CN110275166A - ADMM-based rapid sparse aperture ISAR self-focusing and imaging method - Google Patents
ADMM-based rapid sparse aperture ISAR self-focusing and imaging method Download PDFInfo
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Abstract
The invention belongs to the field of radar signal processing, and particularly relates to an ADMM-based fast sparse aperture ISAR self-focusing and imaging method. The method comprises the following steps: s1 modeling the sparse aperture radar echo; s2 reconstructing a target ISAR image X through ADMM; s3 estimates the initial phase error phi by the minimum entropy criterion. The invention has the following beneficial effects: by the method, the initial phase error can be effectively estimated from the sparse aperture radar echo, ISAR self-focusing is realized, side lobe and grating lobe influence caused by undersampling can be effectively eliminated, and a high-resolution ISAR image is obtained; the robustness is strong, and ISAR self-focusing and imaging can still be realized under the condition of low signal-to-noise ratio; the method has high operation efficiency, can be applied to a real-time ISAR imaging system, and has important engineering application value.
Description
Technical field
The invention belongs to radar signal processing fields, and in particular to one kind is based on alternating direction multiplier (Alternating
Direction Method of Multipliers, ADMM) the ISAR self-focusing of rapid sparse aperture and imaging method.
Background technique
Inverse Synthetic Aperture Radar (ISAR) can obtain the high-resolution two-dimensional image of moving target, compared with optical device,
ISAR has round-the-clock, the round-the-clock, advantage that penetrates by force, has become the important detecting devices of Space object identification, in space
The fields such as targeted surveillance, missile defence, radar astronomy are widely applied.Currently, for complete radar echo signal (or
Claim full aperture signal), the full resolution pricture of traditional ISAR imaging method available moving target, but for sparse
Aperture signal, conventional method fail substantially, still lack effective imaging means.
In ISAR system, many factors will lead to the generation of sparse aperture signal, as ambient noise, receiver noise cause
Part radar return signal-to-noise ratio is low, is unable to satisfy image-forming condition；Under strong Resisting Condition, active, sourceless seism etc. causes part to be returned
The form of nonuniform sampling is presented in wave failure, pulse, forms sparse aperture.In addition, the work of widely applied multifunction radar
Mode will also generate sparse aperture signal, it is however generally that, multifunction radar is to meet multiple target detection, tracking, imaging and identification
Functional requirement, it is necessary to limited radar emission energy is toggled between different target, leads to the letter for irradiating same target
It is number sparse and non-homogeneous, to form sparse aperture signal.Sparse aperture seriously affects traditional ISAR imaging method performance, and one
Aspect, nonuniform sampling cause tradition based on distance-Doppler (RD) the ISAR imaging method of Fast Fourier Transform (FFT) (FFT)
It is influenced by stronger secondary lobe, graing lobe, image resolution ratio reduces；On the other hand, under the conditions of sparse aperture, radar echo pulse
Between coherence reduce, cause traditional ISAR self-focusing method to fail, can not effective compensation target be translatable caused by first phase miss
Difference leads to ISAR image defocus.With the development of compressed sensing technology, existing method introduces compressed sensing technology at present
ISAR imaging, makes full use of the sparsity of ISAR image, by sparse recovery algorithms, is reconstructed from lack sampling radar return
Focus good ISAR image.But existing sparse aperture ISAR imaging method faces the low problem of operation efficiency at present, can not
The demand of real-time ISAR imaging system is adapted to, operation efficiency, which has become, restricts sparse aperture ISAR imaging technique engineer application
Bottleneck, it would be highly desirable to solve.
Summary of the invention
The technical problem to be solved by the present invention is under the conditions of sparse aperture, the decline of conventional RD ISAR imaging method performance,
ISAR picture quality reduce, although and the ISAR imaging method based on compressed sensing technology can obtain high quality ISAR image,
Operation efficiency is low, it is difficult to meet engineering actual demand.
Thinking of the invention is the problem low for sparse aperture ISAR imaging method operation efficiency, proposes one kind and is based on
The rapid sparse aperture ISAR self-focusing of ADMM and imaging method.This method carries out generalization to sparse aperture radar return and builds
Mould passes through l1Norm regularization constraint, which is realized, models the sparse characteristic of ISAR image, on this basis, utilizes ADMM method
It solves and is based on l1The optimization problem of norm regularization constraint.For the operation efficiency for promoting this method, make full use of fourier matrix,
The lower matrix inversion of operation efficiency in iterative process is converted to matrix element by the characteristic of phase error matrix and down-sampled matrix
Plain division, and the iterative solution along distance unit direction is avoided using two-dimentional batch processing mode, further improve operation effect
Rate.Finally in an iterative process, based on the initial phase errors in Minimum Entropy criteria estimation radar return, combining realizes sparse hole
Diameter ISAR self-focusing.
The technical scheme adopted by the invention to solve the technical problem is that: a kind of rapid sparse aperture ISAR based on ADMM
Self-focusing and imaging method, include the following steps (for convenience of succinct, Uniform provisions: matrix or vector indicate with bold-type letter,
To any vector a, aiI-th of element for indicating a, to Arbitrary Matrix A, Ai,jIndicate (i, j) a element of A):
S1 models sparse aperture radar return:
Under the irradiation of higher-frequency radar signal, metal target generally can be equivalent at several discrete the sum of scattering points, it is assumed that
Target includes P scattering point, wherein the coordinate of p-th of scattering point relative target rotation center is (xp,yp), then target is one-dimensional
Range Profile Sequence is represented by the superposition of P scattering point one-dimensional range profile:
WhereinIndicate target one-dimensional range profile sequence,tmIt respectively indicates fast time (i.e. time in arteries and veins) and slow
Time (i.e. time between arteries and veins), σpIndicate the backscattering coefficient of p-th of scattering point of target, j, fc, c be respectively imaginary unit, thunder
Up to transmitting signal carrier frequency and propagation velocity of electromagnetic wave, ω indicates the equivalent revolving speed of target after translational compensation, φ (tm) indicate first phase
Error had not only included the phase error that target translation introduces, but also has included ambient noise phase error.Formula (1) can be further discrete
It turns to:
Wherein, h (m, n) indicates target discrete one-dimensional range profile sequence, and n, m are respectively fast time and slow time serial number: n=
1,2 ..., N, m=1,2 ..., M, N, M are respectively fast time and sum of slow time.PrIndicate that radar emission signal pulse repeats
Frequency.
Under the conditions of sparse aperture, lack sampling form is presented along slow time dimension in radar echo signal, it is assumed that radar returns at this time
Wave includes L pulse (L < M), and it is V that each pulse serial number, which combines the vector to be formed, then hasIt is basic herein
On, the target discrete one-dimensional range profile sequence under the conditions of sparse aperture may be expressed as:
H=ESFx+n (3)
WhereinIndicate target discrete one-dimensional range profile sequence matrixAlong column stack be formed by
Amount, i.e. h=Vec (H), wherein Vec () indicates the vectorization stacked to matrix along column；For piecemeal first phase mistake
Poor matrix:Wherein INIndicate the unit matrix of N × N,Representing matrix Kronecker product,It indicates
Initial phase errors matrix: e=diag [exp (j φ)], wherein diag () expression are made of diagonal matrix, diagonal entry vector
It is made of vector element in bracket, φ indicates initial phase errors vector；For the down-sampled matrix of piecemeal:
WhereinFor down-sampled matrix:For piecemeal Fourier
Matrix:WhereinFor M rank fourier matrix；Indicate target ISAR image
It is stacked along column and is formed by vector, i.e. x=Vec (X)；For the noise vector of column heap poststack.
For convenience of expression, formula (3) show the vector expression of sparse aperture target discrete one-dimensional range profile sequence, still
It is still to be handled by matrix form in the implementation procedure of actual algorithm.Subsequent step will provide the meter of matrix form
Operator expression formula.
S2 reconstructs target ISAR image X by ADMM:
ISAR image only includes usually a small amount of target scattering point, and background is simple, is presented stronger sparse characteristic, therefore can be with
The ISAR image reconstruction under the conditions of sparse aperture is realized using sparse restoration methods.The present invention uses l1Norm regularization method
The sparse characteristic of ISAR image is constrained, with this condition, sparse aperture ISAR image reconstruction is equivalent to solution and seeks as follows
Excellent problem:
Wherein | | | |1、||·||2Respectively l1、l2Norm；λ is regularization parameter, determines the dilute of gained ISAR image
The degree of dredging.Specific step is as follows:
S2.1 solves optimization problem shown in formula (4) by ADMM method:
Optimization problem shown in formula (4) is equivalent to following optimization problem by introducing auxiliary variable z by ADMM method:
It extends Lagrangian formulation are as follows:
Wherein α is Lagrange multiplier, and ρ is to discipline the factor as a warning.ADMM method solves following three subproblems and realizes to formula (4)
Solution:
Wherein k indicates kth time iteration.L is sought respectivelyρ(x, z, α) is led about the single order of x, z, and enabling derivative is that zero can obtain
First and second non trivial solution in formula (7), is shown below:
Wherein S () indicates that Soft Thresholding for Signal function has aleatory variable y and parameter a:
Newer shown in formula (8) is converted to matrix form by S2.2:
In formula (8), first equation includes inverting for the matrix having a size of MN × MN, and operation efficiency is low.To simplify operation,
Consider that matrix E, F, S have the property that
EHE=EEH=ILN (9)
FHF=FFH=IMN (10)
Wherein ILN、IMNThe respectively unit matrix having a size of LN × LN, MN × MN,It is diagonal for diagonal matrix
Line element isFormula (9)-(11) are substituted into first equation in formula (8), can be obtained:
At this point, matrix to be inverted has been converted into diagonal matrix, inverting to it can be realized by matrix element division.Cause
This, the vector form of formula (12) can be expressed as matrix form again, it is shown below:
Wherein Z, A are respectively the matrix form of auxiliary variable z Yu Lagrange multiplier α,Indicate the element of two matrixes
It is divided by respectively.Mask is sampling matrix,Its element value is 1 or 0, respectively indicates extraction or gives up phase
The element of position is answered, then the sampling matrix is multiplied with complete target one-dimensional range profile sequence by each element respectively, can obtain
Obtain the sparse aperture one-dimensional range profile sequence of zero padding.1M×NIndicate all 1's matrix having a size of M × N.Only comprising maximum in formula (13)
Matrix multiplication having a size of M × N, thus compared with (8) first equations of formula, operation efficiency is significantly improved.In addition, formula
(13) f and f inHIt can be realized respectively by FFT and Inverse Fast Fourier Transforms (IFFT), further to promote operation efficiency.
Equally, second and third equation can be further expressed as matrix form in formula (8):
S3 estimates initial phase errors φ by Minimum Entropy criteria:
Initial phase errors φ is estimated by Minimum Entropy criteria in an iterative process, to realize the ISAR under the conditions of sparse aperture certainly
It focuses, is shown below:
Wherein,The entropy for indicating ISAR image obtained by+1 iteration of kth, is defined as follows:
Wherein sum () indicates to sum to each element of matrix in bracket, and ⊙ is the Hadamard product of matrix, i.e. each member of matrix
Element is multiplied respectively；C is ISAR image gross energy: C=sum (| X(k+1)|2), it is unrelated with initial phase errors φ；Const indicate with
Initial phase errors φ unrelated constant.Specific step is as follows:
S3.1 is calculatedInitial phase errors φ about first of pulselDerivative:
Optimization problem shown in formula (16) is solved, is calculated firstInitial phase errors about first of pulse
φlDerivative, be shown below:
Wherein Re () expression takes real in bracket, X(k+1)*Indicate ISAR image X obtained by+1 iteration of kth(k+1)
Conjugation.
S3.2 calculates ISAR image X obtained by+1 iteration of kth(k+1)Initial phase errors φ about first of pulselDerivative:
Include ISAR image X obtained by+1 iteration of kth in formula (18)(k+1)Initial phase errors φ about first of pulselLead
Number calculates as follows:
Wherein 0(l-1)×N、0(L-l)×NRespectively indicate the full null matrix having a size of (l-1) × N Yu (L-l) × N.
S3.3 calculates initial phase errors φ obtained by+1 iteration of kthl (k+1):
Formula (19) are substituted into formula (18), and enable derivativeThe initial phase errors φ of first of pulse can be obtainedl's
Iteration more new-standard cement:
Wherein angle () indicates to take the phase of imaginary number in bracket.
The rapid sparse aperture ISAR self-focusing based on alternating direction multiplier and imaging process be i.e. as a result: loop iteration formula
(13)-(15) and formula (20), until convergence, the X obtained by formula (13) is the ISAR image reconstructed.
Before iterative solution, it is necessary first to carry out Initialize installation to parameter, wherein auxiliary variable Z, Lagrange multiplier A
And initial phase errors matrix e can be initialized as full null matrix, regularization parameter λ is initialized as μ var (H), wherein var ()
For variance operator, μ takes 0.005 < μ < 0.01, disciplines factor ρ=1 as a warning.
What the present invention obtained has the beneficial effect that can be effectively estimated first phase mistake from sparse aperture radar return through the invention
Difference realizes ISAR self-focusing, and can effectively eliminate secondary lobe and the graing lobe influence of lack sampling introducing, obtains ISAR imaging；
ISAR self-focusing and imaging still may be implemented in strong robustness under Low SNR；Operation efficiency is high, can be applied to reality
When ISAR imaging system, have important engineering application value.
Detailed description of the invention
Implementation flow chart Fig. 1 of the invention；
Fig. 2 (a) aircraft plane figure；(b) aircraft scatter times；
Under the conditions of Fig. 3 full aperture: (a) one-dimensional range profile sequence；(b) ISAR image；
ISAR image obtained by algorithms of different under the conditions of Fig. 4 difference sparse aperture；
Algorithm performance under the conditions of Fig. 5 difference sample rate compares: (a) related coefficient；(b) image entropy；(c) time is calculated；
ISAR image obtained by algorithms of different under the conditions of Fig. 6 difference signal-to-noise ratio (SNR)；
Algorithm performance under the conditions of Fig. 7 difference SNR compares: (a) related coefficient；(b) image entropy；(c) time is calculated；
Fig. 8 (a) aircraft optical imagery；(b) trailer-mounted radar；
Under the conditions of Fig. 9 full aperture: (a) one-dimensional range profile sequence；(b) ISAR image；
ISAR image obtained by algorithms of different under the conditions of Figure 10 difference sparse aperture.
Specific embodiment
Invention is further explained with reference to the accompanying drawing:
Fig. 1 is the total process flow of the present invention.
A kind of rapid sparse aperture ISAR imaging method based on ADMM of the present invention, comprising the following steps:
S1 models sparse aperture radar return；
S2 reconstructs target ISAR image X by ADMM；
S3 estimates initial phase errors φ by Minimum Entropy criteria.
It is tested first using emulation data, in experimentation, according to certain aircraft plane figure shown in Fig. 2 (a), structure figures
Scatter times shown in 2 (b).Assuming that target is along rotation center with 0.06rad/s's after carrying out translational compensation to radar return
Revolving speed at the uniform velocity rotates；Radar parameter is provided that centre frequency as 9GHz, and bandwidth 800MHz, pulse is 100 μ s,
Pulse recurrence frequency is 150Hz.If full aperture radar echo pulse number is 256, each pulse includes 256 sampled points.
ISAR imaging is carried out to full aperture radar return data first, as imaging results under the conditions of sparse aperture
Reference.Under the conditions of full aperture, such as Fig. 3 (a), Fig. 3 (b) are shown respectively for target one-dimensional range profile sequence and ISAR image, wherein
ISAR imaging uses conventional RD imaging method (S.Zhang, Y.Liu, and X.Li, " Fast entropy minimization
based autofocusing technique for ISAR imaging,IEEE Trans.Signal Process.,
vol.63,no.13,pp. 34253434,Jul.2015).As seen from the figure, under the conditions of full aperture, conventional RD method can be obtained
The good ISAR image of focusing effect.
Further respectively by random, segmentation in a manner of mixing three kinds the extracting part score from full aperture one-dimensional range profile sequence
According to simulate sparse aperture one-dimensional range profile sequence, as shown in Fig. 4 first row.In experimentation, echo samples rate is set as
0.25, initial phase errors obey mean value be zero, the Gaussian Profile that variance is π, radar return SNR is set as 15dB.The side RD is respectively adopted
Method, AFSBL method (L.Zhao, L.Wang, G.Bi, and L.Yang, " An autofocus technique for
highresolution inverse synthetic aperture radar imagery,IEEE
Trans.Geosci.Remote Sens., vol.52, no.10, pp. 63926403, Oct.2014.) and the present invention mentioned
ADMM method reconstructs target ISAR image from three kinds of sparse aperture data, imaging results respectively as Fig. 4 second and third, four column institutes
Show.As seen from the figure, in three kinds of methods, ISAR image obtained by RD method defocuses substantially, and the mentioned ADMM method of the present invention obtains
Focusing effect optimal ISAR image, especially under the conditions of mixing sparse, ISAR picture obtained by ADMM method obviously compared with
AFSBL method is clear.
Under the conditions of different sample rates, carry out 100 Monte Carlo Experiments respectively, record ISAR pictures obtained by three kinds of algorithms with
Change curve shown in Fig. 3 (b) with reference to the related coefficient of ISAR picture, image entropy and calculating time about sample rate, respectively such as
Fig. 5 (a), Fig. 5 (b) and Fig. 5 (c) are shown.As seen from the figure, the mentioned ADMM method of the present invention is under the conditions of all given sample rates
Highest related coefficient, minimum image entropy are obtained, and the calculating time is maintained within 10s, is promoted than AFSBL method
10-20 times.
Fig. 6 show ISAR imaging knot of three kinds of methods under conditions of radar return SNR is respectively 10dB, 5dB, 0dB
Fruit, wherein sparse aperture one-dimensional range profile sequence is obtained by stochastical sampling, sample rate 0.25.As seen from the figure, when SNR is low
When 5dB, RD and AFSBL method fails substantially, cannot achieve the focusing of ISAR image, and the mentioned ADMM method of the present invention is three
The good ISAR image of focusing effect is obtained under the conditions of kind SNR, shows that it is stronger to the robustness of noise.
Fig. 7 (a), Fig. 7 (b), Fig. 7 (c) are set forth under the conditions of different SNR, and three kinds of methods are 100 Monte Carlos
Averaging of income related coefficient, image entropy and calculating time in experiment.As seen from the figure, the present invention obtains highest phase again
Relationship number, minimum image entropy, and operation efficiency promotes nearly 10 times compared with AFSBL method, further demonstrates its stronger Shandong
Stick and higher operation efficiency.
Algorithm performance verifying is further carried out using certain aircraft measured data.Shown in aircraft optical imagery such as Fig. 8 (a), adopt
It is measured with certain vehicle-mounted X-band radar system, as shown in Fig. 8 (b).The radar signal parameter of transmitting is as follows: centre frequency is
9GHz, bandwidth 1GHz, pulsewidth be 100 μ s, pulse recurrence frequency 100Hz.Full aperture radar return includes 256 pulses,
Each pulse includes 512 sampled points.It is respectively the target one-dimensional range profile under the conditions of full aperture shown in Fig. 9 (a), Fig. 9 (b)
Sequence and ISAR image, the reference as ISAR imaging results under the conditions of sparse aperture.
Using random, segmentation with mix three kinds of modes and extract data from full aperture one-dimensional range profile shown in Fig. 8 (a), with
Sparse aperture one-dimensional range profile sequence is simulated, wherein sample rate is 0.25.Figure 10 gives the mesh under the conditions of three kinds of sparse apertures
Mark the one-dimensional ISAR image as obtained by sequence and three kinds of methods, as seen from the figure, ISAR image obtained by the mentioned ADMM method of the present invention
Focusing effect is better than image obtained by RD and AFSBL method, and closer to ISAR picture shown in Fig. 9 (a), further demonstrate its compared with
Excellent algorithm performance.
The experimental results showed that, the ISAR imaging under the conditions of sparse aperture can be achieved in the present invention above, and gained image focuses effect
Fruit is better than conventional RD method and representative sparse aperture ISAR imaging method, strong to noise robustness, under Low SNR
It stands good, and operation efficiency promotes 10-20 times compared with exemplary process, there is high engineering application value.
Claims (4)
1. a kind of ISAR self-focusing of rapid sparse aperture and imaging method based on ADMM, which is characterized in that this method include with
Lower step:
S1 models sparse aperture radar return:
Under the irradiation of higher-frequency radar signal, metal target generally can be equivalent at several discrete the sum of scattering points, it is assumed that target
Comprising P scattering point, wherein the coordinate of p-th of scattering point relative target rotation center is (xp,yp), then the one-dimensional distance of target
As sequence is represented by the superposition of P scattering point one-dimensional range profile:
WhereinIndicate target one-dimensional range profile sequence,tmRespectively indicate fast time and slow time, σpIndicate target pth
The backscattering coefficient of a scattering point, j, fc, c be respectively imaginary unit, radar emission signal carrier frequency and propagation velocity of electromagnetic wave,
ω indicates the equivalent revolving speed of target after translational compensation, φ (tm) indicate initial phase errors, it had both included the phase that target translation introduces
Error, and include ambient noise phase error；Formula (1) can further discretization are as follows:
Wherein, h (m, n) indicates target discrete one-dimensional range profile sequence, and n, m are respectively fast time and slow time serial number: n=1,
2 ..., N, m=1,2 ..., M, N, M are respectively fast time and sum of slow time, PrIndicate that radar emission signal pulse repeats frequency
Rate；
Under the conditions of sparse aperture, lack sampling form is presented along slow time dimension in radar echo signal, it is assumed that radar return packet at this time
Containing L pulse, it is V that L < M, and each pulse serial number, which combine the vector to be formed, then hasOn this basis, dilute
Target discrete one-dimensional range profile sequence under the conditions of thin aperture may be expressed as:
H=ESFx+n (3)
WhereinIndicate target discrete one-dimensional range profile sequence matrixIt is stacked along column and is formed by vector, i.e.,
H=Vec (H), wherein Vec () indicates the vectorization stacked to matrix along column；For piecemeal initial phase errors matrix:Wherein INIndicate the unit matrix of N × N,Representing matrix Kronecker product,Indicate initial phase errors
Matrix: e=diag [exp (j φ)], wherein diag () expression are made of diagonal matrix vector, and diagonal entry is by bracket
Middle vector element is constituted, and φ indicates initial phase errors vector；For the down-sampled matrix of piecemeal:WhereinFor down-sampled matrix: For piecemeal fourier matrix:WhereinFor M rank fourier matrix；Indicate target ISAR imageAlong column
Stacking is formed by vector, i.e. x=Vec (X)；For the noise vector of column heap poststack；
S2 reconstructs target ISAR image X by ADMM:
Using l1Norm regularization method constrains the sparse characteristic of ISAR image, with this condition, sparse aperture ISAR figure
Following optimization problem is solved as reconstruct is equivalent to:
Wherein | | | |1、||·||2Respectively l1、l2Norm；λ is regularization parameter, determines the sparse journey of gained ISAR image
Degree；Specific step is as follows:
S2.1 solves optimization problem shown in formula (4) by ADMM method:
Optimization problem shown in formula (4) is equivalent to following optimization problem by introducing auxiliary variable z by ADMM method:
It extends Lagrangian formulation are as follows:
Wherein α is Lagrange multiplier, and ρ is to discipline the factor as a warning；ADMM method solves following three subproblems realizations and asks formula (4)
Solution:
Wherein k indicates kth time iteration；L is sought respectivelyρ(x, z, α) is led about the single order of x, z, and enabling derivative is that zero can obtain formula (7)
In first and second non trivial solution, be shown below:
Wherein S () indicates Soft Thresholding for Signal function；
Newer shown in formula (8) is converted to matrix form by S2.2:
In formula (8), first equation includes inverting for the matrix having a size of MN × MN, and operation efficiency is low；To simplify operation, consider
Matrix E, F, S have the property that
EHE=EEH=ILN (9)
FHF=FFH=IMN (10)
Wherein ILN、IMNThe respectively unit matrix having a size of LN × LN, MN × MN,For diagonal matrix, diagonal line element
Element isFormula (9)-(11) are substituted into first equation in formula (8), can be obtained:
At this point, matrix to be inverted has been converted into diagonal matrix, inverting to it can be realized by matrix element division；Therefore,
The vector form of formula (12) can be expressed as matrix form again, be shown below:
Wherein Z, A are respectively the matrix form of auxiliary variable z Yu Lagrange multiplier α,Indicate the element difference of two matrixes
It is divided by, Mask is sampling matrix,Its element value is 1 or 0, respectively indicates extraction or gives up corresponding positions
The sampling matrix is then multiplied with complete target one-dimensional range profile sequence by each element respectively, can be obtained benefit by the element set
Zero sparse aperture one-dimensional range profile sequence, 1M×NIndicate all 1's matrix having a size of M × N；
Equally, second and third equation can be further expressed as matrix form in formula (8):
A(k+1)=A(k)+ρ(X(k+1)-Z(k+1))； (15)
S3 estimates initial phase errors φ by Minimum Entropy criteria:
Initial phase errors φ is estimated by Minimum Entropy criteria in an iterative process, to realize the ISAR autohemagglutination under the conditions of sparse aperture
Coke is shown below:
Wherein,The entropy for indicating ISAR image obtained by+1 iteration of kth, is defined as follows:
Wherein sum () indicates to sum to each element of matrix in bracket, and ⊙ is the Hadamard product of matrix, i.e. matrix each element point
It is not multiplied；C is ISAR image gross energy: C=sum (| X(k+1)|2), it is unrelated with initial phase errors φ；Const indicates to miss with first phase
Poor φ unrelated constant；Specific step is as follows:
S3.1 is calculatedInitial phase errors φ about first of pulselDerivative:
Optimization problem shown in formula (16) is solved, is calculated firstInitial phase errors φ about first of pulsel's
Derivative is shown below:
Wherein Re () expression takes real in bracket, X(k+1)*Indicate ISAR image X obtained by+1 iteration of kth(k+1)Be total to
Yoke；
S3.2 calculates ISAR image X obtained by+1 iteration of kth(k+1)Initial phase errors φ about first of pulselDerivative:
Include ISAR image X obtained by+1 iteration of kth in formula (18)(k+1)Initial phase errors φ about first of pulselDerivative,
It calculates as follows:
Wherein 0(l-1)×N、0(L-l)×NRespectively indicate the full null matrix having a size of (l-1) × N Yu (L-l) × N；
S3.3 calculates initial phase errors φ obtained by+1 iteration of kthl (k+1):
Formula (19) are substituted into formula (18), and enable derivativeThe initial phase errors φ of first of pulse can be obtainedlIteration more
New-standard cement:
Wherein angle () indicates to take the phase of imaginary number in bracket；
The rapid sparse aperture ISAR self-focusing based on alternating direction multiplier and imaging process be i.e. as a result: loop iteration formula (13)-
(15) and formula (20), until convergence, the X obtained by formula (13) are the ISAR image reconstructed.
2. a kind of the rapid sparse aperture ISAR self-focusing based on ADMM and imaging method according to claim 1, feature
It is: before iterative solution, Initialize installation first is carried out to parameter, wherein auxiliary variable Z, Lagrange multiplier A and first phase
Error matrix e can be initialized as full null matrix, and regularization parameter λ is initialized as μ var (H), and wherein var () is variance calculation
Son, μ take 0.005 < μ < 0.01, discipline factor ρ=1 as a warning.
3. a kind of ISAR self-focusing of rapid sparse aperture and imaging method according to claim 1 or claim 2 based on ADMM, special
Sign is: in S2.1, to aleatory variable y and parameter a, has:
4. a kind of ISAR self-focusing of rapid sparse aperture and imaging method according to claim 1 or claim 2 based on ADMM, special
Sign is: in S2.2, f and f in formula (13)HIt can be realized respectively by FFT and IFFT, further to promote operation efficiency.
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| CN111796278A (en) * | 2020-07-02 | 2020-10-20 | 南京理工大学 | Sparse aperture ISAR self-focusing method based on atomic norm and image entropy joint constraint |
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| CN112099010A (en) * | 2020-09-16 | 2020-12-18 | 中国人民解放军国防科技大学 | ISAR (inverse synthetic aperture radar) imaging method for target with micro-motion component based on structured non-convex low-rank representation |
| CN112162280A (en) * | 2020-08-25 | 2021-01-01 | 中国人民解放军空军预警学院雷达士官学校 | SF ISAR one-dimensional high-resolution distance imaging method based on atomic norm minimization |
| CN112684445A (en) * | 2020-12-02 | 2021-04-20 | 中国人民解放军国防科技大学 | MIMO-ISAR three-dimensional imaging method based on MD-ADMM |
| CN112946644A (en) * | 2021-01-28 | 2021-06-11 | 中国人民解放军国防科技大学 | Based on minimizing the convolution weight l1Norm sparse aperture ISAR imaging method |
| CN113075635A (en) * | 2021-03-30 | 2021-07-06 | 南京航空航天大学 | Method for reconstructing target information of frequency agile radar based on coherent accumulation |
| CN114114187A (en) * | 2021-11-18 | 2022-03-01 | 中国人民解放军国防科技大学 | ADMM network direction finding method based on depth expansion under grid mismatch condition |
| CN115421115A (en) * | 2022-05-23 | 2022-12-02 | 中国人民解放军空军预警学院 | Weight-weighted alternating direction multiplier method for combining phase correction and ISAR imaging |
| CN117148347A (en) * | 2023-06-13 | 2023-12-01 | 中国人民解放军空军预警学院 | Two-dimensional joint imaging and self-focusing method based on deep learning network |
| CN113075635B (en) * | 2021-03-30 | 2024-04-12 | 南京航空航天大学 | Method for reconstructing target information of frequency agile radar based on coherent accumulation |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104111458A (en) * | 2014-07-29 | 2014-10-22 | 西安电子科技大学 | Method for compressed sensing synthetic aperture radar imaging based on dual sparse constraints |
| CN105005048A (en) * | 2015-08-07 | 2015-10-28 | 苏州闻捷传感技术有限公司 | Saliency-map-based Laplacian cooperation compression radar imaging method |
| CN106355196A (en) * | 2016-08-23 | 2017-01-25 | 大连理工大学 | Method of identifying synthetic aperture radar image targets based on coupled dictionary learning |
| CN109085589A (en) * | 2018-10-16 | 2018-12-25 | 中国人民解放军国防科技大学 | Sparse aperture ISAR imaging phase self-focusing method based on image quality guidance |
| CN109100718A (en) * | 2018-07-10 | 2018-12-28 | 中国人民解放军国防科技大学 | Sparse aperture ISAR self-focusing and transverse calibration method based on Bayesian learning |
| CN109683161A (en) * | 2018-12-20 | 2019-04-26 | 南京航空航天大学 | A method of the inverse synthetic aperture radar imaging based on depth ADMM network |
| CN109917383A (en) * | 2019-03-28 | 2019-06-21 | 中国人民解放军国防科技大学 | Low signal-to-noise ratio ISAR imaging method based on echo down-sampling accumulation |
-
2019
- 2019-07-12 CN CN201910629019.5A patent/CN110275166B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104111458A (en) * | 2014-07-29 | 2014-10-22 | 西安电子科技大学 | Method for compressed sensing synthetic aperture radar imaging based on dual sparse constraints |
| CN105005048A (en) * | 2015-08-07 | 2015-10-28 | 苏州闻捷传感技术有限公司 | Saliency-map-based Laplacian cooperation compression radar imaging method |
| CN106355196A (en) * | 2016-08-23 | 2017-01-25 | 大连理工大学 | Method of identifying synthetic aperture radar image targets based on coupled dictionary learning |
| CN109100718A (en) * | 2018-07-10 | 2018-12-28 | 中国人民解放军国防科技大学 | Sparse aperture ISAR self-focusing and transverse calibration method based on Bayesian learning |
| CN109085589A (en) * | 2018-10-16 | 2018-12-25 | 中国人民解放军国防科技大学 | Sparse aperture ISAR imaging phase self-focusing method based on image quality guidance |
| CN109683161A (en) * | 2018-12-20 | 2019-04-26 | 南京航空航天大学 | A method of the inverse synthetic aperture radar imaging based on depth ADMM network |
| CN109917383A (en) * | 2019-03-28 | 2019-06-21 | 中国人民解放军国防科技大学 | Low signal-to-noise ratio ISAR imaging method based on echo down-sampling accumulation |
Non-Patent Citations (2)
| Title |
|---|
| CHANGYU HU ET AL.: "Inverse Synthetic Aperture Radar Imaging Using a Deep ADMM Network", 《THE 20TH INTERNATIONAL RADAR SYMPOSIUM IRS 2019》 * |
| 王天云 等: "压缩感知成像雷达研究进展", 《电光与控制》 * |
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