CN109959933B - Multi-baseline circular synthetic aperture radar imaging method based on compressed sensing - Google Patents

Multi-baseline circular synthetic aperture radar imaging method based on compressed sensing Download PDF

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CN109959933B
CN109959933B CN201910292197.3A CN201910292197A CN109959933B CN 109959933 B CN109959933 B CN 109959933B CN 201910292197 A CN201910292197 A CN 201910292197A CN 109959933 B CN109959933 B CN 109959933B
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喻玲娟
林赟
洪文
胡跃虹
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Jiangxi University of Science and Technology
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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
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9017—SAR image acquisition techniques with time domain processing of the SAR signals in azimuth
    • 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
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9005—SAR image acquisition techniques with optical processing of the SAR signals

Abstract

The invention relates to a multi-baseline circular synthetic aperture radar imaging method based on compressed sensing, which comprises the following steps: step S1, deducing a compressed sensing imaging algorithm based on a backward projection inverse operator; step S2, performing two-dimensional plane imaging of the sub-aperture by adopting a compressed sensing algorithm based on a backward projection inverse operator; step S3, adopting a compressed sensing algorithm to focus the sub-aperture in height direction and further completing the correction of the target two-dimensional coordinate position; and step S4, performing coherent accumulation on all the sub-aperture three-dimensional imaging results to obtain a final full-aperture three-dimensional imaging result.

Description

Multi-baseline circular synthetic aperture radar imaging method based on compressed sensing
Technical Field
The invention relates to the field of radar signal processing, in particular to a multi-baseline circular synthetic aperture radar imaging method based on compressed sensing, which solves the problems of large data acquisition amount of a multi-baseline circular synthetic aperture radar and high side lobe after target imaging under the conditions of undersampling and non-uniform sampling, and thus realizes the acquisition of a high-quality three-dimensional imaging result by using a small amount of echo data.
Background
The multi-baseline circular synthetic aperture radar is an imaging radar which carries out multiple circumferential observation on a target in the height direction of the target. The mode can not only obtain the two-dimensional ground distance resolution of the sub-wavelength level, but also has higher height-direction resolution. Due to the excellent characteristics of the multi-baseline circular synthetic aperture radar, the multi-baseline circular synthetic aperture radar has very important significance in the fields of automatic target identification, target detection, high-precision topographic mapping, biomass parameter estimation, artificial target elevation extraction, safety detection and the like.
Although the multi-baseline circular synthetic aperture radar has the potential of realizing three-dimensional high-resolution imaging of a target, the data volume required to be acquired and processed in the mode is large according to the Nyquist sampling criterion, and great challenges are brought to hardware storage and computing resources. In addition, in the data acquisition process of the airborne multi-baseline circular synthetic aperture radar, the radar platform is difficult to keep a standard circular track on a two-dimensional plane and is difficult to keep equal-interval sampling in the height direction. If the acquired echo data is imaged according to the condition that the Nyquist sampling criterion is met, the problem that the side lobe is high after the target imaging is performed is caused.
The compressed sensing theory is different from the traditional Nyquist sampling theorem and is a new sampling and reconstruction theory aiming at sparse or compressible signals. Under the theoretical framework, when the signal has sparsity or compressibility, accurate or approximate reconstruction of a high dimension can be realized only by acquiring or measuring a small number of signal low-dimension projection values. In addition, low data acquisition complexity can be "traded" for high signal reconstruction complexity.
At present, multi-baseline circular synthetic aperture radar imaging based on compressed sensing is researched, and mainly focuses on focusing imaging in the height direction. Ponce et al divide the full aperture data of the multi-baseline circular synthetic aperture radar into a plurality of sub-apertures, perform two-dimensional imaging on each sub-aperture data by using a fast factor back-projection method, then perform height-wise focusing by using a compressed Sensing algorithm, and finally perform incoherent synthesis on the sub-aperture three-dimensional image, thereby realizing three-dimensional high-resolution imaging of forest regions (Ponce O, Prats-Iraola P, Scheiber R, et al. Polarimetric 3-D correlation free multi-circular SAR at P-band [ J ]. IEEE Geoscience and Remote Sensing Letters,2014(4): 803-. Austin et al also uses a height-oriented focusing method based on compressed sensing to realize multi-baseline circular synthetic aperture radar imaging of GOTCHA data and Backhoe data (Austin C D, Ertin E, Moses R L. space Signal methods for 3-D radar imaging [ J ]. IEEE Journal of Selected targets in Signal Processing,2011(3): 408-423).
Disclosure of Invention
The invention aims to provide a multi-baseline circular synthetic aperture radar imaging method based on compressed sensing, which can obtain a high-quality three-dimensional imaging result under the conditions of small echo data quantity and under-sampling and non-uniform sampling.
In order to achieve the above object, the present invention provides a multi-baseline circular synthetic aperture radar imaging method based on compressed sensing, which comprises the following steps:
step S1, deducing a compressed sensing imaging algorithm based on a backward projection inverse operator;
step S2, performing two-dimensional plane imaging of the sub-aperture by adopting a compressed sensing algorithm based on a backward projection inverse operator;
step S3, adopting a compressed sensing algorithm to focus the sub-aperture in height direction and further completing the correction of the target two-dimensional coordinate position;
and step S4, performing coherent accumulation on all the sub-aperture three-dimensional imaging results to obtain a final full-aperture three-dimensional imaging result.
The invention has the beneficial effects that: aiming at the problems that the multi-baseline circular synthetic aperture radar needs large data quantity to be acquired and the side lobe is high after target imaging under the undersampling and non-uniform sampling conditions, the multi-baseline circular synthetic aperture radar imaging method based on compressed sensing is adopted to convert the imaging problem into the problem of solving the optimal solution, and the purpose of acquiring a high-quality three-dimensional imaging result by using a small amount of echo data is achieved.
Drawings
FIG. 1 is a general flowchart of a compressed sensing-based multi-baseline circular synthetic aperture radar imaging method according to the present invention;
FIG. 2 is a diagram of imaging geometry for a multi-baseline circular synthetic aperture radar;
FIG. 3 is a flow chart of the present invention for deriving a compressed sensing imaging algorithm based on a backprojection inverse operator;
FIG. 4 is a flow chart of the present invention for implementing sub-aperture two-dimensional planar imaging by using a compressed sensing imaging algorithm based on a back projection inverse operator;
FIG. 5 is a flow chart of the present invention for implementing sub-aperture height direction focusing by using a compressed sensing algorithm and further completing the correction of the target two-dimensional coordinate position.
Detailed Description
In order that the objects, technical solutions and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in conjunction with the following specific embodiments.
Fig. 1 shows a general flowchart of a multi-baseline circular synthetic aperture radar imaging method based on compressed sensing according to the present invention. The method comprises the following concrete implementation steps:
step S1: the compressed sensing imaging algorithm based on the backward projection inverse operator is deduced and divided into the following four steps:
step S11: and establishing an echo signal model of the multi-baseline circular synthetic aperture radar. In the multi-baseline circular synthetic aperture radar mode, the radar circles around a target areaThe imaging geometry is shown in FIG. 2. Considering that the radar flies around a target by M baselines, the distance from the radar to the center of a target area under each baseline is a constant R cThe azimuth angle of the radar is phi ∈ [0,2 pi ]]. Noting that the interval between the lower visual angles of two adjacent baselines is delta theta, the lower visual angle theta corresponding to the ith baselinemIs thetam＝θ1+(m-1)Δθ，m＝1,2,...M。
Suppose the observed object is a discrete point object where the coordinate position of the nth object is (x)n,yn,zn) Having a scattering coefficient of σnAnd the radar transmits a frequency stepping signal, the echo signal received by the radar under the mth baseline is,
Figure BDA0002025284760000031
where k is 2 pi/λ, and λ is the wavelength.
Step S12: and establishing a two-dimensional imaging model based on a back projection algorithm. The expression for reconstructing each baseline by using a back projection algorithm is as follows,
Figure BDA0002025284760000041
wherein the content of the first and second substances,
Figure BDA0002025284760000042
kc＝2π/λc，λcthe center wavelength.
If the back projection process is expressed by an operator P, the reconstruction process is written in the form of a matrix vector,
Figure BDA0002025284760000043
step S13: and establishing an echo signal observation model based on compressed sensing. The echo signals are written in the form of a matrix vector,
S＝Φσ
wherein phi is
Figure BDA0002025284760000044
A matrix is formed.
Under the theory framework of compressive sensing, the measurement matrix can be selected to be phi, and the sparse matrix is an identity matrix.
Step S14: and deducing a compressed sensing echo signal observation model based on a backward projection inverse operator, and converting the imaging process into an optimization problem.
Combining the back projection reconstruction process and the echo signal observation model based on compressed sensing to obtain
Φ≈P-1
The construction matrix G is such that,
G＝P-1≈Φ
in practical situations, there is noise interference in the process of measuring the echo, so the expression of the compressed sensing echo signal observation model based on the backward projection inverse operator is,
S＝Gσ+n
where n represents observation noise.
Considering further the down-sampling model of the echo data, the observation model may be expressed as,
Figure BDA0002025284760000045
wherein S isDRepresenting the down-sampled echo signal, nDRepresenting the down-sampled observation noise.
Solving the scattering coefficient of the target according to the compressed sensing theory
Figure BDA0002025284760000046
Can be converted to solve forq(q is more than or equal to 0 and less than or equal to 1) optimization problem,
Figure BDA0002025284760000047
satisfy the requirement of
Figure BDA0002025284760000048
Further it may be equivalent to solve the following optimization problem,
Figure BDA0002025284760000049
wherein | · | purple sweetFIs Frobenius norm, Dθ、DfRespectively are down sampling matrixes on an azimuth angle domain and a stepping frequency domain, and lambda is a regularization parameter.
Step S2: the method adopts a compressed sensing algorithm based on a backward projection inverse operator to perform two-dimensional plane imaging of the sub-aperture, and the specific flow is shown in figure 3 and comprises the following four steps:
step S21: dividing the full aperture echo data into a plurality of sub apertures, and acquiring the down-sampled echo data S of each sub apertureD。
Step S22: and determining that the observation matrix is DG and the sparse matrix is an identity matrix I.
Step S23: determining the threshold ratio as gamma, and selecting the amplitude threshold as gamma PS D。
Step S24: and performing compressed sensing reconstruction based on a backward projection inverse operator by adopting a soft threshold iterative algorithm to realize two-dimensional imaging of the sub-aperture.
Step S3: the compressed sensing algorithm is adopted to focus the sub-aperture in the height direction, and the correction of the target two-dimensional coordinate position is further completed, and the specific flow is shown in fig. 4 and comprises the following four steps:
step S31: and establishing a height-direction focusing model based on compressed sensing. Under the mth base line, the two-dimensional imaging result T (x ', y', phi) of any sub-aperture is
Figure BDA0002025284760000051
Wherein the content of the first and second substances,
Figure BDA0002025284760000052
s (x, y) is a two-dimensional window function matched to the finite persistence of the target, fp(x,y,zp(x, y)) represents p scattering points at different heights up at two-dimensional coordinates (x, y) representing a convolution.
Considering phi to 90 deg., the two-dimensional imaging result for any sub-aperture is shown as,
Figure BDA0002025284760000053
when the height-wise sampling meets the nyquist criterion,
Figure BDA0002025284760000054
order to
Figure BDA0002025284760000055
Then
Figure BDA0002025284760000056
Note Tm＝[Tm]，
Figure BDA0002025284760000057
Then
T≈ψf+n
Where n represents observation noise.
Further consider a down-sampled model of the echo data, expressed as,
TD≈Dψf+nD
wherein, TDRepresenting a down-sampled two-dimensional imaging result, nDRepresenting the down-sampled observation noise.
Step S32: and determining the observation matrix as D psi and the sparse matrix as an identity matrix I.
And step S33, performing compressed sensing-based reconstruction by adopting a basis tracking denoising algorithm to realize the height-direction focusing of the sub-aperture.
Step S34, correcting the two-dimensional coordinate position of the target after the height focusing, namely the position of the two-dimensional coordinate of the target after the height focusing by using the relation between the pixel coordinate (x ', y') in the two-dimensional imaging result of the sub-aperture and the real three-dimensional coordinate (x, y, z) of the target
Figure BDA0002025284760000061
And step S4, performing coherent accumulation on all the sub-aperture three-dimensional imaging results to obtain a final full-aperture three-dimensional imaging result.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention.

Claims (3)

1. A multi-baseline circular synthetic aperture radar imaging method based on compressed sensing is characterized by comprising the following steps:
step S1, deducing a compressed sensing imaging algorithm based on a backward projection inverse operator;
step S2, performing two-dimensional plane imaging of the sub-aperture by adopting a compressed sensing algorithm based on a backward projection inverse operator;
step S3, adopting a compressed sensing algorithm to focus the sub-aperture in height direction and further completing the correction of the target two-dimensional coordinate position;
Step S4, performing coherent accumulation on all the sub-aperture three-dimensional imaging results to obtain a final full-aperture three-dimensional imaging result;
the step of deducing the compressed sensing imaging algorithm based on the backward projection inverse operator is as follows:
step S11: establishing an echo signal model of a multi-baseline circular synthetic aperture radar, observing the circumference of the radar around a target area in a multi-baseline circular synthetic aperture radar mode, considering that the radar flies around the target by M baselines, and keeping the distance from the radar to the center of the target area under each baseline constant RcRadar, radarAzimuthal angle is phi ∈ [0,2 π ∈ ]]Noting the interval between the lower visual angles of two adjacent baselines as delta theta, the lower visual angle theta corresponding to the ith baselinemIs thetam＝θ1+(m-1)Δθ，m＝1,2,...M；
Suppose the observed object is a discrete point object where the coordinate position of the nth object is (x)n,yn,zn) Having a scattering coefficient of σnAnd the radar transmits a frequency stepping signal, the echo signal received by the radar under the mth baseline is,
Figure FDA0003059573700000011
wherein k is 2 pi/lambda, and lambda is the wavelength;
step S12: establishing a two-dimensional imaging model based on a back projection algorithm, wherein each base line adopts an expression of reconstructing by the back projection algorithm,
Figure FDA0003059573700000012
wherein the content of the first and second substances,
Figure FDA0003059573700000013
kc＝2π/λc，λcis the center wavelength;
if the back projection process is expressed by an operator P, the reconstruction process is written in the form of a matrix vector,
Figure FDA0003059573700000014
Step S13: establishing an echo signal observation model based on compressed sensing, writing the echo signal into a matrix vector form,
S＝Φσ
wherein phi is
Figure FDA0003059573700000021
A matrix of formations;
under the theory framework of compressed sensing, a measurement matrix can be selected to be phi, and a sparse matrix is an identity matrix;
step S14: deducing a compressed sensing echo signal observation model based on a backward projection inverse operator, and converting an imaging process into an optimization problem;
by combining the backward projection reconstruction process and the echo signal observation model based on compressed sensing, phi is approximately equal to P-1
The construction matrix G is such that,
G＝P-1≈Φ
in practical situations, there is noise interference in the process of measuring the echo, so the expression of the compressed sensing echo signal observation model based on the backward projection inverse operator is,
S＝Gσ+n
wherein n represents observation noise;
considering further the down-sampling model of the echo data, the observation model may be expressed as,
Figure FDA0003059573700000022
wherein S isDRepresenting the down-sampled echo signal, nDRepresenting the downsampled observation noise;
according to the compressive sensing theory, if q is a real number which is more than or equal to 0 and less than or equal to 1, solving the scattering coefficient of the target
Figure FDA0003059573700000023
Can be converted to solve forqThe optimization problem is solved,
Figure FDA0003059573700000024
satisfy the requirement of
Figure FDA0003059573700000025
Further it may be equivalent to solve the following optimization problem,
Figure FDA0003059573700000026
wherein | · | purple sweet FIs Frobenius norm, Dθ、DfRespectively are down sampling matrixes on an azimuth angle domain and a stepping frequency domain, and lambda is a regularization parameter.
2. The multi-baseline circular synthetic aperture radar imaging method based on compressed sensing of claim 1, wherein the step of performing two-dimensional planar imaging of the sub-aperture by using a compressed sensing algorithm based on a backward projection inverse operator comprises:
step S21: dividing the full aperture echo data into a plurality of sub apertures, and acquiring the down-sampled echo data S of each sub apertureD；
Step S22: determining that an observation matrix is DG and a sparse matrix is an identity matrix I;
step S23: determining the threshold ratio as gamma, and selecting the amplitude threshold as gamma PSD；
Step S24: and performing compressed sensing reconstruction based on a backward projection inverse operator by adopting a soft threshold iterative algorithm to realize two-dimensional imaging of the sub-aperture.
3. The multi-baseline circular synthetic aperture radar imaging method based on compressed sensing of claim 1, wherein the step of performing the height-wise focusing of the sub-aperture by using a compressed sensing algorithm and further performing the correction of the two-dimensional coordinate position of the target comprises:
step S31: establishing a height direction focusing model based on compressed sensing; under the mth base line, the two-dimensional imaging result T (x ', y', phi) of any sub-aperture is
Figure FDA0003059573700000031
Wherein the content of the first and second substances,
Figure FDA0003059573700000032
s (x, y) is a two-dimensional window function matched to the finite persistence of the target, fp(x,y,zp(x, y)) represents p scattering points at different heights up at two-dimensional coordinates (x, y) representing a convolution;
considering phi to 90 deg., the two-dimensional imaging result for any sub-aperture is shown as,
Figure FDA0003059573700000033
when the height-wise sampling meets the nyquist criterion,
Figure FDA0003059573700000034
order to
Figure FDA0003059573700000035
Then
Figure FDA0003059573700000036
Note Tm＝[Tm]，
Figure FDA0003059573700000037
Then
T≈ψf+n
Wherein n represents observation noise;
further consider a down-sampled model of the echo data, expressed as,
TD≈Dψf+nD
wherein, TDRepresenting a down-sampled two-dimensional imaging result, nDRepresenting the downsampled observation noise;
step S32: determining an observation matrix as D psi and a sparse matrix as a unit matrix I;
step S33, reconstructing based on compressed sensing by adopting a basis tracking denoising algorithm to realize the height-direction focusing of the sub-aperture;
step S34, correcting the two-dimensional coordinate position of the target after the height focusing, namely the position of the two-dimensional coordinate of the target after the height focusing by using the relation between the pixel coordinate (x ', y') in the two-dimensional imaging result of the sub-aperture and the real three-dimensional coordinate (x, y, z) of the target
Figure FDA0003059573700000041
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