CN110133656B - Three-dimensional SAR sparse imaging method based on decomposition and fusion of co-prime array - Google Patents
Three-dimensional SAR sparse imaging method based on decomposition and fusion of co-prime array Download PDFInfo
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Abstract
The invention discloses a three-dimensional SAR sparse imaging method based on decomposition and fusion of a co-prime array. The method combines the advantages of a co-prime sampling method and a compressed sensing sparse reconstruction method, and by utilizing co-prime sampling, not only can the sampling data be reduced, but also the system is easier to realize compared with the traditional random sampling mode; compared with the traditional sparse imaging method, the method can effectively inhibit grating lobes and false targets and improve the imaging quality.
Description
Technical Field
The invention belongs to the technical field of radar, and particularly relates to the technical field of Synthetic Aperture Radar (SAR) imaging.
Background
Synthetic Aperture Radar (SAR) has become an important means for earth observation at present as a remote sensing imaging technology with all-time, all-weather and abundant information, and is increasingly widely applied in national economy and military fields such as terrain image generation, target detection and reconnaissance, target accurate striking, national earth resource exploration, natural disaster monitoring and the like, and the Synthetic Aperture Radar interference [ J ] earth science progress, 2000,15(6): 734-. The conventional SAR imaging generally only has two-dimensional imaging resolution, and in places with large fluctuation, such as steep mountains and valleys and tall and straight buildings in cities, distortion (shadow occlusion effect, spatial blurring, top-bottom inversion and the like) in the conventional SAR imaging causes some important information (such as height) of the space to be lost, and the imaging result cannot reflect three-dimensional information of an actual scene, so that the three-dimensional imaging has become an urgent requirement for the development of the SAR imaging technology. Currently, three-dimensional imaging technologies include circular SAR (circular SAR) three-dimensional imaging, tomographic SAR (tomogry SAR) three-dimensional imaging, and Array SAR (Array SAR, ASAR) three-dimensional imaging.
The basic principle of array SAR three-dimensional imaging is that an array antenna is added in a cutting track direction, a virtual area array is formed by flying from the cutting track to a platform, so that two-dimensional resolution is obtained, and the third-dimensional resolution is obtained by a pulse compression technology in a distance direction. Compared with circular SAR three-dimensional imaging, the array SAR three-dimensional imaging does not need a circular motion track; compared with the tomography SAR three-dimensional imaging which needs to navigate for multiple times, the array SAR three-dimensional imaging only needs to navigate for one time, so the array SAR three-dimensional imaging has stronger flexibility compared with the tomography SAR and the circumference SAR three-dimensional imaging. The existing array SAR three-dimensional imaging technology plays an important role in the fields of topographic mapping, urban mapping, disaster relief, military exploration and the like.
The resolution of the conventional SAR imaging method based on matched filtering is limited, specifically, the resolution in the distance direction is influenced by the signal bandwidth, the resolution in the track direction is influenced by the length of a synthetic aperture, and the resolution in the cross-track direction is influenced by an array antenna. Especially, the resolution across the track direction needs to be long enough if the resolution is to be improved, and the distance between adjacent array elements needs to be less than half of the signal wavelength in order to avoid grating lobes in the imaging process, so that the number of array elements is huge in the antenna array with fixed length. If the observation scene is sparse, high-resolution imaging of the target scene can be realized by using a small number of samples, but the hardware complexity of the array mode of random sampling is high, and the realization is difficult, while the co-prime array is a sparse array structure formed by a pair of uniform sparse sampling subarrays sharing the first array element and having mutually prime sampling intervals, the array is simple to realize, and the hardware is easy to realize. However, the number and the positions of the array elements in the array antenna determine that the cross correlation between adjacent arrays of the compressed sensing measurement matrix is increased, the signal crosstalk is serious, false targets exist in imaging, and the imaging quality is reduced.
Disclosure of Invention
Aiming at the problems of grating lobes and false targets in sparse imaging, the invention provides a three-dimensional SAR sparse imaging method based on decomposition and fusion of a co-prime array by combining a co-prime sampling technology and an iterative minimization Sparse Bayesian Reconstruction (SBRIM) imaging algorithm. Compared with the traditional random sampling mode, the method provided by the invention has the characteristic of being more convenient for system implementation, and compared with the traditional sparse imaging method, the method provided by the invention can effectively inhibit grating lobes and false targets, and improve the imaging quality.
For the convenience of describing the present invention, the following terms are first defined:
definitions 1 array synthetic Aperture Radar (LASAR)
The array synthetic aperture radar imaging is a synthetic aperture radar technology which fixes a linear array antenna on a load motion platform and is vertical to the motion direction of the platform, combines the motion of the motion platform to synthesize a two-dimensional plane array to realize array two-dimensional plane imaging, and then utilizes the radar beam direction echo delay to realize distance one-dimensional imaging, thereby realizing the three-dimensional imaging of an observation target, and the technology is shown in documents of' Liuzhang, Wang Jing, Nidoku, and the like.
The standard synthetic aperture radar echo data range-wise pulse compression refers to a process of performing signal focusing imaging on a range-wise signal of a synthetic aperture radar by using a synthetic aperture radar to transmit a signal parameter and adopting a matched filtering technology, and is described in the literature, "radar imaging technology, fense, cheng, wang tong, electronic industry press, 2005".
Defining 3, along-track direction, tangential track direction and distance direction of array SAR
The direction of the radar platform motion is called along-track direction (azimuth direction), the direction perpendicular to the along-track direction is called tangential track direction, and the direction perpendicular to the array plane is called distance direction, and the detailed document refers to the research of array three-dimensional synthetic aperture radar sparse imaging technology, wecission, 2013.
Definition 4, fast and slow moments of the array SAR
The time required by the array SAR motion platform to fly through one azimuth synthetic aperture length is called slow time, the radar system transmits and receives pulses with a repetition period of a certain time length, therefore, the slow time can be expressed as a discretization time variable taking a pulse repetition period as a step length, wherein the discretization time variable value of each pulse repetition period is one slow time. The fast time refers to the time interval variable from the sampling of the echo signal within one pulse repetition period. For details, see the literature "synthetic aperture radar imaging principle, edited by piyiming et al, published by electronic technology university press".
Definition 5 standard synthetic aperture radar original echo simulation method
The synthetic aperture radar original echo simulation method refers to a method for simulating an original signal with the characteristics of a synthetic aperture radar echo signal under the condition of certain system parameters based on the synthetic aperture radar imaging principle, and is described in the literature, "zhanpeng, synthetic aperture radar echo signal simulation research, thesis of north-west university of industry, 2004".
Definition 6, synthetic aperture radar imaging space
The synthetic aperture radar projection imaging space refers to an imaging space selected during synthetic aperture radar data imaging, and the synthetic aperture radar imaging needs to project echo data to the imaging space for focusing processing. Generally, the synthetic aperture radar imaging space selects either an oblique plane coordinate system or a horizontal ground coordinate system.
Definition 7 and standard compressed sensing synthetic aperture radar measurement matrix construction method
A compressed sensing synthetic aperture radar measurement matrix construction method is characterized In that under the condition of parameters needed by a given radar system parameter, a platform track parameter, an imaging space parameter and the like, a compressed sensing measurement matrix is constructed by utilizing time delay phases of a synthetic aperture radar system and grid points In an imaging space, the measurement matrix is multiplied by a target real scattering coefficient vector In the imaging space to obtain synthetic aperture radar echo data, and the synthetic aperture radar echo data are defined by 8, and a compressed sensing sparse Reconstruction theory is defined by 2010,109:63-81, Zhang X L, Shi J, et al
If a signal is sparse or compressible, the signal can be reconstructed without distortion using a sampling rate well below that required by the nyquist sampling theorem. If the signal is sparse and the measurement matrix satisfies the incoherent and RIP properties, signal sparse reconstruction using compressed sensing recovery can be achieved by solving the following optimization problem:
wherein the content of the first and second substances,
is the recovered signal, α is the sparse signal, y is the measurement signal, Θ is the measurement matrix, and ε is the noise threshold. For details, the document "research on sparse imaging technology of array three-dimensional synthetic aperture radar, wecisn, 2013".
Definition 9 sparse Bayesian sparse reconstruction (SBRIM) imaging algorithm based on iterative minimization
An Iterative Minimum sparse Bayesian reconstruction (sparse Bayesian Recovery via Iterative Minimum) imaging algorithm was proposed in 2011 by the assistant professor wecistro of the electronics science university. See the document, "array SAR three-dimensional sparse reconstruction imaging algorithm based on Bayesian estimation, Wecisun, 2011"
Define 10, uniform sparse sampling
The uniform sparse sampling refers to dividing a signal according to a certain sampling interval, wherein the sampling interval is greater than or equal to the Nyquist sampling interval. For details, the document entitled "sparse sampling array optimization-based APG-MUSIC Algorithm, Songhu, Jiang 36858"
Definitions 11, coprime sampling
The cross-prime sampling is a special sparse sampling technology, and actually, a pair of samplers with cross-prime sampling intervals are used for carrying out non-uniform time domain undersampling operation on a signal, which is defined as 12 in the literature, "study of cross-prime array signal processing algorithm, Zhoujin, 2018" definition, and cross-prime array
The technique of processing co-prime arrays in signals was first proposed by the group of topics in p.p. vaidyanathan, the basic idea is to adopt two sparse samplers to perform sparse sampling on the received signal, the sampling intervals of the two samplers satisfy the coprime condition in the time domain, the sampling mode breaks through the Nquist sampling theorem, realizes the down sampling of signals simply, combines the concept of prime numbers in the mathematical theory, realizes that the system design of the array divides the co-prime array into two sub-array imaging, the positions of grating lobes in the two sub-images are different, when the distance between two sub-array elements meets the co-prime condition, namely, the method adopts the co-prime array imaging, has better performance on signal output compared with a uniform sparse sampling array, the imaging grating lobes that occur at different locations can be removed and thus can be somewhat attenuated based on co-prime array imaging. See the literature "Vaidyanathan P, Pal P. spark Sensing With Co-Prime Samplers and Arrays [ J ]. IEEE Transactions on Signal Processing,2011,59(2): 573-"
Definition 13, matrix dimension transformation
The dimension transformation of the matrix is to change a known array into a matrix with a specified dimension according to different index rules. Generally, the conversion is performed according to the sequence of the columns, namely, the first column is read, the second column is read, and the storage is performed according to the columns until the storage of the array is completed.
The invention provides a three-dimensional SAR sparse imaging method based on decomposition and fusion of a co-prime array, which comprises the following steps:
step 1, initializing array SAR system parameters:
initializing array SAR system parameters, comprising: the radar carrier wave length is marked as lambda; carrier frequency of radar emission signal, denoted fc(ii) a Bandwidth of radar emission signal, denoted Br(ii) a The pulse time width of radar emission is marked as Tr(ii) a Radar sampling frequency, denoted Fs(ii) a Frequency modulation slope of radar emission signal, noted as fdr(ii) a The central incident angle of the radar beam is recorded as theta; the propagation speed of the electromagnetic waves in the air is marked as C; the height of the array platform is marked as H; the length of the motion track of the azimuth antenna is marked as L _ a; the length of the cross-course array is marked as L _ c; an observation space of the array radar platform is set as a ground three-dimensional coordinate system and is marked as X-Y-Z, wherein X represents a horizontal plane horizontal axis, Y represents a horizontal plane longitudinal axis, and Z represents a horizontal plane vertical axis; the distance direction sampling point number of the radar system is recorded as N R(ii) a Sampling point number of radar azimuth, marked as Ns(ii) a The number of cross-course sampling points is recorded as Nc(ii) a The position of each array element of the array antenna is marked as P (w),
s＝1,2,…,Ns，l＝1,2,…,Nc，w＝1,2,…,NsNcwherein s is the azimuth slow moment, l is the cross-course sampling point position, w is the serial number of each array element of the antenna, NsNcThe total number of array elements of the array antenna is; the fast moment of distance is recorded as tk，tk＝1,2,…,NR(ii) a Position vectors P (w) of each array element of the array antenna are determined in SAR observation scheme design; according to the SAR imaging system scheme and the observation scheme, the parameters of an initialized imaging system required by the SAR imaging method are known;
initializing a scene measurement target space parameter of the array SAR, comprising the following steps: a space rectangular coordinate system X-Y-R formed by a radar beam irradiation field slant distance plane Y-R and a horizontal plane horizontal axis X vertical to the horizontal plane upwards is used as an observation scene target space omega of the array SAR0Wherein, the horizontal plane horizontal axis X and the vertical axis Y of the observation scene target space are the same as the horizontal plane horizontal axis X and the vertical axis Y of the radar platform observation space in the step 1, and R represents the radar distance direction;
observing a target space omega of a scene0Uniformly divided into three-dimensional discrete resolution unit grids with equal size, and recorded as omega 0(i, j, k), wherein i, j, k are natural integers respectively, and i is 1,2, …, NX，j＝1,2,…,NY，k＝1,2,…,NRAnd i is recorded as omega0(i, j, k) the ith cell on the horizontal plane horizontal axis X, j being Ω0(i, j, k) the jth cell on the horizontal plane vertical axis Y, k being denoted as Ω0(i, j, k) the kth cell in the distance direction R, NX、NYAnd NRRespectively recorded as the target space omega of the observation scene0The total number of unit grids in the horizontal axis X, the horizontal vertical axis Y and the distance direction R,
and dr＝C/FsAnd/2 is expressed as the adjacent unit spacing of the unit grid in the horizontal axis X, the horizontal vertical axis Y and the distance direction R respectively, wherein WxFor observing a scene target space omega0Horizontal plane X of the scene size, WyFor observing a scene target space omega0Horizontal plane Y scene range size, C and FsRespectively setting the propagation speed of the electromagnetic wave initialized in the step 1 in the air and the radar sampling frequency; three-dimensional space omega0The dimension of (i, j, k) is NX×NY×NR；
According to the three-dimensional SAR sparse imaging processing method of decomposition and fusion of the co-prime array, target space parameters of an observation scene of the initialized array SAR required by the method are known;
raw echo data of array SAR, denoted as s 0(tk,w)，tk＝1,2,…,NR，w＝1,2,…,NsNcWherein, tkThe fast time of the distance initialized in step 1, w is the serial number of each array element of the antenna, NRNumber of sampling points in the distance direction for initializing the radar system in step 1, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1; in array SAR practical imaging, raw echo data s0(tkW) is provided by a data receiver;
distance direction pulse adopting echo data of synthetic aperture radar in definition 2Compression method for original echo data s0(tk,w)，tk＝1,2,…,NR，w＝1,2,…,NsNcPerforming range-wise pulse compression to obtain range-wise compressed array SAR echo data, and recording the data as src(tk,w)；
Step 4, respectively carrying out uniform sparse sampling and co-prime sampling on the SAR echo data of the array in the step 3 to obtain echo data after uniform sparse sampling and co-prime sampling:
step 4.1, two integers which are mutually prime numbers are initialized and are respectively recorded as prime numbers M1And prime number M2；
Step 4.2, formula
Calculating to obtain a sampling interval M1And then, the total number of sampling points of the SAR array system after uniform sparse sampling is recorded as N1Wherein, in the step (A),
representing the sign of the rounding operation, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1;
echo data s obtained in step 3 after distance compression rc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcUsing the uniform sparse sampling method defined by 10, the sampling interval is M1To obtain corresponding distance compressed echo data s1(tk,w1) And array antenna position P (w)1)，w1＝1,2,…,N1Wherein, tkFor the fast time of the distance initialized in step 1, w1Representing a sampling interval of M1Sequence number of each array element after time-uniform sparse sampling, NRInitializing the distance direction sampling points of the radar system in the step 1;
step 4.3, formula
Calculating to obtain a sampling interval M2And then, the total number of sampling points of the SAR array system after uniform sparse sampling is recorded as N2Wherein
Representing the sign of the rounding operation, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcUsing the uniform sparse sampling method defined by 10, the sampling interval is M2To obtain corresponding distance compressed echo data s2(tk,w2) And array antenna position P (w)2)，w2＝1,2,…,N2Wherein, tkFor the fast time of the distance initialized in step 1, w 2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, NRInitializing the distance direction sampling points of the radar system in the step 1;
step 4.4, adopting a formula N0＝N1+N2And calculating the sampling point number of the SAR array system after the coprime sampling, and recording the sampling point number as N0Wherein N is1The sampling interval obtained for step 4.2 is M1The total number of sampling points N of the SAR array system after uniform sparse sampling2The sampling interval obtained for step 4.3 is M2The total number of sampling points of the SAR array system after uniform sparse sampling is calculated;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcThe relatively prime sampling method in definition 11 is adopted to carry out the relatively prime sampling,obtaining corresponding distance compressed echo data s0(tk,w0) And array antenna position P (w)0)，w0＝1,2,…,N0Wherein, tkFor the fast time of the distance initialized in step 1, w0Indicating the sequence number of each array element after cross-prime sampling, NRNumber of sampling points in the distance direction for initializing the radar system in step 1, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1;
step 5, constructing a measurement matrix according to the data after SAR distance compression after uniform sparse sampling and cross-prime sampling in the step 4 respectively:
Step 5.1, obtaining array SAR system parameters through initialization in step 1, obtaining observation scene target space parameters through initialization in step 2 and obtaining a sampling interval M in step 41Uniformly sparsely sampled array antenna position P (w)1)，w1＝1,2,…,N1Adopting a construction method of defining 7-medium compressed sensing SAR measurement matrix to obtain a sampling interval M1The measurement matrix of the echo data after uniform sparse sampling is marked as A1Measurement matrix A1Of dimension N1×NXNYWherein w is1Representing a sampling interval of M1Sequence number of each array element after time-uniform sparse sampling, N1The sampling interval obtained for step 4.2 is M1The total number of sampling points N of the SAR array system after uniform sparse samplingXAnd NYRespectively initializing the total number of unit grids of the observation scene target space in the horizontal axis X and the horizontal vertical axis Y in the step 2;
step 5.2, obtaining array SAR system parameters through initialization in the step 1, obtaining observation scene target space parameters through initialization in the step 2 and obtaining a sampling interval M in the step 42Uniformly sparsely sampled array antenna position P (w)2)，w2＝1,2,…,N2Adopting a construction method of defining 7-medium compressed sensing SAR measurement matrix to obtain a sampling interval M2The measurement matrix of the echo data after uniform sparse sampling is marked as A 2MeasuringMatrix A2Of dimension N2×NXNYWherein w is2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, N2The sampling interval obtained for step 4.3 is M2The total number of sampling points N of the SAR array system after uniform sparse samplingXAnd NYRespectively initializing the total number of unit grids of the observation scene target space in the horizontal axis X and the horizontal vertical axis Y in the step 2;
step 5.3, utilizing the array SAR system parameters obtained by the initialization in the step 1, the observation scene target space parameters obtained by the initialization in the step 2 and the array antenna position P (w) after the co-prime sampling obtained in the step 40)，w0＝1,2,…,N0Obtaining a measurement matrix of the echo data after the cross-prime sampling by adopting a construction method of defining a 7-medium compressed sensing SAR measurement matrix, and marking the measurement matrix as A0Measurement matrix A0Of dimension N0×NXNYWherein w is0Indicating the sequence number of each array element after cross-prime sampling, N0The total number of sampling points N of the SAR array system after the coprime samplingXAnd NYRespectively initializing the total number of unit grids of the observation scene target space in the horizontal axis X and the horizontal vertical axis Y in the step 2;
step 6, sparse imaging is carried out by adopting a Sparse Bayesian Reconstruction (SBRIM) method based on iterative minimization:
step 6.1, according to the echo signal s 1(tk,w1) And the measurement matrix A1，tk＝1,2,…,NR，w1＝1,2,…,N1Imaging processing is performed by using an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm in definition 9 to obtain a sampling interval M1The imaging result of sparse reconstruction of the echo data after uniform sparse sampling is recorded as
Wherein the content of the first and second substances,
has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w1Representing a sampling interval of M1Sequence number of each array element after time-uniform sparse sampling, N1The sampling interval obtained for step 4.2 is M1The total number of sampling points N of the SAR array system after uniform sparse samplingX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
step 6.2, according to the echo signal s2(tk,w2) And the measurement matrix A2，tk＝1,2,…,NR，w2＝1,2,…,N2Adopting an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm defined 9 to perform imaging processing to obtain a sampling interval M2The imaging result of sparse reconstruction of the echo data after uniform sparse sampling is recorded as
Wherein
Has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, N 2The sampling interval obtained for step 4.3 is M2The total number of sampling points N of the SAR array system after uniform sparse samplingX、NYAnd NRRespectively initializing the target space of the observation scene in the step 2 at the horizontal axis X and the horizontal axisAxis Y and distance to R cell grid total;
step 6.3, according to the echo signal s0(tk,w0) And the measurement matrix A0，tk＝1,2,…,NR，w0＝1,2,…,N0Imaging processing is carried out by adopting an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm defined 9, and an echo data sparse reconstruction imaging result after cross-prime sampling is obtained and recorded as
Wherein
Has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w0Indicating the sequence number of each array element after cross-prime sampling, N0The total number of sampling points N of the SAR array system after the coprime samplingX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
step 7, performing grating lobe suppression fusion on the sparse imaging result obtained after uniform sparse sampling and cross-prime sampling:
initializing a dimension NR×NXNYIs marked as
Wherein
k＝1,2,…,NR，i＝1,2,…,NXNYWherein N isX、NYAnd NRRespectively initializing the target space of the observation scene in the step 2 at the horizontal axis X, the horizontal vertical axis Y and the distance Total number of off-direction R cell grids;
using a formula
k＝1,2,…,NR，i＝1,2,…,NXNYAnd (4) comparing the imaging result obtained in the step (6)
And
are compared element-by-element, wherein,
abs represents absolute value calculation, min represents minimum value calculation, and T represents transposition calculation of a matrix; calculating to obtain alphai(k)、βi(k) And gammai(k) Minimum value of (2)
Will be provided with
Is assigned as
Namely, it is
According to
Get the ith element of the matrix S
Reassigned values;
according to
Obtaining a matrix S after reassignment, wherein S is a sparse reconstruction result after grating lobe fusion suppression, and
and 8, rearranging to obtain a final three-dimensional sparse imaging result:
n obtained in the step 7R×NXNYObtaining a dimension sparse reconstruction result S by adopting a matrix dimension conversion method of definition 13 to obtain NX×NY×NRThe three-dimensional reconstruction result is marked as I, the I is the three-dimensional sparse imaging result after the co-prime array decomposition and fusion, wherein N isX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
and obtaining a three-dimensional SAR sparse imaging result based on array decomposition and fusion, and finishing the whole method.
The invention has the innovation point that a three-dimensional SAR sparse imaging method based on the decomposition and fusion of the co-prime array is provided. The method combines a co-prime sampling technology and an iterative minimization Sparse Bayesian Reconstruction (SBRIM) imaging algorithm, respectively images a co-prime array and sub-arrays of the co-prime array by adopting a compressed sensing iterative minimization Sparse Bayesian Reconstruction (SBRIM) imaging algorithm to obtain three synthetic aperture radar images, and then fuses the obtained imaging results to obtain a final SAR image. Compared with the traditional random sampling method, the method has the characteristic of being more convenient for system implementation, and compared with the traditional sparse imaging method, the method can effectively inhibit grating lobes and false targets and improve the imaging quality.
The method has the advantages that the advantages of a co-prime sampling method and a compressed sensing sparse reconstruction method are combined, the co-prime sampling is utilized, the sampling data can be reduced, the system implementation is more convenient compared with the traditional random sampling method, and in addition, compared with the traditional sparse imaging method, the method can effectively inhibit grating lobes and false targets and improve the imaging quality.
Drawings
FIG. 1 is a process flow diagram of a method provided by the present invention;
FIG. 2 is a table of simulation parameters for an array SAR system used in accordance with an exemplary embodiment of the present invention;
Detailed Description
The invention can be verified by adopting a computer simulation experiment method, and all steps and conclusions are verified to be correct on MATLAB-2017 b. The specific implementation steps are as follows:
step 1, initializing array SAR system parameters:
initializing array SAR system parameters, comprising: radar carrier wavelength, λ ═ 0.08 m; carrier frequency of radar-transmitted signal, fc37.5 GHz; bandwidth of radar emission signal, Br0.8 GHz; the pulse time width of radar emission is marked as Tr2 mus; radar sampling frequency, denoted Fs1.25 GHz; frequency modulation slope of radar emission signal, noted as fdr＝4×1014(ii) a The central incident angle of the radar beam is recorded as theta which is 0 degree; the propagation speed of electromagnetic waves in air is denoted by C3 × 10 8m/s; the height of the array platform is recorded as H, which is 1000 m; the length of the motion track of the azimuth antenna is recorded as L _ a being 3 m; the length of the cross-course array is recorded as L _ c being 3 m; an observation space of the array radar platform is set as a ground three-dimensional coordinate system and is marked as X-Y-Z, wherein X represents a horizontal plane horizontal axis, Y represents a horizontal plane longitudinal axis, and Z represents a horizontal plane vertical axis; the distance of the radar system is counted as NR512; sampling point number of radar azimuth, marked as Ns32; the number of cross-course sampling points is recorded as Nc32; the position of each array element of the array antenna is recorded as
w＝1,2,…,NsNcWherein s is 1,2, …,32, l is 1,2, …,32, w is 1,2, …, NsNcWherein s is the azimuth slow moment, and l is the cross-course samplingThe point position, w is the serial number of each array element of the antenna, NsNc1024 is the total number of array elements of the array antenna; the fast moment of distance is recorded as tk，tk1,2, …, 512; position vectors P (w) of each array element of the array antenna are determined in SAR observation scheme design; according to the SAR imaging system scheme and the observation scheme, the parameters of an initialized imaging system required by the SAR imaging method are known;
initializing a scene measurement target space parameter of the array SAR, comprising the following steps: a space rectangular coordinate system X-Y-R formed by a radar beam irradiation field slant distance plane Y-R and a horizontal plane horizontal axis X vertical to the horizontal plane upwards is used as an observation scene target space omega of the array SAR 0Wherein the horizontal axis X and the longitudinal axis Y of the target space of the observation scene are the same as those of the observation space of the radar platform in the step 1, and R represents the radar distance direction;
target space omega0Uniformly divided into three-dimensional discrete resolution unit grids with equal size, and recorded as omega0(i, j, k), wherein i, j, k are natural integers respectively, and i is 1,2, …, NX，j＝1,2,…,NY，k＝1,2,…,NRAnd i is recorded as omega0(i, j, k) the ith cell on the horizontal plane horizontal axis X, j being Ω0(i, j, k) the jth cell on the horizontal plane vertical axis Y, k being denoted as Ω0(i, j, k) the k-th cell in the distance direction R, NX＝31、NY31 and NRRespectively marked as an observation scene target space omega 5120The total number of unit grids in the horizontal axis X, the horizontal vertical axis Y and the distance direction R,
and dr＝C/Fs/2＝(3×108)/(1.25×109) 0.12 denotes the adjacent cell spacing of the cell grid in the horizontal axis X, the horizontal vertical axis Y and the distance direction R, respectively, Wx31 is the target space omega of the observation scene0Horizontal plane X of the scene size, Wy31 is the target space omega of the observation scene0C is 3 × 108m/s and Fs1.25GHz is respectively the propagation speed of the electromagnetic wave initialized in the step 1 in the air and the radar sampling frequency; three-dimensional space omega0The dimension of (i, j, k) is 31 × 31 × 512;
According to the three-dimensional SAR sparse imaging processing scheme of co-prime array decomposition and fusion, target space parameters of an observation scene of the initialized array SAR required by the method are known;
raw echo data of array SAR, marked as s0(tk,w)，tk＝1,2,…,NR，w＝1,2,…,NsNcWherein t iskThe fast time of the distance initialized in step 1, w is the serial number of each array element of the antenna, N R512 is the number of sampling points in the distance direction of the initialized radar system in step 1, N s32 is the number of sampling points of the radar azimuth direction initialized in the step 1, NcInitializing the number of cross-course sampling points in the step 1 as 32; in array SAR practical imaging, raw echo data s0(tkW) is provided by a data receiver;
original echo data s are compressed by adopting a synthetic aperture radar echo data range direction pulse compression method in definition 20(tk,w)，tk＝1,2,…,NR，w＝1,2,…,NsNcPerforming range-wise pulse compression to obtain range-wise compressed array SAR echo data, and recording the data as src(tk,w)；
Step 4, respectively carrying out uniform sparse sampling and co-prime sampling on the SAR echo data of the array in the step 3 to obtain echo data after uniform sparse sampling and co-prime sampling:
step 4.1, two integers which are mutually prime numbers are initialized and are respectively recorded as prime numbers M 1Equal to 5 and prime number M2＝6；
Step 4.2, using formula
Calculating to obtain a sampling interval of M1When the sum is 5, the total number of sampling points of the SAR array system after uniform sparse sampling is recorded as
Wherein, the first and the second end of the pipe are connected with each other,
representing the sign of the rounding operation, N s32 is the number of sampling points of the radar azimuth direction initialized in the step 1, NcInitializing the number of cross-course sampling points in the step 1 as 32;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcUsing the uniform sparse sampling method defined by 10, the sampling interval is M1Obtaining corresponding distance compressed echo data s through uniform sparse sampling of 51(tk,w1) And array antenna position P (w)1)，w1＝1,2,…,N1Wherein, tkFor the fast time of the distance initialized in step 1, w1Representing a sampling interval of M1Number of each array element after 5-hour uniform sparse sampling, N R512 is the distance sampling points of the radar system initialized in the step 1;
step 4.3, formula
Calculating to obtain a sampling interval M2When the total number of the sampling points of the SAR array system after uniform sparse sampling is 6, the total number is recorded as
Wherein
Representing the sign of the rounding operation, N s32 is the number of sampling points of the radar azimuth direction initialized in the step 1, Nc＝32Initializing the number of cross-course sampling points in the step 1;
Echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcUsing the uniform sparse sampling method defined by 10, the sampling interval is M2Obtaining corresponding distance compressed echo data s through uniform sparse sampling of 62(tk,w2) And array antenna position P (w)2)，w2＝1,2,…,N2Wherein, tkFor the fast time of the distance initialized in step 1, w2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, N R512 is the distance sampling points of the radar system initialized in the step 1;
step 4.4, adopting a formula N0＝N1+N2And calculating the sampling point number of the SAR array system after the coprime sampling, and recording the sampling point number as N0204+ 170-374, where N is1The resulting sampling interval for step 4.2, 204, is M1When the sum is 5, the total number of sampling points of the SAR array system after uniform sparse sampling is N2The resulting sampling interval for step 4.3 is M1702When the sampling point number is 6, the total number of the sampling points of the SAR array system after uniform sparse sampling is obtained;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcAdopting a relatively prime sampling method in the definition 11 to perform relatively prime sampling to obtain corresponding distance-compressed echo data s 0(tk,w0) And array antenna position P (w)0)，w0＝1,2,…,N0Wherein, tkFor the fast time of the distance initialized in step 1, w0Indicating the sequence number of each array element after cross-prime sampling, N R512 is the number of sampling points in the distance direction of the initialized radar system in step 1, NsInitializing radar azimuth sampling points in step 1 as 32，NcInitializing the number of cross-course sampling points in the step 1 as 32;
step 5, constructing a measurement matrix according to the data after SAR distance compression after uniform sparse sampling and cross-prime sampling in the step 4 respectively:
step 5.1, obtaining array SAR system parameters through initialization in step 1, obtaining observation scene target space parameters through initialization in step 2 and obtaining a sampling interval M in step 41Uniformly sparsely sampled array antenna position P (w) of 51)，w1＝1,2,…,N1Adopting a construction method of defining 7-medium compressed sensing SAR measurement matrix to obtain a sampling interval M1A measurement matrix of the echo data after uniform sparse sampling, denoted as a1Measurement matrix A1Of dimension N1×NXNYWherein w is1Representing a sampling interval of M1Number of each array element after 5-hour uniform sparse sampling, N1The resulting sampling interval for step 4.2, 204, is M1When the sum is 5, the total number of sampling points of the SAR array system after uniform sparse sampling is NX31 and N Y31 is the total number of unit grids of the target space of the initialized observation scene in the step 2 on the horizontal axis X and the horizontal vertical axis Y respectively;
step 5.2, obtaining array SAR system parameters through initialization in the step 1, obtaining observation scene target space parameters through initialization in the step 2 and obtaining a sampling interval M in the step 42Uniformly sparsely sampled array antenna position P (w) of 62)，w2＝1,2,…,N2Adopting a construction method of defining 7-medium compressed sensing SAR measurement matrix to obtain a sampling interval M2A measurement matrix of the echo data after uniform sparse sampling, denoted as a2Measurement matrix A2Of dimension N2×NXNYWherein w is2Representing a sampling interval of M2Number of each array element after 6-hour uniform sparse sampling, N2The resulting sampling interval for step 4.3 is M1702When the sum is 6, the total number of sampling points of the SAR array system after uniform sparse sampling is NX31 and NY31 is step 2 respectivelyThe total number of unit grids of an observation scene target space on a horizontal axis X and a horizontal vertical axis Y is initialized;
step 5.3, utilizing the array SAR system parameters obtained by the initialization in the step 1, the observation scene target space parameters obtained by the initialization in the step 2 and the array antenna position P (w) after the co-prime sampling obtained in the step 40)，w0＝1,2,…,N0Obtaining a measurement matrix of the echo data after the cross-prime sampling by adopting a construction method of defining a 7-medium compressed sensing SAR measurement matrix, and marking the measurement matrix as A 0Measuring matrix A0Of dimension N0×NXNYWherein w is0Indicating the sequence number of each array element after cross-prime sampling, N0374 is the total number of sampling points of the SAR array system after the coprime sampling, NX31 and NY31 is the total number of unit grids of the target space of the initialized observation scene in the step 2 on the horizontal axis X and the horizontal vertical axis Y respectively;
step 6, sparse imaging is carried out by adopting a Sparse Bayesian Reconstruction (SBRIM) method based on iterative minimization:
step 6.1, according to the echo signal s1(tk,w1) And the measurement matrix A1，tk＝1,2,…,NR，w1＝1,2,…,N1Adopting an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm defined 9 to perform imaging processing to obtain a sampling interval M1And (5) recording the imaging result of the sparse reconstruction of the echo data after the uniform sparse sampling as
Wherein the content of the first and second substances,
has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w1Representing a sampling intervalIs M1Number of each array element after 5-hour uniform sparse sampling, N1The sampling interval obtained for step 4.2, 204, is M1When the sum is 5, the total number of sampling points of the SAR array system after uniform sparse sampling is NX＝31、NY31 and NRRespectively, 512 represents the total number of unit grids in the horizontal axis X, the horizontal axis Y and the distance direction R of the target space of the observation scene initialized in the step 2, and T represents the transposition operation of the matrix;
Step 6.2, according to the echo signal s2(tk,w2) And the measurement matrix A2，tk＝1,2,…,NR，w2＝1,2,…,N2Adopting an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm defined by 9 to perform imaging processing to obtain a sampling interval M26, recording as the imaging result of sparse reconstruction of the echo data after uniform sparse sampling
Wherein
Has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w2Representing a sampling interval of M2Number of each array element after 6-hour uniform sparse sampling, N2The resulting sampling interval for step 4.3 is M1702When the sum is 6, the total number of sampling points of the SAR array system after uniform sparse sampling is NX＝31、NY31 and NRRespectively, 512 represents the total number of unit grids in the horizontal axis X, the horizontal axis Y and the distance direction R of the target space of the observation scene initialized in the step 2, and T represents the transposition operation of the matrix;
step 6.3, according to the echo signal s0(tk,w0) And the measurement matrix A0，tk＝1,2,…,NR，w0＝1,2,…,N0Imaging processing is carried out by adopting an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm defined 9, and an echo data sparse reconstruction imaging result after cross-prime sampling is obtained and recorded as
Wherein
Has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w0Indicating the sequence number of each array element after cross-prime sampling, N 0374 is the total number of sampling points of the SAR array system after the coprime sampling, NX＝31、NY31 and NRRespectively, 512 represents the total number of unit grids in the horizontal axis X, the horizontal axis Y and the distance direction R of the target space of the observation scene initialized in the step 2, and T represents the transposition operation of the matrix;
step 7, performing grating lobe suppression fusion on the sparse imaging result obtained after uniform sparse sampling and cross-prime sampling:
initializing a dimension NR×NXNYIs marked as
Wherein
k＝1,2,…,NR，i＝1,2,…,NXNYWherein N isX＝31、NY31 and NRRespectively counting the total number of the unit grids in the horizontal axis X, the horizontal axis Y and the distance direction R of the target space of the initial observation scene in the step 2;
using a formula
k＝1,2,…,NR，i＝1,2,…,NXNYAnd (4) comparing the imaging result obtained in the step (6)
And
are compared element-by-element, wherein,
abs represents absolute value calculation, min represents minimum value calculation, and T represents transposition calculation of a matrix; calculating to obtain alphai(k)、βi(k) And gammai(k) Minimum value of (2)
Will be provided with
Is assigned as
Namely, it is
According to
Get the ith element of the matrix S
Reassigned values;
according to
Obtaining a matrix S after reassignment, wherein S is a sparse reconstruction result after grating lobe fusion suppression, and
and 8, rearranging to obtain a final three-dimensional sparse imaging result:
n obtained in the step 7 R×NXNYObtaining a dimension sparse reconstruction result S by adopting a matrix dimension conversion method adopting definition 13 to obtain NX×NY×NRThe three-dimensional reconstruction result is marked as I, the I is the three-dimensional sparse imaging result after the co-prime array decomposition and fusion, wherein N isX＝31、NY31 and NRRespectively counting the total number of the unit grids in the horizontal axis X, the horizontal axis Y and the distance direction R of the target space of the initial observation scene in the step 2;
at this point, the three-dimensional SAR sparse imaging result based on array decomposition and fusion is obtained, and the whole method is finished.
Computer simulation and actual measurement data results prove that by combining the advantages of a co-prime sampling method and a compressed sensing sparse reconstruction method, the invention utilizes co-prime sampling to reduce the sampling data, is more convenient for system realization compared with the traditional random sampling method, and can effectively inhibit grating lobes and false targets and improve the imaging quality compared with the traditional sparse imaging method.
Claims (1)
1. A three-dimensional SAR sparse imaging method based on decomposition and fusion of a co-prime array is characterized by comprising the following steps:
step 1, initializing array SAR system parameters:
initializing array SAR system parameters, comprising: the radar carrier wave length is marked as lambda; carrier frequency of radar emission signal, denoted f c(ii) a Bandwidth of radar emission signal, denoted Br(ii) a The pulse time width of radar emission is marked as Tr(ii) a Radar sampling frequency, denoted Fs(ii) a Radar emissionFrequency modulation slope of signal, noted as fdr(ii) a The central incident angle of the radar beam is recorded as theta; the propagation speed of the electromagnetic waves in the air is marked as C; the height of the array platform is marked as H; the length of the motion track of the azimuth antenna is marked as L _ a; the length of the cross-course array is marked as L _ c; an observation space of the array radar platform is set as a ground three-dimensional coordinate system and is marked as X-Y-Z, wherein X represents a horizontal plane horizontal axis, Y represents a horizontal plane longitudinal axis, and Z represents a horizontal plane vertical axis; the distance direction sampling point number of the radar system is recorded as NR(ii) a Sampling point number of radar azimuth, marked as Ns(ii) a The number of cross-course sampling points is recorded as Nc(ii) a The position of each array element of the array antenna is marked as P (w),
wherein s is the azimuth slow moment, l is the cross-course sampling point position, w is the serial number of each array element of the antenna, NsNcThe total number of array elements of the array antenna is; the fast moment of distance is recorded as tk，tk＝1,2,…,NR(ii) a Position vectors P (w) of each array element of the array antenna are determined in SAR observation scheme design; according to the SAR imaging system scheme and the observation scheme, the parameters of an initialized imaging system required by the SAR imaging method are known;
Step 2, initializing observation scene target space parameters of the array SAR:
initializing a scene measurement target space parameter of the array SAR, comprising the following steps: a space rectangular coordinate system X-Y-R formed by a radar beam irradiation field slant distance plane Y-R and a horizontal plane horizontal axis X vertical to the horizontal plane upwards is used as an observation scene target space omega of the array SAR0Wherein, the horizontal plane horizontal axis X and the vertical axis Y of the observation scene target space are the same as the horizontal plane horizontal axis X and the vertical axis Y of the radar platform observation space in the step 1, and R represents the radar distance direction;
observing a target space omega of a scene0Uniformly divided into three-dimensional discrete resolution unit grids with equal size, and recorded as omega0(i, j, k), wherein i, j, k are natural integers respectively, and i is 1,2, …, NX，j＝1,2,…,NY，k＝1,2,…,NRAnd i is recorded as omega0(i, j, k) in the horizontal planeThe ith cell of the horizontal axis X, j being Ω0(i, j, k) the jth cell on the horizontal plane vertical axis Y, k being denoted as Ω0(i, j, k) the k-th cell in the distance direction R, NX、NYAnd NRRespectively recorded as the target space omega of the observation scene0The total number of unit grids in the horizontal axis X, the horizontal vertical axis Y and the distance direction R,
and dr＝C/FsAnd/2 is expressed as the adjacent unit spacing of the unit grid in the horizontal axis X, the horizontal vertical axis Y and the distance direction R respectively, wherein WxFor observing a scene target space omega 0Horizontal plane X of the scene size, WyFor observing a scene target space omega0Horizontal plane Y scene range size, C and FsRespectively setting the propagation speed of the electromagnetic wave initialized in the step 1 in the air and the radar sampling frequency; three-dimensional space omega0The dimension of (i, j, k) is NX×NY×NR(ii) a Target space parameters of an observation scene of the initialized array SAR are known;
step 3, generating original echo data, and performing range direction pulse compression to obtain echo data after pulse compression:
raw echo data of array SAR, denoted as s0(tk,w)，tk＝1,2,…,NR，w＝1,2,…,NsNcWherein, tkThe fast time of the distance initialized in step 1, w is the serial number of each array element of the antenna, NRNumber of sampling points in the distance direction for initializing the radar system in step 1, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1; in array SAR practical imaging, raw echo data s0(tkW) is provided by a data receiver;
original echo data s are subjected to range direction pulse compression by adopting synthetic aperture radar echo data0(tk,w)，tk＝1,2,…,NR，w＝1,2,…,NsNcPerforming range-wise pulse compression to obtainThe array SAR echo data after the distance direction compression is recorded as src(tk,w)；
Step 4, respectively carrying out uniform sparse sampling and co-prime sampling on the SAR echo data of the array in the step 3 to obtain echo data after uniform sparse sampling and co-prime sampling:
Step 4.1, two integers which are mutually prime numbers are initialized and are respectively recorded as prime numbers M1And prime number M2；
Step 4.2, formula
Calculating to obtain a sampling interval M1And then, the total number of sampling points of the SAR array system after uniform sparse sampling is recorded as N1Wherein, in the step (A),
representing the sign of the rounding operation, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcAdopting a uniform sparse sampling method, and carrying out sampling at an interval of M1To obtain corresponding distance compressed echo data s1(tk,w1) And array antenna position P (w)1)，w1＝1,2,…,N1Wherein, tkFor the fast time of the distance initialized in step 1, w1Representing a sampling interval of M1Sequence number of each array element after time-uniform sparse sampling, NRInitializing the distance direction sampling points of the radar system in the step 1;
step 4.3, formula
Calculating to obtain a sampling interval M2Is uniform in time and uniformityAnd the total number of sampling points of the SAR array system after sparse sampling is recorded as N2Wherein
Representing the sign of the rounding operation, NsInitializing radar azimuth sampling point number N in step 1 cInitializing a cross-course sampling point number in the step 1;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcAdopting a uniform sparse sampling method, and carrying out sampling at an interval of M2To obtain corresponding distance compressed echo data s2(tk,w2) And array antenna position P (w)2)，w2＝1,2,…,N2Wherein, tkFor the fast time of the distance initialized in step 1, w2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, NRInitializing the distance direction sampling points of the radar system in the step 1;
step 4.4, adopting a formula N0＝N1+N2And calculating the sampling point number of the SAR array system after the coprime sampling, and recording the sampling point number as N0Wherein N is1The sampling interval obtained for step 4.2 is M1The total number of sampling points N of the SAR array system after uniform sparse sampling2The sampling interval obtained for step 4.3 is M2The total number of sampling points of the SAR array system after uniform sparse sampling is calculated;
echo data s obtained in step 3 after distance compressionrc(tkW) and the position P (w), t of each array element of the array antenna initialized in the step 1k＝1,2,…,NR，w＝1,2,…,NsNcAdopting a co-prime sampling method to perform co-prime sampling to obtain corresponding distance compressed echo data s 0(tk,w0) And array antenna position P (w)0)，w0＝1,2,…,N0Wherein, tkFor the fast time of the distance initialized in step 1, w0Indicating the sequence number of each array element after cross-prime sampling, NRNumber of sampling points in the distance direction for initializing the radar system in step 1, NsInitializing radar azimuth sampling point number N in step 1cInitializing the number of cross-course sampling points in the step 1;
step 5, constructing a measurement matrix according to the data after SAR distance compression after uniform sparse sampling and cross-prime sampling in the step 4 respectively:
step 5.1, obtaining array SAR system parameters through initialization in step 1, obtaining observation scene target space parameters through initialization in step 2 and obtaining a sampling interval M in step 41Uniformly sparsely sampled array antenna position P (w)1)，w1＝1,2,…,N1Obtaining a sampling interval M by adopting a compressed sensing SAR measurement matrix construction method1The measurement matrix of the echo data after uniform sparse sampling is marked as A1Measurement matrix A1Of dimension N1×NXNYWherein w is1Representing a sampling interval of M1Sequence number of each array element after time-uniform sparse sampling, N1The sampling interval obtained for step 4.2 is M1The total number of sampling points N of the SAR array system after uniform sparse samplingXAnd NYRespectively initializing the total number of unit grids of the observation scene target space in the horizontal axis X and the horizontal vertical axis Y in the step 2;
Step 5.2, obtaining array SAR system parameters through initialization in the step 1, obtaining observation scene target space parameters through initialization in the step 2 and obtaining a sampling interval M in the step 42Uniformly sparsely sampled array antenna position P (w)2)，w2＝1,2,…,N2Obtaining a sampling interval M by adopting a compressed sensing SAR measurement matrix construction method2The measurement matrix of the echo data after uniform sparse sampling is marked as A2Measurement matrix A2Of dimension N2×NXNYWherein w is2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, N2Is the step of4.3 obtaining a sampling interval M2The total number of sampling points N of the SAR array system after uniform sparse samplingXAnd NYRespectively initializing the total number of unit grids of the observation scene target space in the horizontal axis X and the horizontal vertical axis Y in the step 2;
step 5.3, utilizing the array SAR system parameters obtained by the initialization in the step 1, the observation scene target space parameters obtained by the initialization in the step 2 and the array antenna position P (w) after the co-prime sampling obtained in the step 40)，w0＝1,2,…,N0Obtaining a measurement matrix of the echo data after the cross-prime sampling by adopting a compressed sensing SAR measurement matrix construction method, and marking the measurement matrix as A0Measurement matrix A0Of dimension N0×NXNYWherein w is0Indicating the sequence number of each array element after cross-prime sampling, N 0The total number of sampling points N of the SAR array system after the coprime samplingXAnd NYRespectively initializing the total number of unit grids of the observation scene target space in the horizontal axis X and the horizontal vertical axis Y in the step 2;
step 6, sparse imaging is carried out by adopting a Sparse Bayesian Reconstruction (SBRIM) method based on iterative minimization:
step 6.1, according to the echo signal s1(tk,w1) And the measurement matrix A1，tk＝1,2,…,NR，w1＝1,2,…,N1Performing imaging processing by using an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm to obtain a sampling interval M1The imaging result of sparse reconstruction of the echo data after uniform sparse sampling is recorded as
Wherein the content of the first and second substances,
has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w1Representing a sampling interval of M1Sequence number of each array element after time-uniform sparse sampling, N1The sampling interval obtained for step 4.2 is M1The total number of sampling points N of the SAR array system after uniform sparse samplingX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
step 6.2, according to the echo signal s2(tk,w2) And the measurement matrix A2，tk＝1,2,…,NR，w2＝1,2,…,N2Performing imaging processing by using an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm to obtain a sampling interval M 2The sparse reconstruction imaging result of the echo data after the uniform sparse sampling is recorded as
Wherein
Has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w2Representing a sampling interval of M2Sequence number of each array element after time-uniform sparse sampling, N2The sampling interval obtained for step 4.3 is M2The total number of sampling points N of the SAR array system after uniform sparse samplingX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
step 6.3, according to the echo signal s0(tk,w0) And the measurement matrix A0，tk＝1,2,…,NR，w0＝1,2,…,N0Performing imaging processing by using an iterative minimization sparse Bayesian sparse reconstruction (SBRIM) -based imaging algorithm to obtain an echo data sparse reconstruction imaging result after cross-prime sampling, and recording the result as a cross-prime sampling sparse reconstruction imaging result
Wherein
Has a dimension of NR×NXNY，
Dimension NR×1，i＝1,2,…,NXNYWherein t iskFor the fast time of the distance initialized in step 1, w0Indicating the sequence number of each array element after cross-prime sampling, N0The total number of sampling points N of the SAR array system after the coprime samplingX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
step 7, performing grating lobe suppression fusion on the sparse imaging result obtained after uniform sparse sampling and cross-prime sampling:
Initializing a dimension NR×NXNYIs marked as
Wherein
Wherein N isX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
using a formula
The imaging result obtained in the step 6 is processed
And
are compared element-by-element, wherein,
abs represents absolute value calculation, min represents minimum value calculation, and T represents transposition calculation of a matrix; calculating to obtain alphai(k)、βi(k) And gammai(k) Minimum value of (2)
Will be provided with
The k-th element in (b) is assigned a value of
Namely, it is
According to
Get the ith element of the matrix S
Reassigned values;
according to
Obtaining a matrix S after reassignment, wherein S is a sparse reconstruction result after grating lobe fusion suppression, and
and 8, rearranging to obtain a final three-dimensional sparse imaging result:
n obtained in the step 7R×NXNYObtaining a dimension sparse reconstruction result S by adopting a matrix dimension conversion method to obtain NX×NY×NRThe three-dimensional reconstruction result is marked as I, the I is the three-dimensional sparse imaging result after the co-prime array decomposition and fusion, wherein N isX、NYAnd NRRespectively initializing the total number of the grid cells of the observation scene target space in the horizontal axis X, the horizontal longitudinal axis Y and the distance direction R in the step 2;
and obtaining a three-dimensional SAR sparse imaging result based on array decomposition and fusion, and finishing the whole method.
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