CN113835088A - Random radiation radar artifact suppression method for self-adaptive step frequency accumulation - Google Patents

Random radiation radar artifact suppression method for self-adaptive step frequency accumulation Download PDF

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CN113835088A
CN113835088A CN202111121015.XA CN202111121015A CN113835088A CN 113835088 A CN113835088 A CN 113835088A CN 202111121015 A CN202111121015 A CN 202111121015A CN 113835088 A CN113835088 A CN 113835088A
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CN113835088B (en
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张寅�
黄钰林
覃千洋
张永超
毛德庆
张永伟
杨建宇
杨海光
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract

The invention discloses a random radiation radar artifact suppression method for adaptive step frequency accumulation, which specifically comprises the following steps: establishing a random radiation radar echo signal model, and adopting an accumulation method to inhibit correlation and random radiation radar correlation imaging. The method firstly establishes a random radiation radar echo signal model, and analyzes a pseudo target generation mechanism from a mathematical angle; then, by using a self-adaptive step frequency accumulation method, the periodicity and regularity of the single frequency correlation degree when the accumulation is not carried out are broken through aliasing of different frequencies, the correlation degree of an artifact point is reduced, so that a pseudo target is restrained, and the artifact-free target is restored through correlation imaging.

Description

Random radiation radar artifact suppression method for self-adaptive step frequency accumulation
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a random radiation radar imaging artifact suppression method.
Background
Radar imaging has important applications in many fields, such as marine observation, severe weather monitoring, and the like. The random radiation radar is a radar with a new system and can be applied to hovering and addressing of the unmanned aerial vehicle. The observation field of view is increased in the imaging process, so that the false target is interfered with the acquisition of normal target information, and the key problem of randomly radiating the radar is how to restrain the false target.
In documents "y.guo, d.wang, x.he and b.liu", "Super-resolution Imaging method based on random radial array", "2012IEEE International Conference on Imaging Systems and Techniques Proceedings, Manchester, UK,2012, pp.1-6, doi: 10.1109/ist.2012.6403797", the new system of random radiation radar was first proposed, which revealed that it could break through the resolution of conventional real aperture radar, but the authors did not study further. In documents "S.Zhu, A.Zhang, Z.Xu and X.Dong", "radio coherent Imaging With Random Microwave Source", "in IEEE Antennas and Wireless amplification Letters, vol.14, pp.1239-1242,2015, doi: 10.1109/LAWP.2015.2399977", the artifact phenomenon of the Random radiation Radar was found for the first time, but the authors did not further analyze the mechanism of the generation of the false target from the mathematical point of view, and thus, the artifact suppression method could not be further proposed.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a random radiation radar artifact suppression method based on self-adaptive step frequency accumulation.
The specific technical scheme of the invention is as follows: a random radiation radar artifact suppression method for self-adaptive step frequency accumulation specifically comprises the following steps:
step one, establishing a random radiation radar echo signal model,
the random radiation radar comprises a plurality of transmitting antenna array elements and 1 receiving antenna array element, and an antenna is arrangedHeight of ground scene is H, dxAnd dyThe antenna array element spacing of the uniform area array antenna along the x and y directions is respectively represented, P and Q are two point positions in a scene area, and the transmission signal expression of the ith transmission antenna array element is as follows:
Figure BDA0003277048630000011
wherein A isi(t) represents the random amplitude modulated signal of the ith antenna element,
Figure BDA0003277048630000012
random phase signal, T, representing the ith antenna elementrFor transmitting the pulse duration of the signal, fcIs the carrier frequency of the transmitted signal;
let the history of the distance from the ith transmitting antenna to the target point p be RipThen the antenna-to-target time delay is τip＝RipC, c represents the speed of light, and when all the transmitting antenna array transmitting signals reach the target point P, the energy accumulation is expressed as:
Figure BDA0003277048630000021
k, L are points in the observation scene in the distance direction and the direction;
after the radiation field acts on the ground target, the scattering field E of the targets(τipAnd t) is expressed as:
Figure BDA0003277048630000025
wherein, σ (τ)ip) Representing the history of the corresponding distance of the target as RipSo that the echo signal received at the receiving antenna is:
Figure BDA0003277048630000022
wherein, taurpRepresenting the time delay from a target to a receiving antenna r, and dividing an imaging area into K × L small areas;
sampling the received echo data, and the number of sampling points is rho ═ Tr*fsBy transmission of pulse duration TrAnd a sampling frequency fsDetermining that the sampling time vector t is equal to (t)1,t2,…,tρ) Along the sampling instant, the echo data is represented as:
Figure BDA0003277048630000023
wherein, tauir＝τip+τrpRepresenting the total time delay, σ (τ), from the ith transmit antenna to the receive antenna through the target pir) To correspond to the total time delay tauirN ═ N (t) of the scattering coefficient of (c)1),n(t2),...n(tρ)]TRepresenting additive noise;
equation (5) is abbreviated in matrix form:
Rec＝Esσ+N (6)
where Rec is the echo vector, EsThe method comprises the following steps of (1) obtaining a radiation field matrix, wherein sigma is a scattering coefficient vector, and the matrix is in a signal model of a random radiation radar;
step two, inhibiting the correlation degree by adopting an accumulation method,
according to the signal model of the first step, defining the square | χ (x, y) | of the correlation coefficient model of any point Q as the target point P2For the target degree of correlation, i.e.:
Figure BDA0003277048630000024
wherein R isiPFor the history of the distance of the ith transmitting antenna to the target point P, RiQA history of distances to any point Q for the ith transmit antenna;
assuming that the radar continuously transmits eta pulse time-width signals by using frequency hopping interval time T as a period, and eta hops are generatedFrequency point of f1,f2,…,fηAnd obtaining an ith pulse signal model as follows:
Rec[i]＝Es[i]σ+N[i] (8)
wherein, Rec [ i]Echo data vectors for p sample points in the ith pulse, Es[i]Is a random radiation field energy matrix within the ith pulse, N [ i ]]A sampled data vector for the ith impulse noise;
Es[i]decomposed into two matrices B [ i ]]And D [ i ]]Product, B [ i ]]Representing the amplitude-phase matrix of the ith pulse, DI]A time-frequency matrix representing the ith pulse;
correspondingly accumulating the sampling point data of the eta pulses to obtain new data
Figure BDA0003277048630000031
Figure BDA0003277048630000032
In order to ensure that the water-soluble organic acid,
Figure BDA0003277048630000033
Figure BDA0003277048630000034
Figure BDA0003277048630000035
formula (9) is abbreviated:
Figure BDA0003277048630000036
equation (13) is the signal model of adaptive step frequency accumulation;
' handac(x,y)|2Defined as the phase after accumulationThe degree of closeness is further set to | χk(x,y)|2Defined as the correlation when the kth pulse is not accumulated, we can obtain:
Figure BDA0003277048630000041
according to the cauchy inequality:
Figure BDA0003277048630000042
step three, random radiation radar correlation imaging,
according to the equation expression of the echo matrix after accumulation of the formula (13), the matrix is subjected to
Figure BDA0003277048630000043
Is subjected to SVD to obtain
Figure BDA0003277048630000044
Wherein U and V represent unitary matrix of SVD decomposition, and Λ represents matrix
Figure BDA0003277048630000045
The singular value of (a);
after the singular value is subjected to stage inversion, the scattering coefficient of the target is expressed as:
Figure BDA0003277048630000046
wherein Λ' represents a matrix obtained by inverting the diagonal matrix Λ and setting a cutoff value greater than the selection to 0;
and (5) solving the formula (17) to obtain an image without a false target.
The invention has the beneficial effects that: firstly, establishing a random radiation radar echo signal model, and analyzing a pseudo target generation mechanism from a mathematical angle; then, by using a self-adaptive step frequency accumulation method, the periodicity and regularity of the single frequency correlation degree when the accumulation is not carried out are broken through aliasing of different frequencies, the correlation degree of an artifact point is reduced, so that a pseudo target is restrained, and the artifact-free target is restored through correlation imaging.
Drawings
Fig. 1 is a schematic diagram of a geometric model of a random-radiation radar according to an embodiment of the present invention.
Fig. 2 is a diagram illustrating an adaptive step-and-frequency accumulation visualization according to an embodiment of the present invention.
FIG. 3 is a graph of correlation of different accumulation times according to an embodiment of the present invention.
Fig. 4 is a comparison diagram of artifact suppression effect under 20dB signal-to-noise ratio according to an embodiment of the present invention.
Detailed Description
The random radiation radar imaging mainly comprises the steps of transmitting random signals through a plurality of transmitting antenna arrays to obtain more target modulation information, and obtaining high-resolution imaging of a target through an inversion method. The system can realize high-resolution imaging without relative motion with a target, and therefore has important application. At present, research in the field of random radiation radar mainly focuses on a random radiation field construction method and an imaging algorithm so as to improve resolution. However, increasing the observation range of the radar may generate a false target, which may interfere with the acquisition of effective target information, and therefore, it is also important to study methods for suppressing the false target. The method comprises the following steps of firstly, theoretically deducing the reason of the occurrence of a false target; and an inter-pulse adaptive step-frequency accumulation artifact suppression method is provided, and finally the feasibility of the method is verified through simulation. The embodiments of the present invention will be further described with reference to the accompanying drawings.
The simulation experiment of the invention is carried out on MATLAB 2014a, and the effectiveness of the method is verified by the simulation result. The method of the invention is further illustrated below with reference to the figures and examples.
In this embodiment, a geometric model of the random radiation radar of the present invention is shown in fig. 1, an adaptive step-and-frequency accumulation visual diagram is shown in fig. 2, and simulation parameters of the present invention are shown in table 1:
TABLE 1
Carrier frequency 10GHz Signal time width 2us
Bandwidth of signal 2GHz Target spacing 1m
Number of array elements 25 Radar platform height 1km
Sampling frequency 1GHz Frequency hopping interval 10us
Spacing of array elements 1.5m Size of field of view 90m*90m
The method comprises the following specific implementation steps:
step one, establishing a random radiation radar echo signal model,
the random radiation radar comprises a plurality of emissionsThe antenna array element and 1 receiving antenna array element. Let H be 1000m and d be the height of the antenna from the groundxAnd dyIt is 1.5m to represent the antenna array element spacing of the uniform area array antenna along the x and y directions, the circle represents the imaging scene area, P, Q are two point positions in the scene area, then the transmission signal expression of the ith transmission antenna array element is:
Figure BDA0003277048630000051
wherein A isi(t) represents the random amplitude modulated signal of the ith antenna element,
Figure BDA0003277048630000052
random phase signal, T, representing the ith antenna elementrFor transmitting pulses of signal duration 2us, fcIs the carrier frequency of the transmitted signal, 10 GHz.
Let the history of the distance from the ith transmitting antenna to the target point p be RipThen the antenna-to-target time delay is τip＝Rip/c，c＝3*108m/s represents the speed of light. When all the transmit antenna array transmit signals reach the target point P, the energy accumulation is expressed as:
Figure BDA0003277048630000053
k, L are points in the observation scene in the distance direction and the direction;
after the radiation field acts on the ground target, the target scatters the field Es(τipT) can be expressed as:
Figure BDA0003277048630000065
wherein, σ (τ)ip) Representing the history of the corresponding distance of the target as RipThe scattering coefficient of (a), and thus the echo signal received at the receiving antenna, can be expressed as:
Figure BDA0003277048630000061
wherein, taurpRepresenting the time delay from the target to the receiving antenna, the imaging area is divided into 10000 small areas.
Sampling the received echo data, and the number of sampling points is rho ═ Tr*fs2000, pulse duration Tr2us and sampling frequency fsDetermined at 1 GHz. Sampling time vector t ═ t1,t2,…,tρ) Thus, along the sampling instant, the echo data may be represented as
Figure BDA0003277048630000062
Wherein, tauir＝τip+τrpRepresenting the total time delay, σ (τ), from the ith transmit antenna to the receive antenna through the target pir) To correspond to the total time delay tauirN ═ N (t) of the scattering coefficient of (c)1),n(t2),...n(tρ)]TRepresenting additive noise
The equation can also be abbreviated as:
Rec＝Esσ+N (23)
where Rec is the echo vector, EsThe scattering coefficient of the target is obtained by solving a matrix equation set, wherein the matrix is a radiation field matrix, sigma is a scattering coefficient vector and is a signal model of the random radiation radar.
Step two, inhibiting the correlation degree by adopting an accumulation method,
since the time delay from each transmit antenna to the target is small, equation (19) can be approximated as:
Figure BDA0003277048630000063
after carrier frequency removal, (24) can be abbreviated as the following equation:
Figure BDA0003277048630000064
thus EsThe matrix may be decomposed into a product of two matrices B, D, where B is an amplitude-phase matrix containing only amplitude and phase information; d is a time-frequency matrix, which only contains time delay and frequency information, that is:
Es＝BD (26)
wherein the content of the first and second substances,
Figure BDA0003277048630000071
Figure BDA0003277048630000072
partitioning the time-frequency matrix D into blocks according to columns:
D＝[d1 d2 … dKL] (29)
the signal model (23) can be rewritten as:
Figure BDA0003277048630000073
the amplitude and phase are arranged in an orthogonal distribution to minimize redundant information in matrix B, in which case (30) can be deformed
Figure BDA0003277048630000074
Wherein the content of the first and second substances,
Figure BDA0003277048630000075
representing the pseudo-inverse of the magnitude-phase matrix.
The correlation coefficient of the two point i, j position targets in the target area is defined as
Figure BDA0003277048630000076
< - > represents the inner product of two vectors, (-)HRepresenting the conjugate transpose operator. N is a radical ofatRepresenting the total number of transmit antennas. The correlation coefficient of the i and the j positions in the imaging process of the random radiation radar is high, and the correlation with other places is low, namely
χii＝1,χij≈1,χik≈0,k≠i,j (33)
Consists of (32) and (33) in combination, and comprises:
Figure BDA0003277048630000077
as can be seen from equation (34), when the point correlation of two different positions appearing in the imaging region is high, only the sum of the two target coefficients can be solved, but they cannot be solved separately, that is, the strong correlation between the target position in the target region and the pseudo target position will result in that only the linear relationship between the two targets can be solved, and thus two targets cannot be solved separately, which is the mechanism of the appearance of the pseudo target.
According to the signal model of the first step, defining the square | χ (x, y) | of the correlation coefficient model of any point Q as the target point P2For the target correlation, the artifact suppression effect is measured, i.e.:
Figure BDA0003277048630000081
RiPfor the history of the distance of the ith transmitting antenna to the target point P, RiQIs the distance history of the ith transmit antenna to any point Q.
As is understood from the mechanism, since the artifact positions are completely correlated and the correlation is 1, in order to suppress the intensity of the artifact, it is necessary to find a method for reducing the correlation of the artifact positions.
The antenna array is assumed to be a multiple-transmitting-receiving array with M rows and N columns uniformly arranged, so that the number of transmitting antennas is
Nat＝M*N-1 (36)
Supposing that the radar continuously transmits eta pulse time-width signals by using frequency hopping interval time T as a period to generate eta frequency hopping points f1,f2,…,fηAnd step frequency distribution is satisfied, namely the kth pulse frequency hopping satisfies the following equation:
Figure BDA0003277048630000082
the model of the ith pulse signal is obtained as follows:
Rec[i]＝Es[i]σ+N[i] (38)
wherein, Rec [ i]Echo data vectors for p sample points in the ith pulse, Es[i]Is a random radiation field energy matrix within the ith pulse, N [ i ]]Is the sampled data vector of the ith impulse noise. From the foregoing derivation, same reasoning can be seen for Es[i]Can be decomposed into two matrices B [ i ]]And D [ i ]]Product, B [ i ]]Representing the amplitude-phase matrix of the ith pulse, DI]A time-frequency matrix representing the ith pulse.
If the sampling point data of the eta pulses are correspondingly accumulated, new data can be obtained
Figure BDA0003277048630000083
Figure BDA0003277048630000091
Order to
Figure BDA0003277048630000092
Figure BDA0003277048630000093
Figure BDA0003277048630000094
Equation (39) can be abbreviated as:
Figure BDA0003277048630000095
this is the signal model for adaptive step frequency accumulation.
' handac(x,y)|2Defined as the degree of correlation after accumulation, and the correlation function which can be accumulated by the imitative expression (35) is defined as
Figure BDA0003277048630000096
Then is provided with chik(x, y) is the correlation function when the kth pulse is not accumulated, | χk(x,y)|2Defined as the correlation when the k-th pulse is not accumulated, so there are:
Figure BDA0003277048630000097
therefore, the formula (44) can be rewritten as:
Figure BDA0003277048630000098
from the Cauchy inequality:
Figure BDA0003277048630000101
the formula (47) realizes peak value dislocation through different pulse emission frequencies, and balances the peak value dislocation, so that the upper bound of the correlation degree of the artifact after accumulation is reduced powerfully, and the artifact is effectively inhibited.
Step three, random radiation radar correlation imaging,
the step uses a method (TSVD) of truncating singular values to realize the solution of the scattering coefficient of the target.
According to formula (43)Equation expression of echo matrix after accumulation, and pairing matrix
Figure BDA0003277048630000102
Is subjected to SVD to obtain
Figure BDA0003277048630000103
Wherein U and V represent unitary matrix of SVD decomposition, and Λ represents matrix
Figure BDA0003277048630000104
The singular value of (a). After the singular value is subjected to stage inversion, the scattering coefficient of the target can be expressed as
Figure BDA0003277048630000105
Where Λ' represents the matrix obtained by inverting the diagonal matrix Λ and setting the cutoff value greater than the selected value to 0. In this embodiment, an adaptive step-and-frequency accumulation method is adopted, and then the solution is performed by the equation (49), so that the imaging without the false target can be obtained.
To demonstrate the effectiveness of the method, a condition number of 50 was chosen and the signal-to-noise ratio was 20 dB. The experimental scene size was 90m by 90 m. By comparing this method for non-accumulation and different accumulation times, fig. 3 and 4 can be obtained. In which fig. 3 is a correlation diagram of different methods, fig. 3(a) is a correlation diagram of no accumulation, fig. 3(b) is a correlation diagram of accumulation 2 times, fig. 3(c) is a correlation diagram of accumulation 5 times, and fig. 3(d) is a correlation diagram of accumulation 50 times, and it can be seen from fig. 3 that the more the accumulation times, the smaller the correlation of the pseudo target position. Fig. 4 shows imaging diagrams of different methods, fig. 4(a) shows a target scene diagram, fig. 4(b) shows an imaging diagram when no accumulation is performed, fig. 4(c) shows an imaging diagram when 2 times of accumulation are performed, fig. 4(d) shows an imaging diagram when 20 times of accumulation are performed, fig. 4(f) shows an imaging diagram when 50 times of accumulation are performed, and fig. 4(e) shows an imaging diagram when 100 times of accumulation are performed. As can be seen in fig. 4, the intensity of the false target becomes smaller as the number of accumulations increases.
By combining fig. 3 and fig. 4, it is verified that the method of the present invention can effectively reduce the correlation degree of the random radiation radar imaging so as to suppress the false target.

Claims (1)

1. A random radiation radar artifact suppression method for self-adaptive step frequency accumulation specifically comprises the following steps:
step one, establishing a random radiation radar echo signal model,
the random radiation radar comprises a plurality of transmitting antenna array elements and 1 receiving antenna array element, and the height of the antenna from the ground scene is set as H, dxAnd dyThe antenna array element spacing of the uniform area array antenna along the x and y directions is respectively represented, P and Q are two point positions in a scene area, and the transmission signal expression of the ith transmission antenna array element is as follows:
Figure FDA0003277048620000011
wherein A isi(t) represents the random amplitude modulated signal of the ith antenna element,
Figure FDA0003277048620000012
random phase signal, T, representing the ith antenna elementrFor transmitting the pulse duration of the signal, fcIs the carrier frequency of the transmitted signal;
let the history of the distance from the ith transmitting antenna to the target point p be RipThen the antenna-to-target time delay is τip＝RipC, c represents the speed of light, and when all the transmitting antenna array transmitting signals reach the target point P, the energy accumulation is expressed as:
Figure FDA0003277048620000013
k, L are points in the observation scene in the distance direction and the direction;
after the radiation field acts on the ground target, the scattering field E of the targets(τipAnd t) is expressed as:
Figure FDA0003277048620000016
wherein, σ (τ)ip) Representing the history of the corresponding distance of the target as RipSo that the echo signal received at the receiving antenna is:
Figure FDA0003277048620000014
wherein, taurpRepresenting the time delay from a target to a receiving antenna r, and dividing an imaging area into K × L small areas;
sampling the received echo data, and the number of sampling points is rho ═ Tr*fsBy transmission of pulse duration TrAnd a sampling frequency fsDetermining that the sampling time vector t is equal to (t)1,t2,…,tρ) Along the sampling instant, the echo data is represented as:
Figure FDA0003277048620000015
wherein, tauir＝τip+τrpRepresenting the total time delay, σ (τ), from the ith transmit antenna to the receive antenna through the target pir) To correspond to the total time delay tauirN ═ N (t) of the scattering coefficient of (c)1),n(t2),...n(tρ)]TRepresenting additive noise;
equation (5) is abbreviated in matrix form:
Rec＝Esσ+N (6)
where Rec is the echo vector, EsThe method comprises the following steps of (1) obtaining a radiation field matrix, wherein sigma is a scattering coefficient vector, and the matrix is in a signal model of a random radiation radar;
step two, inhibiting the correlation degree by adopting an accumulation method,
according to the signal model of the first step, defining the square | χ (x, y) | of the correlation coefficient model of any point Q as the target point P2For the target degree of correlation, i.e.:
Figure FDA0003277048620000021
wherein R isiPFor the history of the distance of the ith transmitting antenna to the target point P, RiQA history of distances to any point Q for the ith transmit antenna;
assuming that the radar continuously transmits eta pulse time-width signals by using a frequency hopping interval time T as a period, and the generated eta frequency hopping points are f1,f2,…,fηAnd obtaining an ith pulse signal model as follows:
Rec[i]＝Es[i]σ+N[i] (8)
wherein, Rec [ i]Echo data vectors for p sample points in the ith pulse, Es[i]Is a random radiation field energy matrix within the ith pulse, N [ i ]]A sampled data vector for the ith impulse noise;
Es[i]decomposed into two matrices B [ i ]]And D [ i ]]Product, B [ i ]]Representing the amplitude-phase matrix of the ith pulse, DI]A time-frequency matrix representing the ith pulse;
correspondingly accumulating the sampling point data of the eta pulses to obtain new data
Figure FDA0003277048620000022
Figure FDA0003277048620000023
In order to ensure that the water-soluble organic acid,
Figure FDA0003277048620000031
Figure FDA0003277048620000032
Figure FDA0003277048620000033
formula (9) is abbreviated:
Figure FDA0003277048620000034
equation (13) is the signal model of adaptive step frequency accumulation;
' handac(x,y)|2Defined as the accumulated correlation, and then set as | χk(x,y)|2Defined as the correlation when the kth pulse is not accumulated, we can obtain:
Figure FDA0003277048620000035
according to the cauchy inequality:
Figure FDA0003277048620000036
step three, random radiation radar correlation imaging,
according to the equation expression of the echo matrix after accumulation of the formula (13), the matrix is subjected to
Figure FDA0003277048620000037
Is subjected to SVD to obtain
Figure FDA0003277048620000038
Wherein U and V represent unitary matrix of SVD decomposition, and Λ represents matrix
Figure FDA0003277048620000039
The singular value of (a);
after the singular value is subjected to stage inversion, the scattering coefficient of the target is expressed as:
Figure FDA00032770486200000310
wherein Λ' represents a matrix obtained by inverting the diagonal matrix Λ and setting a cutoff value greater than the selection to 0;
and (5) solving the formula (17) to obtain an image without a false target.
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