阅读说明：本技术 一种视频sar成像方法 (Video SAR imaging method ) 是由 安洪阳 王朝栋 杨青 武俊杰 孙稚超 李中余 杨建宇 于 2021-09-14 设计创作，主要内容包括：本发明公开了一种视频SAR成像方法,本发明的方法首先完成视频SAR回波信号模型的构建；然后构建解耦观测模型,并将视频SAR成像问题建模为联合稀疏张量与低秩张量最小化问题,即秩和l-(0)范数联合最小化问题；接着将视频SAR的成像过程转化成l-(1)最小化和张量核范数联合最小化问题；最后利用张量交替方向乘子法进行场景重建,得到成像结果。本发明的方法利用张量交替方向乘子法对欠采样视频SAR回波进行联合低秩与稀疏恢复,与基于快速反投影的视频SAR成像方法相比可以大幅减少数据量；与基于低秩张量恢复的视频SAR成像方法相比,避免了强散射目标对重建性能的影响,提升了成像性能。(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 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 reconstruction performance, and improves imaging performance.)

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, and in a T (T is 1, 2.. T) frame imaging process of the video SAR, assuming that each frame imaging area is an M × N rectangle, M represents the number of azimuth pixel points, N represents the number of distance direction points, then a reflection matrix of the imaging area is represented in a matrix form asWherein the content of the first and second substances,for the (m, n) term, the echo of the t frame is expressed asWherein P and Q respectively represent the total sampling point number of the azimuth direction and the distance direction,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:

wherein the content of the first and second substances,

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_qTo sample at the qth distance, T_aTo synthesize the pore time, K_rFrequency modulation is carried out on the distance direction signals;

step S2: establishing a decoupling observation model,

establishing decoupling observation model based on frequency modulation and scaling algorithmThe following were used:

wherein, Y^(t)Representing the t-th frame echo, X^(t)Which represents the image of the t-th frame,andrespectively representing the distance and azimuth fourier transforms,andrespectively representing a frequency modulation scaling item, a distance direction compression item and an orientation compression item in a frequency modulation scaling algorithm (·)^-1Indicating the reverse process, (.)^*Representing a conjugate calculation;

step S3: modeling as a sparse low-rank tensor joint solution problem,

using decoupled modelsObtaining a video SAR echo model under an undersampling condition as mapping from an imaging scene to an echo:

wherein, theta_aAnd Θ_rAn undersampled matrix representing the azimuth and range directions respectively,for video SAR echo under undersampling conditionT-th frame in (1), the imaging problem is modeled as a joint low rank and sparsity problem, i.e., rank sum₀Norm union minimization problem:

wherein the content of the first and second substances,representing the sparse tensor,representing the low-rank tensor,the t-th frame representing the sparse tensor,a tth frame representing a low rank tensor;

the sum of ranks l in formula (5)₀The norm union minimization problem is converted into tensor nuclear norm and l₁Norm union minimization problem:

in the formula, | · the luminance | |_*Representing tensor kernel norm, | ·| non-woven phosphor₁Is represented by₁A norm;

rewriting equation (6) to the augmented lagrange form:

wherein the content of the first and second substances,the lagrangian operator is represented by,<·,·>expressing tensor inner products, and expressing a penalty coefficient by rho;

step S4: the method combines low rank and sparse tensor recovery, and specifically comprises the following sub-steps:

s41: updating low rank tensor

The low rank tensor update method is as follows:

wherein the content of the first and second substances,

wherein the content of the first and second substances, is composed ofThe t frame data, | · | | non-woven phosphor₂Is represented by₂Norm, | · | luminance_FThe number of the F-norm is expressed,by imaging processes based on frequency modulation algorithmsDecoupled observation modelThe 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

The sparse tensor updating method is as follows:

wherein the content of the first and second substances,

obtaining the value of the updated sparse tensor by using a soft threshold operator;

s43: updating lagrange operators

To pairAccording to the t frame dataThe following is updated:

after all frame updates, get

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_maxIs 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.

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 frame maps, 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", a Video SAR Imaging method Based on Low-Rank Tensor Recovery is provided for the problem of Video SAR Imaging under an undersampling condition, so that the amount of echo data required by Imaging can be greatly reduced, but when a strong scattering target exists in an observation region, the Low-Rank characteristic of a scene is damaged, and therefore 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, 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, and in a T (T is 1, 2.. T) frame imaging process of the video SAR, assuming that each frame imaging area is an M × N rectangle, M is the number of azimuth pixel points, N is the number of distance pixel points, then a reflection matrix of the imaging area is expressed in a matrix form asWherein the content of the first and second substances,for the (m, n) term, the echo of the t frame is expressed asWherein P and Q respectively represent the total sampling point number of the azimuth direction and the distance direction,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:

wherein the content of the first and second substances,

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_qTo sample at the qth distance, T_aTo synthesize the pore time, K_rFrequency modulation is carried out on the distance direction signals;

step S2: establishing a decoupling observation model,

establishing decoupling observation model based on frequency modulation and scaling algorithmThe following were used:

wherein, Y^(t)Representing the t-th frame echo, X^(t)Which represents the image of the t-th frame,andrespectively representing the distance and azimuth fourier transforms,andrespectively representing a frequency modulation scaling item, a distance direction compression item and an orientation compression item in a frequency modulation scaling algorithm (·)^-1Indicating the reverse process, (.)^*Representing a conjugate calculation;

step S3: modeling as a sparse low-rank tensor joint solution problem,

using decoupled modelsObtaining undersampling as a mapping of an imaging scene to an echoVideo SAR echo model under the condition:

wherein, theta_aAnd Θ_rAn undersampled matrix representing the azimuth and range directions respectively,for video SAR echo under undersampling conditionT-th frame in (1), the imaging problem is modeled as a joint low rank and sparsity problem, i.e., rank sum₀Norm union minimization problem:

wherein the content of the first and second substances,representing the sparse tensor,representing the low-rank tensor,the t-th frame representing the sparse tensor,a tth frame representing a low rank tensor;

the sum of ranks l in formula (5)₀The norm union minimization problem is converted into tensor nuclear norm and l₁Norm union minimization problem:

in the formula, | · the luminance | |_*Representing tensor kernel norm, | ·| non-woven phosphor₁Is represented by₁A norm;

rewriting equation (6) to the augmented lagrange form:

wherein the content of the first and second substances,the lagrangian operator is represented by,<·,·>denotes the tensor inner product and p denotes the penalty factor.

Step S4: the method combines low rank and sparse tensor recovery, and specifically comprises the following sub-steps:

s41: updating low rank tensor

The low rank tensor update method is as follows:

wherein the content of the first and second substances,

wherein the content of the first and second substances, is composed ofThe t-th frame data of (a),by imaging based on frequency modulation algorithmProgram for programmingDecoupled observation modelThe 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

The sparse tensor updating method is as follows:

wherein the content of the first and second substances,

and obtaining the value of the updated sparse tensor by using a soft threshold operator.

S43: updating lagrange operators

To pairThe t-th frame data of (1) is updated according to the following formula:

after all frame updates, get

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_maxIs 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 sum₀A norm union minimization problem; the imaging process of the video SAR is then converted into l₁Minimization 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 reconstruction performance, and improves 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 shows the imaging results of the 5 th, 22 th and 30 th frames of the video SAR under the condition of the 60% video SAR echo data volume by the video SAR imaging method according to the embodiment of the present invention.

Detailed Description

The invention mainly adopts a simulation experiment method for verification, and all the 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 SARThe simulation system parameters are shown in table 1.

TABLE 1

Step two: establishing video SAR decoupling observation model

Step three: establishing an azimuthally undersampled echoModeling SAR imaging problems by jointly utilizing low-rank and sparse characteristics of imaging scenes, and carrying out l₀The norm minimization problem and the rank minimization problem are respectively converted into l₁Norm minimization problem and tensor kernel norm minimization problem.

Step four: l obtained in the third step₁The 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.

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.