CN104732224B - SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation - Google Patents
SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation Download PDFInfo
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Abstract
The invention provides a kind of SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation, this method can effectively extract the local Electromagnetic Scattering information carried in SAR target images, under different azimuths, each classification target electromagnetic scattering center and scattering strength are all different, therefore, very strong distinctive is had based on the Zernike features that 2D slice maps are calculated；Meanwhile, SAR target identification methods of the invention apply sparse representation theory to be identified, and it can be very good that input feature vector is reconstructed, and make according to reconstructed error differentiation.In general, SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation are combined the Zernike moment characteristics of 2D slice maps with SRC technologies, target is thus can be very good to be identified, and with the good robustness to noise.
Description
Technical field
The present invention relates to Technology of Radar Target Identification field, more particularly to one kind are sparse based on two-dimentional Zelnick moment characteristics
The SAR target identification methods of expression.
Background technology
Synthetic aperture radar (Synthetic Aperture Radar, abbreviation SAR) technology, be using be mounted in satellite or
Movable radar on aircraft, obtains a kind of pulse radar technology of the geographical band radar target image of high accuracy.Radar target is certainly
Dynamic identification (Synthetic Aperture Radar Auto Targets Recognition, abbreviation SAR-ATR) is much
Managing all has important application value in information analysis techniques field.
The recognition performance of radar target automatic identification, is mainly determined by feature extraction and recognizer.In feature extraction side
Face, by preferable feature extraction, can not only reduce the dimension of data identification, and can retain use with as much as possible
Come the effective information being identified.Due to SAR image some it is unique the characteristics of, such as mirror-reflection, multiple reflection and data sheet
The factor such as non-linear of body, it is difficult to directly extract its linear character as optical imagery.Therefore in order to more effectively realize knowledge
Not, researcher has attempted to a variety of different characteristics being applied in radar target automatic identification field, such as positional information
Feature, sharp peaks characteristic, PCA (Principal Component Analysis, principal component analysis) feature, HOG (Histogram
Of Oriented Gradient, histograms of oriented gradients) feature etc..In terms of recognition methods, traditional recognition methods is main
It is all based on template matches and based on Model Matching.In the matching process based on template, typically schemed with the SAR of target to be measured
The feature of picture is come with known target and the training image based on template is contrasted, to obtain target identification result, but by
There is complex background in SAR image, this is difficult to eliminate and ignore the influence that background image is matched to object, except this it
The change of the outer angle of pitch also increases the difficulty of object matching.In the matching process based on model, usual method is to maintain
The model of physics and concept of one target under different postures, azimuth and deployment conditions, but by object sample institute
Limitation causes to be difficult to be inferred to model parameter, so that being easily caused between training data and tested data does not have very strong statistics
Relation, is just easy to so that radar target recognition have failed in this case；Also, under different expansion conditions, train number
It is also what is be not quite similar according to the operating parameter with tested data, this also largely have impact on the identification to radar target thing
Rate.
The recognition performance of radar target automatic identification how is lifted by better method, always is in field and studies
Important topic.
The content of the invention
For the above-mentioned problems in the prior art, it is required for solve SAR image target identification in the prior art
The problem of estimating azimuth of target, identification limited accuracy is dilute based on two-dimentional Zelnick moment characteristics the invention provides one kind
The SAR target identification methods represented are dredged, the radar target identification method is represented come to non-negative time-frequency plane number using non-negative sparse
According to being modeled and feature extraction, it is not necessary to target bearing angular estimation is carried out to SAR image, while can avoid defocusing or believing
Make an uproar than etc. influence of the factor to target identification effect, improve SAR target identifications accuracy.
To achieve the above object, present invention employs following technological means：
Based on the SAR target identification methods of two-dimentional Zelnick moment characteristics rarefaction representation, comprise the following steps：
1) SAR image of radar target is obtained, and SAR image is rendered as to the SAR 3-D views of three-dimensional, three dimensions point
Not Wei SAR image row pixel coordinate, row pixel coordinate and electromagnetic scattering amplitude；
2) by electromagnetic scattering amplitude dimension be evenly dividing for several amplitudes it is interval, by electromagnetic scattering in SAR 3-D views
The two-dimensional pixel image coordinate of pixel of the amplitude in same amplitude interval is interval in respective magnitudes as SAR 3-D views
Corresponding SAR two-dimensional slice images, so that the SAR three-dimensional image segmentations of radar target are turned into multiple SAR two dimension slicings figures
Picture；
3) the Zelnick moment characteristics of each width SAR two-dimensional slice images of SAR 3-D views are extracted, radar target is constituted
Zelnick Character eigenvector；
4) for the different known radar target of multiclass, the SAR image of multiple known radar targets is gathered respectively as instruction
Practice sample, and according to step 1)~the Zelnick Character eigenvector of each training sample in each classification 3) is extracted respectively, from
And the set composing training sample set of the Zelnick Character eigenvector by each classification each training sample；
5) radar target to be measured is directed to, the SAR image of radar target to be measured is gathered as test sample, according to step 1~3
Extract the Zelnick Character eigenvector of test sample；
6) the Zelnick Character eigenvector for concentrating each training sample using training sample sets up solving sparse linear equations, right
The Zelnick Character eigenvector of test sample carries out sparse linear expression, and solution obtains each in the solving sparse linear equations
Sparse coefficient, is the radar belonging to radar target to be measured by the kind judging belonging to the training sample corresponding to non-zero sparse coefficient
Target classification, realizes the identification to radar target to be measured.
In the above-mentioned SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation, specifically, the step
It is rapid 3) in, the Zelnick moment characteristics b of width SAR two-dimensional slice images expression formula is：
Wherein, r represents that row pixel coordinate in SAR two-dimensional slice images is the pixel (x, y) that y, row pixel coordinate are x
Vector,θ represents the angle of the vector and row pixel coordinate axle of pixel (x, y) in SAR two-dimensional slice images, θ
=tan-1(y/x)；F (r, θ) represents the intensity function of pixel (x, y) in SAR two-dimensional slice images, when SAR two dimension slicing figures
There is pixel at pixel (x, y) position as in, its intensity function f (r, θ)=1, when pixel in SAR two-dimensional slice images
There is no pixel at (x, y) position, then its intensity function f (r, θ)=0；P- | q | it is even number, 0≤| q |≤p, and p >=0；Bpqk
For the coefficient of Zernike Polynomials：
By the Zelnick moment characteristics for each width SAR two-dimensional slice images for extracting SAR 3-D views, radar mesh is obtained
One group of Zelnick Character eigenvector of target.
In the above-mentioned SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation, specifically, the step
It is rapid 6) to be specially：
61) the Zelnick Character eigenvector for concentrating each training sample using training sample sets up following sparse linear
Equation, sparse linear expression is carried out to the Zelnick Character eigenvector of test sample：
Wherein, bzRepresent the Zelnick Character eigenvector of test sample；H represents training sample set, and β represents sparse linear
The sparse coefficient vector of equation, wherein：
H=[h1,h2,…,hi,…,hK]；
hiThe Zelnick Character eigenvector subset of the i-th class known radar target training sample is represented, 1≤i≤K, K is represented
The classification sum of known radar target included in training sample set；And Represent
I-th class known radar target n-thiThe Zelnick Character eigenvector of individual training sample, 1≤ni≤Ni, NiRepresent to be directed to the i-th class
The number for the training sample that known radar target is gathered；
Represent to correspond to the i-th class known radar target n-th in sparse coefficient vectoriThe Zelnick of individual training sample
Character eigenvectorSparse coefficient；
62) withAs sparse coefficient vector optimization aim, withIt is used as constraint
The solving sparse linear equations set up are solved by condition, obtain the optimization aim sparse coefficient vector of the solving sparse linear equations
Value；Wherein, ε is presetting sparse reconstructed error threshold value, | | | |0For L0 norm operators；
63) by optimization aim sparse coefficient vectorThe classification belonging to training sample corresponding to middle non-zero sparse coefficient is sentenced
It is set to the radar target classification belonging to radar target to be measured, realizes the identification to radar target to be measured.
Compared to prior art, the present invention has the advantages that：
1st, the SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation, can effectively be extracted
The local Electromagnetic Scattering information carried in SAR target images, under different azimuths, each classification target electromagnetic scattering
Center and scattering strength are all different, therefore, have very strong discriminating based on the Zernike features that 2D slice maps are calculated
Property.
2nd, the SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation apply rarefaction representation
Theory is identified, and it can be very good that input feature vector is reconstructed, and makes according to reconstructed error differentiation.
3rd, the SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation are 2D slice maps
Zernike moment characteristics are combined with SRC technologies, thus be can be very good target and are identified, and with good to making an uproar
The robustness of sound.
Brief description of the drawings
Fig. 1 is the flow chart of the SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation.
Fig. 2 is the SAR image of the radar target that code name is BMP2 in MSTAR public databases.
Fig. 3 is the SAR image of the radar target that code name is BTR70 in MSTAR public databases.
Fig. 4 is the SAR image of the radar target that code name is T72 in MSTAR public databases.
Fig. 5 is the SAR 3-D views of the radar target that code name is BMP2 in MSTAR public databases.
Fig. 6 is the SAR 3-D views of the radar target that code name is BTR70 in MSTAR public databases.
Fig. 7 is the SAR 3-D views of the radar target that code name is T72 in MSTAR public databases.
Fig. 8 is that the SAR 3-D views of the radar target that code name is BMP2 in MSTAR public databases are interval in different amplitudes
Multiple SAR two-dimensional slice images obtained by upper segmentation.
Fig. 9 is the SAR 3-D views of the radar target that code name is BTR70 in MSTAR public databases in different amplitude areas
Between multiple SAR two-dimensional slice images obtained by upper segmentation.
Figure 10 is that the SAR 3-D views of the radar target that code name is T72 in MSTAR public databases are interval in different amplitudes
Multiple SAR two-dimensional slice images obtained by upper segmentation.
Figure 11 is the antinoise experimental result picture of SAR target identification methods of the present invention in embodiment.
Embodiment
Technical scheme is further described with reference to the accompanying drawings and examples.
The present invention proposes a kind of SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation.One width
Picture element density is the digital SAR image of N rows × N row by N2Individual pixel element composition, and each pixel is except its row, column picture
Outside plain coordinate, electromagnetic scattering amplitude is also carried, therefore SAR image can be expert at pixel coordinate, row pixel coordinate and electromagnetism
The image format of three-dimensional is rendered as in scattering amplitude dimension.One width SAR image can with being shown as three-dimensional (3D) form, due to
Under different azimuths, the Electromagnetic Scattering of different classes of its SAR image of radar target is different, therefore each class target
Scattering center position and amplitude all have a larger difference, therefore be used as the knowledge that feature carries out radar target
Not.But the Electromagnetic Scattering data dimension carried in the SAR image of three dimensional form is too big, it is difficult to directly apply at identification
Reason.Therefore, in the present invention, normalized can be done by the electromagnetic scattering range value to three dimensional form SAR image, then
The section segmentation homogenized in the SAR image to three dimensional form, the SAR two-dimensional slice images extracted remain three-dimensional
Local binarization Electromagnetic Scattering in form SAR image, so that the dimension of Electromagnetic Scattering is significantly contracted
Subtract.And for the extraction of Electromagnetic Scattering in SAR two-dimensional slice images, present invention employs Zelnick (Zernike) square
Feature.Zernike squares can extract the shape facility of image, because Zernike multinomials are orthogonal, therefore for describing figure
The correlation and redundancy of the Zernike features of picture are just special small, and can be rotated in image and the situation full of noise
Under, amplitude can keep constant.Therefore, had based on the Zelnick moment characteristics that SAR two-dimensional slice images are calculated very strong
Distinctive.And in Classification and Identification processing, the identification of SAR targets is realized present invention employs rarefaction representation technology.It is sparse
Expression is the technology of a newly-developed, and its application is very extensive, in the sorting technique (Sparse based on sparse expression
Representation-based Classifier, are abbreviated as SRC) in, test image is projected to what is be made up of training data
On dictionary, so as to obtain a sparse vector, this sparse vector only has seldom nonzero value, and most of is all null value, can be with
Clarification of objective is represented well, therefore can complete the knowledge of radar target by comparing the reconstructed residual based on sparse vector
Not.
Overall flow such as Fig. 1 of SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation
It is shown, specifically include following steps：
1) SAR image of radar target is obtained, and SAR image is rendered as to the SAR 3-D views of three-dimensional, three dimensions point
Not Wei SAR image row pixel coordinate, row pixel coordinate and electromagnetic scattering amplitude.
It is BMP2, BTR70 and T72 radar target that Fig. 2,3,4, which respectively illustrate code name in MSTAR public databases,
SAR image, as shown in Figure 2,3, 4, several pixels that each width SAR image has array arrangement are constituted, a such as width picture
Plain density is the SAR image of N rows × N row by N2Individual pixel element composition, and the pixel of each in SAR image except its row,
Outside row pixel coordinate, also carry electromagnetic scattering amplitude, thus SAR image can be expert at pixel coordinate, row pixel coordinate and
The image format of three-dimensional is rendered as in electromagnetic scattering amplitude dimension, Fig. 5,6,7 item are respectively illustrated in MSTAR public databases
The SAR 3-D views that code name is presented for BMP2, BTR70 and T72 radar target by three-dimensional.
2) by electromagnetic scattering amplitude dimension be evenly dividing for several amplitudes it is interval, by electromagnetic scattering in SAR 3-D views
The two-dimensional pixel image coordinate of pixel of the amplitude in same amplitude interval is interval in respective magnitudes as SAR 3-D views
Corresponding SAR two-dimensional slice images, so that the SAR three-dimensional image segmentations of radar target are turned into multiple SAR two dimension slicings figures
Picture.
The step is actually to carry out the normalized after splitting at equal intervals to electromagnetic scattering amplitude dimension, by segmentation
The normalization of each amplitude interval is considered as a two dimension slicing cut section, and electromagnetic scattering amplitude is same in SAR 3-D views
Pixel in individual amplitude interval is to be considered as falling the pixel in respective two-dimensional cuts into slices cut section, the two dimension of these pixels
Pixel coordinate position is just combined into the two dimensional image for a secondary binaryzation (by the position for having pixel and the position without pixel
It is subject to binaryzation differentiation), using this two dimensional image as SAR 3-D views in the SAR two dimension slicings corresponding to respective magnitudes interval
Image, thus just can obtain multiple SAR two-dimensional slice images that SAR 3-D views split formation on different amplitudes interval.
Fig. 8,9,10 respectively illustrate the SAR graphics for the radar target that code name in MSTAR public databases is BMP2, BTR70 and T72
In multiple SAR two-dimensional slice images as obtained by the segmentation on different amplitudes interval, each width SAR two-dimensional slice images, no picture
The position of vegetarian refreshments represents that the position for having pixel is represented with white with black, to carry out binaryzation differentiation.
3) the Zelnick moment characteristics of each width SAR two-dimensional slice images of SAR 3-D views are extracted, radar target is constituted
Zelnick Character eigenvector.
Present invention employs electromagnetism entrained in Zelnick (Zernike) Moment Feature Extraction SAR two-dimensional slice images
Scattering signatures, to be used as identification feature.The specific extracting mode of the step is as follows：
The Zelnick moment characteristics b of one width SAR two-dimensional slice images can be expressed as：
Wherein, p is exponent number, and q is repeat number, and f (x, y) represents the intensity letter of pixel (x, y) in SAR two-dimensional slice images
Number；Vpq(x, y) is Zernike Polynomials, is defined as：
Vpq(x, y)=Rpq(r)ejqθ,r∈[-1,1]；
Wherein, r represents that row pixel coordinate in SAR two-dimensional slice images is the pixel (x, y) that y, row pixel coordinate are x
Vector,θ represents the angle of the vector and row pixel coordinate axle of pixel (x, y) in SAR two-dimensional slice images, θ
=tan-1(y/x).So represent the polar form of the intensity function f (x, y) of pixel (x, y) in SAR two-dimensional slice images
F (r, θ) is can be expressed as, when having pixel at pixel (x, y) position in SAR two-dimensional slice images, its intensity function f (r,
θ)=1, when there is no pixel at pixel (x, y) position in SAR two-dimensional slice images, then its intensity function f (r, θ)=0, this
Sample has carried out binary conversion treatment by intensity function to SAR two-dimensional slice images.
Zelnick real value radial polynomial is defined as：
Wherein, p- | q | it is even number, 0≤| q |≤p and p >=0, allow s → (p-k)/2, then Zernike Polynomials Vpq(x,y)
Just it can be written to：
Wherein, the coefficient B of Zernike PolynomialspqkIt is defined as：
Therefore, the Zelnick moment characteristics b of SAR two-dimensional slice images is expressed as with polar form：
Wherein ,-π≤θ≤π；Thus the Zelnick moment characteristics of a secondary SAR two-dimensional slice images are just obtained.
The range value of SAR two-dimensional slice images can be expressed as：
WhereinIt is the Zelnick square of SAR two-dimensional slice images after rotating.
Wherein, in the case of q >=0,With | Zp,q|=| Zp,-q| it will set up.According to Zernike squares
Computing Principle, calculates the Zelnick moment characteristics of each width SAR two-dimensional slice images of SAR 3-D views, just constitutes thunder
Up to the Zelnick Character eigenvector of target, the binaryzation SAR two dimensions effectively described in Zelnick Character eigenvector
The Radar Target Scatter central information that sectioning image is included.
4) for the different known radar target of multiclass, the SAR image of multiple known radar targets is gathered respectively as instruction
Practice sample, and according to step 1)~the Zelnick Character eigenvector of each training sample in each classification 3) is extracted respectively, from
And the set composing training sample set of the Zelnick Character eigenvector by each classification each training sample.
5) radar target to be measured is directed to, the SAR image of radar target to be measured is gathered as test sample, according to step 1~3
Extract the Zelnick Character eigenvector of test sample.
6) the Zelnick Character eigenvector for concentrating each training sample using training sample sets up solving sparse linear equations, right
The Zelnick Character eigenvector of test sample carries out sparse linear expression, and solution obtains each in the solving sparse linear equations
Sparse coefficient, is the radar belonging to radar target to be measured by the kind judging belonging to the training sample corresponding to non-zero sparse coefficient
Target classification, realizes the identification to radar target to be measured.
Processing is identified present invention employs rarefaction representation technology, to overcome influence of the noise to identification robustness.It is dilute
It is closely to recover original signal by a base vector to dredge the target represented.For example, the enough samples of given k classification targets
This, is constitutedAny one new test sample y ∈ Rm, category can be passed through well
Represented well in the training sample of its that class：
WhereinDue to new test sample which kind of belongs to is not know
, n different classes of training sample of all K classes is used as base vector, wherein X=[X1,X1,...,XK]∈Rm×n,Then y just can carry out sparse linear by following solving sparse linear equations with all training samples and represent：
Y=X1α1+X2α2+…+XKαK=Xα；
Wherein α=[α1,α2,...αK]∈Rn, due to m<N, therefore the solution of above formula is not unique.Conventional way is to look for
To most sparse solution：
Wherein, | | | |0：The number of nonzero element is calculated, wherein ε is error threshold, but seeks most sparse solution
It is NP-hard problems.Due to the development of compressive sensing theory, if solutionEnough is sparse, then ask most sparse solution just can be with
It is seen as a L0 norm minimum problem：
Wherein | | | |0It is L0 norm operators, that is, calculates the weight of all amplitudes.Using the theory of convex optimization,
There are many algorithms to calculate the L0 norm minimum problems, so as to try to achieve the most sparse solution of solving sparse linear equations.
Based on above-mentioned theory, applied in the present invention, step 6) specific handling process it is as follows：
61) the Zelnick Character eigenvector for concentrating each training sample using training sample sets up following sparse linear
Equation, sparse linear expression is carried out to the Zelnick Character eigenvector of test sample：
Wherein, bzRepresent the Zelnick Character eigenvector of test sample；H represents training sample set, and β represents sparse linear
The sparse coefficient vector of equation, wherein：
H=[h1,h2,…,hi,…,hK]；
hiThe Zelnick Character eigenvector subset of the i-th class known radar target training sample is represented, 1≤i≤K, K is represented
The classification sum of known radar target included in training sample set；And Represent
I-th class known radar target n-thiThe Zelnick Character eigenvector of individual training sample, 1≤ni≤Ni, NiRepresent to be directed to the i-th class
The number for the training sample that known radar target is gathered；
Represent to correspond to the i-th class known radar target n-th in sparse coefficient vectoriThe Zelnick of individual training sample
Character eigenvectorSparse coefficient；
62) withAs sparse coefficient vector optimization aim, withIt is used as constraint
The solving sparse linear equations set up are solved by condition, obtain the optimization aim sparse coefficient vector of the solving sparse linear equations
Value；Wherein, ε is presetting sparse reconstructed error threshold value, | | | |0For L0 norm operators；
63) by optimization aim sparse coefficient vectorThe classification belonging to training sample corresponding to middle non-zero sparse coefficient is sentenced
It is set to the radar target classification belonging to radar target to be measured, realizes the identification to radar target to be measured.
SAR target identification methods of the invention based on two-dimentional Zelnick moment characteristics rarefaction representation can apply to based on meter
Calculation machine programs the radar target recognition systems of self-operating, realizes the radar target recognition of automation.
Technical scheme is further described below by embodiment.
Embodiment：
The present embodiment utilizes the data image that MSTAR public databases are announced, and carrys out the comparative evaluation present invention based on two dimension pool
The SAR target identification methods of Er Nike moment characteristics rarefaction representations and the recognition effect of other Technology of Radar Target Identification.MSTAR is public
Database is completed by the SAR detectors of Santiago National Laboratory X-band altogether, wherein the pixel of all SAR images
Density is all that 128 rows × 128 are arranged, and the resolution ratio with 0.3m × 0.3m is obtained under 15 ° and 17 ° of the angle of pitch respectively.
Include ten class radar targets in MSTAR public databases, this ten classes radar target is ground military vehicle or civilian vehicle,
And outer shape has similarity, its radar target code name is respectively that (amphibious plate armour is detectd by BMP2 (Infantry Tank), BRDM2
Examine car), BTR60 (armoring transfer cart), BTR70 (armored personnel carrier), D7 (agricultural bull-dozer), T62 (T-62 types main website tank),
(carriage motor howitzer is fought by T72 (T-72 types main website tank), ZIL131 (military trucks), ZSU234 (Self propelled Antiaircraft Gun battlebus) and 2S1
Car).Using the radar target image of 17 ° of angles of pitch shootings in MSTAR public databases as the training sample of experiment, 15 ° are bowed
The radar target image that the elevation angle is shot makees sample to be tested, to carry out radar target recognition test.Table I gives MSTAR numbers
According to all training datas in storehouse and the number of samples of test data.The present embodiment therefrom have chosen BMP2, BTR70, T72 this three class
Target is tested, and wherein BMP2 and T72 respectively have three kinds of models.The picture element density of all SAR images be all 128 rows ×
128 row, azimuth is from 0 degree to 360 degree.Meanwhile, in order to embody the superiority of recognition methods of the present invention, except present invention knowledge
Two-dimentional Zelnick moment characteristics (being abbreviated as 2D-Zms) and rarefaction representation sorting technique (being abbreviated as SRC) employed in other method
Outside, principal component analysis feature (being abbreviated as PCA) is also used, (is abbreviated as with SVMs study classification method respectively
SVM) it is combined with K arest neighbors sorting technique (being abbreviated as KNN), tertiary target is identified experiment.Table II-IV is shown respectively
The discrimination statistical result of SRC methods, SVM methods and KNN methods under 2D-Zms features and PCA features in this experiment.From
As can be seen that (i.e. the present invention is based on two-dimentional Zelnick moment characteristics using 2D-Zms feature combination SRC classifying identification methods in table
The SAR target identification methods of rarefaction representation) identification performance be best.
Table I
The discrimination of Table II 2D-Zms Te Zheng ＆PCA feature+SRC methods
The discrimination of Table III 2D-Zms Te Zheng ＆PCA feature+SVM methods
The discrimination of Table IV 2D-Zms Te Zheng ＆PCA feature+KNN methods
Data in from Table II to IV find out that the discrimination of each recognition methods during based on PCA features is used than the present invention
Based on 2D cut into slices Zernike moment characteristics discrimination it is generally lower, and combine SRC recognition methods when, 2D-Zms+
The average criterion correct recognition rata of SRC methods (recognition methods i.e. of the present invention) has reached 97.1%, to be far above PCA features+SRC
The average criterion correct recognition rata 82.6% of method, illustrates the validity of SAR target identification methods of the present invention.Because
PCA features can not response diagram picture well local feature, and these local features are helpful to recognizing, while this hair
2D slice maps proposed in bright method have been effectively maintained the local feature of SAR image, along with high-order Zernike squares can be with
The local message of description image well, meanwhile, the redundancies of Zernike squares yet very little does not result in the waste of feature, therefore I
The Zernike moment characteristics of 2D slice maps that calculate there is very strong discriminating for SAR radar target automatic identifications
Power.
In addition, this experiment is also studied to the noise robustness of recognition methods of the present invention.In order to verify noise robustness,
The Gaussian noise of varying strength is added in experiment in SAR image, Fig. 5 is that the antinoise of SAR target identification methods of the present invention is real
Result figure is tested, it will be seen that when the signal to noise ratio added is higher than 0dB, discrimination also nearly all exceedes from Fig. 5
90%, illustrate that the noise robustness of SAR target identification methods of the present invention is fine.
By above-mentioned experimental verification, show to carry out radar target automatic identification to be proved to be very using 2D-Zernike squares
Effectively.By experiment, the conclusion drawn is as follows：First, the 2D-Zernike that radar target identification method of the present invention is used
Moment characteristics than PCA feature in terms of the redundancy of data it is good, while 2D-Zernike features more have distinctive, this
Outside, the inventive method is rendered as SAR image to carry out two dimension segmentation section after 3D forms, obtains the SAR two dimension slicings of binaryzation
Image, can be very good to retain the local binarization Electromagnetic Scattering of the middle carrying of three dimensional form SAR image, these information pair
In the Classification and Identification of radar target be very important；Second, from experiments it is evident that rarefaction representation classifying identification method with
The combination of 2D-Zernike moment characteristics, it is more more effective than classifying identification methods such as traditional K arest neighbors, SVMs, can be with
Preferably radar target is classified, more accurately radar target recognition result is obtained.
Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with
The present invention is described in detail good embodiment, it will be understood by those within the art that, can be to skill of the invention
Art scheme is modified or equivalent substitution, and without departing from the objective and scope of technical solution of the present invention, it all should cover at this
Among the right of invention.
Claims (3)
1. the SAR target identification methods based on two-dimentional Zelnick moment characteristics rarefaction representation, it is characterised in that including following step
Suddenly：
1) SAR image of radar target is obtained, and SAR image is rendered as the SAR 3-D views of three-dimensional, three dimensions are respectively
Row pixel coordinate, row pixel coordinate and the electromagnetic scattering amplitude of SAR image；
2) by electromagnetic scattering amplitude dimension be evenly dividing for several amplitudes it is interval, by electromagnetic scattering amplitude in SAR 3-D views
The two-dimensional pixel image coordinate of pixel in same amplitude interval is right in the interval institute of respective magnitudes as SAR 3-D views
The SAR two-dimensional slice images answered, so that the SAR three-dimensional image segmentations of radar target are turned into multiple SAR two-dimensional slice images；
3) the Zelnick moment characteristics of each width SAR two-dimensional slice images of SAR 3-D views are extracted, the pool of radar target is constituted
Er Nike Character eigenvectors；
4) for the different known radar target of multiclass, the SAR image of multiple known radar targets is gathered respectively as training sample
This, and according to step 1)~the Zelnick Character eigenvector of each training sample in each classification 3) is extracted respectively, so that by
The set composing training sample set of the Zelnick Character eigenvector of each training sample of each classification；
5) radar target to be measured is directed to, the SAR image of radar target to be measured is gathered as test sample, is extracted according to step 1~3
The Zelnick Character eigenvector of test sample；
6) the Zelnick Character eigenvector for concentrating each training sample using training sample sets up solving sparse linear equations, to test
The Zelnick Character eigenvector of sample carries out sparse linear expression, and solution obtains the sparse of each in the solving sparse linear equations
Coefficient, is the radar target belonging to radar target to be measured by the kind judging belonging to the training sample corresponding to non-zero sparse coefficient
Classification, realizes the identification to radar target to be measured.
2. the SAR target identification methods according to claim 1 based on two-dimentional Zelnick moment characteristics rarefaction representation, its feature
It is, the step 3) in, the Zelnick moment characteristics b of width SAR two-dimensional slice images expression formula is：
<mrow>
<mi>b</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mi>&pi;</mi>
</mfrac>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mi>r</mi>
<mo>=</mo>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>r</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mi>&theta;</mi>
<mo>=</mo>
<mo>-</mo>
<mi>&pi;</mi>
</mrow>
<mrow>
<mi>&theta;</mi>
<mo>=</mo>
<mi>&pi;</mi>
</mrow>
</msubsup>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mi>q</mi>
</mrow>
<mi>p</mi>
</munderover>
<msub>
<mi>B</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
<mi>k</mi>
</mrow>
</msub>
<msup>
<mi>r</mi>
<mi>k</mi>
</msup>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mi>q</mi>
<mi>&theta;</mi>
</mrow>
</msup>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>r</mi>
<mo>,</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mi>r</mi>
<mi>d</mi>
<mi>r</mi>
<mi>d</mi>
<mi>&theta;</mi>
<mo>;</mo>
</mrow>
Wherein, r represent row pixel coordinate in SAR two-dimensional slice images be the pixel (x, y) that y, row pixel coordinate are x to
Amount,θ represents the angle of the vector and row pixel coordinate axle of pixel (x, y) in SAR two-dimensional slice images, θ=
tan-1(y/x)；F (r, θ) represents the intensity function of pixel (x, y) in SAR two-dimensional slice images, when SAR two-dimensional slice images
Have pixel at middle pixel (x, y) position, its intensity function f (r, θ)=1, when pixel in SAR two-dimensional slice images (x,
Y) there is no pixel at position, then its intensity function f (r, θ)=0；P- | q | it is even number, 0≤| q |≤p, and p >=0；BpqkFor pool
The polynomial coefficients of Er Nike：
<mrow>
<msub>
<mi>B</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
<mi>k</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mfrac>
<mrow>
<mi>p</mi>
<mo>-</mo>
<mi>k</mi>
</mrow>
<mn>2</mn>
</mfrac>
</msup>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mo>+</mo>
<mi>k</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
</mrow>
<mo>!</mo>
</mrow>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>p</mi>
<mo>-</mo>
<mi>k</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
<mo>!</mo>
<mo>(</mo>
<mfrac>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mi>q</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
<mo>!</mo>
<mo>(</mo>
<mfrac>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mi>q</mi>
</mrow>
<mn>2</mn>
</mfrac>
<mo>)</mo>
<mo>!</mo>
</mrow>
</mfrac>
<mo>;</mo>
</mrow>
By the Zelnick moment characteristics for each width SAR two-dimensional slice images for extracting SAR 3-D views, radar target is obtained
One group of Zelnick Character eigenvector.
3. the SAR target identification methods according to claim 1 based on two-dimentional Zelnick moment characteristics rarefaction representation, its feature
It is, the step 6) be specially：
61) the Zelnick Character eigenvector for concentrating each training sample using training sample sets up following sparse linear side
Journey, sparse linear expression is carried out to the Zelnick Character eigenvector of test sample：
<mrow>
<msub>
<mi>b</mi>
<mi>z</mi>
</msub>
<mo>=</mo>
<mi>&beta;</mi>
<mo>&times;</mo>
<mi>H</mi>
<mo>=</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>+</mo>
<mo>...</mo>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
</mrow>
</msub>
<mo>+</mo>
<mo>...</mo>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<mo>+</mo>
<mo>...</mo>
<mo>+</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>K</mi>
<mo>,</mo>
<msub>
<mi>N</mi>
<mi>K</mi>
</msub>
</mrow>
</msub>
<msub>
<mi>b</mi>
<mrow>
<mi>K</mi>
<mo>,</mo>
<msub>
<mi>N</mi>
<mi>K</mi>
</msub>
</mrow>
</msub>
<mo>;</mo>
</mrow>
Wherein, bzRepresent the Zelnick Character eigenvector of test sample；H represents training sample set, and β represents solving sparse linear equations
Sparse coefficient vector, wherein：
H=[h1,h2,…,hi,…,hK]；
hiThe Zelnick Character eigenvector subset of the i-th class known radar target training sample, 1≤i≤K are represented, K represents training
The classification sum of known radar target included in sample set；And Represent the i-th class
Known radar target n-thiThe Zelnick Character eigenvector of individual training sample, 1≤ni≤Ni, NiRepresent to be directed to thunder known to the i-th class
The number of the training sample gathered up to target；
<mrow>
<mi>&beta;</mi>
<mo>=</mo>
<mo>&lsqb;</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<msub>
<mi>N</mi>
<mn>1</mn>
</msub>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<msub>
<mi>n</mi>
<mi>i</mi>
</msub>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mrow>
<mi>K</mi>
<mo>,</mo>
<msub>
<mi>N</mi>
<mi>K</mi>
</msub>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>;</mo>
</mrow>
Represent to correspond to the i-th class known radar target n-th in sparse coefficient vectoriThe Zelnick moment characteristics of individual training sample
VectorSparse coefficient；
62) withAs sparse coefficient vector optimization aim, withIt is used as constraint bar
The solving sparse linear equations set up are solved by part, obtain the optimization aim sparse coefficient vector of the solving sparse linear equations's
Value；Wherein, ε is presetting sparse reconstructed error threshold value, | | | |0For L0 norm operators；
63) by optimization aim sparse coefficient vectorThe kind judging belonging to training sample corresponding to middle non-zero sparse coefficient is
Radar target classification belonging to radar target to be measured, realizes the identification to radar target to be measured.
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