CN113777607B - Video SAR imaging method - Google Patents

Video SAR imaging method Download PDF

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CN113777607B
CN113777607B CN202111072571.2A CN202111072571A CN113777607B CN 113777607 B CN113777607 B CN 113777607B CN 202111072571 A CN202111072571 A CN 202111072571A CN 113777607 B CN113777607 B CN 113777607B
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CN113777607A (en
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安洪阳
王朝栋
杨青
武俊杰
孙稚超
李中余
杨建宇
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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
    • 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
    • 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
    • G01S13/9021—SAR image post-processing techniques

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Abstract

The invention discloses a video SAR imaging method, which comprises the steps of firstly completing the construction of a video SAR echo signal model; then, a decoupling observation model is constructed, and a video SAR imaging problem is modeled as a combined sparse tensor and low-rank tensor minimizationProblem, i.e. rank sum 0 A norm union minimization problem; the imaging process of the video SAR is then converted into l 1 Minimization and tensor kernel norm combined minimization problem; and finally, reconstructing a scene by using a tensor alternating direction multiplier method to obtain an imaging result. The method of the invention utilizes a tensor alternating direction multiplier method to carry out combined low-rank and sparse recovery on the undersampled video SAR echo, and compared with a video SAR imaging method based on rapid back projection, the data volume can be greatly reduced; compared with the video SAR imaging method based on low-rank tensor recovery, the method avoids the influence of a strong scattering target on the reconstruction performance, and improves the imaging performance.

Description

Video SAR imaging method
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a video SAR imaging method.
Background
Synthetic Aperture Radar (SAR) is a full-time and all-weather high-resolution imaging system, and can obtain distance high resolution by transmitting large time-width product linear frequency modulation signal and receiving it, and can obtain pulse compression signal by means of matched filtering so as to obtain high resolution in direction of distance.
Compared with the traditional SAR, the video SAR provides unique remote sensing detection capability, and the video of a target area is obtained by observing a scene at a certain frame rate. The video can be used for monitoring and dynamically monitoring the ground for a long time, and detection and indication of moving targets are facilitated, so that the video synthetic aperture radar imaging has wide application prospect.
Under the video SAR working mode, a large number of overlapping apertures exist among frames, the required data volume is huge, and therefore great difficulty is brought to storage, transmission and processing of data, especially to an unmanned aerial vehicle platform and a small satellite platform. In the documents "Processing video-SAR data with the fast backprojection method, IEEE Transactions on Aerospace and Electronic Systems, vol.52, no.6, pp.2838-2848, decumber 2016", a fast backprojection algorithm is proposed to obtain multiple frames, however, this method can only be applied to fully sampled data; in documents of "Video SAR Imaging Based on Low-Rank resistor Recovery, IEEE Transactions on Neural Networks and Learning Systems, vol.32, no.1, pp.188-202, jan.2021", aiming at the problem of Video SAR Imaging under an undersampling condition, a Video SAR Imaging method Based on Low-Rank Tensor Recovery is provided, which can greatly reduce the amount of echo data required by Imaging, but when an observation region has a strong scattering target, the Low-Rank characteristic of a scene is damaged, so that the performance of the method is seriously reduced. Both methods cannot realize accurate imaging of the video SAR under the condition of undersampling.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a video SAR imaging method.
The technical scheme of the invention is as follows: a video SAR imaging method specifically comprises the following steps:
step S0: establishing a video SAR observation model,
the radar platform moves along a straight line, the radar transmits a linear frequency modulation pulse signal at a fixed frequency and receives an echo reflected by an observation area; taking an imaging process with a total frame number of T, in the imaging process of a T (T =1,2.. T) frame of the video SAR, assuming that each frame of imaging area is an M × N rectangle, M is the number of azimuth pixel points, N is the number of distance pixel points, and then a reflection matrix of the imaging area is expressed in a matrix form as
Figure BDA0003260939830000011
Wherein the content of the first and second substances,
Figure BDA0003260939830000012
is (m, n) termThe echo of the t-th frame is represented as
Figure BDA0003260939830000013
Wherein P and Q respectively represent the total sampling point number of the azimuth direction and the distance direction,
Figure BDA0003260939830000014
a complex matrix representing the magnitude of P x Q;
step S1: a video SAR echo model is established,
and establishing a t frame, wherein an echo model of a q distance sampling point at a p azimuth sampling point is as follows:
Figure BDA0003260939830000021
wherein the content of the first and second substances,
Figure BDA0003260939830000022
in the formula, ω a (. And ω) r (. H) envelopes of azimuth and distance, R (p, m, n, t) is the slant distance between the radar and the target at the (m, n) position at the p azimuth instant of the t-th frame, c is the speed of light, λ is the wavelength of the transmitted signal, τ q To sample at the qth distance, T a To synthesize the pore time, K r Frequency modulation is carried out on the distance direction signals;
step S2: establishing a decoupling observation model, and establishing a decoupling observation model,
establishing decoupling observation model based on frequency modulation and scaling algorithm
Figure BDA0003260939830000023
The following were used:
Figure BDA0003260939830000024
wherein Y is (t) Representing the t-th frame echo, X (t) Which represents the image of the t-th frame,
Figure BDA0003260939830000025
and
Figure BDA0003260939830000026
respectively representing the distance and azimuth fourier transforms,
Figure BDA0003260939830000027
and
Figure BDA0003260939830000028
respectively representing a frequency modulation scaling term, a distance direction compression term and an orientation compression term in a frequency modulation scaling algorithm, (. DEG) -1 Indicating the reverse process, (.) * Representing a conjugate calculation;
and step S3: modeling as a sparse low-rank tensor joint solution problem,
using decoupled models
Figure BDA00032609398300000212
Obtaining a video SAR echo model under an undersampling condition as mapping from an imaging scene to an echo:
Figure BDA0003260939830000029
wherein, theta a And Θ r An undersampled matrix representing the azimuth and the range directions respectively,
Figure BDA00032609398300000210
for video SAR echo under undersampling condition
Figure BDA00032609398300000211
In the tth frame, the imaging problem is modeled as a joint low rank and sparseness problem, i.e., rank sum l 0 Norm union minimization problem:
Figure BDA0003260939830000031
wherein the content of the first and second substances,
Figure BDA0003260939830000032
representing the sparse tensor,
Figure BDA0003260939830000033
representing the tensor of low rank order,
Figure BDA0003260939830000034
the t-th frame representing the sparse tensor,
Figure BDA0003260939830000035
a tth frame representing a low rank tensor;
the sum of ranks l in formula (5) 0 The norm union minimization problem is converted into tensor nuclear norm and l 1 Norm union minimization problem:
Figure BDA0003260939830000036
in the formula, | \ | non-counting * Expressing tensor nuclear norm, | · | counting 1 Is represented by 1 A norm;
rewrite equation (6) to the augmented Lagrangian form:
Figure BDA0003260939830000037
wherein the content of the first and second substances,
Figure BDA0003260939830000038
the lagrangian operator is represented by,<·,·>denotes the tensor inner product and p denotes the penalty factor.
And step S4: the method combines low rank and sparse tensor recovery, and specifically comprises the following sub-steps:
s41: updating low rank tensor
Figure BDA0003260939830000039
The updating method of the low rank tensor is as follows:
Figure BDA00032609398300000310
wherein the content of the first and second substances,
Figure BDA00032609398300000311
wherein the content of the first and second substances,
Figure BDA00032609398300000312
Figure BDA00032609398300000313
is composed of
Figure BDA00032609398300000314
The t-th frame data of (a),
Figure BDA00032609398300000315
by imaging processes based on frequency modulation algorithms
Figure BDA00032609398300000316
Decoupled observation model
Figure BDA00032609398300000317
The method comprises the steps of updating a low-rank tensor by using a near-end operator of a tensor nuclear norm;
s42: updating sparse tensors
Figure BDA00032609398300000318
The sparse tensor updating method is as follows:
Figure BDA00032609398300000319
wherein the content of the first and second substances,
Figure BDA0003260939830000041
and obtaining the value of the updated sparse tensor by using a soft threshold operator.
S43: updating lagrange operators
Figure BDA0003260939830000042
To pair
Figure BDA0003260939830000043
The t-th frame data of (1) is updated according to the following formula:
Figure BDA0003260939830000044
after all frame updates, get
Figure BDA0003260939830000045
S44: the penalty parameter p is updated by the processor,
the self-adaptive updating method of the penalty parameter comprises the following steps:
ρ g+1 ＝min(αρ g ,ρ max ) (13)
where ρ is max Is the upper bound of rho, and alpha is a constant equal to or greater than 1;
s45: if the update rates of the low-rank tensor and the sparse tensor are smaller than the predefined value, stopping iteration, otherwise, performing steps S41-S44;
the reconstruction of the imaging scene is finally realized through the steps.
The invention has the beneficial effects that: the method of the invention firstly completes the construction of a video SAR echo signal model; then, a decoupling observation model is constructed, and the video SAR imaging problem is modeled as a combined sparse tensor and low-rank tensor minimization problem, namely rank sum 0 A norm union minimization problem; the imaging process of the video SAR is then converted into l 1 Minimization and tensor kernel norm combined minimization problem; and finally, reconstructing a scene by using a tensor alternating direction multiplier method to obtain an imaging result.The method of the invention utilizes a tensor alternating direction multiplier method to carry out combined low-rank and sparse recovery on the undersampled video SAR echo, and compared with a video SAR imaging method based on rapid back projection, the data volume can be greatly reduced; compared with the video SAR imaging method based on low-rank tensor recovery, the method avoids the influence of a strong scattering target on the reconstruction performance, and improves the imaging performance.
Drawings
Fig. 1 is a schematic view of a video SAR observation geometry according to an embodiment of the present invention.
Fig. 2 is a schematic flow chart of a video SAR imaging method according to an embodiment of the present invention.
Fig. 3 is an imaging result of 5 th, 22 th and 30 th frames of the video SAR in the video SAR imaging method according to the embodiment of the present invention under the condition of the 60% video SAR echo data volume.
Detailed Description
The invention mainly adopts a simulation experiment method for verification, and all steps and conclusions are verified to be correct on Matlab 2020. The present invention will be described in further detail with reference to specific embodiments.
The video SAR observation geometric schematic diagram of the embodiment of the invention is shown in figure 1, a radar platform moves along a straight line, and a radar transmits a chirp signal at a fixed frequency and receives an echo reflected by an observation area.
The specific flow shown is shown in fig. 2, and the implementation steps are as follows:
the method comprises the following steps: further obtaining video SAR echo according to the space geometric structure and echo model of the video SAR
Figure BDA0003260939830000051
The simulation system parameters are shown in table 1.
TABLE 1
Figure BDA0003260939830000052
Step two: establishing a video SAR decoupling observation model
Figure BDA0003260939830000053
Step three: establishing an azimuthally undersampled echo
Figure BDA0003260939830000054
Modeling SAR imaging problems by jointly utilizing low-rank and sparse characteristics of imaging scenes, and carrying out l 0 The norm minimization problem and the rank minimization problem are respectively converted into l 1 Norm minimization problem and tensor kernel norm minimization problem.
Step four: l obtained in the third step 1 The norm minimization and tensor kernel norm minimization problems are rewritten into an augmented lagrange form, a tensor alternating direction multiplier method is used for solving, video SAR imaging scene recovery under the undersampling condition is completed, and the result is shown in fig. 3.
Therefore, the method provided by the invention can realize the high-efficiency accurate focusing of the video SAR echo under the undersampling condition and can obtain the high-precision video SAR result under the condition of obviously reducing the data volume. The method can be applied to the fields of earth remote sensing, resource exploration, geological mapping and the like.

Claims (1)

1. A video SAR imaging method specifically comprises the following steps:
step S0: establishing a video SAR observation model,
the radar platform moves along a straight line, and the radar transmits a linear frequency modulation pulse signal at a fixed frequency and receives an echo reflected by an observation area; taking an imaging process with a total frame number of T, in an imaging process of a T (T =1,2, … T) th frame of the video SAR, assuming that each frame of imaging area is a rectangle of M × N, M represents the number of azimuth direction pixel points, N represents the number of distance direction points, and then a reflection matrix of the imaging area is represented in a matrix form as
Figure FDA0004066955390000011
Wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0004066955390000012
for the (m, n) term, the echo representation of the t-th frameIs composed of
Figure FDA0004066955390000013
Wherein P and Q respectively represent the total sampling point number of the azimuth direction and the distance direction,
Figure FDA0004066955390000014
a complex matrix representing the magnitude of P x Q;
step S1: a video SAR echo model is established,
and establishing a t frame, wherein the echo model of a q distance sampling point at a p azimuth sampling point is as follows:
Figure FDA0004066955390000015
wherein the content of the first and second substances,
Figure FDA0004066955390000016
in the formula, ω a (. And ω) r (. H) envelopes of azimuth and distance, R (p, m, n, t) is the slant distance between the radar and the target at the (m, n) position at the p azimuth instant of the t-th frame, c is the speed of light, λ is the wavelength of the transmitted signal, τ q To sample at the qth distance, T a To synthesize the pore time, K r Frequency modulation is carried out on the distance direction signals;
step S2: establishing a decoupling observation model,
establishing decoupling observation model based on frequency modulation scaling algorithm
Figure FDA00040669553900000112
The following:
Figure FDA0004066955390000017
wherein Y is (t) Representing the t-th frame echo, X (t) Is shown asthe number of the t-frame images,
Figure FDA0004066955390000018
and
Figure FDA0004066955390000019
respectively representing the distance and azimuth fourier transforms,
Figure FDA00040669553900000110
and
Figure FDA00040669553900000111
respectively representing a frequency modulation scaling item, a distance direction compression item and an orientation compression item in a frequency modulation scaling algorithm (·) -1 Indicating the reverse process, (.) * Representing a conjugate calculation;
and step S3: modeling as a sparse low-rank tensor joint solution problem,
using decoupled observation models
Figure FDA0004066955390000021
Obtaining a video SAR echo model under an undersampling condition as mapping from an imaging scene to an echo:
Figure FDA0004066955390000022
wherein, theta a And Θ r An undersampled matrix representing the azimuth and range directions respectively,
Figure FDA0004066955390000023
for video SAR echo under undersampling condition
Figure FDA0004066955390000024
T-th frame in (1), the imaging problem is modeled as a joint low rank and sparsity problem, i.e., rank sum 0 Norm union minimization problem:
Figure FDA0004066955390000025
wherein the content of the first and second substances,
Figure FDA0004066955390000026
representing the sparse tensor,
Figure FDA0004066955390000027
representing the low-rank tensor,
Figure FDA0004066955390000028
the t-th frame representing the sparse tensor,
Figure FDA0004066955390000029
a tth frame representing a low rank tensor;
the sum of ranks in the formula (5) 0 The norm union minimization problem is converted into tensor nuclear norm and l 1 Norm union minimization problem:
Figure FDA00040669553900000210
in the formula, | · the luminance | | * Representing tensor kernel norm, | ·| non-woven phosphor 1 Is represented by 1 A norm;
rewrite equation (6) to the augmented Lagrangian form:
Figure FDA00040669553900000211
wherein the content of the first and second substances,
Figure FDA00040669553900000212
the lagrangian operator is represented by,<·,·>expressing tensor inner products, and expressing a penalty coefficient by rho;
and step S4: the method combines low rank and sparse tensor recovery, and specifically comprises the following sub-steps:
s41: updating low rank tensor
Figure FDA00040669553900000213
The low rank tensor update method is as follows:
Figure FDA00040669553900000214
wherein the content of the first and second substances,
Figure FDA0004066955390000031
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0004066955390000032
Figure FDA0004066955390000033
is composed of
Figure FDA0004066955390000034
The t-th frame data of (a), I | · | purple wind 2 Is represented by 2 Norm, | · | luminance F The number of the F-norm is expressed,
Figure FDA00040669553900000315
by imaging processes based on frequency modulation algorithms
Figure FDA0004066955390000035
Decoupled observation model
Figure FDA0004066955390000036
The method comprises the steps of updating a low-rank tensor by using a near-end operator of a tensor nuclear norm;
s42: updating sparse tensors
Figure FDA0004066955390000037
The sparse tensor updating method is as follows:
Figure FDA0004066955390000038
wherein the content of the first and second substances,
Figure FDA0004066955390000039
obtaining the value of the updated sparse tensor by using a soft threshold operator;
s43: updating lagrange operators
Figure FDA00040669553900000310
To pair
Figure FDA00040669553900000311
The t-th frame data of (1) is updated according to the following formula:
Figure FDA00040669553900000312
after all frame updates, get
Figure FDA00040669553900000313
S44: the penalty parameter p is updated by the processor,
the self-adaptive updating method of the penalty parameter comprises the following steps:
Figure FDA00040669553900000314
where ρ is max Is the upper bound of rho, and alpha is a constant equal to or greater than 1;
s45: if the update rates of the low-rank tensor and the sparse tensor are smaller than the predefined value, stopping iteration, otherwise, performing steps S41-S44;
the reconstruction of the imaging scene is finally realized through the steps.
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