Enhanced imaging method for microwave ESM sparse scanning system

Abstract

The invention discloses an enhanced imaging method for a microwave ESM sparse scanning system, and the method comprises the steps: firstly carrying out the sampling of N * N sampling points in a plane through employing an ESM plane scanning system, and obtaining an N * N-dimensional original phase sample Y and an N * N-dimensional original amplitude sample G; downsampling the original phase sample Y into an initial phase sample yk, and downsampling the original amplitude sample G into an initial amplitude sample D; restoring the initial amplitude sample yk into an N * N-dimensional amplitude sample through K-means clustering and Voronoi micro-grid division, restoring the initial phase sample yk into an N * N phase sample through DCT (Discrete Cosine Transformation) and gradient descent, and reading matlab respectively to obtain an amplitude information graph M and a phase information graph S; and finally, obtaining a radiation source plane diffraction pattern I * through a far and near field transformation algorithm on the amplitude information pattern M and the phase information pattern S. According to the technology, high-resolution reduction of the near-field atlas of the microwave radiation source can be realized on the basis of reducing initial samples, and the technology is expected to be applied to EMI detection and positioning in the electronic industry.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic compatibility detection and image processing in electronic information technology, and in particular relates to an enhanced imaging method for a microwave ESM sparse scanning system. Background Art

[0002] With the rapid development of electronic systems, higher requirements are put forward for the detection of electromagnetic radiation (EMI) of electronic equipment. The interference source location technology based on near field scanning (NFS) is difficult to further improve the detection accuracy due to the limitations of scanning distance and probe size. In contrast, emission source microscopy (ESM) is a new radiation source identification method that can directly measure the far field information (including amplitude information and phase information) of the emission source, and then reversely propagate the near field image on the source surface, so that the position of the emission source can be more accurately calibrated. This technology has higher imaging accuracy and has become a research hotspot in this field. The traditional method is to sample uniform samples on a scanning plane, but due to the large number of sample data, the data acquisition time for each position is long. If the sample size is reduced (for example, sparse scanning is performed), the image resolution obtained by direct inversion is low, so it is of great significance to improve the scanning efficiency while maintaining the required accuracy. Summary of the invention

[0003] The main purpose of the present invention is to provide an enhanced imaging method for a microwave ESM sparse scanning system, so as to solve the problem of high-resolution restoration imaging of the near-field spectrum of a microwave radiation source based on the ESM sparse scanning amplitude information and phase information while reducing the initial samples.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] An enhanced imaging method for a microwave ESM sparse scanning system comprises the following steps:

[0006] (1) The ESM plane scanning system is used to sample N*N sampling points in the plane to obtain the amplitude and phase of each sampling point on the spatial sampling plane. The phase information of all sampling points constitutes an N*N dimensional original phase sample Y, and the amplitude information of all sampling points constitutes an N*N dimensional original amplitude sample G;

[0007] (2) Downsample the original phase sample Y to the initial phase sample y k , downsample the original amplitude sample G to the initial amplitude sample D;

[0008] The original phase sample Y is downsampled to the initial phase sample y kSpecifically, the original phase sample Y is subjected to step-by-step mask convolution processing, each time using a convolution kernel with the same dimension as the original phase sample, that is, forming an N*N mask matrix, defined as Γ (N*N) , then the phase sample Y after mask processing k for:

[0009] Y k =∑∑Y*Γ (N*N) (3)

[0010] For any given sparsity phase information y k , there exists a constant δ K ∈(0,1), so that inequality (4) holds:

[0011]

[0012] Y k is the output information after mask processing, combined with the observation matrix φ, to obtain the initial phase sample y k ;

[0013] The downsampling of the original amplitude sample G to the initial amplitude sample D is specifically to divide the N*N dimensional original amplitude sample G into countless different row vectors and column vectors, and then set the sampling parameters, randomly extract some rows and some columns therefrom, and obtain a random sample with the same dimension as the set sampling parameters, which is recorded as the initial amplitude sample D;

[0014] (3) The initial amplitude sample y is divided into k Restored to N*N dimensional amplitude samples, the initial phase samples y are transformed by DCT transformation and gradient descent k Restored to N*N phase samples, matlab reads N*N dimensional amplitude samples and N*N phase samples respectively to obtain amplitude information graph M and phase information graph S;

[0015] (4) The amplitude information graph M and the phase information graph S can be transformed into the radiation source plane diffraction graph I through the far-field and near-field transformation algorithm. * .

[0016] The present invention restores the initial amplitude sample to an N*N dimensional amplitude sample through K-means clustering and Voronoi micro-grid partitioning, specifically,

[0017] (301-1) Use K-means clustering algorithm to divide the initial amplitude sample set into K clusters, each cluster represents similar sampling points, let C i represents the i-th cluster, then the initial amplitude sample set D is regarded as a set of K clusters, and the i-th cluster in the initial amplitude sample set D is C i, i is a positive integer between 1 and k, that is: D = {C1, C2, ..., C k}, each cluster is a set of similar sampling points, and the jth sampling point in the i-th cluster is x ij , j is a positive integer between 1 and o, that is: C i ={x i1 , x i2 , …, x io}, the optimal number of clusters K is determined by the error square sum SSE model, and the SSE model evaluation expression is:

[0018]

[0019] Among them, p represents the sampling point in the cluster, q i represents the centroid point,

[0020] (301-2) Next, perform Voronoi cell division on each cluster, calculate the Voronoi cell size and gradient parameters of each initial sampling point, and the jth sampling point x in the i-th cluster. ij The size of the Voronoi cell is regarded as the ratio of the area of ​​the cell to the area of ​​all Voronoi cells in the cluster. Let the jth sampling point x in the i-th cluster be ij The unit cell area is V(x ij ), then the sampling point x ij The distribution density S(x ij ) is expressed as:

[0021]

[0022] The gradient is obtained by calculating the change in field strength between adjacent samples. Let x m is the sampling point x ij There are adjacent sampling points with a common cell wall or vertex, and the electric field gradient between the adjacent sampling points can be expressed as:

[0023]

[0024] represents the absolute value of the change in electric field strength, Represents the sampling point x m The electric field strength is obtained by determining the distribution density and gradient value of each cluster sampling point. Based on the distribution density of the sampling points, a reasonable linear image interpolation is performed on the downsampled amplitude sampling points to obtain the reconstructed amplitude sample M.

[0025] The present invention restores the initial phase sample to N*N phase sample by DCT transformation and gradient descent, specifically:

[0026] (302-1) The visualized sparse matrix Ψ is calculated by formulas (11) and (13). According to (9), we know that the known variable y k , Φ, Ψ, that is, to find the initial reconstructed phase sample

[0027]

[0028] Ψ=AYA T (11)

[0029]

[0030] (302-2) After obtaining the initial reconstructed phase sample When , the gradient descent iterative algorithm is used according to formulas (14)-(16) to repair the missing phase data, and the phase sample of the kth iteration is obtained by formula (17):

[0031]

[0032] Among them, F k (·) is the inverse transformation function in the k-th gradient descent process, is the phase sample of the k-1th iteration, S k is the missing phase samples for k iterations, Δ k is the high-dimensional gradient formed by the missing information of the kth iteration, S φ (·) is the measurement operator, is the transposed measurement operator, U k is the feature domain formed by the k-th iteration gradient descent, ρ is the gradient descent step size, F(·) is the inverse transformation function for high-dimensional gradient information, λ is the regularization term coefficient, is the kth iteration phase sample obtained by the gradient descent algorithm;

[0033] (302-3) In each iteration, the mean square error (MSE) and structural similarity (SSIM) are used to evaluate the phase repair image. The degree of closeness to the original phase sample Y, when the degree of closeness between the two meets the preset error threshold, the iteration is stopped, and the corresponding phase repair image is the required N*N phase sample;

[0034]

[0035] Among them, Y i is the ith sample of the original phase sample, is the kth iteration phase sample obtained by gradient descent The i-th sample in , β is The total number of samples in the MSE represents the difference between the original phase sample Y and the kth iteration phase sample The smaller the value, the closer the reconstructed information is to the original information.

[0036]

[0037] Among them, the original phase sample Y and the kth iteration phase sample The mean and standard deviation of Y , and σ Y , It represents the covariance of the original information and the reconstructed information. C1 and C2 are constants used to stabilize the calculation. The value range of SSIM is between [-1, 1]. The closer SSIM is to 1, the better the reconstruction quality.

[0038] The present invention combines the theory of compressed sensing in image processing and adopts two different methods to process the amplitude information and phase information obtained by sparse scanning respectively. The amplitude information divides the initial sample into several clusters through K-means clustering, and then determines the neighbor relationship of each initial sampling point through Voronoi cell micro-grid processing technology, and finally interpolates the unsampled area according to the Voronoi cell neighbor relationship of each sampling point, thereby improving the accuracy of the data and sampling efficiency. The phase information is masked according to local random sampling, and then the image is restored by discrete cosine transform (Discrete Cosine Transform, DCT), and finally the missing data is repaired by gradient descent iterative algorithm. This technology can realize high-resolution restoration of the near-field spectrum of microwave radiation sources on the basis of reducing the initial samples, and is expected to be applied to EMI detection and positioning in the electronics industry. And the quality effect of the reconstructed image is evaluated by the two indicators of mean square error (MSE) and structural similarity (SSIM). This basically solves the limitations of the current research field in far-field scanning sparse processing and imaging restoration of the emission source phase information. This study provides theoretical and methodological support for ESM microwave planar scanning imaging technology in the field of image processing. It also provides a new idea for further exploring random sparse data acquisition processing and imaging enhancement methods. In the experimental phase, we tested the radiation source based on the Elfin5 manipulator ESM detection system. According to the experimental results, under the condition of 50% sampling, the actual ESM reconstructed imaging amplitude phase spectrum structural similarity (SSIM) range is 0.76-0.96, and the pixel error with the original spectrum is controlled within 20 pixels. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a model diagram of the ESM plane scanning system involved in the present invention.

[0040] Figure 2 The present invention relates to a flow chart of an enhanced imaging method for a microwave ESM sparse scanning system.

[0041] Figure 3 A diagram of the step-by-step mask convolution process for the phase information involved in the present invention.

[0042] Figure 4 This is the L-axis SSE curve obtained during the experiment.

[0043] Figure 5 This is the Voronoi micro-grid splitting diagram obtained during the experiment.

[0044] Figure 6 This is the amplitude error curve obtained during the experiment.

[0045] Figure 7 This is the DCT energy transformation diagram obtained during the experiment.

[0046] Figure 8 This is the phase error curve obtained during the experiment.

[0047] Fig. 9 These are the amplitude diagram, phase diagram and diffraction diagram corresponding to the sampling rate during the experiment. Specific embodiments

[0048] The present invention will be further described below through specific embodiments and drawings.

[0049] Example

[0050] An enhanced imaging method for a microwave ESM sparse scanning system, specifically:

[0051] (1) ESM scanning principle

[0052] Figure 1 It is an ESM plane scanning system model. The microwave radiation source radiates. The robotic arm grasps the antenna to complete the precise positioning under the reference plane. The network analyzer is used to sample N*N sampling points in the plane to obtain the amplitude and phase of each sampling point on the spatial sampling plane. The phase information of all sampling points constitutes an N*N-dimensional original phase sample Y, and the amplitude information of all sampling points constitutes an N*N-dimensional original amplitude sample G. Matlab reads the original phase sample Y and the original amplitude sample G respectively to obtain the original phase signal diagram and the original amplitude signal diagram. The original phase information and the original amplitude information are inverted by the far-near field transformation algorithm (that is, the ESM algorithm of two-dimensional Fourier transform) to obtain the radiation source plane diffraction pattern.

[0053] In the ESM scanning scenario, according to the sampling theorem, the sampling frequency must be greater than twice the information frequency in the spatial frequency domain to ensure that the original information is not distorted. Therefore, the phase difference between the two sampling points in the robot arm axis should be less than or equal to π. The corresponding relationship expression is:

[0054]

[0055] sinα=R / L(2)

[0056] In this expression, R and L represent the scanning surface size and the vertical distance between the scanning surface and the detection antenna, respectively. Δs represents the uniform spacing between the sampling points in the scanning surface, and λ is the wavelength. α represents the actual scanning aperture angle. In order to improve the imaging resolution, the distance between the sampling points needs to be small enough. Therefore, the antenna motion step in the scanning aperture should be smaller than the measurement wavelength. On the other hand, Equation (1) can only obtain accurate anti-derivative accuracy when the aperture angle is large. When the aperture angle is close to 90°, the maximum step size is close to λ / 2.

[0057] (2) Downsampling of sparse scanned images

[0058] In order to improve the sampling scanning speed, it is necessary to downsample the original scanning information to achieve the reconstruction of the radiation source diffraction pattern. The purpose of downsampling is to select a suitable observation matrix φ so that the original phase sample Y or the original amplitude sample G is sparse on φ. Specifically, the original phase sample Y or the original amplitude sample G is usually decomposed into several row vectors or column vectors, and some rows and columns are randomly extracted from them based on the given downsampling amplitude to obtain the initial phase sample y k Or initial amplitude sample D.

[0059] (201) Downsampling the original phase sample Y

[0060] Since the original phase samples are continuously changing points, in order to make the derivatized image more accurate before downsampling, it is necessary to add a Mask vector based on the N*N dimensional original phase information Y. The basic principle of the mask is to generate output information by performing a channel-by-channel convolution operation with the input information. Figure 3 As shown, the original phase sample Y is subjected to step-by-step mask convolution processing, and each time a convolution kernel with the same dimension as the original phase sample is used to form an N*N mask matrix, which is defined as Γ (N*N) , then the phase sample Y after mask processing k for:

[0061] Y k =∑∑Y*Γ (N*N) (3)

[0062] In order to ensure high probability and high precision reconstruction of information, the measurement matrix φ needs to satisfy the Restricted Isometry Property (RIP). Taking phase samples as an example, for any given sparsity phase information y k , there exists a constant δ K ∈(0,1), so that inequality (4) holds:

[0063]

[0064] Y k is the output information after mask processing. Combined with the observation matrix φ, the mask information y after downsampling processing can be obtained. k , also called the initial phase sample y k The above inequality shows that the observation matrix φ maintains Y k The norm of Within a certain error range, the sparse information y can be guaranteed k Reliable reconstruction.

[0065] (202) Downsampling the original amplitude sample G

[0066] The N*N dimensional original amplitude sample G is divided into countless different row vectors and column vectors, and then the sampling parameters are set to randomly extract some rows and columns from them to obtain a random sample with the same dimension as the set sampling parameters, which is recorded as the initial amplitude sample D, and the downsampling processing of the amplitude information can be realized. The downsampling processing of the original amplitude information also needs to meet the strict equidistance condition, that is:

[0067]

[0068] The downsampling process of the original amplitude sample G is similar to that of the original phase sample Y. Since the compactness between the amplitude information pixels is small, the ideal imaging state can be restored without mask processing. Mask processing can highlight the specific structure and features of the image, extract important information of the image, select important phase data points, and obtain a reconstructed phase signal graph that is close to the original phase signal graph.

[0069] (3) Restoration of sparse scanned images

[0070] like Figure 2 As shown, the initial amplitude samples are restored to N*N dimensional amplitude samples through K-means clustering and Voronoi micro-grid partitioning, and the initial phase samples are restored to N*N dimensional phase samples through DCT transformation and gradient descent.

[0071] (301) Initial Amplitude Sample Restoration

[0072] The initial amplitude sample D is a small number of sampling points randomly selected from the original amplitude sample G through downsampling. The initial amplitude sample D is classified using the K-means clustering algorithm. The initial amplitude sample set is now divided into K categories. The selection of the K value can be evaluated by the sum of squares due to error (SSE). The initial amplitude sample set is divided into K clusters, each cluster represents similar sampling points, and C is assumed to be i represents the i-th cluster, then the initial amplitude sample set D can be regarded as a set of K clusters, and the i-th cluster in the initial amplitude sample set D is C i , i is a positive integer between 1 and k, that is: D = {C1, C2, ..., C k}, each cluster is a set of similar sampling points, and the jth sampling point in the i-th cluster is x ij , j is a positive integer between 1 and o, that is: C i ={x i1 , x i2 , …, x io}. From this, we can derive the SSE model evaluation expression as:

[0073]

[0074] Among them, p represents the sampling point in the cluster, q i It represents the centroid point (the mean of all samples), SSE is the clustering error of all samples, which represents the quality of clustering. The smaller the SSE, the closer the clustering points are to their center, and the better the clustering effect.

[0075] Due to the limitation of measurement range and accuracy, the number of initial sampling points is small, so regional interpolation is needed to expand the number of initial samples. The optimal number of clusters K is determined by K-means clustering method. Next, Voronoi cell division is performed on each cluster to calculate the Voronoi cell size and gradient parameters of each initial sampling point. The jth sampling point in the i-th cluster is x ij The size of the Voronoi cell can be regarded as the ratio of the area of ​​the cell to the area of ​​all Voronoi cells in the cluster. Let the jth sampling point x in the i-th cluster be ij The unit cell area is V(x ij ), then the sampling point x ij The distribution density S(x ij ) can be expressed as:

[0076]

[0077] The gradient is obtained by calculating the change in field strength between adjacent samples. Let x m is the sampling point x ijThere are adjacent sampling points with a common cell wall or vertex, and the electric field gradient between the adjacent sampling points can be expressed as:

[0078]

[0079] represents the absolute value of the change in electric field strength, Represents the sampling point x m The electric field strength. The distribution density and gradient value of each cluster sampling point can be determined, and the deep interpolation of each Fourier region can be determined based on the calculation results. Generally, deeper interpolation is characterized by lower density and larger gradient. In the deeper interpolation area, multiple points around the sampling point can be selected for interpolation. Conversely, for areas with high Voronoi cell distribution density and small gradient, fewer points around the sampling point can be selected for interpolation. In this way, the accuracy and efficiency of interpolation can be improved.

[0080] Image interpolation is to estimate the grayscale information of unknown pixels based on the grayscale information of known pixels of the initial amplitude sample D. Based on the sampling point distribution density, reasonable linear image interpolation is performed on the downsampled amplitude sampling points to reconstruct the reconstructed amplitude sample M with the same dimension as the original far-field amplitude sample G. Matlab reads the reconstructed amplitude sample M to obtain the reconstructed amplitude signal graph.

[0081] (302) Initial phase sample restoration

[0082] Unlike amplitude, phase information is usually more complex and more sensitive to noise and interference, which makes phase restoration more challenging and difficult. The initial phase sample is a small number of sampling points randomly selected from the original phase sample Y through downsampling. The initial phase sample obtained after downsampling is y k , the information observation matrix φ is determined by the downsampling form, then the mathematical expression of phase reconstruction can be expressed as:

[0083]

[0084] Among them, Ψ is a sparse basis matrix, For the initial reconstructed phase sample, the observation matrix Φ is unrelated to the sparse basis matrix Ψ. The perception matrix τ can be obtained through orthogonalization. Finally, the perception matrix τ is used to perceive the information after sparse transformation. The phase restoration process can be converted into the problem of constructing a sparse basis matrix. A commonly used sparse basis matrix representation method is based on discrete cosine (DCT) transform. The core of constructing a DCT sparse matrix is ​​to identify and utilize the energy compression characteristics of information after DCT transform. When processing information, only high-energy coefficients after transformation can be retained and other coefficients can be set to zero. For a phase sample Y(i, j) of size N*N and sampling position (i, j), the general formula of the two-dimensional DCT transform can be expressed as:

[0085]

[0086] Expanding the above DCT transform formula, it can be expressed as the following matrix form:

[0087] Ψ=AYA T (11)

[0088] The Y variable in the matrix can be regarded as the pixel value at the corresponding position of the original image. A is the transformation matrix. The elements in the matrix can be expressed as:

[0089]

[0090] The expanded expression is:

[0091]

[0092] From formulas (11) and (13), we can calculate the visualization sparse matrix Ψ. According to (9), we know that the known variable y k , Φ, Ψ, the initial reconstructed phase sample can be obtained

[0093] After obtaining the initial reconstruction phase sample When the phase data is missing, the gradient descent iterative algorithm is used to repair the missing phase data, which specifically includes the following steps:

[0094] By inverse transformation function F k (·) The reconstructed phase sample obtained by the k-1th gradient descent Assume that the initial reconstructed phase sample is the reconstructed phase sample obtained by the 0th gradient descent, and outputs the set of missing phase samples S of the kth iteration k ;

[0095]

[0096] Using the measurement operator S φ (·) for S k Independently measure S φ (S k ), the measurement result S φ (Sk ) is subtracted from the multidimensional measurement value W obtained by repeated expansion, and then the difference is measured using the transposition operator Performing the inverse mapping can obtain the k-th high-dimensional gradient information Δ k ;

[0097]

[0098] The kth gradient descent process of the missing phase sample in the feature domain

[0099]

[0100] Among them, F k (·) is the inverse transformation function in the k-th gradient descent process, is the phase sample of the k-1th iteration, S k is the missing phase samples for k iterations, Δ k is the high-dimensional gradient formed by the missing information of the kth iteration, S φ (·) is the measurement operator, is the transposed measurement operator, U k is the feature domain formed by the k-th iteration gradient descent, ρ is the gradient descent step size, and F(·) is the inverse transformation function for high-dimensional gradient information.

[0101] The phase sample of the kth iteration is obtained by formula (17):

[0102]

[0103] Among them, λ is the regularization coefficient, is the kth iteration phase sample obtained by the gradient descent algorithm.

[0104] In each iteration, the gradient of the current phase sample can be calculated, based on the high-dimensional gradient information Update the phase data and calculate the original information Y and the information after iterative processing by combining the residual principle The absolute value of the pixel value difference at the corresponding position. When the residual reaches the preset error threshold, the iteration is stopped to restore the integrity and availability of the image. At this time, the corresponding k-th iteration phase sample The closest to the original phase sample Y, using the closest to the original phase sample Y As the reconstructed phase sample S, matlab reads the reconstructed phase sample S to obtain the reconstructed amplitude signal graph S. Specifically, the mean square error (MSE) and structural similarity index (SSIM) are used to evaluate the phase repair image. How close to the original phase sample Y is.

[0105] The mean square error mainly represents the difference between the reconstructed information and the original information. The specific calculation formula is as follows:

[0106]

[0107] where Y i is the ith sample of the original phase sample, is the kth iteration phase sample obtained by gradient descent The i-th sample in , β is The total number of samples in MSE represents the mean square error between the original information and the reconstructed information. The smaller the value, the closer the reconstructed information is to the original information.

[0108] Structural similarity (SSIM) mainly considers the structural information of the image. This indicator is used to measure the similarity between the reconstructed information and the original information. The calculation formula is as follows:

[0109]

[0110] Among them, the original phase sample Y and the kth iteration phase sample The mean and standard deviation of Y , and σ Y , It represents the covariance of the original information and the reconstructed information. C1 and C2 are constants used to stabilize the calculation. The value range of SSIM is between [-1, 1]. The closer SSIM is to 1, the better the reconstruction quality.

[0111] (4) Reconstruction quality assessment of sparse scanned atlas

[0112] The amplitude information graph M and the phase information graph S can be transformed into the radiation source plane diffraction graph I by the far-field and near-field transformation algorithm. * .

[0113] Example 1

[0114] First, the radiation source is tested based on the Elfin5 manipulator ESM detection system. The number of samples obtained by the initial ESM scan is 1681, including the original amplitude sample G and the original phase sample Y. Then, according to step (2) of the embodiment, the original amplitude sample G and the original phase sample Y are downsampled by 50%. Secondly, according to step (3) of the embodiment, the initial amplitude sample after downsampling is subjected to K-means clustering. Figure 4 The SSE curve shown in Figure 1 gives the value of the optimal cluster number K. The corresponding Voronoi cell parameters are calculated for all sampling points. The cell division results are shown in Figure 1. Figure 5 As shown, Figure 6 The error analysis between the interpolated sampling points and the original data is given. It can be found that the amplitude pixel data is well restored before and after interpolation. Again, for the phase information, the far-field phase restoration is achieved through DCT transformation and gradient descent, and the phase signal map S is reconstructed based on the restored far-field phase. Figure 7 is the energy map of DCT transformation, Figure 8 The curves show the results of each indicator at different iteration times. The horizontal axis represents the number of iterations, and the vertical axis represents the value of the corresponding indicator. Among them, the blue curve represents the MSE value, and the red curve represents the SSIM value. From this, it can be analyzed that when the number of iterations is 10, the value corresponding to the MSE is the smallest. This is the best number of iterations for phase image restoration. When the number of iterations corresponding to the minimum MSE value is 0.96, it is basically close to 1, indicating that the image reconstruction quality is good. Finally, the amplitude information graph M and the phase information graph S can be used to obtain the radiation source plane diffraction graph I through the far-field and near-field transformation algorithm. * . Fig. 9 The corresponding amplitude map, phase map and diffraction map when the sampling rate H is 0.5. Compared with the original image when the sampling rate is H = 1, it can be seen that the amplitude map, phase map and diffraction map reconstructed by downsampling by 50% are similar to the original image. This result shows that this algorithm can achieve high-resolution restoration of the near-field spectrum of microwave radiation sources on the basis of reducing the initial samples, and has good practicality and feasibility. Fig. 9 In the figure, H=0.5 (without masking) refers to the phase signal image obtained by downsampling directly without masking and then restoring and reconstructing the image through DCT transformation and gradient descent. It can be seen that this process cannot restore the ideal imaging.

Claims

1. An enhanced imaging method for a microwave ESM sparse scanning system, characterized in that: The following steps are involved: (1) The ESM plane scanning system is used to sample N*N sampling points in the plane to obtain the amplitude and phase of each sampling point on the spatial sampling plane. The phase information of all sampling points constitutes an N*N dimensional original phase sample Y, and the amplitude information of all sampling points constitutes an N*N dimensional original amplitude sample G; (2) Downsample the original phase sample Y to the initial phase sample y k , downsample the original amplitude sample G to the initial amplitude sample D; The original phase sample Y is downsampled to the initial phase sample y k Specifically, the original phase sample Y is subjected to step-by-step mask convolution processing, each time using a convolution kernel with the same dimension as the original phase sample, that is, forming an N*N mask matrix, defined as Γ (N*N) , then the phase sample Y after mask processing k for: Y k =∑∑Y*Γ (N*N) (3) For any given sparsity phase information y k , there exists a constant δ K ∈(0,1), so that inequality (4) holds: Y k is the output information after mask processing, combined with the observation matrix φ, to obtain the initial phase sample y k ; The downsampling of the original amplitude sample G to the initial amplitude sample D is specifically to divide the N*N dimensional original amplitude sample G into countless different row vectors and column vectors, and then set the sampling parameters, randomly extract some rows and some columns therefrom, and obtain a random sample with the same dimension as the set sampling parameters, which is recorded as the initial amplitude sample D; (3) The initial amplitude sample y is divided into k Restored to N*N dimensional amplitude samples, the initial phase samples y are transformed by DCT transformation and gradient descent k Restored to N*N phase samples, matlab reads N*N dimensional amplitude samples and N*N phase samples respectively to obtain amplitude information graph M and phase information graph S; (4) The amplitude information graph M and the phase information graph S can be transformed into the radiation source plane diffraction graph I through the far-field and near-field transformation algorithm. * .

2. The enhanced imaging method for microwave ESM sparse scanning system according to claim 1, characterized in that: The initial amplitude samples are restored to N*N dimensional amplitude samples through K-means clustering and Voronoi micro-grid partitioning, specifically, (301-1) Use K-means clustering algorithm to divide the initial amplitude sample set into K clusters, each cluster represents similar sampling points, let C i represents the i-th cluster, then the initial amplitude sample set D is regarded as a set of K clusters, and the i-th cluster in the initial amplitude sample set D is C i , i is a positive integer between 1 and k, that is: D = {C1, C2, ..., C k }, each cluster is a set of similar sampling points, and the jth sampling point in the i-th cluster is x ij , j is a positive integer between 1 and o, that is: C i ={x i1 , x i2 , …, x io }, the optimal number of clusters K is determined by the error square sum SSE model, and the SSE model evaluation expression is: Among them, p represents the sampling point in the cluster, q i represents the centroid point, (301-2) Next, perform Voronoi cell division on each cluster, calculate the Voronoi cell size and gradient parameters of each initial sampling point, and the jth sampling point x in the i-th cluster. ij The size of the Voronoi cell is regarded as the ratio of the area of ​​the cell to the area of ​​all Voronoi cells in the cluster. Let the jth sampling point x in the i-th cluster be ij The unit cell area is V(x ij ), then the sampling point x ij The distribution density S(x ij ) is expressed as: The gradient is obtained by calculating the change in field strength between adjacent samples. Let x m is the sampling point x ij There are adjacent sampling points with a common cell wall or vertex, and the electric field gradient between the adjacent sampling points can be expressed as: represents the absolute value of the change in electric field strength, Represents the sampling point x m The electric field strength is obtained by determining the distribution density and gradient value of each cluster sampling point. Based on the distribution density of the sampling points, a reasonable linear image interpolation is performed on the downsampled amplitude sampling points to obtain the reconstructed amplitude sample M.

3. The enhanced imaging method for microwave ESM sparse scanning system according to claim 1, characterized in that: The initial phase samples are restored to N*N phase samples through DCT transformation and gradient descent, specifically: (302-1) The visualized sparse matrix Ψ is calculated by formulas (11) and (13). According to (9), we know that the known variable y k , Φ, Ψ, that is, to find the initial reconstructed phase sample Ψ=YES T (11) (302-2) After obtaining the initial reconstructed phase sample When , the gradient descent iterative algorithm is used according to formulas (14)-(16) to repair the missing phase data, and the phase sample of the kth iteration is obtained by formula (17): Among them, F k (·) is the inverse transformation function in the k-th gradient descent process, is the phase sample of the k-1th iteration, S k is the missing phase samples for k iterations, Δ k is the high-dimensional gradient formed by the missing information of the kth iteration, S φ (·) is the measurement operator, is the transposed measurement operator, U k is the feature domain formed by the k-th iteration gradient descent, ρ is the gradient descent step size, F(·) is the inverse transformation function for high-dimensional gradient information, λ is the regularization term coefficient, is the kth iteration phase sample obtained by the gradient descent algorithm; (302-3) In each iteration, the mean square error (MSE) and structural similarity (SSIM) are used to evaluate the phase repair image. The degree of closeness to the original phase sample Y, when the degree of closeness between the two meets the preset error threshold, the iteration is stopped, and the corresponding phase repair image is the required N*N phase sample; Among them, Y i is the ith sample of the original phase sample, is the kth iteration phase sample obtained by gradient descent The i-th sample in , β is The total number of samples in the MSE represents the difference between the original phase sample Y and the kth iteration phase sample The smaller the value, the closer the reconstructed information is to the original information. Among them, the original phase sample Y and the kth iteration phase sample The mean and standard deviation of Y , and σ Y , It represents the covariance of the original information and the reconstructed information. C1 and C2 are constants used to stabilize the calculation. The value range of SSIM is between [-1, 1]. The closer SSIM is to 1, the better the reconstruction quality.

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