Spatial transform based non-uniform baseline tomographic sar atomic norm three-dimensional imaging

Abstract

To solve the problem that traditional tomographic SAR imaging based on atomic norm is limited to the assumption of uniform array or uniform subarray, resulting in limited application range and mismatch of multi-pass tomographic model, a non-uniform baseline compensation tomographic SAR atomic norm three-dimensional imaging method based on spatial transformation is proposed. Firstly, according to the actual sampling baseline distribution, a dense uniform sampling is constructed and the virtual position closest to the actual sampling is selected. Secondly, the greatest common divisor is calculated according to the unit interval of dense sampling and the interval of virtual position, which is used as the virtual uniform sampling interval after spatial transformation. At this time, the number of uniform sampling obtained is the least. Finally, the spatial transformation matrix is calculated according to the relationship between actual sampling and virtual uniform sampling, and the spatial transformation of the original non-uniform data is completed. Tomographic SAR three-dimensional imaging is realized based on atomic norm.

Description

Technical Field

[0001] This invention aims to provide a spatial transformation method from non-uniform data to uniform data, solving problems such as the limited applicability of subarray sampling assumptions and multi-pass model mismatch in traditional tomographic SAR atomic norm 3D imaging. It is expected to be applied to the field of multi-pass tomographic SAR 3D imaging, including spaceborne, airborne, and vehicle-mounted systems, and to provide a processing method for tomographic SAR atomic norm 3D imaging under non-uniform sampling. Background Technology

[0002] Tomographic Synthetic Aperture Radar (TomoSAR) imaging extends synthetic aperture technology to the height dimension, enabling three-dimensional imaging of observed targets. TomoSAR avoids the overlay problem inherent in traditional two-dimensional imaging by uniquely mapping and projecting the target in three-dimensional space. TomoSAR imaging is typically modeled as a spectrum estimation problem, requiring the estimation of the target's height and scattering (i.e., frequency and amplitude). Currently, compressed sensing (CS) methods are widely used to solve the TomoSAR spectrum estimation problem, achieving non-uniform, super-resolution three-dimensional imaging based on single-look or single-shot data. However, the CS method discretizes the target's elevation distribution and assumes the target falls precisely on the divided grid points. However, the actual target distribution does not perfectly conform to this assumption; it may be distributed at arbitrary elevation locations, not necessarily falling on grid points, leading to decreased reconstruction accuracy and even artifacts—a phenomenon known as "grid mismatch." While this problem can be mitigated by subdividing the grid, grid subdivision enhances the column coherence of the sensing matrix and violates the finite isometric constraint property, degrading CS reconstruction performance. Furthermore, excessive subdivision significantly increases the data dimensionality, causing a surge in computational complexity. In summary, traditional CS processing cannot avoid the problem of decreased estimation accuracy caused by grid mismatch.

[0003] To overcome the influence of grid points, an atomic norm minimization (ANM) method has recently been developed for off-grid sparse estimation of TomoSAR, enabling target frequency estimation in a continuous frequency domain and fundamentally overcoming the limitations of grid points. However, its application in multi-flight tomography processing faces a sampling assumption mismatch problem. The construction of the steering vector in the atomic norm is based on a uniform sampling model, thus it is primarily used in array TomoSAR imaging. However, in multi-flight tomography, due to issues such as flight control precision, the distribution of tomographic samples is usually non-uniform. To address this non-uniform sampling, traditional ANM methods construct a set of virtual dense sampling distributions, assuming that the actual sampling is a subarray distribution of these virtual samples. However, this assumption is inaccurate, leading to impaired estimation capabilities, and the introduction of numerous redundant virtual samples increases computational complexity.

[0004] In summary, current non-uniform baseline TomoSAR atomic norm 3D imaging methods suffer from limitations in applicability and mismatches in multi-flight models. To address these issues, this invention proposes a spatial transformation-based non-uniform baseline tomographic SAR atomic norm 3D imaging method. This method achieves spatial transformation compensation for arbitrary non-uniform data, minimizing virtual uniform sampling and obtaining high-precision TomoSAR atomic norm 3D imaging. The effectiveness of the proposed method has been verified through computer simulations and P-band distributed UAV TomoSAR experiments.

[0005] This invention aims to provide a spatial transformation method from non-uniform data to uniform data, solving problems such as the limited applicability of subarray sampling assumptions and multi-pass model mismatch in traditional tomographic SAR atomic norm 3D imaging. It is expected to be applied to the field of multi-pass tomographic SAR 3D imaging, including spaceborne, airborne, and vehicle-mounted systems, and to provide a processing method for tomographic SAR atomic norm 3D imaging under non-uniform sampling. Summary of the Invention

[0006] The purpose of this invention is to address the limitations of traditional non-uniform baseline tomographic SAR atomic norm 3D imaging, which relies on the subarray sampling assumption based on uniform sampling and suffers from model mismatch in multi-pass tomography. To this end, a non-uniform baseline tomographic SAR atomic norm 3D imaging based on spatial transformation is proposed. This achieves spatial transformation compensation for arbitrary non-uniform data, minimizing virtual uniform sampling and obtaining high-precision tomographic SAR atomic norm 3D imaging. For detailed implementation procedures, please refer to [link to specific implementation details]. Figure 1 .

[0007] The method of the present invention is achieved through the following steps:

[0008] Step 1: Based on the actual sampling baseline distribution, construct a dense and uniform sampling system and select the virtual location closest to the actual sampling.

[0009] Step 2: Calculate the greatest common divisor based on the unit interval of dense sampling and the virtual location spacing to confirm the virtual uniform sampling spacing;

[0010] Step 3: Calculate the spatial transformation matrix based on the relationship between actual sampling and virtual uniform sampling, and complete the resampling of the original non-uniform data;

[0011] Step 4: Achieve TomoSAR atomic norm 3D imaging.

[0012] The advantages of this invention are:

[0013] (1) A non-uniform baseline compensation method based on spatial transformation is proposed, which is applicable to multi-pass tomographic SAR atomic norm three-dimensional imaging.

[0014] (2) Computer simulation and P-band UAV TomoSAR experimental results show that the method has higher accuracy than the traditional method. Attached Figure Description

[0015] Figure 1 Flowchart of TomoSAR Atomic Norm 3D Imaging Based on Spatial Transformation Non-Uniform Baseline

[0016] Figure 2 Schematic diagram of N-time flyby tomographic SAR observations

[0017] Figure 3 Illustration of non-uniform baseline compensation processing

[0018] Figure 4 (a) Single-target and (b) dual-target contrast imaging results

[0019] Figure 5 Comparison of SVD-Wiener, L1 norm, and ANM elevation estimation results. (Solid line) SVD-Wiener. ('o' marker) L1 norm. ('+' marker) ANM. ('*' marker) Setting the true value. (a) Two scatterers with s1 = 4.7m and s2 = 18.09m (SNR = 3dB). (b) Two scatterers with s1 = 4.7m and s2 = 11.40m (SNR = 5dB). (c) Two scatterers with s1 = 4.7m and s2 = 9.38m (SNR = 10dB). (d) Two scatterers with s1 = 4.7m and s2 = 7.37m (SNR = 20dB).

[0020] Figure 6 The diagram illustrates the virtual sampling location distribution based on traditional subarrays and the proposed method. From top to bottom, it shows the actual sampling location distribution, the constructed dense uniform sampling distribution, the equivalent sampling distribution based on traditional subarrays, and the virtual uniform distribution obtained through step one of the proposed method.

[0021] Figure 7 Comparison of RMSE (Reference Mean Squared Error) for (a) single-target and (b) dual-target estimation under 0-25 dB SNR conditions. In the figure, 'o' indicates subarray-based results, and 'Δ' indicates baseline spatial transformation-based estimation results.

[0022] Figure 8 Comparison of detection rates between traditional subarray-based methods and the proposed method. (a) and (b) show the statistical results of single and dual-target detection rates for traditional subarray-based estimation, respectively. (c) and (d) show the results of the baseline compensation method.

[0023] Figure 9 (a) Optical image and (b) Imaging results of the experimental area of ​​Chongqing General Aviation College, China.

[0024] Figure 10(a) Comparison of 3D imaging results of the angular reflection region using traditional CS, (b) traditional ANM, and (c) the proposed method.

[0025] Figure 11 (a) Three-dimensional imaging results of building areas using traditional CS, (b) traditional ANM, and (c) the proposed method.

[0026] Figure 12 (a) Estimation results of the traditional CS, (b) traditional ANM, and (c) the proposed method for target point 2.

[0027] Figure 13 (a) Three-dimensional imaging results of the profile region using traditional CS, (b) traditional ANM, and (c) the proposed method. The black line represents the LiDAR results. Detailed Implementation

[0028] The implementation of the method of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0029] This invention relates to non-uniform baseline tomography SAR atomic norm three-dimensional imaging based on spatial transformation. The processing flow of this algorithm is as follows: Figure 1 As shown, the specific steps include:

[0030] Step 1: Based on the actual sampling baseline distribution, construct a dense and uniform sampling system and select the virtual location closest to the actual sampling.

[0031] Step 2: Calculate the greatest common divisor based on the unit interval of dense sampling and the virtual location spacing to confirm the virtual uniform sampling spacing;

[0032] Step 3: Calculate the spatial transformation matrix based on the relationship between actual sampling and virtual uniform sampling, and complete the resampling of the original non-uniform data;

[0033] Step 4: Achieve TomoSAR atomic norm 3D imaging.

[0034] Step 1: Based on the actual sampling baseline distribution, construct a dense and uniform sampling system and select the virtual location closest to the actual sampling.

[0035] Multi-flight TomoSAR observation diagram as shown below Figure 2 As shown. The SAR system utilizes multi-pass sampling to form an altitude baseline, completing the sampling of the target's tomographic scattering characteristics. Its model is as follows:

[0036] g n =∫ Δs α(x,y,s)·exp(j2πξ n s)ds (1)

[0037] In the formula, α is the scattering function of elevation s, and Δs is the elevation observation range. (x,y) represents the range-azimuth resolution unit after image registration. Spatial frequency ξ n =2b n / λr0 is determined by the vertical baseline b n Let λ and r0 be the radar wavelength and the slant range from the main image to the target, respectively. Since noise ε objectively exists in the observation, the discretized tomographic SAR signal model can be expressed as:

[0038] g=Lα+ε (2)

[0039] In the formula, g is an N×1 observation vector, and N is the number of observations over multiple flights. L is an N×K sampling matrix, where L nk =exp(-j2πξ) n s k ), s k This represents the discrete elevation position, which is discrete into K points in total.

[0040] Since man-made structures are typically sparsely distributed in the tomographic dimension, tomographic imaging can be modeled as a sparse signal recovery problem and solved using the CS method. The height dimension estimate based on L1 norm minimization can be expressed as:

[0041]

[0042] However, traditional CS TomoSAR discretizes the elevation, constructs an elevation grid, and estimates the target's position within the grid. In actual processing, the target does not always fall exactly on a grid point; it can appear at any position on the elevation. This means that the modeling in equation (3) is not sparse, and the estimation results have biases or even a large number of artifacts. This phenomenon is called grid mismatch. To solve this problem, atomic norm based on continuous domain compressed sensing is applied to TomoSAR imaging. It no longer assumes that the target frequency is located on the grid, but rather assumes that it is any value in the normalized frequency. Existing atomic norm methods usually assume that the sampling is uniform, or that it is a subarray of uniform sampling. However, due to factors such as weather and control accuracy, multi-flight sampling is usually non-uniform and very irregular, making it difficult to consider as a subarray of a uniform sampling distribution. Therefore, it is necessary to compensate for the random non-uniform tomographic observation results by resampling.

[0043] Taking 8-point non-uniform sampling as an example, the actual sampling distribution results are as follows: Figure 3 As shown in the first row. First, a virtual dense uniform matrix with extremely small "unit intervals" is constructed, as follows: Figure 3 As shown in the second row, the goal is to ensure that the actual sampling positions fall on or are close to the virtual sampling positions. Based on the principle of proximity, the positions within the virtual dense matrix that are closest to the actual sampling baseline distribution are selected as the subarray distribution, such as... Figure 3As shown in the third row.

[0044] Step 2: Calculate the greatest common divisor based on the unit interval of dense sampling and the virtual location spacing to confirm the virtual uniform sampling spacing;

[0045] Assuming the unit interval of the dense uniform matrix is ​​d, and the sampling interval of the filtered subarray is d, the sampling interval of the subarray is d. sub (i), where i represents the distance between the (i-1)th and ith subarray positions. Calculate d and d sub The greatest common divisor between (i)

[0046] d GCD =[d,d sub (i)] (4)

[0047] In the formula, [※, ※] denotes the operation of finding the greatest common divisor. Let d GCD This serves as the final virtual uniform sampling interval, and the corresponding sampling distribution is constructed.

[0048] It should be noted that in actual processing, due to the randomness of the sampling distribution, d sub (i) The elements may be coprime, resulting in a final greatest common divisor of 1, i.e., a unit interval d. To avoid this, a redundancy range can be set based on the size of d, assuming that there exists a greatest common divisor other than d within this range. For example, ±5d can be set as the redundancy interval, where d... sub (1) = 32d, d sub (2) = 58d, then the greatest common divisor of the two can be considered to be d. GCD =30d. (The last part, "d", appears to be a typo and can be omitted.) GCD As the final interval, a virtual uniform sampling distribution that is closest to the original non-uniform sampling and has the fewest sample numbers can be obtained, such as... Figure 3 As shown in the fourth line.

[0049] Step 3: Calculate the spatial transformation matrix based on the relationship between actual sampling and virtual uniform sampling, and complete the resampling of the original non-uniform data.

[0050] Assuming the compensated virtual uniform sampling result g v If the length is M, then the spatial transformation result of the original observation data can be expressed as:

[0051] g v =Φg (5)

[0052] In the formula, Φ is an M×N dimensional spatial transformation matrix, where M>N. Φ can be solved by solving the following optimization problem:

[0053]

[0054] In the formula, L v It is composed of virtual uniform sampling bvm The sampling matrix formed, L mk =exp(-j2π2b) vm / λr0s k The minimization problem described in equation (6) can be obtained using a general solution method for overdetermined systems. vm The results obtained in steps one and two can then be used to perform spatial transformation of the sampled data using equation (5).

[0055] Step 4: Achieve three-dimensional imaging using tomographic SAR atomic norm.

[0056] The atomic norm minimization problem can be expressed as:

[0057]

[0058] The atomic norm minimization problem above can be transformed into a standard positive semidefinite programming problem (SDP), which can be solved using a standard SDP solver, such as SDPT3 or the Matlab CVX toolkit. Its standard form is expressed as follows:

[0059]

[0060] In the formula, It is a variable in the problem. For the observation results, For regularization parameters, This is a weight matrix, with all parameters known. In the atomic norm minimization, w = 2e0, where e0 is a vector with the first element being 1 and the rest being 0. The function T(u) outputs the complex Hermitian Toeplitz matrix with u as the first column.

[0061]

[0062] If the observation is a subarray with N samples, that is... At this point, the estimated result x only needs to be represented by the corresponding subarray to complete the atomic norm solution based on the traditional subarray sampling assumption, i.e., x→x [N] In the formula, [N] is a subset of [M]. After solving, the Toeplitz matrix of the observation results can be constructed using u, and then the frequency and phase of the target can be obtained using subspace methods such as Root-Music.

[0063] Combining equations (3) and (7), TomoSAR atomic norm three-dimensional imaging can be expressed as:

[0064]

[0065] Equation (10) can be used in the SDP solver to obtain the Toeplitz matrix T(u) containing the elevation target frequency. The frequency estimate f can be obtained using subspace methods, such as Root-Music. k Then the height corresponding to the scattering point is:

[0066] s k =f k H (11)

[0067] In the formula, H represents the unambiguous height corresponding to the virtual uniform array. Finally, based on the elevation estimation results... Estimate the scattering characteristics of the elevation. Assuming K elevation estimates are obtained, the target location is determined by minimizing the penalty function (model order selection). Using the location information, the target amplitude and phase are obtained through least squares, thus completing the non-uniform baseline tomography SAR atomic norm three-dimensional imaging based on spatial transformation.

[0068] Example

[0069] Computer simulation

[0070] Computer simulations were used to verify the off-network phenomenon in traditional CS methods, the detection results of existing subarray-based atomic norm minimization methods, and the detection results of our proposed method. The simulation parameters are shown in the table.

[0071] Table 1 Key Simulation Parameters

[0072] parameter value unit band P - distance 1000 m Baseline -42-28 m Baseline quantity 15 -

[0073] First, simulations compared the imaging capabilities of the traditional CS (based on L1 norm) method and the atomic norm (based on ANM) method under uniform sampling. At a signal-to-noise ratio (SNR) of 15 dB, simulations were performed to determine the imaging capabilities of each method. Figure 4 (a) Single target estimation, target height set at 4.7m, and Figure 4 (b) Estimation of overlapping dual targets, with target heights set at 4.7m and 18.09m. From Figure 4 As can be seen, the traditional CS method, due to the grid effect, results in estimations that deviate somewhat from the true values. Furthermore, due to grid mismatch, the recovered results contain numerous artifacts, affecting image quality. In contrast, the atomic norm method's estimation results are basically consistent with the set values, with a much smaller deviation than the traditional CS method. It also has a stronger ability to represent sparsity and produces almost no artifacts.

[0074] Resolution is one of the important indicators in tomographic imaging. We compared the differences between traditional methods and atomic norm super-resolution capabilities. Figure 5(a) shows the recovery results when SNR = 3dB and the two targets are spaced one resolution apart. It can be seen that the peak positions estimated by the three methods—SVD, L1 norm, and ANM—are basically consistent with the settings. Since the target does not fall on the grid points, the estimated results for the target on the left side of the L1 norm are near the grid points on both sides of the set value. Reducing the target spacing to 0.5 resolutions, the imaging results at SNR = 5dB are as follows... Figure 5 As shown in (b), the SVD method can no longer effectively distinguish between the two targets, but L1 norm and ANM can still effectively differentiate them. However, artifacts begin to appear in the L1 norm and deviate significantly from the true value of the target. With increasing signal-to-noise ratio, L1 norm and ANM can distinguish between two targets that are closer together, such as... Figure 5 (c) shows an SNR of 10 dB with a spacing of 0.35 resolution units, but the L1 norm artifacts are more pronounced. At a higher SNR of 20 dB, the ANM method can even distinguish targets with a spacing of 0.2 resolution units, but the L1 norm estimation results show severe artifacts and cannot effectively distinguish overlapping targets. The results indicate that, under certain SNR conditions, ANM has better sparsity representation and super-resolution capabilities, and can obtain tomographic imaging results of better quality than traditional CS.

[0075] Further validation of the effectiveness of the proposed method is conducted. The baseline settings are as follows: Figure 6 As shown in the first row, a total of 30 observations were collected, distributed between -42m and 46m. Due to limited system control capabilities, the baseline distribution was non-uniform. Traditional ANM (Application Not Mitigation) uses a uniformly dense array to find locations adjacent to the actual samples as virtual sampling locations, thus equating the original non-uniform result to a subarray of the uniform array, such as... Figure 6 As shown in the second and third rows, this paper proposes to construct a virtual uniform sampling distribution based on the nearest grid point and the maximum interval, and then perform spatial transformation on the original data. Compared with traditional methods, this approach simultaneously processes the data during array transformation; furthermore, it utilizes the greatest common divisor to obtain the maximum interval when constructing the uniform matrix, reducing the length of the virtual uniform matrix and thus lowering complexity. The final sampling distribution of the proposed method is shown in the figure. Figure 6 As shown in the fourth line.

[0076] After equivalent and spatial compensation transformations of the samples, the estimation accuracy (RMSE) of the two methods was compared and analyzed at SNRs of 0, 5, 10, 15, 20, and 25 dB. The results of 500 Monte Carlo simulations are as follows: Figure 7 As shown, in the simulation, the target position is randomly distributed within the unambiguous range for each test. The single-target estimation case is as follows: Figure 7(a) At lower SNRs, the results based on the subarray deteriorate significantly. As the SNR increases, the subarray-based method gradually improves and begins to approach the proposed method; after 5 dB, the performance of both methods becomes essentially equal. The dual-target estimation results are shown below. Figure 7 As shown in (b), the results based on subarrays deteriorate more severely, and the estimation accuracy of the two methods only tends to be consistent when SNR = 15dB. The above results indicate that under low signal-to-noise ratio conditions, the traditional subarray-based ANM method has unstable estimation results and limited accuracy, especially when there is dual-target overlay, its estimation capability is insufficient.

[0077] Furthermore, we compared the detection estimation performance in the 0-25dB range when the sampling quantity was 10, 20, and 30. Here, the criterion for successful detection is defined as the estimated target quantity matching the set value, and the result deviation being less than the resolution length; otherwise, the detection is considered a failure. The statistical results are as follows: Figure 8 As shown, triangles, squares, and circles represent the cases when the number of samples N is 10, 20, and 30, respectively. Figure 8 (a) and (c) show the detection probabilities of the subarray and baseline compensation method for the single-target case. When there is only one target to be estimated, the detection performance of the two methods is similar. However, the spatial transformation method performs better under low signal-to-noise ratio and low sampling number conditions. Figure 8 (b) and (d) show the detection probabilities for the two-target case. It can be seen that the subarray-based method exhibits significant performance degradation when only 10 samples are collected. With 20 and 30 samples, the baseline spatial transformation method achieves a detection rate exceeding 90% at an SNR of 10 dB, while the subarray-based method requires an SNR of 15 dB. In summary, the proposed baseline spatial transformation method demonstrates better estimation accuracy and stability.

[0078] P-band UAV TomoSAR Experiment

[0079] In March 2021, TomoSAR experimental data from an unmanned aerial vehicle (UAV) was successfully acquired from Chongqing General Aviation College in China. The system operated in the P-band, acquiring 30 tracks of data between altitudes of 170-260m. The primary observation area was the college campus, and the corresponding optical maps and SAR imaging results are shown below. Figure 9 As shown in (a) and (b), with a system viewpoint θ = 70°, a scene center slant distance of 656.2 m, and a baseline length Δb of approximately 90 m, the corresponding elevation resolution ρ is... s It is 2.54m. The dashed border indicates areas of buildings with significant overlap, while the solid border indicates corner locations.

[0080] Tomographic imaging was performed using the traditional CS method, the traditional ANM method, and the proposed method, respectively, with the results of two-dimensional elevation staining as follows: Figure 10As shown. Due to the influence of grid mismatch, the traditional CS method exhibits significant estimation fluctuations, such as... Figure 10 As shown in (a), the estimation results using ANM are much more uniform and smooth. However, traditional ANM methods based on the subarray sampling assumption have more noise compared to the proposed method, such as... Figure 10 As shown in (b)(c).

[0081] The two-dimensional elevation coloring results of the building area obtained by the three methods are as follows: Figure 11 As shown, the three methods exhibit significant differences. The estimation results based on the traditional gridded CS method show obvious noise in the elevation, and the elevation estimation results for the building in the upper right corner show a clear stepped distribution trend. In contrast, (b) and (c) based on the atomic norm show significantly less noise. The noise is caused by artifacts in the elevation estimation. Numerous artifacts introduce false target points in the height-dimensional imaging, and due to gridding issues, it is difficult to ensure that the grid points in the estimation results match the actual elevation. This combination leads to instability in the model selection method, resulting in noise. Compared to (b), the proposed method (c) significantly reduces the number of outliers in the overall image, as seen in the lower left region. For areas with severe overlay, such as rooftops and floors, (c) shows a smoother and more stable distribution, and it has a stronger ability to preserve the texture of the building's height distribution, maintaining a more complete elevation estimation of the rooftops. In summary, the proposed method demonstrates superior performance in the presence of target overlay.

[0082] Two typical targets were selected to further verify the analysis results. Target 2 is a point target, shown by the black circle in the figure, and target 3 is a profile, shown by the blue dashed line in the figure. Target 2 is located in the rooftop area, where the rooftop and ground areas will overlap, which can be used as a reference for estimating the recovery performance of overlapping targets. Profile line 3 crosses the rooftop areas of two buildings and has a relatively obvious geometric structure, which can be used as a reference for 3D imaging quality assessment. The estimation results of target 2 are compared with... Figure 12 As shown in the figure. It can be seen that in the overlapping region, the proposed method can effectively distinguish overlapping targets and recover the target elevation, while the traditional method can only obtain one target height. The profile result of target 3 is shown in the figure. Figure 13 As shown, the solid line represents the target LiDAR result, which serves as the comparison benchmark. It is clearly visible that the traditional CS method suffers from grid effects, exhibiting a stepped characteristic in the estimation results and failing to ideally recover the structural features of the target. The ANM-based method preserves the building's structural features better, but due to severe overlapping in this building area, the traditional ANM method produces a significant amount of noise. The proposed method significantly suppresses noise and outliers and effectively recovers the sloping structure of the building on the right. Table 2 shows a comparison of the accuracy of the three methods compared to LiDAR data. It can be seen that the proposed method achieves the best estimation accuracy, reaching 4.13m.

[0083] Table 2 Comparison of Building Area Estimation Accuracy

[0084] Traditional CS Traditional ANM The proposed method RMSE(m) 4.90 4.54 4.13

Claims

1. A non-uniform baseline tomography SAR atomic norm three-dimensional imaging based on spatial transformation, characterized in that, Includes the following steps: Step 1: Based on the actual sampling baseline distribution, construct a dense and uniform sampling system and select the virtual location closest to the actual sampling. In step one, the random non-uniform tomographic observation results are compensated and resampled. First, a virtual dense uniform matrix with a very small "unit interval" is constructed to make the actual sampling position fall on or close to the virtual sampling position as much as possible. Then, based on the principle of proximity, the position in the virtual dense array that is closest to the actual sampling baseline distribution is selected as the subarray distribution; Step 2: Calculate the greatest common divisor based on the unit interval of dense sampling and the virtual location spacing to confirm the virtual uniform sampling spacing; In step two, the method for calculating the virtual uniform sampling interval is as follows: Assuming the unit interval of the dense uniform matrix is ​​d, and the sampling interval of the filtered subarray is d, the sampling interval of the subarray is d. sub (i), where i represents the distance between the (i-1)th and ith subarray positions; calculate d and d sub The greatest common divisor among (i) is: d GCD =[d,d sub (i)]; In the formula, [※, ※] denotes the operation of finding the greatest common divisor; Step 3: Calculate the spatial transformation matrix based on the relationship between actual sampling and virtual uniform sampling, and complete the resampling of the original non-uniform data; In step three, the method for resampling the original non-uniform data is as follows: Assuming the compensated virtual uniform sampling result g v If the length is M, then the spatial transformation result of the original observation data can be expressed as: g v =Φg; In the formula, Φ is an M×N dimensional spatial transformation matrix, and Φ can be obtained by solving the following optimization problem: ； In the formula, L v It is a sampling matrix composed of virtual uniform sampling, L mk =exp(-j2π2b vm / λr0s k ); Step 4: Implement TomoSAR atomic norm 3D imaging; represented as: .

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