CN111562578A - Distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint - Google Patents

Distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint Download PDF

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CN111562578A
CN111562578A CN202010142064.0A CN202010142064A CN111562578A CN 111562578 A CN111562578 A CN 111562578A CN 202010142064 A CN202010142064 A CN 202010142064A CN 111562578 A CN111562578 A CN 111562578A
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刘辉
李葛爽
张刚强
孟庆华
申红旗
吴飞飞
李伟亭
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North China University of Water Resources and Electric Power
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Abstract

The invention provides a distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint, which adopts a sparse representation theory to represent a complex scene as the combination of amplitude and phase, utilizes two items of prior information of three-dimensional scene sparsity and scene amplitude as real number, adds a scene amplitude real value constraint item into a regularization reconstruction model, and utilizes a quasi-Newton algorithm to estimate the scene amplitude and phase respectively, thereby completing three-dimensional reconstruction which is more in line with the actual situation; according to the method, amplitude real value constraint is added to the regularized reconstruction model, so that the measurement model is more reasonable, the method accords with the actual situation, and high-resolution three-dimensional imaging with higher super-resolution capability and stronger robustness can be realized.

Description

Distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint
Technical Field
The invention relates to a distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint, and belongs to the field of design and application according to three-dimensional imaging.
Background
The array SAR technology is characterized in that transmitting and receiving separately-arranged array antennas are sparsely arranged on a cross-course, the three-dimensional resolution of the azimuth direction, the elevation direction (equivalent to the distance direction of a traditional SAR system) and the cross-course of an observed object is realized by adopting a sky-bottom observation mode and respectively through a synthetic aperture technology, a pulse compression technology and a beam forming technology, and the regional information perceptibility of a radar is greatly improved. The technology can realize the three-dimensional reconstruction of an observation area by a single straight-line navigation downward-looking imaging mode, and effectively solves the problems of machine bottom dead zone, shadow, geometric distortion, left and right blurring and the like of the traditional SAR technology; meanwhile, the problems of excessive navigation, difficult control of motion trail and the like of other 3D-SAR (multi-baseline chromatography SAR, circular SAR and the like) technologies are eliminated.
Research on array SAR technology is carried out abroad by the German space navigation center (DLR), the German applied scientific research institute (FGAN), the university of Georgia technology, the American Sandia laboratory, the French defense research program, and the like, but the three-dimensional imaging result is not published. In China, the research of the array SAR technology just starts. In terms of three-dimensional imaging algorithms, three main categories are distinguished. The first type is that the traditional SAR imaging technology is used for reference, azimuth-elevation two-dimensional compression is completed firstly, and then cross-navigation compression is performed, the algorithm introduces more approximation to the echo distance course, and the imaging precision is low; the second type is that three-dimensional reconstruction is directly carried out on three-dimensional echo data, and the algorithm does not approximate the distance process, so that the imaging precision is higher, but the timeliness is not strong; and the third type is to use the super-resolution idea for reference, realize high-resolution three-dimensional imaging through low sampling signals, and the algorithm is complex, and the imaging precision and timeliness are to be further verified. However, the third method for realizing high-resolution three-dimensional imaging through sparse sampling is a future development direction due to the influence of cross-course resolution.
Sparse representation theory can achieve accurate recovery of the signal with a sparse signal much lower than the Nyquist sampling frequency. However, in the traditional sparse representation method, the real part and the imaginary part of a complex scene are respectively processed, and the constraint condition that the amplitude sparsity and the amplitude of the scene are real numbers is ignored. The invention researches the sparse representation imaging algorithm of the array SAR by using the prior information with the real scene amplitude, and has important significance for further reducing the array element number, the system cost and the physical realization of the array SAR system.
Disclosure of Invention
The invention aims to provide a distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint, which adopts a sparse representation theory to represent a complex scene as the combination of amplitude and phase, utilizes two items of prior information of three-dimensional scene sparsity and real scene amplitude, adds a scene amplitude real value constraint item into a regularization reconstruction model, and utilizes a quasi-Newton algorithm to estimate the scene amplitude and phase respectively, thereby completing three-dimensional reconstruction which is more in line with the actual situation.
A distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint mainly comprises the following steps:
step R1, constructing a sparse array SAR complex signal linear measurement model:
and step R2, performing sparse three-dimensional reconstruction by means of a quasi-Newton algorithm.
In the step R1, based on the full array linear array, the distributed array SAR sparse representation three-dimensional imaging algorithm considering the real-valued constraint of the scene amplitude may be represented as the following steps, after the echo data of the ith receiving array element of the array SAR is subjected to range-wise compression, range migration correction and azimuth compression
Figure BDA0002401394650000021
In the formula, t is the fast time of the distance direction, N is the slow time of the azimuth direction, N is the number of space resolution units on the course crossing of the observation scene, and sigmaj(t, n) is the complex scattering coefficient of the cross-course target after two-dimensional compression, fiFor the response frequency corresponding to the ith array element across the course, i.e.
fi＝yi/(λR0) (2)
In the formula, yiThe coordinates of the ith antenna element in the cross-heading direction,
Figure BDA0002401394650000022
represents the slant distance between the projection point of the scattering point on the azimuth-distance plane and the reference origin:
conversion into vector form
S(t,n,i)＝ψ(t,n)Tα(t,n) (3)
In the formula (I), the compound is shown in the specification,
ψi(t,n)＝[exp(j2πfiy1),exp(j2πfiy2),…,exp(j2πfiyN)]T(4)
α(t,n)＝[α1(t,n),α2(t,n),…,αΝ(t,n)]T(5)
ψi(t, N) is a linear projection vector of the ith array element with dimension N × 1, α (t, N) is a cross-heading target complex scattering coefficient vector and passes through
Figure BDA0002401394650000023
α are sparse, so the distributed array SAR echo S is also sparse under the basis function ψ, introducing the measurement matrix Φ ∈ RK×N(K is the array element number of the sparse linear array, N is the array element number of the full array), and the value is K rows corresponding to the N × N unit matrix selected according to the sparse array element position;
Figure BDA0002401394650000031
then the formula (6) can be changed to
Sv＝ΦΨα＝Θα (8)
In the formula, SvIn order to obtain the thinned-out echo of the S, theta-phi psi is a projection matrix;
according to the sparse representation theory, the scene alpha can be obtained by sparse reconstruction of the formula (9)
Figure BDA0002401394650000032
In the formula, | · the luminance | |1Is represented by1A norm;
however, alpha is a complex scene, the traditional method is to take the real part and the imaginary part of a complex signal to be processed respectively, and the method considers the amplitude sparsity of the SAR scene concentrated in low frequency and expresses the scene as the combination of amplitude and phase
α＝G|α| (10)
In the formula (I), the compound is shown in the specification,
Figure BDA0002401394650000033
is a diagonal matrix of the grid,
Figure BDA0002401394650000034
is α phase, | α | is α amplitude;
assume that scene amplitude can be sparsely represented by a base P containing a sparse representation and a sparse coefficient beta
|α|＝Pβ (11)
The scene is expressed as a combination of amplitude and phase, and the distributed array SAR linear measurement model can be finally expressed as the combination of amplitude and phase, and the constraint condition that | α | ═ P β itself is a real number is added
Figure BDA0002401394650000035
Wherein P comprises a DCT group and β is a conjugate of β.
In the step R2, for the distributed array SAR linear measurement model, a sparse three-dimensional reconstruction is performed by using a quasi-newton algorithm, which includes the following specific steps:
step 1, an imaging result obtained by a three-dimensional RD imaging algorithm is used as an initial value of a scene alpha, and initial values of G and beta are obtained according to a formula (10) and a formula (11);
step 2, selecting a proper basis, and representing the basis corresponding to the real value amplitude by using the real value coefficient;
step 3, converting the constrained optimization problem represented by the formula (12) into an unconstrained optimization problem according to G, and estimating beta by using a quasi-Newton algorithm
Figure BDA0002401394650000036
In the formula, λ1、λ2Is a regularization parameter;
and 4, resolving the equation (14) by using a quasi-Newton algorithm according to the estimated value of the beta, and re-estimating the G
Figure BDA0002401394650000041
Where Q is diag { α }, γ is a vector of diagonal elements of G, and λ is3Is a regularization parameter;
and 5, repeating the steps 3 to 4, and terminating the iteration when the change of the beta and the gamma is smaller than a preset threshold value.
Compared with the prior art, the method has the following advantages:
according to the distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint, a complex scene is represented as the combination of amplitude and phase by adopting a sparse representation theory, two items of prior information that three-dimensional scene sparsity and scene amplitude are real numbers are utilized, a scene amplitude real value constraint item is added into a regularization reconstruction model, and the scene amplitude and the phase are respectively estimated by utilizing a quasi-Newton algorithm, so that three-dimensional reconstruction which is more consistent with the actual situation is completed; according to the method, amplitude real value constraint is added to the regularized reconstruction model, so that the measurement model is more reasonable, the method accords with the actual situation, and high-resolution three-dimensional imaging with higher super-resolution capability and stronger robustness can be realized.
Drawings
Fig. 1 shows sparsity in three-dimensional space.
FIG. 2 is a flow chart of a distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real-valued constraint.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects solved by the present application more clear and obvious, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The indefinite article "a" or "an" as used herein does not exclude a plurality, and the term "and/or" may comprise any and all combinations of one or more of the associated listed items.
As shown in fig. 1 and fig. 2, in the real three-dimensional world, the scattering target (as shown in fig. 1) occupies only a small part of the whole space, and has sparsity, and the array SAR has three-dimensional resolution. Therefore, the sparsity of the scattering target is also kept in the three-dimensional imaging space, namely, the scattering coefficient of only K elements in the target echo signal is a nonzero value.
The idea of sparse representation can be used for reference, high-precision three-dimensional reconstruction of a target area can be realized by only using a small amount of sparse array element echo data, the number of array elements is greatly reduced, and the bottleneck that the cross-course dimension resolution is too low is solved. The flow of the distributed array SAR sparse representation three-dimensional imaging algorithm considering the scene amplitude real value constraint is shown in FIG. 2.
A distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint mainly comprises the following steps:
step R1, constructing a sparse array SAR complex signal linear measurement model:
and step R2, performing sparse three-dimensional reconstruction by means of a quasi-Newton algorithm.
In the step R1, based on the full array linear array, the distributed array SAR sparse representation three-dimensional imaging algorithm considering the real-valued constraint of the scene amplitude may be represented as the following steps, after the echo data of the ith receiving array element of the array SAR is subjected to range-wise compression, range migration correction and azimuth compression
Figure BDA0002401394650000051
In the formula, t is the fast time of the distance direction, N is the slow time of the azimuth direction, N is the number of space resolution units on the course crossing of the observation scene, and sigmaj(t, n) is the complex scattering coefficient of the cross-course target after two-dimensional compression, fiFor the response frequency corresponding to the ith array element across the course, i.e.
fi＝yi/(λR0) (2)
In the formula, yiThe coordinates of the ith antenna element in the cross-heading direction,
Figure BDA0002401394650000052
represents the slant distance between the projection point of the scattering point on the azimuth-distance plane and the reference origin:
conversion into vector form
S(t,n,i)＝ψ(t,n)Tα(t,n) (3)
In the formula (I), the compound is shown in the specification,
ψi(t,n)＝[exp(j2πfiy1),exp(j2πfiy2),…,exp(j2πfiyN)]T(4)
α(t,n)＝[α1(t,n),α2(t,n),…,αΝ(t,n)]T(5)
ψi(t, N) is a linear projection vector of the ith array element with dimension N × 1, α (t, N) is a cross-heading target complex scattering coefficient vector and passes through
Figure BDA0002401394650000053
α are sparse, so the distributed array SAR echo S is also at the basis function ψSparse, introducing a measurement matrix Φ ∈ RK×N(K is the array element number of the sparse linear array, N is the array element number of the full array), and the value is K rows corresponding to the N × N unit matrix selected according to the sparse array element position;
Figure BDA0002401394650000054
then the formula (6) can be changed to
Sv＝ΦΨα＝Θα (8)
In the formula, SvIn order to obtain the thinned-out echo of the S, theta-phi psi is a projection matrix;
according to the sparse representation theory, the scene alpha can be obtained by sparse reconstruction of the formula (9)
Figure BDA0002401394650000061
In the formula, | · the luminance | |1Is represented by1A norm;
however, alpha is a complex scene, the traditional method is to take the real part and the imaginary part of a complex signal to be processed respectively, and the method considers the amplitude sparsity of the SAR scene concentrated in low frequency and expresses the scene as the combination of amplitude and phase
α＝G|α| (10)
In the formula (I), the compound is shown in the specification,
Figure BDA0002401394650000062
is a diagonal matrix of the grid,
Figure BDA0002401394650000063
is α phase, | α | is α amplitude;
assume that scene amplitude can be sparsely represented by a base P containing a sparse representation and a sparse coefficient beta
|α|＝Pβ (11)
The scene is expressed as a combination of amplitude and phase, and the distributed array SAR linear measurement model can be finally expressed as the combination of amplitude and phase, and the constraint condition that | α | ═ P β itself is a real number is added
Figure BDA0002401394650000064
Wherein P comprises a DCT group and β is a conjugate of β.
In the step R2, for the distributed array SAR linear measurement model, a sparse three-dimensional reconstruction is performed by using a quasi-newton algorithm, which includes the following specific steps:
step 1, an imaging result obtained by a three-dimensional RD imaging algorithm is used as an initial value of a scene alpha, and initial values of G and beta are obtained according to a formula (10) and a formula (11);
step 2, selecting a proper basis, and representing the basis corresponding to the real value amplitude by using the real value coefficient;
step 3, converting the constrained optimization problem represented by the formula (12) into an unconstrained optimization problem according to G, and estimating beta by using a quasi-Newton algorithm
Figure BDA0002401394650000065
In the formula, λ1、λ2Is a regularization parameter;
and 4, resolving the equation (14) by using a quasi-Newton algorithm according to the estimated value of the beta, and re-estimating the G
Figure BDA0002401394650000066
Where Q is diag { α }, γ is a vector of diagonal elements of G, and λ is3Is a regularization parameter;
and 5, repeating the steps 3 to 4, and terminating the iteration when the change of the beta and the gamma is smaller than a preset threshold value.
The working principle of the application is as follows:
the algorithm adopts a sparse representation theory, a complex scene is represented as a combination of amplitude and phase, two items of prior information of three-dimensional scene sparsity and real scene amplitude are utilized, a scene amplitude real value constraint item is added into a regularized reconstruction model, and the scene amplitude and the phase are respectively estimated by using a quasi-Newton algorithm, so that three-dimensional reconstruction which is more in line with the actual situation is completed; according to the method, amplitude real value constraint is added to the regularized reconstruction model, so that the measurement model is more reasonable, the method accords with the actual situation, and high-resolution three-dimensional imaging with higher super-resolution capability and stronger robustness can be realized.
The foregoing is illustrative of one or more embodiments provided in connection with the detailed description and is not intended to limit the disclosure to the particular embodiments disclosed herein. Similar or identical methods, structures, etc. as used herein, or any technical deduction or replacement thereof based on the idea of the present application should be considered as the protection scope of the present application.

Claims (3)

1. A distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real value constraint is characterized by mainly comprising the following steps:
step R1, constructing a sparse array SAR complex signal linear measurement model:
and step R2, performing sparse three-dimensional reconstruction by means of a quasi-Newton algorithm.
2. The distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real-valued constraints is characterized in that in the step R1, on the basis of a full array linear array, echo data of the ith receiving array element of the array SAR can be represented as distance compression, distance migration correction and azimuth compression after distance compression, distance migration correction and azimuth compression
Figure FDA0002401394640000011
In the formula, t is the fast time of the distance direction, N is the slow time of the azimuth direction, N is the number of space resolution units on the course crossing of the observation scene, and sigmaj(t, n) is the complex scattering coefficient of the cross-course target after two-dimensional compression, fiFor the response frequency corresponding to the ith array element across the course, i.e.
fi＝yi/(λR0) (2)
In the formula, yiThe coordinates of the ith antenna element in the cross-heading direction,
Figure FDA0002401394640000012
represents the slant distance between the projection point of the scattering point on the azimuth-distance plane and the reference origin:
conversion into vector form
S(t,n,i)＝ψ(t,n)Tα(t,n) (3)
In the formula (I), the compound is shown in the specification,
ψi(t,n)＝[exp(j2πfiy1),exp(j2πfiy2),…,exp(j2πfiyN)]T(4)
α(t,n)＝[α1(t,n),α2(t,n),…,αΝ(t,n)]T(5)
ψi(t, N) is a linear projection vector of the ith array element with the dimension of N × 1, α (t, N) is a cross-heading target complex scattering coefficient vector passing through
Figure FDA0002401394640000013
α are sparse, so the distributed array SAR echo S is also sparse under the basis function ψ, introducing the measurement matrix Φ ∈ RK×N(K is the array element number of the sparse linear array, N is the array element number of the full array), and the value is K rows corresponding to the N × N unit matrix selected according to the sparse array element position;
Figure FDA0002401394640000014
then the formula (6) can be changed to
Sv＝ΦΨα＝Θα (8)
In the formula, SvIn order to obtain the thinned-out echo of the S, theta-phi psi is a projection matrix;
according to the sparse representation theory, the scene alpha can be obtained by sparse reconstruction of the formula (9)
Figure FDA0002401394640000021
In the formula, | · the luminance | |1Is represented by1A norm;
however, alpha is a complex scene, the traditional method is to take the real part and the imaginary part of a complex signal to be processed respectively, and the method considers the amplitude sparsity of the SAR scene concentrated in low frequency and expresses the scene as the combination of amplitude and phase
α＝G|α| (10)
In the formula (I), the compound is shown in the specification,
Figure FDA0002401394640000022
is a diagonal matrix of the grid,
Figure FDA0002401394640000023
is α phase, | α | is α amplitude;
assume that scene amplitude can be sparsely represented by a base P containing a sparse representation and a sparse coefficient beta
|α|＝Pβ (11)
The scene is expressed as a combination of amplitude and phase, and the distributed array SAR linear measurement model can be finally expressed as the combination of amplitude and phase, and the constraint condition that | α | ═ P β itself is a real number is added
Figure FDA0002401394640000024
Wherein P comprises a DCT group and β is a conjugate of β.
3. The distributed array SAR sparse representation three-dimensional imaging algorithm considering scene amplitude real-value constraint is characterized in that in the step R2, sparse three-dimensional reconstruction is carried out on a distributed array SAR linear measurement model by means of a quasi-Newton algorithm, and the specific steps are as follows:
step 1, an imaging result obtained by a three-dimensional RD imaging algorithm is used as an initial value of a scene alpha, and initial values of G and beta are obtained according to a formula (10) and a formula (11);
step 2, selecting a proper basis, and representing the basis corresponding to the real value amplitude by using the real value coefficient;
step 3, converting the constrained optimization problem represented by the formula (12) into an unconstrained optimization problem according to G, and estimating beta by using a quasi-Newton algorithm
Figure FDA0002401394640000025
In the formula, λ1、λ2Is a regularization parameter;
and 4, resolving the equation (14) by using a quasi-Newton algorithm according to the estimated value of the beta, and re-estimating the G
Figure FDA0002401394640000026
Where Q ═ diag { | α | }, γ is a vector consisting of G diagonal elements, λ3Is a regularization parameter;
and 5, repeating the steps 3 to 4, and terminating the iteration when the change of the beta and the gamma is smaller than a preset threshold value.
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