i,j); The process of performing iFFT2 transformation on the solution results to obtain the pre-unwrapped result of the original interference phase map is as follows: In the formula, The result is the pre-unwrapping result, iFFT2(·) is the two-dimensional inverse fast Fourier transform, and δ is the frequency domain pre-unwrapping result.

10. The phase unwrapping system for large gradient deformation regions in mining areas according to claim 7, characterized in that, In the complex conjugate module, the process of obtaining the noise phase map by multiplying the original interference phase map and the pre-unwrapped result by complex conjugate to dilute the interference fringes is as follows: In the formula, This is the original interferometric phase diagram. To pre-detach the results, Represents the multiplication operation, and conj(·) represents taking the conjugate complex number. This is a noise phase diagram.

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