A method for estimating a scattering center parameter of a SAR image

Abstract

The application relates to a SAR image scattering center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit, and comprises the following steps: obtaining an original SAR image and performing pretreatment to obtain original frequency domain echo data; according to the original frequency domain echo data, using a point scattering center model and an OMP algorithm to initialize a key area where target scattering centers are located, obtaining an initial scattering center position parameter set and an initial scattering center energy proportion; according to the initial scattering center position parameter set and the initial scattering center energy proportion, based on an attribute scattering center model and an SOMP algorithm, attribute parameter extraction is performed, and a scattering center attribute parameter estimation result, a scattering center coefficient estimation result and a scattering center energy proportion sequence are output. Compared with the prior art, the scattering center parameter can be efficiently extracted, and meaningful target scattering component attribute information can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar, and particularly relates to a SAR image scattering center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit. BACKGROUND

[0002] Synthetic Aperture Radar (SAR) provides a kind of all-weather and all-day technical method for target detection and identification, and with the improvement of SAR imaging resolution, it is more and more important to extract scattering features with geometric and physical meanings from SAR echo data. Scattering center is a basic feature of radar target scattering in high frequency region. The modeling of local scattering center has experienced the development process from point scattering model to geometrical theory of diffraction (GTD), then to attributed scattering center model (ASCM) and three-dimensional geometric model scattering primitive. The trend of modeling of scattering center is to establish a model with higher parameter dimension, better physical characteristic representation ability and richer physical and geometric information. The modeling of high-dimensional scattering center helps to promote the researches of radar target automatic identification, inverse scattering and radar target three-dimensional reconstruction.

[0003] The attributed scattering center model models the relationship between scattering echo and frequency, angle, local attribute (such as length, azimuth angle, type, etc.) of scattering component. Due to high dimension of model parameters, the feature extraction problem is a high-dimensional nonlinear parameter estimation problem, and the calculation complexity is very high.

[0004] The traditional image domain attributed scattering center extraction method depends on the accuracy of image segmentation, and mostly uses the technical means of scattering center segmentation-approximate maximum likelihood, so that the robustness and accuracy of feature extraction result cannot be guaranteed. Converting the SAR image to frequency echo domain and using sparse constraint or heuristic optimization method to automatically estimate the number and parameters of scattering center can avoid the problem of image segmentation, but the problem of large calculation amount of frequency domain method cannot be ignored, which seriously restricts its practical application. Based on the idea of frequency domain extraction, a series of methods have been proposed, including methods based on sparse Bayesian learning, non-parametric Bayesian estimation, genetic algorithm and traditional OMP, although some efficiency improving skills are used, but the problem of high complexity still exists. SUMMARY

[0005] The application aims to provide a SAR image scattering center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit, to solve the problems of high memory occupation in the scattering parameter dictionary, long scattering center parameter estimation time and redundant calculation in the prior art, efficiently extract the scattering center parameter and obtain meaningful target scattering component attribute information.

[0006] The application aims to provide a SAR image scattering center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit, to solve the problems of high memory occupation in the scattering parameter dictionary, long scattering center parameter estimation time and redundant calculation in the prior art, efficiently extract the scattering center parameter and obtain meaningful target scattering component attribute information.

[0007] The application aims to provide a SAR image scattering center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit, to solve the problems of high memory occupation in the scattering parameter dictionary, long scattering center parameter estimation time and redundant calculation in the prior art, efficiently extract the scattering center parameter and obtain meaningful target scattering component attribute information.

[0008] S1, obtaining an original SAR image and performing preprocessing to obtain original frequency domain echo data;

[0009] S2, initializing a key region where a target scattering center is located by using a point scattering center model and an OMP algorithm according to the original frequency domain echo data, to obtain an initial scattering center position parameter set and an initial scattering center energy proportion;

[0010] S3, performing attribute parameter extraction based on an attribute scattering center model and an SOMP algorithm according to the initial scattering center position parameter set and the initial scattering center energy proportion, and outputting a scattering center attribute parameter estimation result, a scattering center coefficient estimation result and a scattering center energy proportion sequence.

[0011] The step S1 specifically comprises:

[0012] The original SAR image is obtained, and inverse processing is performed on the imaging process according to the parameters used in SAR imaging, to obtain original frequency domain echo data corresponding to the original SAR image, wherein the inverse processing comprises inverse Fourier transform, zero removal and window removal operations.

[0013] The step S2 comprises the following steps:

[0014] S21, determining the value range of the parameter x and the parameter y in the point scattering center according to the bandwidth, the frequency dimension sampling number, the azimuth accumulation angle, the azimuth sampling number parameters used in radar echo acquisition: (-x m / 2,x m / 2), (-y m / 2,y m / 2), wherein x m is the range imaging range, and y m is the azimuth imaging range;

[0015] S22, setting an initial position parameter grid (Δx, Δy), and constructing a position parameter dictionary Θ0={(x, y)|x∈[-x m / 2:Δx:xm / 2],y∈[-y m / 2:Δy:y m / 2]};

[0016] S23. Construct a scattering atom dictionary D(Θ0) based on the point scattering center model. The scattering atom dictionary is a two-dimensional matrix, with the i-th column d... i for The normalized vectorized atom, wherein the point scattering center model is:

[0017]

[0018] Where f is the frequency sample value, It is the azimuth angle sample value, and c is the speed of light;

[0019] S24. Based on the vectorized s0 of the original frequency domain echo data E0 and the scattering atom dictionary D(Θ0), the original orthogonal matching pursuit algorithm OMP is used to extract the initial position parameter set of the point scattering center, and output the initial scattering center position parameter set and the initial scattering center energy ratio.

[0020] The vectorization of the original frequency domain echo data E0 is s0 = vec(E0), where vec() represents flattening the original M×N matrix into an MN×1 vector.

[0021] The scattering atom dictionary D(Θ0) is generated as follows: D(Θ0) = [d1, d2, ..., d i ,…,d C ],in,

[0022]

[0023] θ i It is the i-th parameter combination in the candidate parameter set Θ0. It is a point scattering center model, which is θ in step S23. i =(x i ,y i C is the number of parameter combinations in Θ0~(x,y).

[0024] The original Orthogonal Matching Pursuit (OMP) algorithm includes the following steps:

[0025] S241. Initialize the candidate parameter set Θ0, the scattering atom dictionary D(Θ0), set the iteration number k = 1, the scattered echo residual vector r = s, and estimate the parameter set. δ0 = 0, δ1 = 1;

[0026] S242. Determine ε0 based on the signal-to-noise ratio of the SAR image;

[0027] S243, calculate the inner product similarity c=D of each scattering center atom and the scattering echo residual H (Θ)·r, (·) H represents the conjugate transpose;

[0028] S244, determine the atom with the maximum inner product similarity that is is the first parameter atom in Θ0, which is added to the estimation result

[0029] S245, calculate the least square estimation amplitude of the atom with the maximum inner product similarity get the current estimated scattering echo vector update the scattering echo residual vector to update the energy proportion of the scattering atom extracted in this iteration wherein represents the Moore-Penrose pseudo-inverse operation;

[0030] S246, judge whether δ k -δ k-1 > ε0, if yes, update the iteration number k=k+1, and return to step S243, and the iteration is performed to extract the scattering center parameters, otherwise, execute step S247;

[0031] S247, output the parameter estimation result based on the point scattering model Let it be the initial scattering center position parameter set output, and output the initial scattering center energy proportion sequence δ1.

[0032] The attribute scattering center model is:

[0033]

[0034] wherein f is a frequency sampling point, f c is the radar center frequency, is an azimuth angle sampling point, is a scattering center orientation angle parameter, α is a scattering center surface curvature parameter, c is the speed of light, γ is a scattering center feature related to frequency parameter, x, y are scattering center position parameters.

[0035] The step S3 adopts the idea of alternating optimization to step-by-step optimize and refine the scattering center attribute parameters to be estimated Based on the L0 norm optimization parameter estimation based on the serial orthogonal matching pursuit algorithm SOMP.

[0036] The step S3 includes the following steps:

[0037] S31, to Coarse estimation of parameters: using the initial set of scattering center position parameters As an initial value, expand upon it. The estimation, construction Where L=[0:ΔL:L max ], It is a set containing combinations of values ​​for (x, y), L max The maximum length parameter of the scattering center is determined based on the initial value of y. These are the minimum and maximum orientation angle values ​​determined based on the composite angle. As parameters for candidate scattering atoms, based on the initial scattering center energy proportion sequence δ1, the SOMP method was used to... Estimation is performed to obtain the estimated parameter set. and energy percentage sequence δ2;

[0038] S32, to Parameters are further refined and estimated: As an initial value, the coarse mesh is refined based on it. For the coarsely estimated parameter values The parameter values ​​are extrapolated to the left and right by Dθ / 2 from the coarse estimate, where Dθ is the total range of the refined estimate extension, thus constructing... by As parameters for candidate scattering atoms, based on the energy percentage sequence δ2, the SOMP method was used to... By performing refined estimation, a set of estimated parameters is obtained. and energy percentage sequence δ3;

[0039] S33. Estimate the α parameter: Using this as an initial value, we extend the estimate of α to construct... Where α∈{-1,-1 / 2,0,1 / 2,1}, with As parameters for candidate scattering atoms, α is estimated using the SOMP method based on the energy percentage sequence δ3, resulting in an estimated parameter set. and energy percentage sequence δ4;

[0040] S34. Estimate the γ parameter: Using this as an initial value, we extend the estimate of γ to construct... by As parameters for candidate scattering atoms, γ is estimated using the SOMP method based on the energy percentage sequence δ4, resulting in the final estimated parameter set. That is, the estimation results of the scattering center attribute parameters.

[0041] The SOMP based on the energy proportion sequence of the scattering center atoms extracted in the previous stage in the alternating optimization process includes the following steps:

[0042] 1) initialize the input scattering echo vector s, the estimated parameter set output by the previous stage j j=1, 2, 3, 4, the energy proportion δ of the scattering atoms extracted in the previous stage in descending order c , the minimum comparison number N of SOMP h , the minimum energy proportion ε of the scattering center corresponding to the stop iteration set according to the signal-to-noise ratio of the SAR image, initialize k=1 and r=s, δ0=0, δ1=1;

[0043] 2) according to the of the data of the previous stage c ={δ1, δ2,..., δ i ,...,δ C}, generate corresponding Θ j1 , corresponding Θ j2 ..., wherein Θ ji is determined according to and the refined grid, and the estimated parameter result of the above stage is taken as the center, each parameter is expanded to a certain range to the left and right, and the parameter atom set obtained by re-refining the value according to the refined grid is obtained;

[0044] 3) determine the iteration threshold ε;

[0045] 4) generate a dynamic dictionary: SOMP algorithm generates a scattering atom dictionary of the refined parameter dictionary set corresponding to the parameter atom of the previous stage according to the energy proportion of the scattering atom extracted in the previous stage, k=1 initializes the current scattering atom dictionary as D=D(Θ j1 ), and then generates D(Θ j2 ), D(Θ j3 ), …, D(Θ jC ) in turn to add to the current scattering atom dictionary;

[0046] 5) perform the serialized orthogonal matching pursuit operation: the dictionary D(Θ ji ) generated by a Θ ji is called an atom cluster, the number of atom clusters contained in the current scattering atom dictionary is obtained, denoted as N cluster ; calculate the inner product similarity c=D H ·r of the current scattering atom dictionary and the scattering echo residue, obtain the serial number of the atom with the maximum inner product similarity ​The atomic cluster number is Let the current maximum inner product similarity According to the defined SOMP algorithm, N h Parameters, comparison and N h The size of N, if now ≥N h Then it is considered that the atomic cluster where the currently extracted scattering atom is located is more than the subsequent N h Each atomic cluster should be better, retaining the extracted scattering atom results. If N now <N h Then execute the iterative operations 51)-53) until N is satisfied. now ≥N h :51) According to δ c The order of the dictionary is refined using the largest parameter Θ that has not yet been used to generate a dictionary. j(i+1) Generate a dictionary of scattering atoms D t =D(Θ) j(i+1) ), and incorporate it into the current scattering atom dictionary D=[D,D t ];52) Calculate the residual of the scattered echo and D t Inner product correlation Get c max =max|c|; 53) If c * >c max Then let N now =N now +1, continue iterating through steps 51)-53) until N. now ≥N h If c * ≤c max Then let N now =0, update c * =c max Update the index of the currently extracted scattering atoms. Then update the cluster number of the currently extracted scattering atom to... Continue iterating through steps 51)-53) until N. now ≥N h ;

[0047] 6) Perform the elimination operation on the atom clusters from which the scattering atoms have been extracted, and update the relevant variables simultaneously: 61) Eliminate the extracted atom clusters, that is, let That is, the atomic cluster number is 62) Update the extraction results by using the partial dictionary corresponding to the atoms. calculate Thus updating the scattered echo margin Calculate the energy proportion of the scattering center atom extracted in this round of SOMP iteration

[0048] 7) Determine whether to meet the stop iteration condition delta k -delta k-1 Epsilon, if yes, execute step 8), otherwise, update k=k+1, return to step 4) for the next round of SOMP scattering center extraction iteration;

[0049] 8) Output the scattering center parameter estimation result The scattering center coefficient estimation result sigma and the scattering center energy proportion sequence delta, complete the scattering center parameter extraction in this alternating optimization phase.

[0050] Compared with the prior art, the present application has the following beneficial effects:

[0051] (1) Automatically initialize the main scattering center region from the frequency domain echo:

[0052] The existing SAR image target region is mainly based on the image highlight region segmentation method, using the pixel not being zero as the segmentation standard; while the present application uses the extraction of the point scattering model as the target region initialization method, which can automatically initialize the main scattering center region from the frequency domain echo without image segmentation.

[0053] (2) Realize a more efficient serialized orthogonal matching pursuit parameter estimation method:

[0054] Considering the importance of the energy proportion order information of the scattering center extracted in the previous stage when the redundant dictionary is split into multiple stages of optimization under the alternating optimization condition, the energy proportion order information is added to the matching pursuit process, and a serialized orthogonal matching pursuit method is proposed: the refined dictionary is generated dynamically according to the energy proportion order, the memory occupation of the dictionary is reduced during each inner product projection calculation; the serialized orthogonal matching pursuit operation limits the number of minimum comparison atom clusters, and there is no need to compare the global inner product projection size relationship; the extracted atom cluster is eliminated, and the redundant calculation is reduced. Through the above improvements, the efficiency of the attribute scattering center frequency domain extraction method can be significantly improved under the condition of ensuring a certain accuracy.

[0055] (3) Both electromagnetic scattering simulation data and measured data can extract the physical and geometric information of the target:

[0056] The present application can extract attribute scattering center parameter information with certain physical and geometric significance under the condition of ensuring a certain accuracy. For electromagnetic simulation data, the scattering mechanism information with certain reference value can be obtained according to the combination of the estimated values of the length parameter and the surface curvature parameter; for MSTAR measured data, the geometric parameter information of the scattering center of the main scattering component of the target can be obtained. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 Flow chart of the method of the present application;

[0058] Figure 2 SAR image with zero and window removal of raw echo data of the present application, where (a) is the original SAR image converted to frequency domain, (b) is the frequency domain image with zero and window removal based on (a);

[0059] Figure 3 SAR image of noisy SLICY with SLICY model and simulation for electromagnetic simulation data generation, where (a) is the geometry of SLICY model and radar measurement geometry, (b) is the electromagnetic simulation SAR image of SLICY model;

[0060] Figure 4 Optical image, original SAR image and echo image of ten classes of targets in MSTAR data set;

[0061] Figure 5 Flow chart of the sequential orthogonal matching pursuit algorithm SOMP;

[0062] Figure 6 SAR image and corresponding geometric scatterer diagram of two-dimensional plane for reconstruction of scattering center of electromagnetic simulation data, where (a) is the reconstructed SAR image according to the extracted mathematical scattering center parameters, (b) is the geometric shape of the basic scatterer on the two-dimensional plane according to the extracted attribute scattering center parameters;

[0063] Figure 7 SAR image echo image reconstructed from the extracted scattering center of MSTAR data. DETAILED DESCRIPTION

[0064] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present application, and detailed implementation and specific operation process are given, but the protection scope of the present application is not limited to the following embodiments.

[0065] The two-dimensional attribute scattering center model describes the relationship between the scattering center response and the frequency, the azimuth angle, the scattering center position, the target length, the orientation angle, the target surface curvature and the frequency correlation coefficient. Considering the sparsity of the scattering center in the backscattering field, the scattering center extraction can be expressed as a sparse representation problem in the frequency domain. Considering the high dimension of the parameters, the complexity of the traditional orthogonal matching pursuit method is high, and the following methods are used to reduce the complexity under the premise of ensuring a certain accuracy: a simple point scattering model OMP method is used for rough estimation to determine the key area of the target; an alternating optimization distribution estimation parameter is used; a sequential OMP (SOMP) method using the energy ratio relationship of the scattering center extraction result of the previous step of alternating optimization is proposed to reduce the complexity; in the SOMP, a refinement dictionary is generated one by one according to the energy ratio order to reduce the size of the dictionary, the orthogonal matching pursuit operation with a smaller number of times is used to reduce the calculation amount, and the extracted atomic cluster is used to eliminate the repeated extraction. Through the above improvements, the target scattering center parameters with certain geometric and physical significance can be efficiently extracted.

[0066] Based on the above idea, the embodiment provides a SAR image scattering center parameter estimation method based on alternating optimization and sequential orthogonal matching pursuit, as shown in Figure 1 , including the following steps:

[0067] S1, obtaining an original SAR image and performing preprocessing to obtain original frequency domain echo data.

[0068] The data used in the embodiment includes two types, which are electromagnetic calculation software simulation data and MSTAR target measured data.

[0069] Specifically, an original SAR image I0 is obtained, and inverse processing is performed on the imaging process according to the parameters used in SAR imaging, to obtain original frequency domain echo data E0 corresponding to the original SAR image, wherein the inverse processing includes inverse Fourier transform, zero removal and window operation.

[0070] For simulation data, the zero filling number and the window function are known, and for measured data, the zero filling number and the window function can be estimated. The image of the original echo data after zero removal and window operation is as shown in Figure 2 .

[0071] S2, according to the original frequency domain echo data, using a point scattering center model and an OMP algorithm to initialize a key area of the target scattering center, to obtain an initial scattering center position parameter set and an initial scattering center energy ratio.

[0072] S21, according to the bandwidth, the frequency dimension sampling number, the azimuth accumulation angle and the azimuth sampling number parameters used in radar echo acquisition, the value range of the parameter x and the parameter y in the point scattering center is determined: (-x m / 2, x m / 2), (-y m / 2, y m / 2), where x m is the range imaging range, y m is the azimuth imaging range.

[0073] S22, set the initial position parameter grid (Δx, Δy), and construct the position parameter dictionary Θ0={(x, y) | x∈[-x m / 2:Δx:x m / 2], y∈[-y m / 2:Δy:y m / 2}.

[0074] S23, construct the scattering atom dictionary D(Θ0) according to the point scattering center model, the scattering atom dictionary is a two-dimensional matrix, the i-th column d i is the normalized vectorized atom of , where the point scattering center model is:

[0075]

[0076] where f is the frequency sampling value, is the azimuth angle sampling value, and c is the speed of light.

[0077] S24, according to the vectorization s0 of the original frequency domain echo data E0 and the scattering atom dictionary D(Θ0), use the original orthogonal matching pursuit algorithm OMP to extract the initial position parameter set of the point scattering center, output the initial scattering center position parameter set and the initial scattering center energy proportion δ1.

[0078] The vectorization s0 of the original frequency domain echo data E0 is s0=vec(E0), where vec() represents flattening the original M×N matrix into an MN×1 vector.

[0079] The generation mode of the scattering atom dictionary D(Θ0) is D(Θ0)=[d1,d2,…,d i ,…,d C ], where

[0080]

[0081] θ i is the i-th parameter combination in the candidate parameter set Θ0, is the point scattering center model, which is θ i =(x i ,y i ) in step S23, and C is the number of parameter combinations in Θ0~(x,y).

[0082] The original Orthogonal Matching Pursuit (OMP) algorithm described in step S24 includes the following steps:

[0083] S241. Initialize the candidate parameter set Θ0, the scattering atom dictionary D(Θ0), set the iteration number k = 1, the scattered echo residual vector r = s, and estimate the parameter set. δ0 = 0, δ1 = 1;

[0084] S242. Determine ε0 based on the signal-to-noise ratio of the SAR image. Specifically, determine ε0 based on the energy amplitude relationship between the target area and the background area of ​​the SAR image.

[0085] S243. Calculate the inner product similarity c = D between each scattering center atom and the residual of the scattered echo. H (Θ)·r,(·) H Represents conjugate transpose;

[0086] S244. Determine the atom with the highest inner product similarity. Right now It is the first in Θ0 Each parameter atom is added to the estimation result.

[0087] S245. Calculate the least squares estimate of the atom with the highest inner product similarity. Obtain the current estimated scattered echo vector Update the scattered echo residual vector as follows Update the percentage of scattered atom energies extracted in this iteration. in Represents the Moore-Penrose pseudo-inverse operation;

[0088] S246. Determine whether δ is satisfied. k -δ k-1 If ε > 0, then update the iteration count k = k + 1 and return to step S243 to iteratively extract the scattering center parameters; otherwise, execute step S247.

[0089] S247. Output the parameter estimation results based on the point scattering model. Let it be the initial set of scattering center position parameters. Output the initial scattering center energy percentage sequence δ1.

[0090] This embodiment provides examples of attribute scattering center extraction for two types of data: electromagnetic simulation data and MSTAR measured data.

[0091] The appropriate parameter ε0 is selected as the stop iteration parameter used in determining the initial position parameter of S2 from the signal-to-noise ratio of the SAR image. For the SLICY model of the electromagnetic simulation data, 10 dB of noise is added, and for the measured MSTAR data, appropriate selection is made. Here, for the simulation data, the noise is relatively small, and ε0=0.0005 is taken, and for the MSTAR data, ε0=0.001 is taken. According to the radar parameters, the position parameter grid used to construct the dictionary is selected, and here, for the electromagnetic simulation data, x=[-2.5:0.05:2.5] and y=[-2.5:0.05:2.5] are initialized. For the MSTAR data, x=[-6.5:0.3:6.5] and y=[-6.5:0.3:6.5] are initialized. The scattering atom dictionary D(Θ0) is constructed according to the point scattering model. The OMP method is used to extract the coarse estimates of the parameters x and y The initial value of the position of the scattering center as S3 is extracted.

[0092] The SLICY model used for the electromagnetic simulation data generation and the simulated SAR image of the noisy SLICY are shown in FIG. 1. Figure 3 The optical images, the original SAR images, and the echo images of the ten types of targets in the MSTAR data set are shown in FIG. 2. Figure 4

[0093] S3, according to the initial scattering center position parameter set and the initial scattering center energy proportion, the attribute parameter extraction is carried out based on the attribute scattering center model and the SOMP algorithm, and the scattering center attribute parameter estimation result, the scattering center coefficient estimation result, and the scattering center energy proportion sequence are output.

[0094] The two-dimensional attribute scattering center model models the response relationship of the single-station radar backscattering field in the frequency domain with respect to the frequency and the angle. The attribute scattering center model of a single scattering center is:

[0095]

[0096] where f is the frequency sampling point, f c is the radar center frequency, is the azimuth angle sampling point, is the scattering center orientation angle parameter, a is the scattering center surface curvature parameter, c is the speed of light, γ is the scattering center feature related to the frequency, x and y are the scattering center position parameters.

[0097] The total scattering field of the target can be represented as the superposition of a finite number of P attribute scattering centers plus noise, that is:

[0098]

[0099] where E i ​This is the scattered field of a single attribute scattering center, and N is the noise matrix. The attribute parameters θ of each of the P attribute scattering centers are retrieved from the total scattered echo E. i This is an ill-conditioned and multi-solution problem. Considering the sparsity of the target scattering centers, the scattering center extraction problem can be represented as a sparse representation problem to obtain a feasible solution. This can be transformed into solving the following L0 norm optimization problem:

[0100]

[0101] Where s is the vectorized total scattering field, and D is a dictionary generated based on the attribute scattering center model, with the parameter set of the dictionary being Θ = {θ1, θ2, ..., θ...}. i ,...,θ Q}, where σ is a sparse vector and the values ​​at non-zero positions represent the magnitude A of the attribute scattering center. i .

[0102] The commonly used OMP algorithm for L0 optimization problems has high complexity, limiting its practical application. Firstly, we consider using alternating parameter optimization to break down the parameter estimation problem into four steps. Simultaneously, we utilize prior energy order information from the previous stage's scattering atoms and employ the improved Serialized Orthogonal Matching Pursuit (SOMP) algorithm to perform L0-norm-based parameter estimation. Specifically, this includes the following steps:

[0103] S31, to Coarse estimation of parameters: using the initial set of scattering center position parameters As an initial value, expand upon it. The estimation, construction

[0104] Specifically, the range of values ​​for L is determined based on the coarsely estimated y-parameter results, and the range is determined based on the radar parameters. The range of values ​​for L is [0:ΔL:L]. max ], It is a set containing combinations of values ​​for (x, y), L max The maximum length parameter of the scattering center is determined based on the initial value of y. It is a coarse estimate of x and y values, determined based on the minimum and maximum orientation angles of the composite angle. As parameters for candidate scattering atoms, the generation of coarse meshes is related to... The parameter dictionary is then used to generate a scattering atom dictionary based on the initial scattering center energy proportion sequence δ1, and the SOMP method is used to analyze the scattering atoms. Estimation is performed to obtain the estimated parameter set. And the energy percentage sequence δ2.

[0105] In this embodiment, the maximum length of the electromagnetic simulation data is taken as L. max =1, the maximum length of MSTAR data is set to L. max =3. Determined based on radar parameters. The range of values ​​for which this value is derived is given by the simulation data. measured data

[0106] S32, to Parameters are further refined and estimated: As an initial value, the coarse mesh is refined based on it. For the coarsely estimated parameter values The parameter values ​​are extrapolated to the left and right by Dθ / 2 from the coarse estimate, where Dθ is the total range of the refined estimate extension, thus constructing... by As parameters for candidate scattering atoms, based on the energy percentage sequence δ2, the SOMP method was used to... By performing refined estimation, a set of estimated parameters is obtained. And the energy percentage sequence δ3.

[0107] In this embodiment, the position grid Δx = d x / 2,Δy=d y / 2, where d x ,d y This represents the resolution in both the range and azimuth directions.

[0108] S33. Estimate the α parameter: Using this as an initial value, we extend the estimate of α to construct... Where α∈{-1,-1 / 2,0,1 / 2,1}, with As parameters for candidate scattering atoms, α is estimated using the SOMP method based on the energy percentage sequence δ3, resulting in an estimated parameter set. And the energy percentage sequence δ4.

[0109] S34. Estimate the γ parameter: Using this as an initial value, we extend the estimate of γ to construct... by As parameters for candidate scattering atoms, γ is estimated using the SOMP method based on the energy percentage sequence δ4, resulting in the final estimated parameter set. That is, the estimation results of the scattering center attribute parameters.

[0110] In this embodiment, the maximum value of the azimuth dependence factor γ in both the simulated data and the measured data is taken as γ. max =1e-9.

[0111] Steps S31-S34 all use the SOMP algorithm, which is an improved OMP algorithm that fully considers the energy order of the candidate scattering centers in the previous stage, and is suitable for extracting scattering centers with the sparse representation property combined with alternating optimization. The SOMP algorithm is improved in three aspects: a) dictionary dynamic generation: generating refined parameter clusters and the corresponding scattering dictionary in order; b) serialized orthogonal matching pursuit: comparing the inner product projection size only with a small number of energy-ordered adjacent atomic clusters; and c) atomic cluster elimination of extracted atoms, which reduces the complexity of the algorithm, while experiments show that it can guarantee a certain parameter extraction accuracy. Specifically, as shown in FIG. 8, the SOMP algorithm includes the following steps: Figure 5

[0112] 1) Initialize the input scattering echo vector s, the estimated parameter set output by the previous stage j j = 1, 2, 3, 4, the energy proportion of the scattering atoms extracted in the previous stage in descending order δ c , the minimum comparison number N of SOMP h , the minimum energy proportion ε of the scattering center corresponding to the stop iteration set according to the signal-to-noise ratio of the SAR image, initialize k = 1, r = s, δ0= 0, δ1= 1;

[0113] 2) According to the energy order δ c of the data in the previous stage i = {δ1, δ2,..., δ C ,..., δ j1}, generate corresponding Θ j2 , corresponding Θ ji ……, wherein Θ j1 is determined according to and the refined grid, and the estimation parameter result in the above stage is taken as the center, each parameter is expanded to a certain range to the left and right, and the parameter atom set obtained by re-refining the value according to the refined grid;

[0114] 3) Determine the iteration threshold ε;

[0115] 4) Generate a dynamic dictionary: the SOMP algorithm generates a scattering atom dictionary of the refined parameter dictionary set corresponding to the parameter atom of the previous stage according to the energy proportion of the scattering atom extracted in the previous stage each time, initializes the current scattering atom dictionary as D = D(Θ j2 ) when k = 1, and then generates D(Θ j3 ), D(Θ jC ), and D(Θ ji ) in turn to add to the current scattering atom dictionary; ​

[0116] 5) Perform orthogonal matching tracing operation for serialization: convert a Θ ji The generated dictionary D(Θ) ji A cluster of atoms is called an atom cluster. The number of atom clusters contained in the current scattering atom dictionary is denoted as N. cluster Calculate the inner product similarity c = D between the current scattering atom dictionary and the scattering echo margin. H ·r, retrieves the index of the atom with the highest inner product similarity. Get The atomic cluster number is Let the current maximum inner product similarity According to the defined SOMP algorithm, N h Parameters, comparison and N h The size of N, if now ≥N h Then it is considered that the atomic cluster where the currently extracted scattering atom is located is more than the subsequent N h Each atomic cluster should be better, retaining the extracted scattering atom results. If N now <N h Then execute the iterative operations 51)-53) until N is satisfied. now ≥N h :51) According to δ c The order of the dictionary is refined using the largest parameter Θ that has not yet been used to generate a dictionary. j(i+1) Generate a dictionary of scattering atoms D t =D(Θ) j(i+1) ), and incorporate it into the current scattering atom dictionary D=[D,D t ];52) Calculate the residual of the scattered echo and D t Inner product correlation Get c max =max|c|; 53) If c * >c max Then let N now =N now +1, continue iterating through steps 51)-53) until N. now ≥N h If c * ≤c max Then let N now =0, update c * =c max Update the index of the currently extracted scattering atoms. Then update the cluster number of the currently extracted scattering atom to... Continue iterating through steps 51)-53) until N. now ≥Nh ;

[0117] 6) Perform the elimination operation on the atom clusters from which the scattering atoms have been extracted, and update the relevant variables simultaneously: 61) Eliminate the extracted atom clusters, that is, let That is, the atomic cluster number is 62) Update the extraction results by using the partial dictionary corresponding to the atoms. calculate Thus updating the scattered echo margin Calculate the energy percentage of the scattering center atom extracted in this round of SOMP iteration.

[0118]

[0119] 7) Determine if the stopping iteration condition δ is met. k -δ k-1 If ≤ε, then proceed to step 8); otherwise, update k = k + 1 and return to step 4) for the next round of SOMP scattering center extraction iteration.

[0120] 8) Output scattering center parameter estimation results The scattering center coefficient estimation result σ and the scattering center energy proportion sequence δ complete the extraction of scattering center parameters in this alternating optimization stage.

[0121] The following uses S32 as an example. The SOMP process will be explained in detail using the example of refining parameter estimates:

[0122] S321. Initialize the input scattered echo vector s, and the estimated parameter set output by j in the previous stage. The energy percentage δ² of the scattering atoms extracted in the previous stage in descending order, and the minimum number of SOMP comparisons N h Based on the signal-to-noise ratio of the SAR image, the minimum energy percentage ε of the scattering center corresponding to the stopping iteration is set, and k = 1, r = s is initialized. δ0 = 0, δ1 = 1;

[0123] S322, Based on the data from the previous stage The corresponding descending energy order δ2={δ1,δ2,...,δ i ,...,δ C}, generated sequentially The corresponding Θ 21 , The corresponding Θ 2i ..., of which Θ 2i It is based on and refine the mesh The above-mentioned estimated parameter results are confirmed. For each parameter, the value is extended to a certain range to the left and right and is refined according to the refined grid The parameter atom set obtained by re-refining the value is obtained.

[0124] S323, determine the iteration threshold ε;

[0125] S324, generate a dynamic dictionary: the SOMP algorithm generates a scattering atom dictionary of the refined parameter dictionary set corresponding to the previous stage parameter atom energy proportion extracted each time, k=1 initializes the current scattering atom dictionary as D=D(Θ 21 ), and thereafter generates D(Θ 22 ), D(Θ 23 ), …, D(Θ 2C ) in turn and adds them to the current scattering atom dictionary.

[0126] S325, perform a serialized orthogonal matching pursuit operation: take one Θ 2i generated dictionary D(Θ 2i ) as an atom cluster, obtain the number of atom clusters contained in the current scattering atom dictionary, denoted as N cluster ; calculate the inner product similarity c=D H ·r of the current scattering atom dictionary and the scattering echo residual, and obtain the serial number of the atom with the largest inner product similarity. Obtain the atom cluster serial number where is located. Let the current maximum inner product similarity be According to the N h parameters defined by the SOMP algorithm, compare and N h , if N now ≥N h , it is considered that the atom cluster where the current extracted scattering atom is located is better than the subsequent N h atom clusters, and the extracted scattering atom result is retained. If N now <N h , perform the iteration operations of 51)-53) until N now ≥N h : 51) according to the order in δ c , use the largest parameter dictionary Θ 2(i+1) that has not been generated yet to generate a scattering atom dictionary D t =D(Θ 2(i+1) ), and incorporate it into the current scattering atom dictionary D=[D,D t ]; 52) calculate the inner product relevance of the scattering echo residual and D t ; obtain cmax = max |c|; 53) if c * > c max , let N now = N now + 1, continue the iteration of steps 51) - 53) until N now ≥ N h ; if c * ≤ c max , let N now = 0, update c * = c max , update the serial number of the current extracted scattering atom update the serial number of the atomic cluster where the current extracted scattering atom is located as continue the iteration of steps 51) - 53) until N now ≥ N h ;

[0127] S326, perform the operation of atomic cluster elimination of the extracted scattering atom, and update the related variables: 61) the extracted atomic cluster is eliminated, that is, let is the partial dictionary corresponding to the atom with the atomic cluster serial number , 62) update the extraction result calculate , thereby updating the scattering echo residual calculate the energy proportion occupied by the scattering center atom extracted in this round of SOMP iteration

[0128] S327, judge whether the stop iteration condition δ k - δ k-1 ≤ ε is met, if yes, execute step S328, otherwise, update k = k + 1, and return to step S324 to perform the next round of SOMP scattering center extraction iteration;

[0129] S328, output the scattering center parameter estimation result the energy proportion sequence δ3, and the scattering center coefficient estimation result σ3, complete the scattering center parameter extraction in this alternating optimization phase.

[0130] According to the scattering center parameter estimation result and the scattering center coefficient estimation result σ, the zero padding and windowing imaging can be performed again to obtain the reconstructed SAR image of the scattering center extraction result.

[0131] The effects of the embodiment can be illustrated by the following simulation and measured data results:

[0132] A. Experimental data:

[0133] The electromagnetic simulation data used in the experiment was a sLICY model of an ideal material calculated using the PO algorithm, which included typical scattering types such as first-order surfaces, dihedral surfaces, trihedral surfaces, and cap-shaped surfaces. The measured data consisted of ten categories of ground vehicle data from publicly available MSTAR data, with one image from each category. The electromagnetic simulation data had a higher resolution, while the MSTAR data had a lower resolution. Specific radar parameters are shown in Table 1.

[0134] Table 1

[0135] Class Center Frequency Bandwidth Synthesis Angle Frequency to Sampling Number Azimuth to Sampling Number EM Simulation Data 10 GHz 3 GHz 8 degrees 101 101 MSTAR Measured Data 9.6 GHz 491.95 MHz 2.93 degrees Varies by Target Varies by Target

[0136] B. Experimental Results:

[0137] The scattering centers of the simulation data and measured data were extracted using the method proposed in this invention, following the steps outlined above. For the electromagnetic simulation data, the scattering center extraction results are as follows: Figure 6 As shown, where Figure 6 (a) shows the result of reconstructing the echo using the extracted scattering center parameters according to the model, referred to as the reconstructed image. Figure 6 (b) shows the results extracted from A diagram showing the size and type of the scatterer plotted on a two-dimensional plane for the seven parameters is provided. Table 2 also shows the time and memory used to extract the attribute scattering centers from the simulation data using the OMP and SOMP algorithms, respectively.

[0138] For MSTAR data of ten target categories, the proposed method was also used to extract attribute scattering centers. The total echo of the extracted scattering centers and the reconstructed image are shown below. Figure 7 As shown in Table 3, the complexity of the improved SOMP algorithm and the original OMP algorithm were also compared.

[0139] Table 2

[0140] Algorithm Time Max Memory Usage Reconstruction Energy Ratio OMP 117.357 11.02 GB 0.809 SOMP 88.837 3.791 GB 0.791

[0141] Table 3

[0142]

[0143]

[0144] C. Analysis of Experimental Results:

[0145] contrast Figure 6 (a) and Figure 3 (b) shows that the original SAR image and the reconstructed image with extracted attribute scattering centers have a high degree of fit to the original image. Figure 6(b) The estimated SLICY model distribution scatterer length is close to the original model, especially for the case of high resolution and not too low signal-to-noise ratio, the scatterer type in the target can be correctly judged according to the (L, α) parameters.

[0146] Comparison Figure 7 and Figure 4 The echo image and SAR image of the original MSTAR data and the echo image and SAR image reconstructed according to the attribute scatter center extraction result are basically consistent in the target area, meanwhile the background noise in the echo is filtered out, and the scatter center feature accurately and completely describes the target shape.

[0147] According to the comparison results of the original OMP and improved SOMP algorithms in Tables 2 and 3, it can be seen that the method proposed in the application has obvious advantages in the time occupancy and maximum memory consumption of the algorithm, and the parameter extraction result still has good physical meaning and geometric description performance.

[0148] The experimental results show that the application can more efficiently use the sparse representation method in the frequency domain to extract the attribute scatter center, and the extracted scatter center parameters can obtain the scatter type result with physical meaning under the condition of high resolution and not too low signal-to-noise ratio, and the extraction result can geometrically characterize the target on the measured data.

[0149] The above describes the preferred embodiments of the application in detail. It should be understood that those skilled in the art can make many modifications and changes without creative labor according to the concept of the application. Therefore, any technical solution obtained by logical analysis, reasoning or limited experiment on the basis of the prior art according to the concept of the application should be within the protection scope determined by the claims.

Claims

1. A SAR image scattering center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit, characterized in that, The method comprises the following steps: S1, obtaining an original SAR image and pre-processing to obtain original frequency domain echo data; S2, according to the original frequency domain echo data, using a point scattering center model and an OMP algorithm to initialize a key area where a target scattering center is located, to obtain an initial scattering center position parameter set and an initial scattering center energy proportion; S3, according to the initial scattering center position parameter set and the initial scattering center energy proportion, attribute parameter extraction is performed based on an attribute scattering center model and an SOMP algorithm, to output a scattering center attribute parameter estimation result, a scattering center coefficient estimation result and a scattering center energy proportion sequence; The SOMP based on the scattering center atom energy proportion sequence extracted in the last stage in the alternating optimization process comprises the following steps: 1) initialization of the input scattering echo vector s, the estimated parameter set output by the last stage j j = 1, 2, 3, 4, the energy proportion δ of the scattering atoms extracted in the last stage in descending order c , the minimum comparison number N of SOMP h , the minimum energy proportion ε of the scattering center corresponding to the stop iteration set according to the signal-to-noise ratio of the SAR image, initialization k = 1, r = s, δ0=0, δ1=1; 2) according to the data of the last stage corresponding descending energy order δ c = {δ1, δ2,..., δ i ..., δ C}, sequentially generate corresponding Θ j1 , corresponding Θ j2 ..., wherein Θ ji is determined according to and the refined grid, and the parameter estimation result of the above stage is taken as the center, each parameter value is expanded to a certain range on the left and right, and the parameter atom set obtained by re-refining the value according to the refined grid; 3) determining an iteration threshold ε; 4) Generating dynamic dictionary: SOMP algorithm generates a scattering atom dictionary of the refined parameter dictionary set corresponding to the previous stage parameter atom according to the scattering atom energy proportion extracted in the previous stage, and initializes the current scattering atom dictionary as D=D(Θ j1 ) when k=1, and then generates D(Θ j2 ), D(Θ j3 ), …, D(Θ jC ) in turn and adds them to the current scattering atom dictionary; 5) Perform orthogonal matching tracing operation for serialization: convert a Θ ji The generated dictionary D(Θ) ji A cluster of atoms is called an atom cluster. The number of atom clusters contained in the current scattering atom dictionary is denoted as N. cluster ; Calculate the inner product similarity c = D between the current scattering atom dictionary and the scattering echo margin. H ·r, retrieves the index of the atom with the highest inner product similarity. Get The atomic cluster number is Let the current maximum inner product similarity According to the defined SOMP algorithm, N h Parameters, comparison and N h The size of N, if now ≥N h Then it is considered that the atomic cluster where the currently extracted scattering atom is located is more than the subsequent N h Each atomic cluster should be better, retaining the extracted scattering atom results. If N now <N h Then execute the iterative operations 51)-53) until N is satisfied. now ≥N h :51) According to δ c The order of the dictionary is refined using the largest parameter Θ that has not yet been used to generate a dictionary. j(i+1) Generate a dictionary of scattering atoms D t =D(Θ) j(i+1) ), and incorporate it into the current scattering atom dictionary D=[D,D t ];52) Calculate the residual of the scattered echo and D t Inner product correlation Get c max =max|c|; 53) If c * >c max Then let N now =N now +1, continue iterating through steps 51)-53) until N. now ≥N h If c * ≤c max Then let N now =0, update c * =c max Update the index of the currently extracted scattering atoms. Then update the cluster number of the currently extracted scattering atom to... Continue iterating through steps 51)-53) until N. now ≥N h ; 6) Perform the operation of extracted atom cluster cancellation, while updating the relevant variables: 61) Extracted atom cluster cancellation, i.e. let i.e. the partial dictionary corresponding to the atom with atom cluster number 62) Update the extraction result Calculate Thus, update the scattered echo residual Calculate the energy proportion occupied by the scattering center atom extracted in this round of SOMP iteration 7) judge whether the stop iteration condition δ k - δ k-1 ≤ ε, if yes, execute step 8), otherwise, update k = k + 1, return to step 4) for the next round of SOMP scattering center extraction iteration; 8) output the scatter center parameter estimation results The scatter center coefficient estimation results σ and the scatter center energy proportion sequence δ complete the scatter center parameter extraction of the present alternating optimization phase.

2. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 1, characterized in that, The step S1 is specifically: An original SAR image is obtained, and according to the parameters used in SAR imaging, inverse processing is performed on the imaging process to obtain original frequency domain echo data corresponding to the original SAR image, wherein the inverse processing includes inverse Fourier transform, zero removal and window removal operations.

3. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 1, characterized in that, The step S2 comprises the following steps: S21, according to the bandwidth used when collecting the radar echo, the frequency dimension sampling number, the azimuth accumulation angle, the azimuth sampling number parameters, the value range of the parameter x and the parameter y in the point scattering center is determined: (-x m / 2,x m / 2), (-y m / 2,y m / 2), wherein x m is the distance direction imaging range, and y m is the azimuth direction imaging range; S22, set the initial position parameter grid (Δx, Δy), construct the position parameter dictionary Θ0= {(x, y) | x ∈ [-x m / 2:Δx:x m / 2], y ∈ [-y m / 2:Δy:y m / 2]}; S23. Constructing a scattering atom dictionary D(Θ0) according to the point scatter center model, the scattering atom dictionary being a two-dimensional matrix, the i-th column d i is a normalized vectorized atom, wherein the point scatter center model is: is a normalized vectorized atom, wherein the point scatter center model is: where f is the frequency sample value, is the azimuth angle sample value, and c is the speed of light. S24, according to the vectorization s0 of the original frequency domain echo data E0 and the scattering atom dictionary D(Θ0), an initial position parameter set of a point scattering center is extracted by using an original orthogonal matching pursuit algorithm OMP, and an initial scattering center position parameter set and an initial scattering center energy proportion are output.

4. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 3, characterized in that, The vectorization s0 of the original frequency domain echo data E0 is vec(E0), and vec() represents flattening the original M×N matrix into an MN×1 vector.

5. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 4, characterized in that, The scattering atom dictionary D(Θ0) is generated in the manner D(Θ0) = [d1, d2,..., d i ,…,d C ], wherein, θ i is the i-th parameter combination in the candidate parameter set Θ0, is the point scatter center model, i.e. θ i = (x i ,y i ) in step S23. C is the number of parameter combinations in Θ0~(x,y).

6. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 3, characterized in that, The original orthogonal matching pursuit algorithm OMP comprises the following steps: S241, initialize candidate parameter set Θ0, scattering atom dictionary D(Θ0), set iteration number k = 1, scattering echo residual vector r = s, estimated parameter set δ0= 0, δ1= 1; S242, according to the SAR image signal-to-noise ratio, ε0 is determined; S243、compute the inner product similarity c = D of each scatterer atom with the scattered echo residual H (Θ) · r, (·) H denotes the conjugate transpose; S244. Determine the atom with the highest inner product similarity. Right now It is the first in Θ0 Each parameter atom is added to the estimation result. S245、calculating a least square estimation amplitude of the atom with the largest inner product similarity obtaining a current estimation scattering echo vector updating the scattering echo residual vector as updating the energy proportion of the scattering atom extracted in this iteration wherein denotes Moore-Penrose pseudo-inverse operation; S246, judging whether δ k - δ k-1 > ε0, if yes, updating iteration number k = k + 1, and returning to step S243, the iteration is performed for extraction of the scattering center parameter, otherwise, step S247 is executed; S247、output the parameter estimation result based on the point scattering model Let it be the initial scattering center position parameter set Output, output the initial scattering center energy proportion sequence δ1 at the same time.

7. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 1, characterized in that, The attribute scattering center model is: where f is the frequency sampling point, f c is the radar center frequency, is the azimuth angle sampling point, is the scattering center orientation angle parameter, a is the scattering center surface curvature parameter, c is the speed of light, γ is the scattering center characteristic parameter related to frequency, x, y are the scattering center position parameters.

8. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 7, characterized in that, The step S3 adopts the idea of alternating optimization to optimize and refine the to-be-estimated scattering center attribute parameters step by step The parameter estimation based on L0 norm optimization is performed based on a serialized orthogonal matching pursuit algorithm SOMP.

9. The SAR image scatter center parameter estimation method based on alternating optimization and serialized orthogonal matching pursuit according to claim 7, characterized in that, The step S3 comprises the following steps: S31, to coarsely estimate parameters: with an initial set of scattering center position parameters as initial values, on the basis of which the estimation of is expanded, to construct where L = [0: ΔL: L max ], is a set containing combinations of (x, y) values, L max is a maximum length parameter of the scattering center determined according to the initial value of y, is the minimum and maximum orientation angle values determined according to the synthetic angle, to as the candidate scattering atom parameters, based on the initial scattering center energy proportion sequence δ1, use the SOMP method to estimate to obtain the estimated parameter set and the energy proportion sequence δ2; S32, to refine the estimation of parameters: to Δx, Δy, ΔL, as initial values, on the basis of which the coarse grid is refined, the value of the parameter of the coarse estimate Each parameter value of is extrapolated to the left and right by Dθ / 2, Dθ is the total range of the refined estimate expansion, thereby constructing to As the candidate scattering atom parameter, based on the energy proportion sequence δ2, the SOMP method is used to refine the estimation, and the estimated parameter set is obtained and the energy proportion sequence δ3; S33, estimating the parameter a: taking As an initial value, on the basis of which the estimation of a is expanded, the parameter set Wherein a ∈ {-1, -1 / 2, 0, 1 / 2, 1}, so that As the parameter of the candidate scattering atom, based on the energy proportion sequence δ3, the SOMP method is used to estimate a, and the estimated parameter set And the energy proportion sequence δ4; S34, estimate the parameter γ: take As the initial value, on the basis of which the estimate of γ is expanded, construct Take As the parameter of the candidate scattering atom, based on the energy proportion sequence δ4, estimate γ using the SOMP method to obtain the final estimated parameter set That is, the scattering center attribute parameter estimation result.

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