CN113625275A - Sparse aperture radar image two-dimensional joint reconstruction method - Google Patents
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Abstract
A two-dimensional joint reconstruction method for a sparse aperture radar image comprises the following steps: step S1, an ISAR imaging model is constructed, the ISAR imaging model is suitable for obtaining target echoes and obtaining an MXN slow time dimension range image sequence matrix S based on the target echoes, and the ISAR imaging model is also suitable for carrying out Fourier transformation on the slow time dimension range image sequence matrix S to obtain an initial two-dimensional ISAR image matrix S of the target2D(ii) a Step S2, constructing a single-polarization random sparse aperture model which is suitable for the initial two-dimensional ISAR image matrix S2DPerforming sparse selection to obtain a QXN sparse aperture measurement signal matrix SfStep S3, measuring a signal matrix S according to the sparse aperture by adopting a 2D-OMP methodfAnd performing sparse reconstruction to output an ISAR reconstructed image matrix. The sparse aperture radar image two-dimensional joint reconstruction method can reduce the complexity of image reconstruction and reduce the time of image reconstruction.
Description
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a two-dimensional joint reconstruction method for a sparse aperture radar image.
Background
ISAR (inverse synthetic aperture radar) imaging is one of important means for researching target characteristics, and has important significance for identifying parameters such as target length, size, shape and scattering characteristics. In the conventional ISAR imaging, the data volume is large, and great burden is brought to a radar system in the aspects of signal generation equipment, signal processing equipment, data storage and the like.
In 2006, the compressed sensing theory proposed by Donoho, cans, Romberg and Tao et al fully utilizes the sparsity or compressibility of signals to acquire and reconstruct the signals, breaks through the limit of nyquist sampling theorem, and can greatly reduce the storage amount of information. In 2007, r.baraniuk et al, university of rice, introduced compressed sensing into high-resolution radar for the first time, from which the corresponding basic research was developed. The compressed sensing reconstruction algorithm belongs to a convex optimization problem, and a greedy algorithm represented by an Orthogonal Matching Pursuit (OMP) algorithm is most widely applied. However, the method introduces a Kronecker product in the process of converting from two dimensions to one dimensions, which results in excessive calculation complexity, and in practice, the received radar echo may have data loss and the image reconstruction time is long.
Disclosure of Invention
The invention aims to solve the technical problem of high image reconstruction complexity and long time in the prior art, and provides a two-dimensional combined reconstruction method for a sparse aperture radar image.
In order to solve the technical problem, the invention provides a two-dimensional joint reconstruction method for a sparse aperture radar image, which comprises the following steps: step S1: constructing an ISAR imaging model, the ISARThe image model is suitable for acquiring target echoes and acquiring an MxN slow time dimension range image sequence matrix S based on the target echoes, and the ISAR imaging model is also suitable for performing Fourier transform on the slow time dimension range image sequence matrix S to acquire an initial two-dimensional ISAR image matrix S of the target2D(ii) a Wherein S ═ ψ S2DPhi is an mxm inverse fourier transform matrix, S ═ S0，s1，...，sM-1]T，smIs a range profile sequence of 1 XN, M is more than or equal to 0 and less than M; step S2: constructing a single-polarized random sparse aperture model adapted to the initial two-dimensional ISAR image matrix S2DPerforming sparse selection to obtain a QXN sparse aperture measurement signal matrix Sf，Sf＝PS＝PψS2D＝ΦS2DPhi is a perception matrix, and P is a decimation matrix; step S3: measuring a signal matrix S according to a sparse aperture by adopting a 2D-OMP methodfAnd performing sparse reconstruction to output an ISAR reconstructed image matrix.
Optionally, the step of obtaining an M × N slow time dimension range image sequence matrix S based on the target echo includes: sequentially performing Decirp processing and inverse Fourier transform on the target echo to obtain corresponding tmOne-dimensional range profile sequence of the target echo at the moment; combining a plurality of one-dimensional range profile sequences at different moments to form a slow time-range profile matrix of the target; and carrying out envelope alignment and phase correction on the slow time-range profile matrix, and recording the processed slow time-range profile matrix as an MXN matrix S to obtain an MXN slow time dimension range profile sequence matrix S.
Optionally, the signal transmitted by the radar is a chirp signal, which is expressed as:
wherein f is0Is the signal carrier frequency of the chirp signal, k is the chirp rate,
the fast time variable is T, the pulse width of the linear frequency modulation signal is k ═ B/T, and B is the signal bandwidth of the linear frequency modulation signal; t is tmIs a slow time variable, tm＝mTd，TdThe pulse repetition interval of the linear frequency modulation signal is shown, M is a pulse serial number, M is more than or equal to 0 and less than M, M is the total imaging observation pulse number, M is an integer, and M is an integer which is more than or equal to 0 and less than M; t is the total time of the process,
t is more than or equal to 0 and less than or equal to TA，TAFor total imaging observation time, TA＝M*Td。
Optionally, target echo after radar-transmitted signal is reflected by target
Expressed as:
wherein A isiIs the echo amplitude of the target echo, c is the electromagnetic wave propagation rate, j is an imaginary number unit, and the radar sampling rate is fsThe number of sampling points N of the radar in a single pulse is expressed as N ═ fsT；Ri(tm) Is tmThe ith scatter point P (x) at time instanti，yi) Distance from the radar.
Optionally, the signal matrix S is measured according to the sparse aperture by using a 2D-OMP methodfThe step of performing sparse reconstruction includes: step S31: residual matrix RlInitial amount of (R)o＝SfIndex set ΛlInitialization set of
Setting the loop count l of step S31 to 0; step S32: obtaining a perception matrix phi and a residual matrix RlMaximum correlation element of, gets abs (Φ)HRl) Coordinates (p, q) corresponding to the maximum element, wherein p is the row of the maximum element, and q is the column of the maximum element; and updates index set Al＝Al-1Andgate { (p, q) }; step S33: renewing the rarefaction
Sparse solution
The position of the non-zero element in (1) is represented by index set AlThe scattering coefficient Γ is determined by the following method: order to
As an index set ΛlWherein all column sequence numbers satisfy q ═ qmA subset of elements organized in order; wherein q ismIs AlAll distinct column elements;
wherein
Is phi middle by
The resulting matrix is indexed by the row element of (a),
is SfIn the formula qmA matrix of indices; step S34: updating residual matrices
If L is less than or equal to L, returning to the step S32, otherwise, finishing the reconstruction and outputting a reconstructed image
The technical scheme of the invention has the following beneficial effects:
according to the two-dimensional joint reconstruction method for the sparse aperture radar image, the random sparse aperture radar is used for image reconstruction, the calculated amount is reduced, and a foundation is provided for the research of a time domain diversity-based full polarization radar imaging method. The invention provides a two-dimensional joint reconstruction method of a sparse aperture radar image by combining with actual needs, and aims at random sparse aperture radar ISAR image reconstruction to perform two-dimensional joint orthogonal matching pursuit (2D-OMP) based on a compressed sensing theory, so that the complexity of image reconstruction is reduced and the time is short.
Drawings
FIG. 1 is a general flowchart of a random sparse aperture radar based image reconstruction method proposed by the present invention;
FIG. 2 is a schematic diagram of an ISAR imaging model;
FIG. 3 is a schematic diagram of a random sparse aperture decimation method;
FIG. 4 is a flow chart of a 2D-OMP process;
FIG. 5 is a Jacobian 42 aircraft target scattering point model diagram for simulation according to the present invention;
FIG. 6 is a radar image reconstructed using the RD method;
fig. 7(a) and 7(b) are radar images reconstructed by using the RD method after aperture extraction is performed on the echo matrix, and the aperture extraction ratios are respectively 25% and 50%;
fig. 8(a) and 8(b) are radar images reconstructed by a 2D-OMP method after the aperture extraction of the echo matrix according to the present invention, where the aperture extraction ratio is 25% and 50%, respectively.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further 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 invention and are not intended to limit the scope of the invention.
An embodiment of the present invention provides a two-dimensional joint reconstruction method for a sparse aperture radar image, which, with reference to fig. 1, includes:
step S1: the method comprises the steps of constructing an ISAR imaging model, wherein the ISAR imaging model is suitable for obtaining target echoes and obtaining an MxN slow time dimension range image sequence matrix S based on the target echoes, and is also suitable for carrying out Fourier transformation on the slow time dimension range image sequence matrix S to obtain an initial two-dimensional ISAR image matrix S of a target20(ii) a Wherein S ═ ψ S2DPhi is an mxm inverse fourier transform matrix, S ═ S0，s1，...，sM-1]T，smIs a range profile sequence of 1 XN, M is more than or equal to 0 and less than M;
step S2: constructing a single-polarized random sparse aperture model adapted to the initial two-dimensional ISAR image matrix S2DPerforming sparse selection to obtain a QXN sparse aperture measurement signal matrix Sf，Sf＝PS＝PψS2D＝ΦS2DPhi is a perception matrix, and P is a decimation matrix;
step S3: measuring a signal matrix S according to a sparse aperture by adopting a 2D-OMP methodfAnd performing sparse reconstruction to output an ISAR reconstructed image matrix.
In step S1, ISAR imaging employs the classical turntable model, and the scene setup is as shown in fig. 2. A global rectangular coordinate system X-Y is established by taking a radar as an origin, a rectangular coordinate system X-O-Y is established by taking a centroid O of a target as the origin, the spatial directivity of the rectangular coordinate system X-O-Y is fixed, the rectangular coordinate system X-O-Y is parallel to the global coordinate system X-Y, the X axis is parallel to the X axis, and the Y axis is parallel to the Y axis. The distance from the radar to the center of mass of the target is R0Assuming that the target translation is precisely compensated, the target azimuth α is 90 °. The motion of the object is translated into rotation about the object's center of mass at an angular velocity ω.
The signal transmitted by the radar is a chirp signal, which is expressed as:
wherein f is0Is the signal carrier frequency of the chirp signal, k is the chirp rate,
for fast time variables, T is the pulse width of the chirp signal, B is the signal bandwidth of the chirp signal, and B ═ kT. t is tmIs a slow time variable, tm＝mTd，TdIs the pulse repetition interval of the chirp signal, m is the pulse number, 0M is more than or equal to M, M is the total imaging observation pulse number, M is an integer, and M is an integer which is more than or equal to 0 and less than M. t is the total time of the process,
t is more than or equal to 0 and less than or equal to TA，TAFor total imaging observation time, TA＝M*Td. The slow time is a scale in which time is discretized at pulse repetition intervals, and the fast time is a scale of signal time within each slow time interval.
Imaging target composed of NTOne scattering point for the ith scattering point P (x)i，yi) In one embodiment, the "stop-and-go" model is sampled, ignoring the ith scatter point P (x)i，yi) Equivalent rotation amount in any pulse repetition interval, at tmThe ith scatter point P (x) at time instanti，yi) Distance from radar is Ri(tm)，Ri(tm) Expressed as:
Ri(tm)＝R0+yicos(ωtm)+xisin(ωtm) (formula 2)
It should be noted that the "stop-and-go" model is a relatively basic model in ISAR imaging, i.e., the internal approximation of the pulse considers the target not to rotate, and the rotation occurs between the pulses.
Due to the rotation angle ω t of the target during the imaging observationmSmaller, (formula 2) can be written as (formula 3)
Ri(tm)＝R0+yi+xiωtm(formula 3)
Target echo after radar-transmitted signal is reflected by target
Can be expressed as:
wherein A isiThe echo amplitude of the target echo, c the electromagnetic wave propagation rate, and j the imaginary unit.
Radar sampling rate of fsThe number of sampling points N of the radar in a single pulse is expressed as N ═ fsAnd T. Radar reception of tmTarget echo of time
Then, echo to the target
Sequentially carrying out Decirp processing and inverse Fourier transform to obtain corresponding tmTarget echo of time
A one-dimensional range profile sequence; combining a plurality of one-dimensional range profile sequences at different moments to form a slow time-range profile matrix of the target; and carrying out envelope alignment and phase correction on the slow time-range profile matrix, and recording the processed slow time-range profile matrix as an MxN matrix S, namely obtaining the MxN slow time dimension range profile sequence matrix S.
S＝[s0，s1，...，sM-1]T(formula 5)
Wherein s ismThe range image sequence after envelope alignment and phase correction of a 1 XN one-dimensional range image sequence.
The Dechirp processing is to mix the target echo and a reference signal so as to complete the deskew processing, and the inverse Fourier transform is to convert the target echo from a frequency domain to a time domain.
In one embodiment, the envelope alignment method is a frequency domain correlation method and a time domain correlation method, and the core method is to correlate one-dimensional distance images obtained by two different pulses and compensate according to the relative position of the obtained correlation maximum value. In one embodiment, the method of phase correction is a method of single-bit auto-focus.
According to the ISAR imaging principle, fast Fourier transform is carried out on the range image sequence matrix S with the slow time dimension to obtain the initial value of the targetFirst two-dimensional ISAR image matrix S2D。
S＝ψS2D(formula 6)
S2DAn initial two-dimensional ISAR image matrix of M × N, and ψ is an Inverse Fast Fourier Transform (IFFT) matrix of M × M.
Wherein, WMExp (j2 pi/M), M is the total number of imaging observation pulses, and M is an integer.
In step S2, a single-polarized random sparse aperture model is constructed, which is adapted to the initial two-dimensional ISAR image matrix S2DPerforming sparse selection to obtain a QXN sparse aperture measurement signal matrix Sf，Sf＝PS＝PψS2D＝ΦS2DWhere Φ is P ψ, the perceptual matrix, and P the decimation matrix.
Under the condition of sparse aperture, Q apertures are extracted from M complete apertures for imaging observation (Q < M), the essence is that a Q multiplied by M extraction matrix P is constructed to carry out sparse selection on full aperture data, and the construction principle is shown in FIG. 3. According to fig. 3, the decimation matrix P is considered to be obtained by decimating Q rows from the M × M identity matrix I, and is represented as:
for the initial two-dimensional ISAR image matrix S2DPerforming sparse selection to obtain a QXN sparse aperture measurement signal matrix Sf。
Sf＝PS＝PψS2D＝ΦS2D(formula 9)
And phi is P psi as a perception matrix.
According to the target scattering theory, a radar target generally consists of a limited number of strong scattering points in a high-frequency area, and the limited number of strong scattering points of the radar target have sparsity compared with the whole imaging area, so that in one case, the following sparse optimization problem is solved by adopting compressed sensing processing:
||Sf-ΦS2D||Fless than or equal to epsilon (formula 10)
There is a minimum of S2DM of1Norm min | | S2D||1So that | | Sf-ΦS2D||FLess than or equal to threshold Epsilon, min | | S2D||1s.t.||Sf-ΦS2D||F≤ε。
Wherein | · | purple sweet1Representation matrix m1Norm, | · | luminanceFRepresenting the norm F-norm, epsilon is a threshold value related to the noise level. m is1The norm is defined as:
the definition of the F norm is
ε is a small value, and the smaller the ε is set, the more accurate the estimate.
The above optimization problem is different from the conventional sparse optimization problem in that the reconstructed image and the measurement signal are in a matrix form, while the signal model of the conventional reconstruction problem is in a vector form. One of the simplest ways to solve this problem is to vectorize the matrix by columns, which translates into a one-dimensional optimization problem, i.e.
sf＝Φvs2D(formula 11)
Wherein s isf＝vec(Sf)，sfA vector of QNx 1; s2D＝vec(S2D)，S2DIs a vector of MN x 1, and the vector,
Φvis a dictionary matrix of QN x MN,
represents the Kronecker product of the matrix.
For the sparse optimization problem expressed by the above formula, more classical compressed sensing algorithms can be used, such as a convex optimization algorithm, a matching pursuit algorithm (MP), an orthogonal matching pursuit algorithm (OMP), a bayesian learning algorithm, and the like. The OMP algorithm has outstanding calculation efficiency and higher reconstruction precision, and meets the real-time signal processing requirement of the radar system.
It should be noted that, although the original problem is solved by using the vectorization method to perform dimension reduction processing, the calculation amount is increased compared with the original model, because a Kronecker product is introduced in the dimension reduction process, the matrix dimension is explosively increased under the condition of a large bandwidth. If the optimal solution (equation 11) can be directly obtained without converting to one dimension, the computational complexity can be effectively reduced.
In step S3, a sparse aperture measurement signal matrix S is inputfSensing matrix phi and ISAR image sparsity L; and (3) outputting: reconstructing an image
Step S31: residual matrix RlInitial amount of (R)o＝SfIndex set Al(l is an integer of 0 or more) initialization set
(index set A)lIs an empty set), the loop count l of step S31 is set to 0:
step S32: obtaining a perception matrix phi and a residual matrix RlOf the maximum correlation element, specifically, acquisition abs (Φ)HR1) Coordinates (p, q) corresponding to the middle-largest element, whereinHShowing matrix conjugate transpose, wherein p is the row where the largest element is located, and q is the column where the largest element is located; and updates index set Λl＝Λl-1∩{(p，q)}；
Step S33: renewing the rarefaction
Sparse solution
By the index set ΛlThe scattering coefficient Γ was determined to be obtained by:
order to
As an index set ΛlWherein all column sequence numbers satisfy q ═ qmThe elements are grouped in order as subsets. Wherein q ismIs ΛlAll distinct column elements.
Wherein
Is phi middle by
The resulting matrix is indexed by the row element of (a),
is SfIn the formula qmA matrix of indices.
Is based on
Is obtained by selecting a specific row of the matrix.
Is based on
Is obtained by selecting a specific column of the matrix.
ΛlIs a set, each element of which is a coordinate (p, q),
is ΛlThe principle of selecting elements is as follows: selecting ΛlAll elements in q which are not identical are grouped into a new set
Step S34: updating residual matrices
If L is less than or equal to L, returning to the step S32, otherwise, finishing the reconstruction and outputting a reconstructed image
And finishing the whole process of reconstructing the ISAR image. The effectiveness of the reconstruction method is proved by a simulation test.
As shown in FIG. 5, the invention uses a 330-point Yake 42 airplane scattering point model to carry out simulation experiments, and the sparsity L is set to be 500. Fig. 8(a) and (b) are respectively ISAR images reconstructed by the 2D-OMP method proposed by the present invention when the extraction ratio is 25% and 50%, and the results show that when the number of randomly extracted apertures accounts for 25% of the original number of apertures, the reconstructed ISAR images can still reflect the real shape of the target, which conforms to the simulation setup, and shows the effectiveness of the method of the present invention.
The above description is only an example of the present invention and should not be taken as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A two-dimensional joint reconstruction method for a sparse aperture radar image is characterized by comprising the following steps:
step S1, constructing an ISAR imaging model, wherein the ISAR imaging model is suitable for acquiring target echoes and acquiring an MXN slow time dimension range image sequence matrix S based on the target echoes, and the ISAR imaging model is also suitable for performing Fourier transformation on the slow time dimension range image sequence matrix S to acquire an initial two-dimensional ISAR image matrix S of a target2D(ii) a Wherein S ═ ψ S2DPhi is an mxm inverse fourier transform matrix, S ═ S0,s1,…，sM-1]T，smIs a range profile sequence of 1 XN, M is more than or equal to 0 and less than M;
step S2, constructing a single-polarization random sparse aperture model which is suitable for the initial two-dimensional ISAR image matrix S2DPerforming sparse selection to obtain a QXN sparse aperture measurement signal matrix Sf，Sf＝PS＝PψS2D＝ΦS2DPhi is a perception matrix, and P is a decimation matrix;
step S3, measuring a signal matrix S according to the sparse aperture by adopting a 2D-OMP methodfAnd performing sparse reconstruction to output an ISAR reconstructed image matrix.
2. The sparse aperture radar image two-dimensional joint reconstruction method of claim 1, wherein the step of obtaining an mxn slow time dimension range image sequence matrix S based on target echoes comprises: sequentially performing Decirp processing and inverse Fourier transform on the target echo to obtain corresponding tmOne-dimensional range profile sequence of the target echo at the moment; combining a plurality of one-dimensional range profile sequences at different moments to form a slow time-range profile matrix of the target; envelope alignment and phase correction are carried out on the slow time-range profile matrix, the processed slow time-range profile matrix is recorded as an MXN matrix S, and an MXN slow time dimension range profile sequence is obtainedAnd (5) matrix S.
3. The sparse aperture radar image two-dimensional joint reconstruction method of claim 1, wherein the signals transmitted by the radar are chirp signals expressed as:
wherein f is0Is the signal carrier frequency of the chirp signal, k is the chirp rate,
the fast time variable is T, the pulse width of the linear frequency modulation signal is k ═ B/T, and B is the signal bandwidth of the linear frequency modulation signal; t is tmIs a slow time variable, tm＝mTd，TdThe pulse repetition interval of the linear frequency modulation signal is shown, M is a pulse serial number, M is more than or equal to 0 and less than M, M is the total imaging observation pulse number, M is an integer, and M is an integer which is more than or equal to 0 and less than M; t is the total time of the process,
t is more than or equal to 0 and less than or equal to TA，TAFor total imaging observation time, TA＝M*Td。
4. The sparse aperture radar image two-dimensional joint reconstruction method of claim 3,
target echo after radar-transmitted signal is reflected by target
Expressed as:
wherein A isiIs the echo amplitude of the target echo, c is the electromagnetic wave propagation rate, j is an imaginary number unit, and the radar sampling rate is fsRadar, radarThe number of sampling points N within a single pulse is denoted N ═ fsT；Ri(tm) Is tmThe ith scatter point P (x) at time instanti,yi) Distance from the radar.
5. The sparse aperture radar image two-dimensional joint reconstruction method of claim 1, wherein a 2D-OMP method is used to measure a signal matrix S from the sparse aperturefThe step of performing sparse reconstruction includes:
step S31: residual matrix RlInitial amount of (R)o＝SfIndex set ΛlInitialization set of
Setting the loop count l of step S31 to 0;
step S32: obtaining a perception matrix phi and a residual matrix RlMaximum correlation element of, gets abs (Φ)HRl) Coordinates (p, q) corresponding to the maximum element, wherein p is the row of the maximum element, and q is the column of the maximum element; and updates index set Λl＝Λl-1∩{(p,q)}；
Step S33: renewing the rarefaction
Sparse solution
By the index set ΛlThe scattering coefficient Γ was determined to be obtained by: order to
As an index set ΛlWherein all column sequence numbers satisfy q ═ qmA subset of elements organized in order; wherein q ismIs ΛlAll distinct column elements;
wherein
Is phi middle by
The resulting matrix is indexed by the row element of (a),
is SfIn the formula qmA matrix of indices;
step S34: updating residual matrices
If L is less than or equal to L, returning to the step S32, otherwise, finishing the reconstruction and outputting a reconstructed image
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