CN111679277B - Multi-baseline chromatography SAR three-dimensional imaging method based on SBRIM algorithm - Google Patents

Multi-baseline chromatography SAR three-dimensional imaging method based on SBRIM algorithm Download PDF

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CN111679277B
CN111679277B CN202010467200.3A CN202010467200A CN111679277B CN 111679277 B CN111679277 B CN 111679277B CN 202010467200 A CN202010467200 A CN 202010467200A CN 111679277 B CN111679277 B CN 111679277B
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CN111679277A (en
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张晓玲
陈益飞
张星月
师君
韦顺军
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a multi-baseline chromatography SAR three-dimensional imaging method based on an SBRIM algorithm, which is characterized in that the SBRIM algorithm is introduced into the multi-baseline chromatography SAR three-dimensional imaging, firstly, distance-azimuth two-dimensional SAR imaging is carried out on data obtained by each voyage, then, image registration is carried out on the obtained SAR imaging, and an observation vector is obtained; obtaining a measurement matrix according to a chromatography direction signal measurement model, initializing SBRIM algorithm parameters, and calculating a diagonal matrix; and then estimating a scattering coefficient vector and noise power, and finally judging whether the iteration termination condition is met or not, and reconstructing a height direction signal by finishing the operation until the termination condition is reached to obtain a three-dimensional imaging result. Compared with the traditional sparse reconstruction algorithm, the method has the advantages that the advantages of three-dimensional imaging of the traditional algorithm under sparse aerial distribution can be kept, the number of algorithm parameters is reduced, the chromatographic resolution is improved, the three-dimensional image can be reconstructed under less observation data, and the precision of signal sparse reconstruction is improved.

Description

Multi-baseline chromatography SAR three-dimensional imaging method based on SBRIM algorithm
The technical field is as follows:
the invention belongs to the technical field of radar, and particularly relates to the technical field of three-dimensional imaging in a chromatography synthetic aperture radar.
Technical background:
synthetic Aperture Radar (SAR) is a high-resolution Radar that can acquire two-dimensional high-resolution images of ground targets around the clock and all the day. The traditional SAR imaging technology cannot acquire three-dimensional information of an observation space, and the problems of shielding, space blurring, top-bottom inversion and the like exist in the imaging process, so that three-dimensional imaging becomes an urgent requirement for the development of the SAR imaging technology. The multi-baseline tomography SAR three-dimensional imaging technology is an extension of the traditional two-dimensional SAR imaging technology, and aperture synthesis is carried out on an SAR image sequence acquired by multiple-time flying over in the tomography direction, so that the traditional SAR imaging is extended to the third dimension, the resolution in the tomography direction is obtained, and the three-dimensional imaging of a scene is realized. The multi-baseline chromatography SAR has gained wide attention and application in various fields, and has become a hotspot for researching SAR technologies at home and abroad.
In the tomography SAR imaging processing, in order to realize high-resolution three-dimensional imaging, the acquired data must meet the sampling theorem, however, in practical situations, the number of the navigated is insufficient or non-uniform, and the traditional three-dimensional imaging method is difficult to meet the practical requirements. To address this problem, r.bamler, xx.zhu, a.budillon et al apply a compressive sensing method to tomographic SAR imaging. The current sparse reconstruction algorithms include Orthogonal Matching Pursuit (OMP), Bayesian Compressive Sensing (BCS) imaging algorithm, and the like. The OMP algorithm is widely used due to the advantages of simple structure, low calculation complexity and short operation time, but the OMP algorithm needs to preset sparsity, and needs to carry out approximate estimation of the sparsity in the actual imaging processing, which can cause inaccurate reconstruction result and bring serious reconstruction error; the BCS algorithm selects different prior probability distributions of different observation models, can construct a reconstruction model of a sparse signal more flexibly, and has better estimation performance and flexibility compared with an OMP algorithm, but the BCS algorithm needs to set a plurality of algorithm parameters, and the performance of the BCS algorithm is reduced due to improper selection of the algorithm parameters. Therefore, under less observation data, in order to reconstruct a three-dimensional image and improve the precision of signal sparse reconstruction, the invention provides a multi-baseline chromatography SAR three-dimensional imaging method based on an Iterative minimization Bayesian Iterative reconstruction (SBRIM) algorithm.
The invention content is as follows:
the invention discloses a multi-baseline chromatography SAR three-dimensional imaging method based on an SBRIM algorithm, which is characterized in that the SBRIM algorithm is introduced into the multi-baseline chromatography SAR three-dimensional imaging, firstly, distance-azimuth two-dimensional SAR imaging is carried out on data obtained by each voyage, then, image registration is carried out on the obtained SAR imaging, an observation vector is obtained, then, a measurement matrix is obtained according to a chromatography direction signal measurement model, then, SBRIM algorithm parameters are initialized, an iteration stop condition is set, a diagonal matrix is calculated, then, a scattering coefficient vector is estimated, then, noise power is estimated, finally, whether the iteration stop condition is met or not is judged, and a height direction signal is reconstructed after the operation is finished until the termination condition is reached, so that a three-dimensional imaging result is obtained. The method can reconstruct a three-dimensional image under less observation data, and improve the precision of signal sparse reconstruction.
For the convenience of describing the present invention, the following terms are first defined:
definition 1 synthetic aperture radar
The synthetic aperture radar is a synthetic aperture radar technology which fixes a radar on a load motion platform, combines the motion of the platform to synthesize an equivalent array to realize the resolution in the array direction, and then realizes one-dimensional distance imaging by utilizing the radar beam to delay echoes, thereby realizing two-dimensional imaging of an observed target. See the literature "synthetic aperture radar imaging principle", edited by buzz, electronic technology university press.
Definition 2, vertical baseline and parallel baseline of synthetic aperture radar
The synthetic aperture radar baseline length refers to the distance between two antennas in the synthetic aperture radar system, the vertical baseline refers to the component of the actual baseline which is vertical to the radar sight line in the track method plane, and the parallel baseline refers to the component of the actual baseline which is parallel to the radar sight line in the track method plane. In the invention, the vertical baseline of the synthetic aperture radar system is marked as b⊥Parallel base line is denoted as b||. See the literature "synthetic aperture radar imaging principle", edited by buzz, electronic technology university press.
Definition 3, norm
Let X be a complex field
Figure GDA0003516052250000021
Upper linear space, wherein
Figure GDA0003516052250000022
Represents a complex field if it satisfies the following properties: the | | | X | |, is greater than or equal to 0, and only X | | | 0 when | | X | | |, 0; i | aX | ═ a | | | | | X | |, where a is an arbitrary constant; i X1+X2||≤||X1||+||X2If is called X norm in X space, X is1And X2As any two values in X space. For an N × 1-dimensional discrete signal vector X ═ X1,x2,...,xN]TWhere T is the sign of the transpose operation, L of the vector XPNorm expression is
Figure GDA0003516052250000023
Wherein xiFor the ith element of vector X, Σ | represents the sign of the sum of absolute values operation, L of vector X2Norm expression is
Figure GDA0003516052250000024
See the literature "matrix theory", editions of Huangting, etc., the first edition of higher education publishers, for details.
Definition 4: diagonal matrix
The square matrix with all zero elements except the main diagonal is called diagonal matrixArray, if the main diagonal element is a1,a2,...,anThen the corresponding diagonal matrix is diag { a }1,a2,...,an}. See "matrix theory", Huang Ting Zhu, etc., higher education Press for details.
Definition 5, conjugate transpose
The conjugate transpose is to transpose the complex matrix and take the conjugate, denoted as AHAnd the calculation can be carried out by a standard conjugate transpose method. See "linear algebra", university of peer department of mathematics, higher education press for details.
Definition 6, standard matrix inversion method
Assuming matrix a and matrix B, if AB ═ E, where E is the identity matrix, then matrix B is said to be the right inverse of matrix a, and matrix B is usually written as a-1Calculating the matrix A by a standard matrix inversion method according to the matrix A-1. See "matrix theory", Huang Ting Zhu, etc., higher education Press for details.
Definition 7 and 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 8 and standard two-dimensional SAR imaging method
The purpose of the imaging process is to obtain corresponding point targets from the signal space and distinguish the point targets from adjacent targets, thereby reconstructing a target space corresponding to the scene. The standard two-dimensional SAR imaging method is a process of focusing and imaging an echo data signal of a synthetic aperture radar by using parameters such as a synthetic aperture radar transmitting signal and adopting technologies such as matched filtering. Details are found in the literature "Piyamii, Yangjianyu, Yusheng, etc. the imaging principle of synthetic aperture radar [ M ]. Chengdu, university of electronic science and technology, Press, 2007, 44-65"
Definition 9, compressed sensing sparse reconstruction theory
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:
Figure GDA0003516052250000031
wherein the content of the first and second substances,
Figure GDA0003516052250000032
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 10, 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"
The invention provides a multi-baseline chromatography SAR three-dimensional imaging method based on an SBRIM algorithm, which comprises the following steps:
step 1, initializing parameters of a multi-baseline chromatography SAR system
Initializing multi-baseline tomosynthesis SAR system parameters includes: the number of voyage times is marked as N; vertical base line, denoted b⊥nParallel base line, denoted b||nN is 1,2,., N, where N is the number of flights; carrier frequency of radar emission signal fc(ii) a The frequency modulation slope of the radar emission signal is fdr(ii) a The pulse repetition frequency of the radar system is PRF; the bandwidth of the radar emission signal is marked as Br(ii) a The propagation speed of the electromagnetic waves in the air is marked as C; the fast time of the distance is marked as T, T is 1,2, T, T is the total number of the fast time of the distance,the azimuth slow time is recorded as l, wherein l is 1,2, K, and K is the total number of the azimuth slow time; the parameters are all standard parameters of the SAR system and are determined in the design of a multi-baseline chromatography SAR observation scheme; according to the multi-baseline tomographic SAR imaging system scheme and the observation scheme, initialized imaging system parameters required by the SAR imaging method are known.
Step 2: observation scene target space parameter for initializing multi-baseline chromatography SAR
Initializing observation scene target space parameters of the multi-baseline tomography SAR comprises the following steps: taking a space rectangular coordinate system formed by a ground plane of a radar beam irradiation area and a unit vector vertical to the ground plane upwards as an observation scene target space omega of the multi-baseline tomography SAR, wherein omega is Mx×My×MzA pixel; uniformly dividing an observation scene target space omega into three-dimensional unit grids with equal size, called resolution units, and respectively recording the side lengths of the three-dimensional unit grids in the horizontal transverse direction, the horizontal longitudinal direction and the height direction as dx，dyAnd dzThe number of unit grids in the observation scene target space in the horizontal transverse direction, the horizontal longitudinal direction and the height direction is Mx,MyAnd MzThe unit grid size is the traditional theoretical imaging resolution of the multi-baseline chromatography SAR system; a two-dimensional plane imaging space is formed by the horizontal transverse direction and the horizontal longitudinal direction, and the position of the mth element of the tth equidistant stereo unit grid on the two-dimensional plane imaging space is recorded as
Figure GDA0003516052250000041
Wherein m is (m)y-1)Mx+mxM is the t-th equidistant solid unit grid height of the two-dimensional plane-dimensional imaging space to the total number of the solid unit grids, and M is Mx·My，mx＝1,...,Mx，my＝1,...,MyT is the total number of the fast-going moments initialized in step 1.
Recording the scattering coefficient of the mth element of the tth equidistant stereo unit grid in the target space of the observation scene as deltatmM1, 2,., M, T1, 2,., T; using a formula
Figure GDA0003516052250000051
Calculating to obtain a scattering coefficient matrix, and recording the scattering coefficient matrix as delta, wherein the scattering coefficient matrix delta is composed of M rows and T columns, T is the total number of the distance fast-forward moments obtained by initialization in the step 1, M is the total number of the T-th equidistant stereo unit grid array of the two-dimensional planar imaging space to the stereo unit grid, and M is equal to Mx·My(ii) a According to the SAR imaging method processing scheme of the multi-baseline tomography SAR based on the SBRIM algorithm, the observation scene target space parameters required for initializing the multi-baseline tomography SAR are known.
Step 3, generating original echo data, and performing range-azimuth two-dimensional SAR imaging on each echo data acquired by navigation
The N-th raw echo data of the multi-baseline SAR at the l-th azimuth slow time and the T-th range fast time is denoted as s (T, l, N), T being 1, 2.
Performing distance-direction two-dimensional SAR imaging on the original echo data s (t, l, n) by adopting a standard two-dimensional SAR imaging method in definition 8 to obtain image data of each voyage
Figure GDA0003516052250000052
T is 1,2, T, l is 1,2, T, K, N is 1,2, N, where T is the total number of the distance fast moments initialized in step 1, T is the distance fast moments, K is the total number of the azimuth slow moments initialized in step 1, l is the azimuth slow moments, N is the number of times of flight initialized in step 1, and N is a sequence number of flight.
Step 4, carrying out image registration on the obtained SAR imaging, and carrying out deskew processing to obtain an observation vector
And (2) registering the image sequences acquired by each flight in the step 3 by using a conventional image registration method, so that the same distance-orientation unit corresponds to the same scattering point in the target scene, and obtaining a registered image sequence h (T, l, N), wherein T is 1, 2.
Using a formula
Figure GDA0003516052250000053
N1, 2, N, calculating the slope distance R of each passing platform from the reference pointn(s) wherein the target position of the chromatographic orientation point is (r)0S) each passing radar platform is in the position of (b)||n,b⊥n). Using a formula
Figure GDA0003516052250000054
N is 1,2, N, and a deskewed observation signal vector g (t, l, N) is calculated, where h (t, l, N) is a registered image sequence, and R is a registered image sequencen(0) Is a reference point (r)00) a reference slant distance to each navigation radar platform, where T is 1,2,., T, l is 1,2,., K, N is 1,2,., N, where T is a total number of fast-going moments of distances initialized in step 1, T is a total number of fast-going moments of distances, K is a total number of slow-going moments of azimuth initialized in step 1, l is a slow-going moment of azimuth, N is a number of navigation times initialized in step 1, and N is a navigation sequence number.
And 5: constructing an observation vector matrix
Using g ═ g1,g2,...,gN]TConstructing an observation vector matrix, wherein gnG (T, l, N), T1, 2, a, T, l 1,2, a, K, N1, 2, a, N, T being the signal after deskewing in step 4, T being the total number of distance fast times initialized in step 1, T being the total number of distance fast times, K being the total number of azimuth slow times initialized in step 1, l being the azimuth slow time, N being the number of times of flight initialized in step 1, N being each flight number.
Step 6, discretizing a scene target and constructing a measurement matrix
Using the formula
Figure GDA0003516052250000061
Calculating to obtain the spatial frequency of the nth orbital tomography direction, and recording as xinN is 1,2,. cndot.n; discretizing the position of the scene target in tomography by D uniform points sdD1, 2, D, using the formula
Figure GDA0003516052250000062
Calculating to obtain a measurement matrix, and recording as phi; wherein the target position of the chromatographic directional point is (r)0,s)，b⊥nFor the vertical baseline of the nth track auxiliary image initialized in step 1 with respect to the main image, b||nFor the parallel baseline of the nth track side image initialized in step 1 with respect to the main image, fcC is the propagation speed of the electromagnetic wave initialized in the step 1 in the air.
Step 7, initializing SBRIM algorithm parameters
The initialization parameters of the SBRIM algorithm comprise: a weighting coefficient, noted as α; reconstructing an error threshold, and recording as epsilon; noise power, denoted as β; total number of iterations, denoted Iiter(ii) a The iteration times are marked as k; the smoothing factor is recorded as eta; the diagonal matrix control parameter is marked as p; using a formula
Figure GDA0003516052250000063
Calculating to obtain an initialized signal estimation value
Figure GDA0003516052250000064
Wherein g is the observation vector matrix in step 5, Φ is the measurement matrix in step 6, and H is the conjugate transpose operator in definition 5.
Step 8, calculating a diagonal matrix
Updating iteration times, calculating to obtain updated iteration times by adopting a formula k which is k +1, and marking as k; using the formula
Figure GDA0003516052250000071
Calculating to obtain a diagonal matrix of the kth iteration, and recording the diagonal matrix as Lambda(k). Wherein N is the number of voyages initialized in step 1, p is the diagonal matrix control parameter initialized in step 7, η is the smoothing factor initialized in step 7,
Figure GDA0003516052250000072
for the scattering coefficient estimate for the ith satellite orbit data in the k-1 iteration cycle, diag {. cndot } is the sign of the diagonal matrix operation in definition 4.
Step 9, estimating scattering coefficient vector
Using the formula alpha(k)＝αβ(k)Calculating to obtain the kth iteration weighting coefficient which is marked as alpha(k)(ii) a Using a formula
Figure GDA0003516052250000073
Calculating to obtain a scattering coefficient vector of the kth iteration, and recording as
Figure GDA0003516052250000074
Where α is the weighting factor initialized in step 7, β(k)For the noise power of the kth iteration, g is the observation vector matrix in step 5, Φ is the measurement matrix in step 6, Λ(k)For the diagonal matrix of the kth iteration in step 7, H is the sign of the conjugate transpose operation in definition 5, (-)-1To define the standard matrix inversion operator in 6.
Step 10, estimating noise power
Using a formula
Figure GDA0003516052250000075
Calculating to obtain the kth iterative noise power which is marked as beta(k). N is the number of voyages initialized in step 1, g is the observation vector matrix in step 5, phi is the measurement matrix in step 6,
Figure GDA0003516052250000076
is the scattering coefficient vector of the kth iteration in step 9, | · | | calving2Is L in definition 32The norm solves the operator.
Step 11, judging whether the iteration termination condition is met, reconstructing height direction information to obtain the final three-dimensional imaging result if the iteration termination condition is met
Figure GDA0003516052250000077
And k is less than or equal to IiterThen, the steps 8 to 11 are continuously executed.
If not satisfied with
Figure GDA0003516052250000078
And k is less than or equal to IiterEither condition, the algorithm iteration terminates, then the output
Figure GDA0003516052250000079
The obtained K iteration scattering coefficient of the SBRIM algorithm
Figure GDA00035160522500000710
Namely the final three-dimensional imaging result of the multi-baseline chromatography SAR. Where ε is the reconstruction error threshold initialized in step 7, IiterFor the total number of iterations initialized in step 7,
Figure GDA00035160522500000711
the vector of scattering coefficient of the kth iteration in step 9, | · | | computationally2Is L in definition 32The norm solves the operator. Through the steps, a multi-baseline tomography SAR three-dimensional imaging result based on the SBRIM algorithm is obtained.
The invention has the innovation points that a multi-baseline tomography SAR three-dimensional imaging method based on an SBRIM algorithm is provided, and aims at the problems of low resolution and fuzziness of the traditional three-dimensional imaging algorithm caused by insufficient number of navigated objects and nonuniform navigated objects in the tomography SAR three-dimensional imaging process.
Compared with the traditional sparse reconstruction algorithm, the method has the advantages that the advantages of three-dimensional imaging under sparse aerial distribution of the traditional algorithm can be kept, the number of algorithm parameters is reduced, the chromatographic resolution is improved, the three-dimensional image can be reconstructed under less observation data, the precision of signal sparse reconstruction is improved, and in addition, a more stable imaging effect can be obtained under the condition of low signal to noise ratio.
Drawings
FIG. 1 is a schematic block flow diagram of a method provided by the present invention;
fig. 2 shows a tomography SAR three-dimensional imaging simulation parameter of the method provided by the present invention.
Detailed Description
The invention mainly adopts a simulation experiment method for verification, and all steps and conclusions are verified to be correct on MATLAB R2017b software. The specific implementation steps are as follows:
step 1, initializing parameters of a multi-baseline chromatography SAR system
Initializing multi-baseline tomosynthesis SAR system parameters includes: the number of voyages is recorded as N-21; vertical base line, denoted b⊥nWherein b is⊥1＝2000m，b⊥n＝(b⊥1-n 200+200) m, n 1, 2.., 21; parallel base lines, denoted b||nWherein b is||1＝0m，b||n0m, n 1,2, 21; carrier frequency of radar emission signal fc10 GHz; the frequency modulation slope of the radar emission signal is fdr＝2×1015Hz/s; the pulse repetition frequency of the radar system is PRF 1024; the bandwidth of the radar emission signal is marked as Br200 MHz; the propagation speed of electromagnetic waves in air is denoted by C3 × 108m/s; the fast time of the distance direction is marked as T, T is 1,2, the.. the T, T is 1024 and is the total number of the fast time of the distance direction, the slow time of the azimuth direction is marked as l, l is 1,2, the.. the K, K is 2048 and is the total number of the slow time of the azimuth direction; the parameters are all standard parameters of the SAR system and are determined in the design of a multi-baseline chromatography SAR observation scheme; according to the multi-baseline tomographic SAR imaging system scheme and the observation scheme, initialized imaging system parameters required by the SAR imaging method are known.
Step 2: observation scene target space parameter for initializing multi-baseline chromatography SAR
Initializing observation scene target space parameters of the array SAR comprises the following steps: taking a space rectangular coordinate system formed by a ground plane of a radar beam irradiation area and a unit vector vertical to the ground plane upwards as an observation scene target space omega of the array SAR; Ω is 101 × 101 × 101 pixels; uniformly dividing an observation scene target space omega into three-dimensional unit grids with equal size, called resolution units, and respectively recording the side lengths of the three-dimensional unit grids in the horizontal transverse direction, the horizontal longitudinal direction and the height direction as dx＝1m，dy1m and dzThe unit grid number of the observation scene space in the horizontal transverse direction, the horizontal longitudinal direction and the height direction is M respectively as 1Mx＝51,My51 and Mz512, the unit grid size is the traditional theoretical imaging resolution of the array SAR system; the horizontal transverse direction and the horizontal longitudinal direction form an array plane dimension imaging space, and the position of the mth element of the tth equidistant stereo unit grid on the array plane dimension imaging space is recorded as
Figure GDA0003516052250000091
Wherein m is 51 (m)y-1)+mxM is the total number of t-th equidistant stereo unit grid array to stereo unit grid of the array plane dimension imaging space, M is Mx×My＝2601，mx＝1,...,51，my＝1,...,51，t＝1,2,...,1024；
Recording the scattering coefficient of the mth element of the tth equidistant stereo unit grid in the target space of the observation scene as delta tm1,2,., 2601, t 1,2,.., 1024; using a formula
Figure GDA0003516052250000092
Calculating to obtain a scattering coefficient matrix, and recording the scattering coefficient matrix as delta, wherein the scattering coefficient matrix delta consists of 2601 rows and 1024 columns; according to the SAR imaging method processing scheme of the multi-baseline tomography SAR based on the SBRIM algorithm, the observation scene target space parameters required for initializing the multi-baseline tomography SAR are known.
Step 3, generating original echo data, and performing range-azimuth two-dimensional SAR imaging on each echo data acquired by navigation
The n-th navigated raw echo data of the multi-baseline SAR in the l-th azimuth slow time and the t-th distance fast time is marked as s (t, l, n), t is 1,2, 1, 1024, l is 1,2, 2048, n is 1,2, 21, wherein t is the distance fast time, l is the azimuth slow time, and n is each navigating sequence number; in multi-baseline tomography SAR real imaging, raw echo data s (t, l, n) is provided by a data receiver.
Distance-direction two-dimensional SAR imaging method for original echo data s (t, l, n) in definition 8 is adopted to carry out distance-direction two-dimensional SAR imagingSAR imaging to obtain image data of each voyage
Figure GDA0003516052250000093
t 1,2, 1, 1024, l 1,2, 2048, n 1,2, 21, where t is the time instant of the fast direction, l is the time instant of the slow direction, and n is the respective flight sequence number.
Step 4, carrying out image registration on the obtained SAR imaging, and carrying out deskew processing to obtain an observation vector
And (3) registering the image sequences acquired by each navigation in the step (3) by using a traditional image registration method, so that the same distance-orientation unit corresponds to the same scattering point in the target scene, and obtaining a registered image sequence h (t, l, n), wherein t is 1,2,., 1024, l is 1,2,., 2048, and n is 1,2,., 21, t is a fast moment of the distance direction, l is a slow moment of the orientation direction, and n is a sequence number of each navigation.
Using a formula
Figure GDA0003516052250000101
n 1,2, 21, calculating the slope distance R of each passing platform from the reference pointn(s) wherein the target position of the chromatographic orientation point is (r)0S) each passing radar platform is in the position of (b)||n,b⊥n). Using a formula
Figure GDA0003516052250000102
n is 1,2, 21, and calculating a deskewed observation signal vector g (t, l, n), where h (t, l, n) is a registered image sequence, and R isn(0) Is a reference point (r)00) a reference slant distance to each passing radar platform, t 1,2,.., 1024, l 1,2,., 2048, n 1,2,. once, 21, where t is a fast time of distance, l is a slow time of azimuth, and n is each passing sequence number.
And 5: constructing an observation vector matrix
Using g ═ g1,g2,...,gN]TConstructing an observation vector matrix, wherein gnG (t, l, n), t 1,2,., 1024, l 1,2,., 2048, n 1,2,., 21, which is the signal after the deskew process in step 4, t is the fast time of the distance direction, l is the slow time of the directionAnd n is each navigation serial number.
Step 6, discretizing a scene target and constructing a measurement matrix
According to the formula
Figure GDA0003516052250000103
Calculating to obtain the spatial frequency of the nth orbital tomography direction, and recording as xi n1,2, ·, 21; and then discretizing the position of the scene target in the tomography direction by D-101 uniform points sd1,2, 101, using the formula
Figure GDA0003516052250000104
Calculating to obtain a measurement matrix, and recording as phi; wherein the target position of the chromatographic directional point is (r)0,s)，b⊥n＝(b⊥1N 200+200) m, n 1,2, 21, the vertical baseline of the nth track sub-image with respect to the main image initialized in step 1, b||n0m, n 1,2, 21, which is the parallel baseline of the nth track sub-image initialized in step 1 with respect to the main image, fcThe carrier frequency of the radar transmission signal initialized in step 1 is 10GHz, and C is 3 × 108And m/s is the propagation speed of the electromagnetic wave initialized in the step 1 in the air.
Step 7, initializing SBRIM algorithm parameters
The initialization parameters of the SBRIM algorithm comprise: the weighting coefficient is recorded as alpha being 1; the reconstruction error threshold is marked as epsilon 10-5(ii) a Noise power, noted as β ═ 1; total number of iterations, denoted Iiter100; the iteration times are recorded as k being 0; smoothing factor, noted as η 10-6(ii) a The diagonal matrix control parameter is recorded as p 1; according to the formula
Figure GDA0003516052250000111
Calculating to obtain an initialized signal estimation value
Figure GDA0003516052250000112
Wherein g is the observation vector matrix in step 5, Φ is the measurement matrix in step 6, and H is the conjugate transpose operator in definition 5.
Step 8, calculating a diagonal matrix
Updating iteration times, calculating to obtain updated iteration times according to a formula k which is k +1, and recording as k; according to the formula
Figure GDA0003516052250000113
Calculating to obtain a diagonal matrix of the kth iteration, and recording the diagonal matrix as Lambda(k). Where N ═ 21 is the number of flights initialized in step 1, p ═ 1 is the diagonal matrix control parameter initialized in step 7, and η ═ 10-6For the smoothing factor initialized in step 7,
Figure GDA0003516052250000114
for the scattering coefficient estimate for the ith satellite orbit data in the k-1 iteration cycle, diag {. cndot } is the sign of the diagonal matrix operation in definition 4.
Step 9, estimating scattering coefficient vector
According to the formula alpha(k)＝αβ(k)Calculating to obtain the kth iteration weighting coefficient which is marked as alpha(k)(ii) a According to the formula
Figure GDA0003516052250000115
Calculating to obtain a scattering coefficient vector of the kth iteration, and recording as
Figure GDA0003516052250000116
Where α ═ 1 is the weighting coefficient initialized in step 7, β(k)For the noise power of the kth iteration, g is the observation vector matrix in step 5, Φ is the measurement matrix in step 6, Λ(k)For the diagonal matrix of the kth iteration in step 7, H is the sign of the conjugate transpose operation in definition 5, (-)-1To define the standard matrix inversion operator in 6.
Step 10, estimating noise power
Using a formula
Figure GDA0003516052250000117
Calculating to obtain the kth iterative noise power which is marked as beta(k). Wherein N-21 is in step 1Initializing the obtained navigation times, g is an observation vector matrix in the step 5, phi is a measurement matrix in the step 4,
Figure GDA0003516052250000118
the vector of scattering coefficient of the kth iteration in step 9, | · | | computationally2Is L in definition 32The norm solves the operator.
Step 11, judging whether the iteration termination condition is met, reconstructing height direction information to obtain the final three-dimensional imaging result if the iteration termination condition is met
Figure GDA0003516052250000121
And k is less than or equal to IiterThen, the steps 8 to 11 are continuously executed.
If not satisfied with
Figure GDA0003516052250000122
And k is less than or equal to IiterEither condition, the algorithm iteration terminates, then the output
Figure GDA0003516052250000123
The obtained K iteration scattering coefficient of the SBRIM algorithm
Figure GDA0003516052250000124
Namely the final three-dimensional imaging result of the multi-baseline chromatography SAR. Wherein ε is 10-5For the reconstruction error threshold initialized in step 7, Iiter100 is the total number of iterations initialized in step 7,
Figure GDA0003516052250000125
the vector of scattering coefficient of the kth iteration in step 9, | · | | computationally2Is L in definition 32The norm solves the operator. Through the steps, a multi-baseline tomography SAR three-dimensional imaging result based on the SBRIM algorithm can be obtained.
The invention introduces the SBRIM algorithm into the tomography SAR imaging by using a small amount of navigation data and conducts sparse reconstruction in the tomography direction to obtain the three-dimensional imaging result of a target scene, compared with the traditional sparse reconstruction method which constructs a measurement matrix by using all echo data, the invention reduces the algorithm operation amount, improves the tomography direction resolution and the signal sparse reconstruction precision, and can obtain more stable imaging effect under the condition of low signal to noise ratio.

Claims (1)

1. A multi-baseline chromatography SAR three-dimensional imaging method based on an SBRIM algorithm is characterized by comprising the following steps:
step 1, initializing parameters of a multi-baseline chromatography SAR system
Initializing multi-baseline tomosynthesis SAR system parameters includes: the number of voyage times is marked as N; vertical base line, denoted b⊥nParallel base line, denoted b||nN is 1,2, …, N, where N is the number of flights; carrier frequency of radar emission signal fc(ii) a The frequency modulation slope of the radar emission signal is fdr(ii) a The pulse repetition frequency of the radar system is PRF; the bandwidth of the radar emission signal is marked as Br(ii) a The propagation speed of the electromagnetic waves in the air is marked as C; distance fast time is marked as T, T is 1,2, …, T, T is the total distance fast time, azimuth slow time is marked as l, l is 1,2, …, K, K is the total azimuth slow time; the parameters are all standard parameters of the SAR system and are determined in the design of a multi-baseline chromatography SAR observation scheme; according to the multi-baseline tomography 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: observation scene target space parameter for initializing multi-baseline chromatography SAR
Initializing observation scene target space parameters of the multi-baseline tomography SAR comprises the following steps: a spatial rectangular coordinate system formed by a ground plane of a radar beam irradiation area and a unit vector vertical to the ground plane upwards is used as an observation scene target space omega of the multi-baseline tomography SAR, wherein omega is Mx×My×MzA pixel; uniformly dividing an observation scene target space omega into three-dimensional unit grids with equal size, called resolution units, and respectively recording the side lengths of the three-dimensional unit grids in the horizontal transverse direction, the horizontal longitudinal direction and the height direction as dx，dyAnd dzObserving the horizontal and horizontal direction of the target space of the sceneThe number of the horizontal and vertical unit grids is Mx,MyAnd MzThe unit grid size is the traditional theoretical imaging resolution of the multi-baseline chromatography SAR system; a two-dimensional plane imaging space is formed by the horizontal transverse direction and the horizontal longitudinal direction, and the position of the mth element of the tth equidistant stereo unit grid on the two-dimensional plane imaging space is recorded as
Figure FDA0003516052240000011
Wherein m is (m)y-1)Mx+mxM is the t-th equidistant solid cell grid height to the total solid cell grid number of the two-dimensional planar imaging space, M is 1, …, Mx·My，mx＝1,…,Mx，my＝1,…,MyT is 1, …, and T is the total number of the distance fast time obtained by initialization in step 1;
recording the scattering coefficient of the mth element of the tth equidistant stereo unit grid in the target space of the observation scene as
Figure FDA0003516052240000012
Figure FDA0003516052240000013
Using a formula
Figure FDA0003516052240000014
Calculating to obtain a scattering coefficient matrix, and recording the scattering coefficient matrix as delta, wherein the scattering coefficient matrix delta is composed of M rows and T columns, T is the total number of the distance fast-forward moments obtained by initialization in the step 1, M is the total number of the T-th equidistant stereo unit grid array of the two-dimensional planar imaging space to the stereo unit grid, and M is equal to Mx·My(ii) a According to the SAR imaging method processing scheme of the multi-baseline tomography SAR based on the SBRIM algorithm, target space parameters of an observation scene for initializing the multi-baseline tomography SAR are known;
step 3, generating original echo data, and performing range-azimuth two-dimensional SAR imaging on each echo data acquired by navigation
The nth navigated raw echo data of the multi-baseline SAR at the l-th azimuth slow time and the T-th range fast time is denoted as s (T, l, N), T is 1,2, …, T, l is 1,2, …, K, N is 1,2, …, N; in the multi-baseline chromatography SAR actual imaging, original echo data s (t, l, n) is provided by a data receiver;
performing distance-direction two-dimensional SAR imaging on the original echo data s (t, l, n) by adopting a two-dimensional SAR imaging method to obtain image data of each voyage
Figure FDA0003516052240000021
Wherein T is the total number of the distance fast moments initialized in the step 1, T is the distance fast moments, K is the total number of the azimuth slow moments initialized in the step 1, l is the azimuth slow moment, N is the number of voyage times initialized in the step 1, and N is each voyage serial number;
step 4, carrying out image registration on the obtained SAR imaging, and carrying out deskew processing to obtain an observation vector
Registering the image sequences acquired in each voyage in step 3 by using a conventional image registration method, so that the same distance-orientation unit corresponds to the same scattering point in the target scene, and obtaining a registered image sequence h (T, l, N), where T is 1,2, …, T, l is 1,2, …, K, N is 1,2, …, N;
using a formula
Figure FDA0003516052240000022
Calculating the slope distance R between each navigation platform and the reference pointn(s) wherein the target position of the chromatographic orientation point is (r)0S) each passing radar platform is in the position of (b)||n,b⊥n) (ii) a Using a formula
Figure FDA0003516052240000023
Calculating to obtain a de-skewed observation signal vector g (t, l, n), wherein h (t, l, n) is a registered image sequence, and Rn(0) Is a reference point (r)00) reference slope to each of the airborne radar platforms, T1, 2, …, T, l 1,2, …, K, N1, 2, …, N, where T is the total number of fast-forward moments initialized in step 1, and T is the total number of fast-forward momentsAt a fast moment, K is the total number of azimuth slow moments obtained by initialization in the step 1, l is the azimuth slow moment, N is the total number of voyages obtained by initialization in the step 1, and N is a voyage serial number;
and 5: constructing an observation vector matrix
Using g ═ g1,g2,...,gN]TConstructing an observation vector matrix, wherein gnG (T, l, N), T1, 2, …, T, l 1,2, …, K, N1, 2, …, N, and N, where T is the total number of fast-direction moments initialized in step 1, K is the total number of slow-direction moments initialized in step 1, l is the slow-direction moment, N is the number of voyages initialized in step 1, and N is the number of voyages;
step 6, discretizing a scene target and constructing a measurement matrix
Using a formula
Figure FDA0003516052240000031
Calculating to obtain the spatial frequency of the nth orbital tomography direction, and recording as xinN is 1,2, …, N; discretizing the position of the scene target in a chromatography position by D uniform points sdD is 1,2, …, D, using the formula
Figure FDA0003516052240000032
Calculating to obtain a measurement matrix, and recording as phi; wherein the target position of the chromatographic directional point is (r)0,s)，b⊥nFor the vertical baseline of the nth track auxiliary image initialized in step 1 with respect to the main image, b||nFor the parallel baseline of the nth track side image initialized in step 1 with respect to the main image, fcC is the transmission speed of the electromagnetic wave initialized in the step 1 in the air;
step 7, initializing SBRIM algorithm parameters
The initialization parameters of the SBRIM algorithm comprise: a weighting coefficient, noted as α; reconstructing an error threshold, and recording as epsilon; noise power, denoted as β; total number of iterations denoted Iiter(ii) a The iteration times are marked as k; flat plateSlip factor, denoted as η; the diagonal matrix control parameter is marked as p; using a formula
Figure FDA0003516052240000033
Calculating to obtain an initialized signal estimation value
Figure FDA0003516052240000034
Wherein g is an observation vector matrix in the step 5, phi is a measurement matrix in the step 6, and H is a conjugate transpose operation symbol;
step 8, calculating a diagonal matrix
Updating iteration times, calculating to obtain updated iteration times by adopting a formula k which is k +1, and marking as k; using a formula
Figure FDA0003516052240000035
Calculating to obtain a diagonal matrix of the kth iteration, and recording the diagonal matrix as Lambda(k)(ii) a Wherein
N is the number of voyages initialized in the step 1, p is the diagonal matrix control parameter initialized in the step 7, eta is the smoothing factor initialized in the step 7,
Figure FDA0003516052240000041
the scattering coefficient estimation value of the ith satellite orbit data in the (k-1) th iteration cycle is shown, and diag {. cndot } is a diagonal matrix operation symbol;
step 9, estimating scattering coefficient vector
Using the formula alpha(k)＝αβ(k)Calculating to obtain the kth iteration weighting coefficient which is marked as alpha(k)(ii) a Using a formula
Figure FDA0003516052240000042
Calculating to obtain a scattering coefficient vector of the kth iteration, and recording as
Figure FDA0003516052240000043
Where α is the weighting factor initialized in step 7, β(k)Noise work for the kth iterationThe ratio g is the observation vector matrix in step 5, phi is the measurement matrix in step 6, lambda(k)For the diagonal matrix of the kth iteration in step 7, H is the conjugate transpose symbol, (. cndot.)-1Matrix inversion operators;
step 10, estimating noise power
Using a formula
Figure FDA0003516052240000044
Calculating to obtain the kth iterative noise power which is marked as beta(k)(ii) a Wherein N is the navigation times initialized in the step 1, g is the observation vector matrix in the step 5, phi is the measurement matrix in the step 6,
Figure FDA0003516052240000045
the vector of scattering coefficient of the kth iteration in step 9, | · | | computationally2Is L2The norm solves the operator;
step 11, judging whether the iteration termination condition is met, reconstructing height direction information to obtain a final three-dimensional imaging result
If it is not
Figure FDA0003516052240000046
And k is less than or equal to IiterContinuing to execute the steps 8-11;
if not satisfied with
Figure FDA0003516052240000047
And k is less than or equal to IiterEither condition, the algorithm iteration terminates, then the output
Figure FDA0003516052240000048
The obtained K iteration scattering coefficient of the SBRIM algorithm
Figure FDA0003516052240000049
The three-dimensional imaging result is the final three-dimensional imaging result of the multi-baseline chromatography SAR; where ε is the reconstruction error threshold initialized in step 7, IiterFor the iteration initialized in step 7The total number of the first and second batteries,
Figure FDA00035160522400000410
the vector of scattering coefficient of the kth iteration in step 9, | · | | computationally2Is L2The norm solves the operator; through the steps, a multi-baseline tomography SAR three-dimensional imaging result based on the SBRIM algorithm is obtained.
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