Tomosar imaging method combining common point focusing and subspace spectrum estimation

Abstract

The application discloses a kind of tomographic SAR imaging methods for combining same-name point focusing and subspace spectrum estimation, comprising: based on the Euclidean distance between main flight image and multiple other flight images, complex coherence coefficient and phase correlation, weight is calculated to calculate score;According to weight calculation score, determine the registration data matrix, and according to the registration data matrix, sliding window covariance matrix smoothing processing is carried out, to obtain the smoothed covariance matrix;Symmetric processing is carried out to the smoothed covariance matrix, to construct weighting factor;Eigenvalue decomposition is carried out to the smoothed covariance matrix, to construct noise subspace;Based on measurement matrix, weighting factor and noise subspace, spectrum estimation is carried out, to complete a kind of keeping good same-name point focusing precision and three-dimensional imaging quality tomographic SAR imaging.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a tomographic SAR (Synthetic Aperture Radar) imaging method that combines corresponding point focusing and subspace spectrum estimation. Background Technology

[0002] With the acceleration of urbanization, synthetic aperture radar plays an increasingly prominent role in high-resolution remote sensing monitoring. In particular, in urban environments with complex building structures and variable ground object scattering characteristics, three-dimensional tomographic SAR (TomoSAR) imaging technology has become an important means of identifying and reconstructing targets.

[0003] In traditional tomographic synthetic aperture radar (SAR) methods, the observation dimension is mainly established in the vertical direction, i.e., the elevation direction, and 3D reconstruction of the target scene is performed using techniques such as spectral estimation or compressed sensing. Common spectral estimation methods include nonparametric methods based on Fast Fourier Transform (FFT), beamforming (BF), minimum variance (Capon), and multiple signal classification (MUSIC).

[0004] Tomographic SAR imaging, based on 2D SAR observation data from multiple orbits and different viewpoints, achieves spatial reconstruction of scatterers in the elevation direction. Its imaging performance largely depends on high-precision registration between SAR images from multiple flights. In practical applications, registration errors exist between airborne multi-flight SAR data, especially in areas with drastic viewpoint changes and complex scattering characteristics. Simply relying on image registration is insufficient to achieve pixel-level alignment, severely impacting the quality of 3D imaging. Therefore, introducing a more robust corresponding point extraction mechanism and effective noise suppression strategies during tomographic inversion has become a key technical challenge for improving the reconstruction accuracy of TomoSAR.

[0005] Among them, the multiple signal classification algorithm, as a high-resolution spectral estimation method based on feature subspace decomposition, has super-resolution capabilities and can effectively separate coherent scatterers, making it a more refined tomographic focusing technique in complex urban environments. The MUSIC method uses the covariance matrix of the received signal for feature decomposition, orthogonally separating the signal subspace and noise subspace, and constructs a response vector in the elevation search space. It then identifies the location of scatterers through spectral function search, exhibiting higher elevation resolution and noise resistance.

[0006] Traditional MUSIC tomography methods primarily involve using an image from a specific flight as the master image. Image registration techniques are then employed to precisely register images from other flights to the master image's reference coordinate system, ensuring consistency of the same scattering point in the image domain across different viewpoints. For any pixel (x, y) in the master image, a corresponding slant range difference model and elevation response vector are constructed by combining the orbital parameters, baseline configuration, and wavelength from different flights. A signal matrix is ​​then constructed from the registered complex pixel values ​​from multiple flights, and the covariance matrix is ​​calculated. The spectral function exhibits sharp peaks at the actual scatterer elevations. Spectral peak detection allows estimation of the elevation positions of multiple master scatterers, achieving super-resolution 3D imaging. The above steps are repeated for all pixels in the entire image, acquiring MUSIC elevation inversion results pixel-by-pixel, ultimately reconstructing a 3D point cloud image.

[0007] Traditional MUSIC algorithms typically rely on eigenvalue decomposition of the original covariance matrix, making them susceptible to noise, data perturbations, and covariance matrix estimation errors. This leads to unstable spectral estimation, especially under conditions of low signal-to-noise ratio or limited sampled data. Furthermore, traditional MUSIC methods lack full utilization of data structure and prior information, and do not employ additional smoothing or enhancement mechanisms to improve the quality of the covariance matrix, thus affecting the resolution of weak scatterers or close-range targets. Simultaneously, in scenarios such as tomographic SAR imaging, where there are viewing angle variations and speckle noise, directly using traditional MUSIC can easily result in positioning errors and spurious peaks, affecting the final imaging accuracy. Secondly, the focusing accuracy of corresponding points often exhibits instability, severely impacting image quality.

[0008] Therefore, how to provide a tomographic SAR imaging method that maintains good focusing accuracy of corresponding points and three-dimensional imaging quality has become an important issue. Summary of the Invention

[0009] To address the aforementioned problems in the existing technology, this invention provides a tomographic SAR imaging method that combines corresponding point focusing and subspace spectrum estimation.

[0010] The technical problem to be solved by this invention is achieved through the following technical solution:

[0011] In a first aspect, the present invention provides a tomographic SAR imaging method that combines corresponding point focusing and subspace spectrum estimation, the tomographic SAR imaging method comprising:

[0012] The score is calculated based on the weights of the Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images.

[0013] The registered data matrix is ​​determined by calculating the score based on the weights, and the registered data matrix is ​​then smoothed by a sliding window covariance matrix to obtain the smoothed covariance matrix.

[0014] The smoothed covariance matrix is ​​symmetrically processed to construct a weighting factor;

[0015] The smoothed covariance matrix is ​​subjected to eigenvalue decomposition to construct a noise subspace;

[0016] Based on the measurement matrix, the weighting factor, and the noise subspace, spectral estimation is performed to complete three-dimensional tomographic SAR imaging.

[0017] Optionally, a score is calculated based on weights derived from the Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images, including:

[0018] The Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images are weighted according to an initial threshold and preset weights to obtain an intermediate weight score; the preset weights include preset weights for Euclidean distance, complex coherence coefficient, and phase correlation.

[0019] The step of iteratively updating and determining the intermediate weight calculation score continues until the intermediate weight calculation score is less than a preset threshold. Then, the intermediate weight calculation score in the current iteration is determined as the weight calculation score.

[0020] Optionally, the method for determining the preset weights includes:

[0021]

[0022] Where i∈{1,2,3}, λ1 represents the preset weight of Euclidean distance, λ2 represents the preset weight of complex coherence coefficient, and λ3 represents the preset weight of phase correlation. Let λ represent the value of the t-th iteration. i ; Let λ represent the (t+1)th iteration. i ΔS represents the gradient of the score calculated using intermediate weights; η represents the learning rate.

[0023] Optionally, the smoothed covariance matrix is ​​symmetrically processed to construct weighting factors, including:

[0024] The antisymmetric permutation matrix and the smoothed covariance matrix are symmetrically processed to obtain the symmetric covariance matrix.

[0025] The weighting factor is constructed by processing the symmetric covariance matrix using a diagonal matrix function.

[0026] Optionally, spectral estimation is performed based on the measurement matrix, the weighting factor, and the noise subspace to complete three-dimensional tomographic SAR imaging, including:

[0027] Substituting the measurement matrix, the weighting factor, and the noise subspace into the MUSIC spectrum calculation formula, spectral estimation is performed to complete three-dimensional tomographic SAR imaging.

[0028] Optionally, the MUSIC spectrum calculation formula includes:

[0029]

[0030] Among them, P MUSIC (θ i ) represents the i-th elevation candidate point θ i Spectral estimate; a(θ) i ) represents the i-th column in the measurement matrix, representing the i-th candidate elevation point θ. i The direction vector; W represents the weighting factor; E n The superscript H represents the noise subspace; the superscript H indicates the conjugate transpose operation of the matrix.

[0031] Secondly, the present invention provides a tomographic SAR imaging device that combines corresponding point focusing and subspace spectrum estimation, the tomographic SAR imaging device comprising:

[0032] The calculation module is used to calculate the weights and scores based on the Euclidean distance, complex coherence coefficient and phase correlation between the main flight image and multiple other flight images;

[0033] The smoothing module is used to calculate the score based on the weights to determine the registered data matrix, and to perform sliding window covariance matrix smoothing based on the registered data matrix to obtain the smoothed covariance matrix.

[0034] A symmetry processing module is used to perform symmetry processing on the smoothed covariance matrix to construct weighting factors;

[0035] The eigenvalue decomposition module is used to perform eigenvalue decomposition on the smoothed covariance matrix to construct a noise subspace.

[0036] The spectrum estimation module is used to perform spectrum estimation based on the measurement matrix, the weighting factor, and the noise subspace to complete three-dimensional tomographic SAR imaging.

[0037] This invention provides a tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation. It calculates scores based on weighted calculations of Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images. By integrating the characteristics of Euclidean distance, phase correlation, and complex coherence coefficient, high-precision corresponding point focusing is achieved. The method employs a sliding window covariance matrix smoothing technique, effectively improving the statistical stability of the covariance matrix and significantly suppressing interference from high-frequency noise and local abrupt changes. Introducing a weighting factor enhances robustness under signal-to-noise ratio, increases main lobe intensity, and suppresses side lobes. Therefore, the tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation provided by this invention maintains good corresponding point focusing accuracy and 3D imaging quality even in complex scenarios such as urban areas, providing theoretical support and engineering feasibility for high-precision TomoSAR imaging tasks.

[0038] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating a tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation provided in an embodiment of the present invention.

[0040] Figure 2 This is a schematic diagram of the adaptive corresponding point focusing process provided in an embodiment of the present invention;

[0041] Figure 3 This is a schematic diagram of the subspace enhancement process provided in an embodiment of the present invention;

[0042] Figure 4 This is a first imaging comparison diagram between the tomographic SAR imaging method provided in this embodiment of the invention and the existing tomographic SAR imaging method;

[0043] Figure 5 This is a second imaging comparison diagram between the tomographic SAR imaging method provided in this embodiment of the invention and the existing tomographic SAR imaging method;

[0044] Figure 6 This is a schematic diagram of the structure of a tomographic SAR imaging device that combines corresponding point focusing and subspace spectrum estimation according to an embodiment of the present invention. Detailed Implementation

[0045] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0046] To address the issues of unstable focusing accuracy and poor imaging precision at corresponding points in existing tomographic SAR imaging methods, this invention provides a tomographic SAR imaging method that combines corresponding point focusing with subspace spectrum estimation. (See [link to relevant documentation]). Figure 1 , Figure 1 This is a flowchart illustrating a tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation provided by an embodiment of the present invention, specifically including the following steps:

[0047] Step S101: Calculate the weights and scores based on the Euclidean distance, complex coherence coefficient, and phase correlation between the master overpass image and other overpass images.

[0048] In this embodiment of the invention, "flyover" refers to the process by which a SAR platform, such as a satellite or aircraft, performs a single continuous imaging of a certain area of ​​the ground while flying along a predetermined orbit. A "flyover image" refers to a radar image of a strip or specific shape generated each time a flight is over. The "main flyover image" refers to a selected flyover image, and "other flyover images" refer to other flyover images besides the main flyover image.

[0049] See Figure 2 , Figure 2 This is a flowchart illustrating the adaptive corresponding point focusing process provided in this embodiment of the invention. The process involves calculating a score based on the Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images, including:

[0050] The Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images are weighted according to the initial threshold and preset weights to obtain the intermediate weight score; the preset weights include the preset weights for Euclidean distance, complex coherence coefficient, and phase correlation.

[0051] The process involves iteratively updating the intermediate weight calculation score until the intermediate weight calculation score is less than a preset threshold. Then, the intermediate weight calculation score in the current iteration is determined as the weight calculation score.

[0052] The methods for determining the preset weights include:

[0053] First, set the initial weights, and then update the weights iteratively as follows:

[0054]

[0055] Where i∈{1,2,3}, λ1 represents the preset weight of Euclidean distance, λ2 represents the preset weight of complex coherence coefficient, and λ3 represents the preset weight of phase correlation; the superscript t indicates the iteration number. Let λ represent the (t+1)th iteration. i ; Let λ represent the value of the t-th iteration. i ΔS represents the gradient of the score calculated by the intermediate weights, i.e., the score of the focus point of the same name; η represents the learning rate (which decreases with iteration).

[0056] The weight update strategy provided in this embodiment of the invention is simple in form, involving only one multiplication and addition operation, making it computationally convenient and suitable for efficient implementation in large-scale data processing tasks. Mechanistically, this method can dynamically adjust the weights according to changes in the scoring function, avoiding the rigidity problem caused by fixed weight updates, and possessing good flexibility and adaptability. As iteration progresses, the algorithm can gradually enhance its responsiveness to high-contribution features, effectively suppressing invalid or noisy features, thereby improving the focusing accuracy and robustness of corresponding points. Furthermore, the weight evolution process reflects the changing trend of the data structure with iteration, helping the algorithm achieve stable convergence in the search space, improving overall imaging quality and algorithm reliability.

[0057] When the number of iterations reaches the preset number, the weight under that iteration is used as the preset weight. The preset number of iterations can be set by technical personnel based on experience.

[0058] In this embodiment of the invention, a preset threshold is determined because, in SAR tomography, a single focusing index of a corresponding point is insufficient to comprehensively measure the focusing quality of that point. Therefore, an overall scoring function is adopted, which integrates spatial geometric consistency, complex coherence coefficient, and coherent scattering characteristics to ensure that the corresponding points achieve global optimization.

[0059] The specific method for calculating the weights and scores is as follows:

[0060] score=λ1×Euc+λ2×coh+λ3×pha;

[0061] Where score represents the score calculated by the intermediate weight; λ1 represents the preset weight of the Euclidean distance; Euc represents the Euclidean distance; λ2 represents the preset weight of the complex coherence coefficient; coh represents the complex coherence coefficient; λ3 represents the preset weight of the phase correlation; and pha represents the phase correlation.

[0062] Minimum search method:

[0063] best match = argminscore;

[0064] Here, best match represents the best matching operation; argmin is used to represent the parameter value of a function that achieves the minimum value in its domain.

[0065] When the intermediate weight calculation score is less than the preset threshold, i.e. lower than the preset standard, the iteration is terminated, and the intermediate weight calculation score under the current iteration is determined to be the optimal weight calculation score. At this time, the pixel in the main flight image is the same pixel in other flight images.

[0066] Traditional algorithms typically focus only on the image registration process, neglecting subtle differences in scattering characteristics and viewing angle variations across different flight data, easily leading to mismatches in local areas. In contrast, this invention introduces an iterative optimization mechanism, combined with a pixel-by-pixel level matching adjustment strategy, to dynamically update the focusing weights of corresponding points. This allows the matching process to gradually converge to the optimal solution under multi-scale and multi-feature constraints, significantly improving the accuracy and robustness of corresponding point focusing. This invention designs a dynamically weighted corresponding point focusing framework based on an iterative optimization mechanism. By updating the weights of each feature factor in successive rounds, the corresponding point focusing results gradually converge to the global optimum. This method is particularly suitable for complex SAR imaging scenarios such as densely built-up areas and forest cover, effectively improving the algorithm's robustness to non-ideal conditions. The iteration automatically terminates when the error falls below a preset standard, effectively avoiding redundant calculations and significantly improving overall computational efficiency.

[0067] In this embodiment of the invention, during the iterative optimization process, Euclidean distance is used as a key constraint to ensure the spatial geometric consistency of corresponding points, effectively avoid geometric mismatch, and improve the accuracy of spatial constraints.

[0068] Geometric constraint-assisted focusing of corresponding points: Euclidean distance can constrain the three-dimensional positional relationship of corresponding points and suppress the offset caused by noise or local disturbance.

[0069] The formula for calculating Euclidean distance is as follows:

[0070]

[0071] Among them, amp n (r,x) is the pixel at position (r,x) in the selected master overpass image; uv (r,x) is the pixel at position (r,x) in other overpass images; r is the x-coordinate of the pixel in the overpass image, and x is the y-coordinate of the pixel in the overpass image; N represents the total number of overpasses; L1 represents the size of the overpass image.

[0072] In this embodiment of the invention, in SAR tomography, corresponding points not only need to be aligned at the pixel level, but also need to maintain correctness in physical space. The complex coherence coefficient, as an important indicator for measuring the similarity of corresponding points, can effectively improve the rationality of focusing on target corresponding points.

[0073] The complex coherence coefficient is used to measure the consistency of the scatterer response in SAR observations from different expeditions. High coherence implies stable scattering characteristics, which helps to improve the reliability of corresponding points.

[0074] The formula for calculating the complex coherence coefficient is:

[0075]

[0076] Where Coh represents the complex coherence coefficient.

[0077] In this embodiment of the invention, the scattering characteristics of corresponding points in SAR tomography are mainly reflected in phase information. Therefore, introducing phase correlation as a focusing constraint for corresponding points helps to improve the focusing degree of coherent information and make the focusing process of corresponding points more accurate and robust.

[0078] In SAR images from different expeditions, the amplitude may vary due to changes in imaging conditions, but phase information is more stable. Using phase correlation for focusing on corresponding points can ensure that the scattering characteristics of corresponding points remain physically consistent.

[0079] Compared to directly using amplitude-based focusing, phase-based focusing is more resistant to speckle noise interference, improves the robustness of focusing, and enhances noise immunity.

[0080] Compared to traditional methods, this strategy performs better in focusing on the same points of complex or non-rigid targets such as urban buildings and forests. It can adapt to the scattering characteristics of different targets, is suitable for complex scenes, and can improve the accuracy of 3D reconstruction.

[0081] The formula for calculating phase correlation is:

[0082]

[0083] (u=1,2,…,N,v=1,2,…,L1,u≠n)

[0084] Where Pha represents phase correlation; R n (m) is the reference slant range of the selected master overpass image, R p (m) is the reference slant distance for other flight images.

[0085] In this embodiment of the invention, Euclidean distance is used to constrain spatial geometric position to prevent geometric mismatch, and multi-pixel information is integrated to ensure accurate spatial alignment of corresponding points.

[0086] By constraining the complex coherence coefficient, we can ensure that corresponding points meet the scattering consistency, thereby improving accuracy and tomographic imaging precision.

[0087] Phase correlation is used to measure the consistency of target scattering characteristics in multi-view imaging. Phase corresponding point focusing is adopted, and coherent information is used to improve the robustness of corresponding point focusing, reduce the impact of noise, and enhance the stability of corresponding points between images across cruises.

[0088] Step S102: Calculate the score based on the weights to determine the registered data matrix, and perform sliding window covariance matrix smoothing based on the registered data matrix to obtain the smoothed covariance matrix.

[0089] See Figure 3 , Figure 3 This is a flowchart illustrating the subspace enhancement process provided in this embodiment of the invention. The scores are calculated based on weights to obtain the corresponding points passed through the route. The complex values ​​of the corresponding points passed through the route are stored to obtain the registered data matrix. Where M refers to the number of sampling points in the elevation direction, and each row in the registered data matrix is ​​a channel / sub-aperture, and each column is a fast time or frequency point.

[0090] Let the sliding window length be L = N, and the total number of sliding operations be K = N - L + 1. The k-th subarray is:

[0091]

[0092] The corresponding covariance matrix is:

[0093]

[0094] Finally, the smoothed covariance matrix after sliding window covariance matrix smoothing is:

[0095]

[0096] The smoothing of the covariance matrix of the sliding subarray effectively improves the statistical stability of the covariance matrix by weighted averaging of multiple local subarrays, significantly suppressing interference from high-frequency noise and local abrupt changes. This method reduces the impact of random noise on spectral estimation by fusing local redundant information, thereby enhancing the robustness and discriminative power of spectral peak identification.

[0097] Step S103: Perform symmetric processing on the smoothed covariance matrix to construct weighting factors.

[0098] Traditional methods lack symmetry and may suffer from numerical errors due to the non-Hermitian nature of the covariance matrix. In this embodiment of the invention, the forward and backward smooth fusion can be achieved by introducing an antisymmetric permutation matrix, which effectively improves the Hermitian nature and numerical stability of the covariance matrix. This not only enhances the orthogonality of the signal and noise subspaces but also significantly suppresses the interference of non-ideal terms on imaging quality, making it particularly suitable for accurate 3D reconstruction in low signal-to-noise ratio and complex scattering environments.

[0099] In one implementation, the smoothed covariance matrix is ​​symmetrically processed to construct weighting factors, including:

[0100] The symmetric covariance matrix is ​​obtained by performing symmetric processing on the antisymmetric permutation matrix and the smoothed covariance matrix.

[0101] Weighting factors are constructed by processing the symmetric covariance matrix using diagonal matrix functions.

[0102] Specifically, the aforementioned R smooth The smoothed covariance matrix has dimensions N×N, and the size of the antisymmetric permutation matrix J is based on R. smooth The antisymmetric permutation matrix J is determined to be:

[0103]

[0104] After obtaining the smoothed covariance matrix and the antisymmetric permutation matrix, the symmetric covariance matrix R1 is determined as follows:

[0105]

[0106] Based on this, the symmetric covariance matrix is ​​processed by the diagonal matrix function diag(·), and the weighting factor W is constructed, including:

[0107]

[0108] in, It represents the set of real numbers.

[0109] In this embodiment of the invention, the weighting factor can suppress high-energy noise channels and improve the main lobe focusing and side lobe suppression capabilities, which is particularly effective in sparse / occluded environments.

[0110] Introducing Hermitian symmetry processing to construct an inverse covariance matrix effectively enhances the positive definiteness and symmetry of the matrix, which helps to construct a purer noise subspace and improve the spectral peak resolution capability in multi-target scenarios.

[0111] Step S104: Perform eigenvalue decomposition on the smoothed covariance matrix to construct the noise subspace.

[0112] In this embodiment of the invention, eigenvalue decomposition of the smoothed covariance matrix includes:

[0113]

[0114] Among them, U s The eigenvector matrix representing the signal subspace; Λ s U represents the eigenvalue matrix corresponding to the signal subspace; NThe eigenvector matrix representing the noise subspace; Λ N This represents the eigenvalue matrix corresponding to the noise subspace; the superscript H indicates the conjugate transpose operation of the matrix.

[0115] Based on the above eigenvalue decomposition results, the signal space and noise space are separated:

[0116] Suppose there are d signal sources in the observed signal. Then the first d largest eigenvalues ​​correspond to the signal subspace, and the remaining Md smaller eigenvalues ​​correspond to the noise subspace E. n :

[0117] E n =[e d+1 ,e d+2 ,…e M ];

[0118] By extracting the principal components of the signal, signals and noise can be accurately distinguished. Extraction of the noise subspace En can significantly improve spectral estimation results, making the MUSIC method more accurate. The role of the noise subspace is to reduce the influence of noise, thereby more accurately identifying scatterers.

[0119] Step S105: Perform spectral estimation based on the measurement matrix, weighting factor, and noise subspace to complete three-dimensional tomographic SAR imaging.

[0120] The measurement matrix is ​​mainly used to obtain low-dimensional observation data from high-dimensional observation signals. It is a key bridge for mapping the distribution of scatterers in the elevation direction to echo data at multiple observation angles.

[0121] In this embodiment of the invention, the measurement matrix, weighting factor, and noise subspace are substituted into the MUSIC spectrum calculation formula for spectrum estimation, including:

[0122]

[0123] Among them, P MUSIC (θ i ) represents the spectral estimate of the i-th column in the measurement matrix; a(θ) i ) represents the i-th column in the measurement matrix, representing the i-th direction θ. i Or elevation candidate point θ i The direction vector; the superscript H indicates the conjugate transpose operation of the matrix.

[0124] In tomographic SAR, the three-dimensional structure of a target can be estimated based on spectral values, thus enabling tomographic SAR imaging.

[0125] In this embodiment of the invention, a weighted score is calculated based on the Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images. By integrating the characteristics of Euclidean distance, phase correlation, and complex coherence coefficient, high-precision corresponding point focusing is achieved. The statistical stability of the covariance matrix is ​​effectively improved by employing a sliding window covariance matrix smoothing method, significantly suppressing interference from high-frequency noise and local abrupt changes. By introducing a weighting factor, robustness under signal-to-noise ratio is improved, increasing the main lobe intensity and suppressing side lobes. Based on this, the tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation provided by this embodiment of the invention can maintain good corresponding point focusing accuracy and 3D imaging quality even in complex scenarios such as urban areas, providing theoretical support and an engineering feasibility basis for high-precision TomoSAR imaging tasks.

[0126] The simulation experiment of a tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation provided by the embodiments of the present invention is as follows:

[0127] See Figure 4 and Figure 5 , Figure 4 This is a schematic diagram comparing the first imaging method of the tomographic SAR imaging method provided in this embodiment of the invention with existing tomographic SAR imaging methods. Figure 5 This is a second imaging comparison diagram between the tomographic SAR imaging method provided in this embodiment of the invention and existing tomographic SAR imaging methods, including MUSIC, Capon, CS-OMP, ANM, and ISTA. Figure 4 and Figure 5 It can be seen that the imaging effect and accuracy of the tomographic SAR imaging method provided in this embodiment of the invention are significantly better than those of existing tomographic SAR imaging methods.

[0128] Refer to Table 1, which is a comparison table of the performance indicators between the tomographic SAR imaging method provided in this embodiment of the invention and existing tomographic SAR imaging methods, as detailed below:

[0129] Table 1 Comparison of Indicators

[0130] Dispersion K-neighborhood point cloud entropy This method 0.0412 3.7049 MUSIC 0.1248 4.0158 Capon 0.0827 4.0441 CS-OMP 0.0779 3.8654 ANM 0.1209 3.8889 ISTA 0.0854 3.7434

[0131] This invention proposes an adaptive weighting mechanism that, during the spectral estimation process, effectively enhances the main lobe energy focusing based on the local signal-to-noise distribution, while suppressing side lobe leakage and spurious peak interference, thereby improving the overall spectral resolution and imaging stability.

[0132] This invention introduces a corresponding point focusing scoring mechanism based on fused features. Building upon traditional image registration strategies, it constructs a comprehensive scoring function (including Euclidean distance, complex coherence coefficient, and phase correlation) to impose full-dimensional constraints, significantly reducing corresponding point focusing errors and achieving accurate point localization. Subsequently, a sliding subarray is used for covariance matrix smoothing to construct a cleaner noise subspace. Adaptive weighting is then applied for multi-signal classification in 3D tomographic SAR imaging, ultimately significantly improving point cloud reconstruction quality and effectively reducing elevation estimation errors. Specifically, the dispersion reaches 0.0412, nearly half that of the best result of 0.0779 achieved by other methods, demonstrating higher focusing accuracy. The K-neighborhood point cloud entropy is 3.7049, superior to the lowest value of 3.8654 achieved by other methods, fully demonstrating the advantages of this method in terms of structural clarity and information integration.

[0133] Based on the same inventive concept, embodiments of the present invention also provide a tomographic SAR imaging device that combines corresponding point focusing and subspace spectrum estimation, see [link to relevant documentation]. Figure 6 , Figure 6 This is a schematic diagram of a tomographic SAR imaging device that combines corresponding point focusing and subspace spectrum estimation according to an embodiment of the present invention. The tomographic SAR imaging device includes:

[0134] Calculation module 601 is used to calculate the weight and score based on the Euclidean distance, complex coherence coefficient and phase correlation between the main flight image and multiple other flight images;

[0135] The smoothing module 602 is used to calculate the score based on the weights to determine the registered data matrix, and to perform sliding window covariance matrix smoothing based on the registered data matrix to obtain the smoothed covariance matrix.

[0136] The symmetry processing module 603 is used to perform symmetry processing on the smoothed covariance matrix to construct weighting factors;

[0137] The eigenvalue decomposition module 604 is used to perform eigenvalue decomposition on the smoothed covariance matrix to construct a noise subspace.

[0138] The spectrum estimation module 605 is used to perform spectrum estimation based on the measurement matrix, the weighting factor and the noise subspace to complete three-dimensional tomographic SAR imaging.

[0139] In this embodiment of the invention, a weighted score is calculated based on the Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images. By integrating the characteristics of Euclidean distance, phase correlation, and complex coherence coefficient, high-precision corresponding point focusing is achieved. The statistical stability of the covariance matrix is ​​effectively improved by employing a sliding window covariance matrix smoothing method, significantly suppressing interference from high-frequency noise and local abrupt changes. By introducing a weighting factor, robustness under signal-to-noise ratio is improved, increasing the main lobe intensity and suppressing side lobes. Based on this, the tomographic SAR imaging method combining corresponding point focusing and subspace spectrum estimation provided by this embodiment of the invention can maintain good corresponding point focusing accuracy and 3D imaging quality even in complex scenarios such as urban areas, providing theoretical support and an engineering feasibility basis for high-precision TomoSAR imaging tasks.

[0140] Optional, a calculation module, specifically used for:

[0141] The Euclidean distance, complex coherence coefficient, and phase correlation between the main flight image and multiple other flight images are weighted according to an initial threshold and preset weights to obtain an intermediate weight calculation score. The preset weights include preset weights for Euclidean distance, complex coherence coefficient, and phase correlation. The intermediate weight calculation score is determined iteratively until it is less than a preset threshold, at which point the intermediate weight calculation score in the current iteration is determined as the weight calculation score.

[0142] Optionally, the method for determining the preset weights includes:

[0143]

[0144] Where i∈{1,2,3}, λ1 represents the preset weight of Euclidean distance, λ2 represents the preset weight of complex coherence coefficient, and λ3 represents the preset weight of phase correlation. Let λ represent the value of the t-th iteration. i ; Let λ represent the (t+1)th iteration. i ΔS represents the gradient of the score calculated using intermediate weights; η represents the learning rate.

[0145] Optional, symmetric processing module, specifically used for:

[0146] The antisymmetric permutation matrix and the smoothed covariance matrix are symmetrically processed to obtain a symmetric covariance matrix; the symmetric covariance matrix is ​​then processed by a diagonal matrix function to construct a weighting factor.

[0147] Optional, spectral estimation module, specifically used for:

[0148] Substituting the measurement matrix, the weighting factor, and the noise subspace into the MUSIC spectrum calculation formula, spectral estimation is performed to complete three-dimensional tomographic SAR imaging.

[0149] Optionally, the MUSIC spectrum calculation formula includes:

[0150]

[0151] Among them, P MUSIC (θ i ) represents the i-th elevation candidate point θ i Spectral estimate; a(θ) i ) represents the i-th column in the measurement matrix, representing the i-th candidate elevation point θ. i The direction vector; W represents the weighting factor; E n The superscript H represents the noise subspace; the superscript H indicates the conjugate transpose operation of the matrix.

[0152] It should be noted that the terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention.

[0153] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0154] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings and the disclosure in carrying out the claimed invention. In the description of the invention, the word "comprising" does not exclude other components or steps, "a" or "an" does not exclude a plurality, and "a plurality" means two or more, unless otherwise explicitly specified. Furthermore, while different embodiments may describe certain measures, this does not mean that these measures cannot be combined to produce good results.

[0155] As the device embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.

[0156] It should be noted that the apparatus of the present invention is an apparatus that applies the above-mentioned tomographic SAR imaging method of combined corresponding point focusing and subspace spectrum estimation. Therefore, all embodiments of the above-mentioned tomographic SAR imaging method of combined corresponding point focusing and subspace spectrum estimation are applicable to this apparatus and can achieve the same or similar beneficial effects.

[0157] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A tomographic SAR imaging method combining named spot focusing with subspace spectral estimation, characterized by, The tomographic SAR imaging method comprises: The weight calculation score is calculated based on the Euclidean distance, complex coherence and phase correlation between the main flight image and the multiple other flight images; A post-registration data matrix is determined according to the weight calculation score, and a sliding window covariance matrix smoothing process is performed according to the post-registration data matrix to obtain a smoothed covariance matrix; Symmetric processing is performed on the smoothed covariance matrix to construct a weighting factor; Eigenvalue decomposition is performed on the smoothed covariance matrix to construct a noise subspace; Spectral estimation is performed based on the measurement matrix, the weighting factor and the noise subspace to complete three-dimensional tomographic SAR imaging.

2. The tomographic SAR imaging method of claim 1, characterized in that, The weight calculation score is calculated based on the Euclidean distance, complex coherence and phase correlation between the main flight image and the multiple other flight images, comprising: The weight calculation score is calculated based on the Euclidean distance, complex coherence and phase correlation between the main flight image and the multiple other flight images, comprising: The step of determining the intermediate weight calculation score is iteratively updated until the intermediate weight calculation score is less than a preset threshold, and the intermediate weight calculation score under the current iteration is determined as the weight calculation score.

3. The tomographic SAR imaging method of claim 2, wherein, The determination method of the preset weight comprises: wherein i∈{1,2,3}, λ1 represents a preset weight of the Euclidean distance, λ2 represents a preset weight of the complex coherence coefficient, and λ3 represents a preset weight of the phase correlation; denotes λ i of the tth iteration denotes λ i of the (t+1)th iteration; ΔS represents a gradient of the intermediate weight calculation score; and η represents a learning rate.

4. The tomographic SAR imaging method of claim 1, wherein, Symmetric processing is performed on the smoothed covariance matrix to construct a weighting factor, comprising: Symmetric processing is performed on the smoothed covariance matrix to construct a weighting factor, comprising: Symmetric processing is performed on the smoothed covariance matrix to construct a weighting factor, comprising:

5. The tomographic SAR imaging method of claim 1, wherein, Spectral estimation is performed based on the measurement matrix, the weighting factor and the noise subspace to complete three-dimensional tomographic SAR imaging, comprising: Spectral estimation is performed based on the measurement matrix, the weighting factor and the noise subspace to complete three-dimensional tomographic SAR imaging, comprising:

6. The tomographic SAR imaging method of claim 5, wherein, The MUSIC spectral calculation formula comprises: where P MUSIC (θ i ) denotes the spectral estimate of the i-th elevation candidate point θ i ; a(θ i ) denotes the i-th column in the measurement matrix, representing the direction vector of the i-th elevation candidate point θ i ; W denotes the weighting factor; E n denotes the noise subspace; the superscript H denotes the conjugate transpose operation of a matrix.

7. A tomographic SAR imaging apparatus combining named spot focusing with subspace spectral estimation, characterized by The tomographic SAR imaging device comprises: The calculation module is configured to calculate a weight calculation score based on the Euclidean distance, complex coherence and phase correlation between the main flight image and the multiple other flight images; The smoothing module is configured to determine a post-registration data matrix according to the weight calculation score, and perform a sliding window covariance matrix smoothing process according to the post-registration data matrix to obtain a smoothed covariance matrix; The symmetric processing module is configured to perform symmetric processing on the smoothed covariance matrix to construct a weighting factor; The eigenvalue decomposition module is configured to perform eigenvalue decomposition on the smoothed covariance matrix to construct a noise subspace; The spectral estimation module is configured to perform spectral estimation based on the measurement matrix, the weighting factor and the noise subspace to complete three-dimensional tomographic SAR imaging.

8. The tomographic SAR imaging apparatus as claimed in claim 7, characterized in that The calculation module is specifically configured to: The initial threshold and the preset weight are used to weight and allocate the Euclidean distance, the complex coherence coefficient and the phase correlation between the main flight image and the multiple other flight images to obtain an intermediate weight calculation score; the preset weight includes a preset weight of the Euclidean distance, a preset weight of the complex coherence coefficient and a preset weight of the phase correlation; the step of determining the intermediate weight calculation score is iteratively updated until the intermediate weight calculation score is less than a preset threshold, and the intermediate weight calculation score under the current iteration is determined as the weight calculation score.

9. The tomographic SAR imaging apparatus as claimed in claim 8, characterized in that The determination manner of the preset weight includes: wherein i∈{1,2,3}, λ1 represents a preset weight of the Euclidean distance, λ2 represents a preset weight of the complex coherence coefficient, and λ3 represents a preset weight of the phase correlation; denotes λ i of the tth iteration denotes λ i of the (t+1)th iteration; ΔS represents a gradient of the intermediate weight calculation score; and η represents a learning rate.

10. The tomographic SAR imaging apparatus as claimed in claim 7, characterized in that The symmetry processing module is specifically configured to: Symmetry processing is performed according to the anti-symmetry permutation matrix and the smoothed covariance matrix to obtain a symmetrized covariance matrix; the symmetrized covariance matrix is processed through a processing diagonal matrix function to construct a weighting factor.

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