CN108931770B - ISAR imaging method based on multi-dimensional beta process linear regression - Google Patents

ISAR imaging method based on multi-dimensional beta process linear regression Download PDF

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CN108931770B
CN108931770B CN201810539702.5A CN201810539702A CN108931770B CN 108931770 B CN108931770 B CN 108931770B CN 201810539702 A CN201810539702 A CN 201810539702A CN 108931770 B CN108931770 B CN 108931770B
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CN108931770A (en
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白雪茹
彭鑫
张毓
赵志强
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904—SAR modes
    • G01S13/9064—Inverse SAR [ISAR]

Abstract

The invention discloses an ISAR imaging method based on multi-dimensional beta process linear regression, which mainly solves the problem that the prior art is low in imaging quality when the signal-to-noise ratio is low and data is defective. The scheme comprises the following steps: 1) receiving ISAR echo and performing range direction pulse compression to obtain an echo matrix; 2) performing sliding window processing on the echo matrix to generate a data matrix; 3) establishing a multi-dimensional beta process linear regression model for each distance unit in the data matrix; 4) solving a multi-dimensional beta process linear regression model by using a Gibbs sampling method to obtain a weight vector and a sparse binary vector of a data matrix; 5) and obtaining an imaging matrix by the weight vector and the sparse binary vector, transposing the imaging matrix and taking the mean value to obtain an ISAR image. The method can obtain the inverse synthetic aperture radar ISAR image with high quality and good focusing under the conditions of echo loss and low signal-to-noise ratio, and can be used for target feature extraction or identification.

Description

ISAR imaging method based on multi-dimensional beta process linear regression
Technical Field
The invention belongs to the technical field of radars, and further relates to an ISAR (inverse synthetic aperture radar) imaging method for target feature extraction or identification.
Background
The inverse synthetic aperture radar ISAR has the characteristics of all-weather, high resolution, long distance and the like, and plays an important role in the observation of aviation and aerospace targets. However, when the target cannot be continuously observed due to the limitation of the radar operation mode, the azimuth echo is damaged. In addition, when the inverse synthetic aperture radar ISAR detects a small long-distance target, the echo signal-to-noise ratio is low, so that a high-quality imaging result is difficult to obtain.
The northwest university of industry disclosed a motorized target compressive sensing ISAR imaging method in its patent document entitled "motorized target compressive sensing ISAR imaging method" (publication No.: CN102841350A, application No.: 201210347782.7). The method comprises the following specific steps: performing distance compression, motion compensation and migration correction on the echo data to obtain a complex matrix, and generating a Gaussian random matrix to perform dimension reduction observation on the complex matrix; solving a1 norm convex optimization equation for each column of the inverse synthetic aperture radar to obtain an ISAR imaging result of the inverse synthetic aperture radar at one moment; and traversing each imaging moment to realize the ISAR imaging of the maneuvering target in each time interval. However, the method has the disadvantages that the inverse synthetic aperture radar ISAR imaging result at each moment is obtained by solving the 1 norm convex optimization equation, the sparse representation weight vector capacity is insufficient, the estimated parameter error is large, false points are easy to generate under the conditions of echo loss and low signal-to-noise ratio, and the inverse synthetic aperture radar ISAR image with good focus cannot be obtained.
Liu H C, Jiu B, Liu H W in its published article "Superresolution ISAR Imaging Based on Sparse Bayesian Learning" 2014,52(8):5005 + 5013 proposed an ISAR super-resolution Imaging method Based on Sparse Bayesian Learning SBL. The method is based on a sparse signal representation theory, converts the inverse synthetic aperture radar ISAR high-resolution imaging problem into a sparse signal reconstruction problem, establishes a sparse Gaussian-gamma level prior model for weight vectors, obtains parameter estimation through a maximized boundary likelihood function, and finally realizes inverse synthetic aperture radar ISAR imaging. However, the method still has the disadvantages that because the model established by the method for the weight vector is not accurate enough, the environment prior information cannot be fully utilized, and the inverse synthetic aperture radar ISAR image with good focusing cannot be obtained under the condition of low signal-to-noise ratio.
Disclosure of Invention
The invention aims to provide an inverse synthetic aperture radar imaging method based on multi-dimensional beta process linear regression aiming at the defects of the prior art so as to reduce false points under the conditions of echo defect and low signal-to-noise ratio and improve ISAR imaging quality.
The basic idea of the invention is as follows: based on a sparse signal reconstruction theory, the inverse synthetic aperture radar imaging problem is converted into a sparse linear regression problem, a multi-dimensional beta process is adopted to model a target echo, a Gibbs sampling algorithm is further adopted to solve model parameters, and finally target two-dimensional imaging is achieved. The implementation scheme comprises the following steps:
the ISAR imaging method based on the multi-dimensional beta process linear regression comprises the following steps:
(1) transmitting linear frequency modulation signals to a moving target through an inverse synthetic aperture radar, and acquiring defect echoes of the transmitted linear frequency modulation signals in a noise environment, wherein the number of distance sampling points is NrThe number of sampling points in the azimuth direction is NaTo obtain an Nr×NaDefect echo matrix S ofrWherein the column sequence number corresponding to the defective column vector is t1,...,tp；
(2) From defect echo matrix SrGenerating a real transpose echo matrix:
Figure BDA0001679016740000021
wherein R represents a real number set, NdRepresenting the number of azimuth effective samples, NmTaking the number of the sliding window;
(3) constructing a real Fourier dictionary:
Figure BDA0001679016740000022
(4) constructing a weight matrix by taking random numbers which are subjected to standard normal distribution as elements
Figure BDA0001679016740000023
Obtaining weight vector W of mth layer of the mth column of all rows in weight matrix W by utilizing gamma-Gaussian distribution:rmPrior distribution of
Figure BDA0001679016740000024
Wherein, the' represents all elements of the dimension in the matrix, P (-) represents probability density,
Figure BDA0001679016740000027
probability density, λ, representing a Gaussian distributionwRepresenting the accuracy of the weights in the probability distribution, -1 representing the inversion operation, INaWith a representation dimension of NaUnit matrix of (1), weight accuracy lambdawThe prior distribution of (a) is: p (lambda)w) Gamma (c, d), Gamma (·) represents Gamma distribution, c represents weight shape parameter, d represents weight scale parameter;
(5) constructing a sparse binary matrix with 0 as an element
Figure BDA0001679016740000025
Obtaining sparse binary vector Z of the mth layer of all rows and lines in sparse binary matrix Z by utilizing beta-Bernoulli distribution:rmPrior distribution of
Figure BDA0001679016740000026
Where Π represents a multiplication operation, and n represents a binary vector Z:rmN ═ 1.. NaBernoulli (·) denotes the probability density of the Bernoulli distribution, πnA probability parameter representing a bernoulli distribution whose prior distribution is: p (pi)n)＝Beta(a/Na,b(Na-1)/Na) Beta (·) represents Beta distribution, a is alpha hyper-parameter, b is Beta hyper-parameter;
(6) constructing a multi-dimensional beta process linear regression model of each distance unit according to the following formula:
Figure BDA0001679016740000031
S:rmsignal vectors, phi, representing the m-th layer of all rows and columns of the real transposed echo matrix S::mFourier dictionary matrix, ε, representing all rows and all columns of the mth layer of a real Fourier dictionary Φ:rmRepresenting a signal vector S:rmThe corresponding noise vector is set to be the corresponding noise vector,
Figure BDA0001679016740000032
represents a dot product;
(7) obtaining a noise vector epsilon using a gamma-Gaussian distribution:rmPrior distribution of
Figure BDA0001679016740000033
λεIndicating the accuracy of the noise, IKRepresenting an identity matrix with dimension K, noise accuracy lambdaεThe prior distribution of (a) is:
P(λε) Gamma (e, f), where e represents a noise shape parameter and f represents a noise scale parameter;
(8) updating the sparse binary matrix Z and the weight matrix W by using a Gibbs sampling method to obtain an updated sparse binary matrix Z 'and an updated weight matrix W';
(9) using the updated sparse binary matrix Z 'and the updated weight matrix W' to obtain a real sparse vector matrix: x ═ Z 'W';
(10) generating a complex sparse vector matrix according to the real sparse vector matrix X: x ═ X1+jX2Wherein X is1Representing a in a real sparse vector matrix X1A matrix of all layer elements of all rows and columns, a1＝1,...Na，X2Representing a in a real sparse vector matrix X2A matrix of all layer elements of all rows and columns, a2＝Na+1,...2Na；
(11) Generating an imaging matrix according to the complex sparse vector matrix X':
Figure BDA0001679016740000034
where | · | | denotes a modulo operation, X'::mRepresenting a matrix formed by the m-th layer elements of all rows and all columns in the complex sparse vector matrix X';
(12) and transposing the imaging matrix SI to obtain an inverse synthetic aperture radar imaging result.
The invention has the following advantages:
1. the invention is based on the Bayesian nonparametric method, fully utilizes the prior information of the environment, overcomes the limitation of the prior Bayesian parameter model on parameter fixation during signal modeling, enables the model to be more flexible and improves the imaging quality of the inverse synthetic aperture radar.
2. The invention adopts a multidimensional beta process to model the signal, adopts a sliding window method to process the echo signal in different time segments, and carries out average processing on a plurality of images, thereby effectively reducing the interference of false points and obtaining the inverse synthetic aperture radar image with good focus.
The technical solution of the present invention is described in further detail below with reference to the accompanying drawings and the detailed description.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a graph of distance and time after the defective echo distance is compressed;
FIG. 3 is a diagram showing the results of imaging a defect echo using a prior art range-Doppler imaging method;
fig. 4 is a graph of the imaging results after reconstruction of defect echoes using the present invention.
Detailed Description
The technical solution and effects of the present invention will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of the invention are as follows:
step 1, defect echo matrix S in noise environment is recorded by inverse synthetic aperture radarr。
The inverse synthetic aperture radar transmits electromagnetic waves, the electromagnetic waves are reflected after meeting a target in the transmission process, the reflected echoes are interfered by noise in the transmission process and are received by a radar receiver, and a defect echo matrix S is obtainedrWherein the number of distance sampling points is NrThe number of sampling points in the azimuth direction is NaThe defective column vector corresponds to the column number t1,...,tp。
Step 2, defect echo matrix SrProcessing to obtain a distance direction pulse compressed matrix Sd。
(2a) Taking the distance from the inverse synthetic aperture radar to the scene center as a reference distance, taking a linear frequency modulation signal which has the same carrier frequency and frequency modulation rate as the transmitted linear frequency modulation signal and the distance of which is the reference distance as a reference signal, conjugating the reference signal, and multiplying the conjugated reference signal by a received echo signal to obtain a matrix after linear frequency demodulation:
Figure BDA0001679016740000041
wherein the content of the first and second substances,
Figure BDA0001679016740000042
for a fast time of distance, tmFor azimuth slow time, Sref(. is) a reference signal, SrdFor the matrix after the line-released tone, a conjugate operation is represented;
(2b) deleting matrix S after line-released tone modulationrdA middle defective column vector, to obtain an Nr×NdEffective echo matrix S ofeIn which N isdRepresenting the number of azimuth valid samples;
(2c) for effective echo matrix SeFourier transform is carried out along the distance dimension to obtain a matrix S after distance direction pulse compressiond；
Step 3, compressing the matrix S in the distance direction pulsedSelecting a distance unit without target echo, and calculating to obtain a distance direction pulse compressed matrix SdAverage noise accuracy λ ofεInitial value of (2)
Figure BDA0001679016740000051
(3a) Setting the initial value of the row subscript i to be 1;
(3b) according to the distance direction pulse compressed matrix SdCalculating a distance direction pulse compressed matrix SdMiddle ith row vector SdiNoise power of
Figure BDA0001679016740000052
Wherein Sdi(u) represents the distance-wise pulse-compressed matrix SdIth row vector SdiThe u-th element of (1), wherein | · | | | represents a modulo operation;
(3c) root of herbaceous plantAccording to the noise power PiCalculating to obtain a matrix S after the distance direction pulse compressiondIth row vector SdiStandard deviation of noise of
Figure BDA0001679016740000053
(3d) Taking 5 lines of range bins without target echoes, comparing the line subscripts i with 5, if i is less than or equal to 5, making i equal to i +1, returning to the step (3b), and if i is greater than 5, executing the step (3 e);
(3e) calculating to obtain an average noise standard deviation according to the noise standard deviation:
Figure BDA0001679016740000054
(3f) according to mean noise standard deviation σnCalculating to obtain average noise precision lambdaεInitial value of (a):
Figure BDA0001679016740000055
step 4, compressing the matrix S according to the distance direction pulsedGenerating a real transpose echo matrix:
Figure BDA0001679016740000056
(4a) for the distance direction pulse compressed matrix SdTransposing to obtain a complex transpose echo matrix Sc；
(4b) Setting the number N of values of the sliding windowmWindow length L-N-5d-Nm+1, the window function sliding step Sp is 1, and the data window initial value Ld＝1；
(4c) Selecting a complex transpose echo matrix ScL todGo to LdThe elements of all the columns of the + L-1 row are taken as a three-dimensional echo matrix SwL todA layer;
(4d) initializing the data window with an initial value LdAnd the number N of values of the sliding windowmMaking a comparison if Ld<NmThen let Ld＝Ld+ Sp, return to step (4b), ifLd≥NmStopping circulation to obtain a spliced three-dimensional echo matrix Sw；
(4e) From a three-dimensional echo matrix SwConstructing a real transpose echo matrix
Figure BDA0001679016740000061
Where Re (. cndot.) represents the real part and Re (. cndot.) represents the imaginary part.
Step 5, constructing a real Fourier dictionary:
Figure BDA0001679016740000062
(5a) to be provided with
Figure BDA0001679016740000063
Is an element, with a construction dimension of Na×NaComplex fourier dictionary of phicWherein e is(·)Denotes an exponent based on a natural constant, j denotes an imaginary unit, and q denotes a complex Fourier dictionary ΦcL denotes a complex Fourier dictionary phicThe value ranges of the row sequence number q and the column sequence number l are [ -N [ ]a/2,Na/2-1]；
(5b) Deleting complex Fourier dictionary phicT th of (1)1,...,tpLine, get dimension Nd×NaEffective fourier dictionary of phie；
(5c) Using window functions to the effective Fourier dictionary phiePerforming sliding window value taking, and splicing to obtain a three-dimensional dictionary matrix phiw，
Figure BDA0001679016740000064
(5c1) Setting the number N of values of the sliding windowmWindow length L-N-5d-Nm+1, window function sliding step Sp equal to 1, dictionary window initial value Ldic＝1；
(5c2) Selecting an effective Fourier dictionary phieL todicGo to LdicTaking the matrix of all columns of the + L-1 row as a three-dimensional dictionary matrix phiwL todicA layer;
(5c3) initializing the dictionary window to LdicAnd the number N of values of the sliding windowmMaking a comparison if Ldic<NmThen let Ldic＝Ldic+ Sp, return to step (3c2), if Ls≥NpStopping circulation to obtain three-dimensional dictionary matrix phiw；
(5d) According to a three-dimensional dictionary matrix phiwConstructing a real Fourier dictionary:
Figure BDA0001679016740000065
Figure BDA0001679016740000066
and 6, establishing a multi-dimensional beta process linear regression model for each distance unit in the real transfer echo matrix S.
(6a) Constructing a weight matrix by taking random numbers which are subjected to standard normal distribution as elements
Figure BDA0001679016740000067
(6b) Obtaining weight precision lambda by utilizing gamma distributionwThe prior distribution of (a) is: p (lambda)w) Gamma (c, d), where Gamma (·) denotes Gamma distribution, P (·) denotes probability density, c denotes weight shape parameter, and d denotes weight scale parameter;
(6c) obtaining the mth layer weight vector W of the mth column of all rows in the weight matrix W by utilizing gamma-Gaussian distribution:rmPrior distribution of (a):
Figure BDA0001679016740000071
wherein "means all elements of the dimension in the matrix,
Figure BDA0001679016740000072
representing the probability density of the gaussian distribution, -1 representing the inversion operation,
Figure BDA0001679016740000073
with a representation dimension of NaThe identity matrix of (1);
(6d) constructing a sparse binary matrix with 0 as an element
Figure BDA0001679016740000074
(6e) Obtaining a probability parameter pi by utilizing beta distributionnThe prior distribution of (a) is: p (pi)n)＝Beta(a/Na,b(Na-1)/Na) Wherein Beta (·) represents Beta distribution, a is alpha hyper-parameter, b is Beta hyper-parameter;
(6f) obtaining sparse binary vector Z of the mth layer of all rows and lines in sparse binary matrix Z by utilizing beta-Bernoulli distribution:rmPrior distribution of (a):
Figure BDA0001679016740000075
where Π represents the multiplication operation, and n represents the binary vector Z:rmN ═ 1.. NaBernoulli (·) denotes the probability density of Bernoulli distribution;
(6g) modeling each range cell in the real echo matrix S according to:
Figure BDA0001679016740000076
wherein S:rmSignal vectors, phi, representing the m-th layer of all rows and columns of the real transposed echo matrix S::mFourier dictionary matrix, ε, representing all rows and all columns of the mth layer of a real Fourier dictionary Φ:rmRepresenting a signal vector S:rmThe corresponding noise vector is set to be the corresponding noise vector,
Figure BDA0001679016740000077
represents a dot product;
(6h) obtaining noise accuracy lambda using gamma distributionεThe prior distribution of (a) is: p (lambda)ε) Gamma (e, f), where e represents a noise shape parameter and f represents a noise scale parameter;
(6i) obtaining a noise vector epsilon using a gamma-Gaussian distribution:rmThe prior distribution of (a) is:
Figure BDA0001679016740000078
wherein IKRepresenting an identity matrix of dimension K.
And 7, updating the sparse binary matrix Z and the weight matrix W by using a Gibbs sampling method to obtain an updated sparse binary matrix Z 'and an updated weight matrix W'.
(7a) Setting the initial value of the iteration number k to be 1, the maximum iteration number maximum to be 15, the initial value of the row subscript n to be 1, the initial value of the column subscript r to be 1, the initial value of the layer subscript m to be 1, and assigning the value of the sparse binary matrix Z to the initial value of the sparse binary matrix
Figure BDA0001679016740000081
Assigning the value of the weight matrix W to the initial value of the weight matrix
Figure BDA0001679016740000082
Setting an initial value pi of a probability parameter vector pi(0)Is a vector with 0.01 element, weight precision lambdawInitial value of (2)
Figure BDA0001679016740000083
Initial value c of weight shape parameter c(0)＝1×10-6Initial value d of weight scale parameter d(0)＝1×10-6Alpha over-parameter a is 5 × 103The beta hyperparameter b is 1000; initial value e of noise shape parameter e(0)＝1×10-6Initial value f of noise scale parameter f(0)＝1×10-6；
(7b) Computing a k-th iteration sparse binary vector
Figure BDA0001679016740000084
The nth element of
Figure BDA0001679016740000085
Distribution of (a):
Figure BDA0001679016740000086
wherein "-" means subject to，n＝1,...Na，
Figure BDA0001679016740000087
Figure BDA0001679016740000088
(k-1) denotes the k-1 st iteration;
(7c) according to the distribution
Figure BDA0001679016740000089
Randomly generating a value as a sparse binary vector at the kth iteration
Figure BDA00016790167400000810
The nth element of
Figure BDA00016790167400000811
A value of (d);
(7d) the layer subscript m and the sliding window value number NmFor comparison, if m>NmIf yes, making m equal to 1 and executing the step (7e), otherwise, making the layer subscript m equal to m +1 and returning to the step (7 b);
(7e) calculating weight vector in k iteration
Figure BDA00016790167400000812
The nth element of (1)
Figure BDA00016790167400000813
Distribution of (a):
Figure BDA00016790167400000814
wherein the content of the first and second substances,
Figure BDA00016790167400000815
Figure BDA00016790167400000816
(7f) according to the distribution
Figure BDA00016790167400000817
Randomly generating a value as a weight vector at the k-th iteration
Figure BDA00016790167400000818
The nth element of (1)
Figure BDA00016790167400000819
A value of (d);
(7g) the layer subscript m and the sliding window value number NmFor comparison, if m>NmIf yes, making m equal to 1, and executing the step (7h), otherwise, making the layer subscript m equal to m +1, and returning to the step (7 e);
(7h) calculating probability parameter vector pi at kth iteration(k)The nth element of (1)
Figure BDA0001679016740000091
Distribution of (a):
Figure BDA0001679016740000092
(7i) according to the distribution
Figure BDA0001679016740000093
Randomly generating a value as a probability parameter vector pi at the kth iteration(k)The nth element of (1)
Figure BDA0001679016740000094
A value of (d);
(7j) the subscript n of the row and a three-dimensional echo matrix SwNumber of lines Nd-Nm+1 comparison, if n>Nd-NmIf +1, executing step (7k), otherwise, making the row index n equal to n +1, and returning to step (7 b);
(7k) calculating weight value precision in k iteration
Figure BDA0001679016740000095
And noise accuracy at kth iteration
Figure BDA0001679016740000096
(7k1) Calculating weight value precision in k iteration
Figure BDA0001679016740000097
Probability distribution of (2):
Figure BDA0001679016740000098
(7k2) according to probability distribution
Figure BDA0001679016740000099
Randomly generating a value as weight precision in the k iteration
Figure BDA00016790167400000910
A value of (d);
(7k3) calculating the value of the weight shape parameter in the k iteration:
Figure BDA00016790167400000911
calculating the value of the weight scale parameter in the k iteration:
Figure BDA00016790167400000912
(7k4) computing noise precision at kth iteration
Figure BDA00016790167400000913
Distribution of (a):
Figure BDA00016790167400000914
(7k5) according to the distribution
Figure BDA00016790167400000915
Randomly generating a value as the noise precision at the kth iteration
Figure BDA00016790167400000916
A value of (d);
(7k6) calculating the value of the noise shape parameter at the kth iteration:
Figure BDA0001679016740000101
calculating the value of the noise scale parameter at the kth iteration:
Figure BDA0001679016740000102
(7l) comparing the iteration number k with the maximum iteration number maximum, stopping iteration if k is greater than the maximum, executing the step (7m), and returning to the step (7b) if the iteration number k is equal to k + 1;
(7m) taking the column index r and the number of distance sampling points as NrBy comparison, if r>NrStopping iteration to obtain an updated sparse binary matrix
Figure BDA0001679016740000103
And the updated weight matrix
Figure BDA0001679016740000104
Otherwise, making the column subscript r ═ r +1, and returning to the step (7 b);
and 8, obtaining an imaging result according to the updated sparse binary matrix Z 'and the updated weight matrix W' in the step 7.
(8a) Using the updated sparse binary matrix Z 'and the updated weight matrix W' to obtain a real sparse vector matrix:
Figure BDA0001679016740000106
(8b) generating a complex sparse vector matrix according to the real sparse vector matrix X: x ═ X1+jX2Wherein X is1Representing a in a real sparse vector matrix X1A matrix of all layer elements of all rows and columns, a1＝1,...Na，X2Representing a in a real sparse vector matrix X2A matrix of all layer elements of all rows and columns, a2＝Na+1,...2Na；
(8c) Root of herbaceous plantGenerating an imaging matrix according to the complex sparse vector matrix X':
Figure BDA0001679016740000105
X′::mrepresenting a matrix formed by the m-th layer elements of all rows and all columns in the complex sparse vector matrix X';
(8d) and transposing the imaging matrix SI to obtain an inverse synthetic aperture radar imaging result.
The effects of the present invention can be further illustrated by the following simulations:
1. simulation parameters
The radar works in the C wave band, the carrier frequency is 5.52GHz, the target is a Yark-42 airplane, and the bandwidth of the radar is 400 MHz. The defect rate of echo data is 50%, and the signal-to-noise ratio is 0 dB.
2. Simulation content and results
Simulation 1: the distance pulse compressed image is drawn with a defect occurring in the 1 st to 80 th, 207 th to 320 th and 451 th to 512 th lines of the echo data after the distance pulse compression, and the result is shown in fig. 2. The abscissa represents the slow time after the defective echo data is pressed to the pulse along the distance, and the ordinate represents the distance unit after the defective echo data is pressed to the pulse along the distance, so that as can be seen from fig. 2, the defective echo has a large influence on the azimuth pulse compression.
Simulation 2: the range-doppler imaging method in the prior art is used to image the defect echo after the range-oriented pulse pressure, and the imaging result is drawn, and the result is shown in fig. 3. Wherein the abscissa represents the azimuthal distribution of the imaging results and the ordinate represents the distance distribution of the imaging results. It can be seen from fig. 3 that the range-doppler imaging method in the prior art has more side lobes and unclear target geometry.
Simulation 3: the distance pulse pressure defect echo is reconstructed by using the method, and the imaging result is drawn as shown in figure 4. Wherein the abscissa represents the azimuthal distribution of the imaging results and the ordinate represents the distance distribution of the imaging results. As can be seen from FIG. 4, the imaging result obtained by the invention can clearly show the geometric structure of the airplane target, and the image focusing effect is good.
The simulation results show that the inverse synthetic aperture radar ISAR high-resolution imaging problem is converted into the sparse vector reconstruction problem based on the sparse signal reconstruction theory, a multi-dimensional beta process linear regression model is established, the model is solved by using a Gibbs sampling method, the sparsity of target scattering point distribution and the prior information of noise are fully utilized, and the inverse synthetic aperture radar ISAR image with high quality and good focusing can be obtained under the conditions of echo loss and low signal to noise ratio.

Claims (9)

1. The ISAR imaging method based on the multi-dimensional beta process linear regression comprises the following steps:
(1) transmitting linear frequency modulation signals to a moving target through an inverse synthetic aperture radar, and acquiring defect echoes of the transmitted linear frequency modulation signals in a noise environment, wherein the number of distance sampling points is NrThe number of sampling points in the azimuth direction is NaTo obtain an Nr×NaDefect echo matrix S ofrWherein the column sequence number corresponding to the defective column vector is t1,...,tp；
(2) From defect echo matrix SrGenerating a real transpose echo matrix:
Figure FDA0003537330500000011
wherein R represents a real number set, NdRepresenting the number of azimuth effective samples, NmTaking the number of the sliding window;
(3) constructing a real Fourier dictionary:
Figure FDA0003537330500000012
(4) constructing a weight matrix by taking random numbers which are subjected to standard normal distribution as elements
Figure FDA0003537330500000013
Obtaining weight vector W of mth layer of the mth column of all rows in weight matrix W by utilizing gamma-Gaussian distribution:rmPrior distribution of
Figure FDA0003537330500000014
Wherein, the' represents all elements of the dimension in the matrix, P (-) represents probability density,
Figure FDA0003537330500000015
probability density, λ, representing a Gaussian distributionwRepresenting the weight accuracy in the probability distribution, -1 represents the inversion operation,
Figure FDA0003537330500000016
with a representation dimension of NaUnit matrix of (1), weight accuracy lambdawThe prior distribution of (a) is: p (lambda)w) Gamma (c, d), Gamma (·) represents Gamma distribution, c represents weight shape parameter, d represents weight scale parameter;
(5) constructing a sparse binary matrix with 0 as an element
Figure FDA0003537330500000017
Obtaining sparse binary vector Z of the mth layer of all rows and lines in sparse binary matrix Z by utilizing beta-Bernoulli distribution:rmPrior distribution of
Figure FDA0003537330500000018
Where Π represents a multiplication operation, and n represents a binary vector Z:rmN ═ 1.. NaBernoulli (·) denotes the probability density of the Bernoulli distribution, πnA probability parameter representing a bernoulli distribution whose prior distribution is: p (pi)n)＝Beta(a/Na,b(Na-1)/Na) Beta (·) represents Beta distribution, a is alpha hyper-parameter, b is Beta hyper-parameter;
(6) constructing a multi-dimensional beta process linear regression model of each distance unit according to the following formula:
Figure FDA0003537330500000024
S:rmsignal direction of the mth layer of all rows and columns of the real transposed echo matrix SAmount of phi::mFourier dictionary matrix, ε, representing all rows and all columns of the mth layer of a real Fourier dictionary Φ:rmRepresenting a signal vector S:rmThe corresponding noise vector is set to be the corresponding noise vector,
Figure FDA0003537330500000025
represents a dot product;
(7) obtaining a noise vector epsilon using a gamma-Gaussian distribution:rmPrior distribution of
Figure FDA0003537330500000021
λεIndicating the accuracy of the noise, IKRepresenting an identity matrix with dimension K, noise accuracy lambdaεThe prior distribution of (a) is: p (lambda)ε) Gamma (e, f), where e represents a noise shape parameter and f represents a noise scale parameter;
(8) updating the sparse binary matrix Z and the weight matrix W by using a Gibbs sampling method to obtain an updated sparse binary matrix Z 'and an updated weight matrix W';
(9) using the updated sparse binary matrix Z 'and the updated weight matrix W' to obtain a real sparse vector matrix:
Figure FDA0003537330500000026
(10) generating a complex sparse vector matrix according to the real sparse vector matrix X: x ═ X1+jX2Wherein X is1Representing a in a real sparse vector matrix X1A matrix of all layer elements of all rows and columns, a1＝1,...Na，X2Representing a in a real sparse vector matrix X2A matrix of all layer elements of all rows and columns, a2＝Na+1,...2Na；
(11) Generating an imaging matrix according to the complex sparse vector matrix X':
Figure FDA0003537330500000022
where | l | · | represents a modulo operation,X′::mrepresenting a matrix formed by the m-th layer elements of all rows and all columns in the complex sparse vector matrix X';
(12) and transposing the imaging matrix SI to obtain an inverse synthetic aperture radar imaging result.
2. The method of claim 1, wherein step (2) is based on a defect echo matrix SrGenerating a real-transformed echo matrix
Figure FDA0003537330500000023
The method comprises the following steps:
(2a) to defect echo matrix SrPerforming line-breaking frequency modulation to obtain matrix S after line-breaking frequency modulationrd；
(2b) According to the column number t corresponding to the defect column vector1,...,tpDeleting the matrix S after the line-released tonerdA middle defective column vector, to obtain an Nr×NdEffective echo matrix S of dimensioneIn which N isdRepresenting the number of azimuth valid samples;
(2c) for effective echo matrix SeFourier transform is carried out along the distance dimension to obtain a matrix S after distance direction pulse compressiond；
(2d) Matrix S after range-wise pulse compressiondSelecting a distance unit without target echo, and calculating to obtain a distance direction pulse compressed matrix SdAverage noise accuracy λ ofnInitial value of (2)
Figure FDA0003537330500000031
(2e) For the distance direction pulse compressed matrix SdTransposing to obtain a complex transpose echo matrix Sc；
(2f) Using window function to complex inversion echo matrix ScPerforming sliding window value taking to obtain a spliced three-dimensional echo matrix Sw，
Figure FDA0003537330500000032
C represents a complex set, where NmTaking the number of the sliding window;
(2g) from a three-dimensional echo matrix SwConstructing a real transpose echo matrix
Figure FDA0003537330500000033
Figure FDA0003537330500000034
Where Re (. cndot.) represents the real part and Re (. cndot.) represents the imaginary part.
3. The method of claim 2, wherein step (2a) comprises applying a defect echo matrix SrPerforming line-breaking frequency modulation to obtain matrix S after line-breaking frequency modulationrdThe method comprises the following implementation steps:
(2a1) taking the distance from the inverse synthetic aperture radar to the center of the scene as a reference distance, and taking a linear frequency modulation signal which has the same carrier frequency and frequency modulation rate as the transmission signal of the inverse synthetic aperture radar and the distance of the reference distance as a reference signal Sref；
(2a2) Reference signal SrefTaking the defect echo matrix S after conjugation and receptionrMultiplying to obtain matrix S after line-breaking tone modulationrd。
4. The method of claim 2, wherein the distance-wise pulse-compressed matrix S in step (2d)dSelecting a distance unit without target echo, and calculating to obtain a distance direction pulse compressed matrix SdAverage noise accuracy λ ofεInitial value of (2)
Figure FDA0003537330500000035
The method comprises the following implementation steps:
(2d1) setting the initial value of the row subscript i to be 1;
(2d2) according to the distance direction pulse compressed matrix SdCalculating a distance direction pulse compressed matrix SdMiddle ith row vector SdiNoise power of
Figure FDA0003537330500000041
Wherein Sdi(u) represents the distance-wise pulse-compressed matrix SdIth row vector SdiThe u-th element in (1), i | · | |, represents the modulo operation;
(2d3) according to noise power PiCalculating to obtain a matrix S after the distance direction pulse compressiondIth row vector SdiStandard deviation of noise of
Figure FDA0003537330500000042
(2d4) Taking 5 lines of range bins without target echoes, comparing the line index i with 5, if i is less than 5, making i equal to i +1, and returning to the step (2d 2); if i is more than or equal to 5, executing the step (2d 5);
(2d5) calculating to obtain an average noise standard deviation according to the noise standard deviation:
Figure FDA0003537330500000043
(2d6) according to mean noise standard deviation σnCalculating to obtain average noise precision lambdaεInitial value of (2)
Figure FDA0003537330500000044
Figure FDA0003537330500000045
5. The method of claim 2, wherein step (2f) uses a window function on the complex echo matrix ScPerforming sliding window value taking to obtain a spliced three-dimensional echo matrix SwThe method comprises the following implementation steps:
(2f1) setting the number N of values of the sliding windowmWindow length L-N-5d-Nm+1, the window function sliding step Sp is 1, and the data window initial value Ld＝1；
(2f2) Selecting a complex transpose echo matrix ScL todGo to LdThe elements of all the columns of the + L-1 row are taken as a three-dimensional echo matrix SwL todA layer;
(2f3) initializing the data window with an initial value LdAnd the number N of values of the sliding windowmMaking a comparison if Ld＜NmThen let Ld＝Ld+ Sp, return to step (2f 2); if L isd≥NmStopping circulation to obtain a spliced three-dimensional echo matrix Sw。
6. The method of claim 1, wherein the step (3) of constructing a real fourier dictionary comprises:
Figure FDA0003537330500000051
the method comprises the following steps:
(3a) to be provided with
Figure FDA0003537330500000052
Is an element, with a construction dimension of Na×NaComplex fourier dictionary of phicWherein e is(·)Denotes an exponent based on a natural constant, j denotes an imaginary unit, and q denotes a complex Fourier dictionary ΦcL denotes a complex Fourier dictionary phicThe value ranges of the row sequence number q and the column sequence number l are [ -N [ ]a/2,Na/2-1]；
(3b) Deleting complex Fourier dictionary phicT th of (1)1,...,tpLine, get dimension Nd×NaEffective fourier dictionary of phie；
(3c) Using window functions to the effective Fourier dictionary phiePerforming sliding window value taking and splicing to obtain a three-dimensional dictionary matrix
Figure FDA0003537330500000053
(3d) According to a three-dimensional dictionary matrix phiwConstructing a real Fourier dictionary
Figure FDA0003537330500000054
Figure FDA0003537330500000055
7. The method of claim 6, wherein in step (3c), the window function is applied to the effective Fourier dictionary ΦePerforming sliding window value taking, and splicing to obtain a three-dimensional dictionary matrix phiwThe method comprises the following specific steps:
(3c1) setting the number N of values of the sliding windowmWindow length L-N-5d-Nm+1, window function sliding step Sp equal to 1, dictionary window initial value Ldic＝1；
(3c2) Selecting an effective Fourier dictionary phieL todicGo to LdicTaking the matrix of all columns of the + L-1 row as a three-dimensional dictionary matrix phiwL todicA layer;
(3c3) initializing the dictionary window to LdicAnd the number N of values of the sliding windowmMaking a comparison if Ldic＜NmThen let Ldic＝Ldic+ Sp, return to step (3c2), if Ls≥NpStopping circulation to obtain three-dimensional dictionary matrix phiw。
8. The method according to claim 1, wherein in the step (8), updating the sparse binary matrix Z and the weight matrix W by using a Gibbs sampling method to obtain an updated sparse binary matrix Z 'and an updated weight matrix W', and the specific steps are as follows:
(8a) setting the initial value of the iteration number k to be 1, the maximum iteration number maximum to be 15, the initial value of the row subscript n to be 1, the initial value of the column subscript r to be 1, the initial value of the layer subscript m to be 1, and assigning the value of the sparse binary matrix Z to the initial value of the sparse binary matrix
Figure FDA0003537330500000061
Assigning the value of the weight matrix W to the initial value of the weight matrix
Figure FDA0003537330500000062
Setting an initial value pi of a probability parameter vector pi(0)Is a vector with 0.01 element, weight precision lambdawInitial value of (2)
Figure FDA0003537330500000063
Initial value c of weight shape parameter c(0)＝1×10-6Initial value d of weight scale parameter d(0)＝1×10-6Alpha over-parameter a is 5 × 103The beta hyperparameter b is 1000; initial value e of noise shape parameter e(0)＝1×10-6Initial value f of noise scale parameter f(0)＝1×10-6；
(8b) Computing a k-th iteration sparse binary vector
Figure FDA0003537330500000064
The nth element of
Figure FDA0003537330500000065
Distribution of (a):
Figure FDA0003537330500000066
wherein "-" means subject to, N ═ 1a，
Figure FDA0003537330500000067
Figure FDA0003537330500000068
(k-1) denotes the k-1 st iteration;
(8c) according to the distribution
Figure FDA0003537330500000069
Randomly generating a value as a sparse binary vector at the kth iteration
Figure FDA00035373305000000610
The nth element of
Figure FDA00035373305000000611
A value of (d);
(8d) the layer subscript m and the sliding window value number NmMaking a comparison if m > NmIf yes, making m equal to 1 and executing the step (8e), otherwise, making the layer subscript m equal to m +1 and returning to the step (8 b);
(8e) calculating weight vector in k iteration
Figure FDA00035373305000000612
The nth element of (1)
Figure FDA00035373305000000613
Distribution of (a):
Figure FDA00035373305000000614
wherein the content of the first and second substances,
Figure FDA00035373305000000615
Figure FDA00035373305000000616
(8f) according to the distribution
Figure FDA00035373305000000617
Randomly generating a value as a weight vector at the k-th iteration
Figure FDA0003537330500000071
The nth element of (1)
Figure FDA0003537330500000072
A value of (d);
(8g) the layer subscript m and the sliding window value number NmMaking a comparison if m > NmIf yes, making m equal to 1, and executing the step (8h), otherwise, making the layer subscript m equal to m +1, and returning to the step (8 e);
(8h) calculating probability parameter vector pi at kth iteration(k)The nth element of (1)
Figure FDA0003537330500000073
Distribution of (a):
Figure FDA0003537330500000074
(8i) according to the distribution
Figure FDA0003537330500000075
Randomly generating a value as a probability parameter vector pi at the kth iteration(k)The nth element of (1)
Figure FDA0003537330500000076
A value of (d);
(8j) the subscript n of the row and a three-dimensional echo matrix SwNumber of lines Nd-Nm+1 comparison, if N > Nd-NmIf +1, executing step (8k), otherwise, making the row index n equal to n +1, and returning to step (8 b);
(8k) calculating weight value precision in k iteration
Figure FDA0003537330500000077
And noise accuracy at kth iteration
Figure FDA0003537330500000078
(8l) comparing the iteration number k with the maximum iteration number maximum, stopping iteration if k is greater than maximum, executing the step (8m), and returning to the step (8b) if the iteration number k is equal to k + 1;
(8m) taking the column index r and the number of distance sampling points as NrBy comparison, if r > NrStopping iteration to obtain an updated sparse binary matrix
Figure FDA0003537330500000079
And the updated weight matrix
Figure FDA00035373305000000710
Otherwise, let the column index r be r +1, return to step (8 b).
9. The method according to claim 8, wherein in step (8k), weight precision is calculated for the kth iteration
Figure FDA00035373305000000711
And noise accuracy at kth iteration
Figure FDA00035373305000000712
The method comprises the following specific steps:
(8k1) calculating weight value precision in k iteration
Figure FDA00035373305000000713
Probability distribution of (2):
Figure FDA00035373305000000714
wherein: c. C(k-1)Represents the weight shape parameter at the k-1 iteration, d(k-1)Represents the weight scale parameter, N, at the k-1 iterationaNumber of sampling points representing azimuth, NmThe number of the sliding window values is represented,
Figure FDA00035373305000000715
representing a weight vector in the k iteration;
(8k2) according to probability distribution
Figure FDA0003537330500000081
Randomly generating a value as weight precision in the k iteration
Figure FDA0003537330500000082
A value of (d);
(8k3) calculating the value of the weight shape parameter in the k iteration:
Figure FDA0003537330500000083
calculating the value of the weight scale parameter in the k iteration:
Figure FDA0003537330500000084
(8k4) computing noise precision at kth iteration
Figure FDA0003537330500000085
Distribution of (a):
Figure FDA0003537330500000086
wherein: e.g. of the type(k-1)Representing the noise shape parameter at the k-1 iteration, f(k-1)Representing the noise scale parameter at the k-1 iteration, NrThe number of distance-wise sampling points is represented,
Figure FDA0003537330500000087
representing the sparse binary vector at the kth iteration, S:rmSignal vectors, phi, representing the m-th layer of all rows and columns of the real transposed echo matrix S::mA fourier dictionary matrix representing the m-th layer of all rows and all columns of the real fourier dictionary Φ,
Figure FDA0003537330500000088
2 norm is taken;
(8k5) according to the distribution
Figure FDA0003537330500000089
Randomly generating a value as the noise precision at the kth iteration
Figure FDA00035373305000000810
A value of (d);
(8k6) calculating the value of the noise shape parameter at the kth iteration:
Figure FDA00035373305000000811
calculating the value of the noise scale parameter at the kth iteration:
Figure FDA00035373305000000812
. 。
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