Fast high-resolution imaging method based on whirling electromagnetic waves

Abstract

The application discloses a kind of fast high-resolution imaging methods based on vortex electromagnetic wave, which constructs the two-dimensional imaging model of pitch angle and azimuth angle based on concentric circular ring array, realizes low-rank decomposition to the received echo and observation matrix by means of spherical harmonics function, introduces orthogonal matching pursuit algorithm to the scattering point in observation plane for target reconstruction, so as to realize the two-dimensional joint imaging of radar target pitch angle and azimuth angle.The imaging mode of joint OMP algorithm and spherical harmonic decomposition proposed in the application can realize higher imaging resolution compared with the traditional generalized inverse solution mode, while greatly reducing the operation amount of imaging process, effectively saving calculation time.

Description

Technical Field

[0001] This invention relates to the field of radar target imaging, and more specifically to a fast, high-resolution imaging method based on vortex electromagnetic waves. Background Technology

[0002] With the continuous development of modern science and technology, people have increasingly higher requirements for the resolution of radar imaging. However, traditional radar imaging technology requires the relative motion between the radar and the target to form a virtual aperture, which severely restricts the improvement of radar's overall detection capabilities. Vortex electromagnetic waves, due to their special helical wavefront structure and the infinity and orthogonality of their mode numbers, introduce new rotational degrees of freedom for target imaging, providing a feasible way to break through the bottleneck of traditional radar imaging technology.

[0003] Two-dimensional imaging results of vortex electromagnetic waves regarding elevation and azimuth angles can be easily obtained by solving the imaging model equations. However, the massive amount of data makes solving the equations using generalized inverse methods time-consuming, and the imaging results obtained using this method often have poor resolution. Currently, many sparse reconstruction methods exist to accurately solve for target parameters, which can significantly improve the resolution of the reconstructed image. However, on the one hand, the transmission of a large number of OAM modes in the sparse reconstruction model requires sufficient time to accumulate; on the other hand, the large-scale scenes in sparse imaging also increase computational costs. Both factors significantly increase the computational time complexity.

[0004] Therefore, achieving high-resolution imaging of vortex electromagnetic waves while reducing the computational time cost during the imaging process is of great research significance and practical application value for the development of radar imaging technology. Summary of the Invention

[0005] The purpose of this invention is to provide a fast, high-resolution imaging method based on vortex electromagnetic waves, which can reduce the imaging computation time while achieving high-resolution imaging of vortex electromagnetic waves.

[0006] The technical solution for achieving the objective of this invention is as follows: Firstly, this invention provides a fast, high-resolution imaging method based on vortex electromagnetic waves, comprising the following steps:

[0007] Step 1: Determine the order of the spherical harmonic expansion by fitting the results before and after the expansion.

[0008] Step 2: Construct the echo model under plane wave spherical harmonic expansion;

[0009] Step 3: Estimate the scattering coefficient of the observation area using the orthogonal matching pursuit method;

[0010] Step 4: Output a two-dimensional target image with elevation and azimuth angles.

[0011] In a second aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described in the first aspect.

[0012] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0013] Fourthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in the first aspect.

[0014] Compared with existing technologies, the advantages of this invention are as follows: This invention provides a fast, high-resolution imaging method based on vortex electromagnetic waves. A two-dimensional imaging model of the echo signal's elevation and azimuth angles is constructed using a concentric ring array. Low-rank decomposition of the observation matrix using spherical harmonic functions significantly reduces the time cost in imaging computation. Simultaneously, the OMP algorithm is introduced to reconstruct the two-dimensional angular information of each scattering point, achieving two-dimensional high-resolution imaging of vortex electromagnetic waves with respect to elevation and azimuth angles. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of a vortex electromagnetic wave observation model.

[0016] Figure 2 The graph shows the variation of the spherical harmonic expansion order under different influencing factors, where (a) shows the variation of the spherical harmonic expansion order with frequency, and (b) shows the variation of the spherical harmonic expansion order with array radius.

[0017] Figure 3 The image shows the two-dimensional imaging results of the elevation and azimuth angles of the two target points.

[0018] Figure 4 The images show the elevation angle imaging results, where (a) is the imaging result under the direct inversion method and (b) is the imaging result under the plane wave spherical harmonic expansion.

[0019] Figure 5 A comparison of imaging time for the direct inversion method and the plane wave spherical harmonic expansion method. Detailed Implementation

[0020] A fast, high-resolution imaging method based on vortex electromagnetic waves includes the following steps:

[0021] Step 1: Determine the order of the spherical harmonic expansion by fitting the results before and after the expansion.

[0022] In physics, plane waves can be expressed as a linear combination of spherical waves using the spherical harmonic expansion formula. This can be further generalized to a spherical harmonic expansion of plane waves using the spherical harmonic function addition formula, facilitating discussion and research in practical applications. The order of the expansion during imaging can be determined based on the fitting results before and after the spherical harmonic expansion. Specifically, the fitting operation involves illuminating the target with a single-mode OAM beam at a given system operating frequency and array radius, and observing the decomposition order when the echo after spherical harmonic decomposition matches the original echo. This order is the desired spherical harmonic expansion order.

[0023] The specific expression for the spherical harmonic expansion of a plane wave is:

[0024]

[0025] Where k is the wave number, i is the imaginary part, r is the array radius, l,m are the orders of the spherical harmonic expansion in the global coordinate system, Y(·) is the spherical harmonic function, and j(·) is the spherical Bessel function of the first kind.

[0026] Based on the fitting results before and after the spherical harmonic expansion, a reasonable order of spherical harmonic expansion is determined.

[0027] Adopting such Figure 1 The UCCA array shown receives the echo reflected from the scattering point. The decomposition order required for the spherical harmonic expansion of the echo is investigated under different frequencies and array radii. The order required for the subsequent plane wave spherical harmonic expansion is determined based on the factors affecting the change of the decomposition order. Figure 2 Simulation results show that the decomposition order required for spherical harmonic decomposition is related to the frequency of the emitted electromagnetic wave and the array radius of the concentric ring array, and increases continuously with the increase of the emission frequency and the array radius.

[0028] Step 2: Construct the echo model under plane wave spherical harmonic expansion;

[0029] like Figure 1 The diagram shows a multiple-transmitter, multiple-receiver model, with both the transmitting and receiving arrays using UCCA arrays. The echo model under plane wave spherical harmonic expansion is as follows:

[0030]

[0031] in,

[0032]

[0033]

[0034]

[0035] A(m), B(m), and C represent the positive mode OAM wave, the negative mode OAM wave, and the Gaussian beam, respectively. These three decompositions describe the echo spherical harmonic expansion of the vortex electromagnetic wave in different modes (positive order mode, negative order mode, and zero mode).

[0036] Among them, the distribution sequence I s Let k be the induced current generated on the target when an incident wave of arbitrary mode is applied, where k is the wave number, i is the imaginary part, and r is the wave number. s Let be the radii of the concentric ring array (UCCA), l be the order of the spherical harmonic decomposition, m be the topological charge, and θ and . These represent the elevation and azimuth angles of each scattering point from the origin in spherical coordinates. It contains the elevation and azimuth angles of each array element from the origin in spherical coordinates, Y(·) is a spherical harmonic function, and j(·) is a spherical Bessel function of the first kind.

[0037] Step 3: Estimate the scattering coefficient of the observation area using the Orthogonal Matching Pursuit (OMP) algorithm;

[0038] Considering that radar targets are typically composed of several independent high-frequency scatterers, sparse recovery theory can be applied to the reconstruction of the detected target. By meshing the observation area and combining the spherical harmonic decomposition methods for echoes in various modes mentioned above, the sparse representation model for vortex electromagnetic wave imaging can be constructed as follows:

[0039]

[0040] in, The echo received by the receiving antenna. For the observation matrix, is the target scattering coefficient vector, representing target information; M is the total number of modes emitted by the system, and l is the order of the spherical harmonic expansion; observation matrix. Each row represents the echo of a certain vortex electromagnetic wave mode under each grid, and each column represents the echo of a certain grid under each vortex electromagnetic wave mode. Let be the decomposition vector of each scattering point in the spherical harmonic expansion. Let be the decomposition vector of each array element in the spherical harmonic expansion.

[0041] For the imaging model equations mentioned above, the OMP algorithm is used to solve the equations and quickly reconstruct the two-dimensional angular information of each scattering point.

[0042] Step 4: Output a two-dimensional target image with elevation and azimuth angles.

[0043] Based on the imaging equations before and after spherical harmonic decomposition shown above, it can be observed that the original observation matrix is ​​M×Q, which is the total number of modes traversed during imaging multiplied by the total number of grids in the observation area. The resulting matrix typically has a large amount of data, making the process of obtaining the imaging equation using the generalized inverse method extremely time-consuming. However, by performing low-rank decomposition on the echoes under different modes, the original observation matrix can be decomposed into the product of two matrices, M×L and L×Q. Calculations show that the computational complexity of the original solution process is M×Q, while the computational complexity after spherical harmonic expansion becomes L×(M+Q). Since the order L of the spherical harmonic decomposition is always less than the dimension of the original observation matrix, the time cost of the imaging computation process is significantly reduced.

[0044] For the aforementioned sparse representation model of radar imaging, the sparse recovery method can accurately solve for the target parameters, thereby significantly improving the resolution of the reconstructed image. The OMP algorithm, as a sparse recovery method, has a significant advantage in computational speed compared to other sparse recovery methods.

[0045] The core idea of ​​the OMP algorithm is to find the observation matrix in each iteration. China to echo The column contributing the most is selected and updated in the support set. The sparse solution is then estimated using the least squares method to obtain a new iterative residual. This process is repeated iteratively to find the column vector most similar to the residual. As a sparse recovery method, the number of iterations in the OMP algorithm depends on the number of scattering points in the observed scene, thus enabling high-resolution reconstruction of the target's two-dimensional angular information in a relatively short time.

[0046] The beneficial effects of this invention are illustrated below with simulation examples.

[0047] Assume the frequency of the emitted electromagnetic wave is 1 GHz and the wave number k is 20.9440. The UCCA array consists of two rings with radii of 1.35 meters and 1.45 meters, respectively, each ring composed of 20 array elements arranged at equal intervals. There are two independent scattering points in space, P1(10°, 50°) and P2(20°, 50°), and the ergodic mode number is set to -10:10. Figure 3 This figure shows the two-dimensional imaging results of the elevation and azimuth angles of two scattering points in space. As can be seen from this figure, the present invention can achieve high-resolution two-dimensional imaging of the target with fewer modes.

[0048] Algorithm resolution simulation: In order to compare the imaging method of this invention with existing methods, Figure 4The blurred images in the elevation direction under both the proposed method and the direct inversion method were simulated, with the simulation parameters consistent with those described above. A comparison of the simulation results shows that the imaging resolution under the direct inversion method is not high, and there is also the phenomenon of imaging target errors, while the method of this invention can achieve high-resolution imaging of the simulated target.

[0049] Algorithm Efficiency Simulation: The use of plane wave spherical harmonic expansion and the OMP algorithm in this invention aims to address the computational efficiency issue when the observation matrix data volume is large. To demonstrate the significant contribution of this invention to improving imaging efficiency, the time required to achieve complete imaging using this invention is compared with the time required to achieve complete imaging using the direct inversion method. Figure 5 A bar chart comparing the time consumption of the two methods was plotted. The frequency of the emitted electromagnetic wave in the simulation was 1 GHz, and the wave number k was 20.9440. The radii of the circular rings set in the UCCA array were 0.4 meters and 0.5 meters, respectively, with each ring consisting of 20 array elements arranged equidistantly. A scattering point P3 (25°, 50°) was set in the simulation, and the entire imaging observation plane was divided into a 100×100 grid. As the number of modes traversed during the imaging process increases, the data volume of the entire observation matrix also increases, which means that the time consumed by the entire imaging process also increases. Four cases of mode number variation were set in the simulation: -10:10, -20:20, -50:50, and -100:100. The bar chart comparing the imaging time of the direct inversion method and the plane wave spherical harmonic expansion method is shown below. Figure 5 As shown. Figure 5 This indicates that, under real-valued computation, the imaging algorithm in this invention can improve computational efficiency by more than 50%, which greatly reduces the time cost in imaging computation.

[0050] This invention provides a fast, high-resolution imaging method based on vortex electromagnetic waves. A two-dimensional imaging model with elevation and azimuth angles is constructed using a concentric ring array. Low-rank decomposition of the observation matrix is ​​performed using spherical harmonic functions, and the OMP algorithm is introduced to achieve high-resolution target reconstruction within the observation plane. Compared with traditional imaging methods, this invention can significantly reduce the computational load during the imaging process while achieving high-resolution imaging, greatly reducing the time cost of imaging.

Claims

1. A fast, high-resolution imaging method based on vortex electromagnetic waves, characterized in that, Includes the following steps: Step 1: Determine the order of the spherical harmonic expansion by fitting the results before and after the expansion. The order of the spherical harmonic expansion during the imaging process is determined based on the fitting results before and after the spherical harmonic expansion. The specific fitting operation is as follows: under the set system operating frequency and array radius, the target is illuminated with a single-mode OAM beam, and the decomposition order is observed when the echo after spherical harmonic decomposition is consistent with the original echo. This order is the spherical harmonic expansion order to be sought. Step 2: Construct the echo model under plane wave spherical harmonic expansion; Step 3: Estimate the scattering coefficient of the observation area using the orthogonal matching pursuit method; construct a sparse representation model for vortex electromagnetic wave imaging: ； in, The echo received by the receiving antenna. For the observation matrix, The target scattering coefficient vector represents target information; M is the total number of modes emitted by the system; the observation matrix... Each row represents the echo of a certain vortex electromagnetic wave mode under each grid, and each column represents the echo of a certain grid under each vortex electromagnetic wave mode. Let be the decomposition vector of each scattering point in the spherical harmonic expansion. For each element in the spherical harmonic expansion, decompose the vectors. The OMP algorithm is used to solve the equations and reconstruct the two-dimensional angular information of each scattering point; Step 4: Output a two-dimensional target image with elevation and azimuth angles.

2. The fast, high-resolution imaging method based on vortex electromagnetic waves according to claim 1, characterized in that, In step 1, the specific expression for the spherical harmonic expansion of a plane wave is: ； Where k is the wave number and i is the imaginary part. Let l be the array radius, and l,m be the order of the spherical harmonic expansion in the global coordinate system. It is a spherical harmonic function. It is a Bessel function of the first kind of sphere.

3. The fast, high-resolution imaging method based on vortex electromagnetic waves according to claim 2, characterized in that, Step 2: Constructing the echo model under plane wave spherical harmonic expansion: ； in, , ， ； , , These represent the echo spherical harmonic expansion under positive order modes, negative order modes, and zero mode, respectively; Among them, the distribution sequence The induced current generated on the target when an incident wave of any mode is applied. Let be the radii of the concentric ring array, l be the order of the spherical harmonic decomposition, and m be the topological charge number. and These represent the elevation and azimuth angles of each scattering point from the origin in spherical coordinates. It includes the elevation and azimuth angles of each array element from the origin in spherical coordinates.

4. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-3.

6. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method described in any one of claims 1-3.

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