CN109444880A - A kind of SAR target identification method based on the fusion of multiple features low-rank representation - Google Patents
A kind of SAR target identification method based on the fusion of multiple features low-rank representation Download PDFInfo
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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
- 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
- G01S7/411—Identification of targets based on measurements of radar reflectivity
Abstract
The invention discloses a kind of SAR target identification methods based on the fusion of multiple features low-rank representation, low-rank representation model is applied in the target identification problem under SAR configuration, combine identification SAR target using multiple features low-rank representation, improve accuracy of identification, furthermore, the invention also provides a kind of new two-graded fusion strategies, this convergence strategy has sufficiently excavated the contribution of the multi-faceted correlation and multiple features of SAR image to identification, and two stage decision fusion further improves the robustness of proposed method.
Description
Technical field
The present invention relates to Technology of Radar Target Identification field more particularly to it is a kind of based on multiple features low-rank representation fusion
SAR target identification method.
Background technique
It is special based on synthetic aperture radar (SAR) round-the-clock, work that is round-the-clock and not influenced by weather, illumination condition
Point, SAR have been widely used for civilian and military field.SAR automatic target detection (SARATR) technology is in SAR image target
It plays an important role in processing and interpretation.
Common SAR target identification method includes: the method for (1) based on template matching, and this method passes through training image structure
Build a series of reference picture (airspace or time domain), i.e. template.These templates are stored in advance, constitute template library.It is needing
When identification, SAR target image to be identified for one first will be all in the test image and template library
Template is matched, and is then grouped into the test image in the class where most similar template therewith.However, this method needs
A large amount of template is stored in advance, computation burden is very heavy.(2) based on the method for model, this is one used in MSTAR project
Kind recognition methods.This method comprises the concrete steps that: firstly, extracting the feature of unknown object, releasing one according to mathematical model
A little relevant candidate targets, then assume the classification and posture of these targets respectively；Then, model construction is passed through to candidate target
Technology carries out three-dimensional imaging, extracts scattering center model, and one-step prediction of going forward side by side identifies clarification of objective, regards target to be identified as
Fixed reference feature；It is finally matched and is adjudicated.However, this method is the biggest problems are that need accurate estimation scattering model
Parameter to noise-sensitive and is not easy to realize.(3) based on the method for indicating study, with the development of machine learning, indicate that study is made
For an important branch in machine learning field, based on its outstanding properties in signal processing and data mining by
Person's concern.
Rarefaction representation and compressed sensing are the current hot research topics indicated in study.Rarefaction representation and compressed sensing are carved
What is drawn is the sparsity of vector, but in practical applications, we will face various data, such as image, video, these data days
It is exactly so matrix.For the measurement of matrix sparsity, if continuing to apply the sparsity of vector, they are launched into vector to locate
Reason, that will destroy the inside of data as a result, can lead to the problem of in many applications a large amount of.In addition, traditional SAR target identification
Original image is mostly only utilized in algorithm, and the dimension of one side original image is excessively high to reduce subsequent classifier performance；It is another
There is a large amount of redundancy in aspect original image；These all limit the performance of target identification.In addition, it is contemplated that every a kind of special
Sign is different the contribution of identification, has had document to prove that the robustness of identification can be improved in multiple features fusion.Although conventional
Fusion method can obtain certain effect, but without excavating the strong correlation between the adjacent SAR image in orientation.
In conclusion how to provide a kind of new SAR target identification method, the identification during SAR target identification is improved
Precision and robustness always are the important topic studied in the art.
Summary of the invention
In view of the above shortcomings of the prior art, the invention discloses a kind of based on the fusion of multiple features low-rank representation
Low-rank representation model is applied in the target identification problem under SAR configuration, utilizes multiple features low-rank by SAR target identification method
It indicates joint identification SAR target, improves accuracy of identification, in addition, the invention also provides a kind of new two-graded fusion strategy, this
One convergence strategy has sufficiently excavated the contribution of the multi-faceted correlation and multiple features of SAR image to identification, and two stage decision melts
Conjunction further improves the robustness of proposed method.
In order to solve the above technical problems, present invention employs the following technical solutions:
A kind of SAR target identification method based on the fusion of multiple features low-rank representation, includes the following steps:
(1) the known radar target different for N class, acquires the SAR image in multiple orientation of every class known radar target,
Using the SAR image of each known radar target as a training sample, using the set of all training samples as training sample
Collection, extracts the Gabor transformation feature, PCA feature and Wavelet Transform Feature of each training sample respectively；
(2) it is directed to radar target to be measured, the SAR image in multiple orientation of radar target to be measured is acquired, by each SAR image
As a test sample, using the set of all test samples as test sample collection, each test sample is extracted respectively
Gabor transformation feature, PCA feature and Wavelet Transform Feature；
(3) the Gabor transformation feature based on training sample set, PCA feature and Wavelet Transform Feature obtain characteristics dictionary；
(4) Gabor transformation feature, PCA feature and Wavelet Transform Feature based on training sample set and test sample collection are asked
The low-rank representation coefficient matrix of test sample collection；
(5) the low-rank representation coefficient matrix based on characteristics dictionary and test sample collection acquires test sample and concentrates each test specimens
First prediction label of Gabor transformation feature originally, PCA feature and Wavelet Transform Feature；
(6) the of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature is concentrated to test sample
One prediction label, which carries out multi-faceted neighborhood, votes to obtain test sample and concentrates the Gabor transformation feature of each test sample, PCA feature
And the second prediction label of Wavelet Transform Feature；
(7) the of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature is concentrated to test sample
Two prediction labels carry out Bayesian Fusion, obtain the final class label of test sample collection, realize the identification to radar target to be measured.
Preferably, in step (3):
Characteristics dictionary is Xk, XkIndicate corresponding k-th of the eigenmatrix of N class training sample, whereinK is characterized types index, k=1, and 2,3, k-th of eigenmatrix of c class sample be
Preferably, in step (4):
Based on formulaSeek the low-rank table of test sample collection
Show coefficient matrix Wk(y), wherein α and β is respectively noise term coefficient and regularization term coefficient, | | | |FRepresenting matrix
Frobenius norm,C class training sample relative toLow-rank representation coefficient matrix,Refer to and eliminates
Corresponding k-th of the eigenmatrix of N class training sample of c class training sample, 1≤c≤N, EkIt is noise matrix, AkIt indicates to include instruction
Practice the eigenmatrix of sample set and test sample collection, Ak=[Xk,Yk], YkIndicate corresponding k-th of feature square of all test samples
Battle array, wherein characteristics dictionary Xk, XkIndicate corresponding k-th of the eigenmatrix of N class training sample, whereinK is characterized types index, k=1, and 2,3, the low-rank representation coefficient matrix of kth kind feature is Wk,
Middle Wk=[Wk(x),Wk(y)]。
Preferably, the acquiring method of the first prediction label of k-th of feature of i-th of test sample is such as in step (5)
Under:
Wi k(y)The low-rank representation coefficient matrix W of test sample collection under k-th of featurek(y)In i-th column, indicate i-th
Test sampleIn characteristics dictionary XkUnder expression coefficient vector, according to Wi k(y)Maximum coefficient value set coefficient threshold ρ, to the
I test sampleWith the azimuth of its corresponding training sample of low-rank representation coefficient maximum valueCentered on, and the side of setting
Parallactic angle contiguous range V obtains azimuth in all kinds of training samples and is inSubset in sectionIt finds every
A training sample subsetIn Wi k(y)In corresponding coefficient subsetWhereinGeneration
Table c class training sample subsetCorresponding coefficient subset,
Work as satisfactionThen determine i-th of test sampleThe first prediction label be rk；
Wherein, AndFor intermediate parameters, 1≤q≤Q.
Preferably, as follows in the acquiring method of the second prediction label of k-th of feature of i-th of the test sample of step (6):
Wi k(y)It is the low-rank representation coefficient matrix W of the test sample collection under k-th of featurek(y) the i-th column vector in, table
Show i-th of test sampleIn characteristics dictionary XkUnder expression coefficient vector, with the azimuth of the test sampleCentered on set
A fixed orientation neighborhoodQ be field angle, obtain be in the neighborhood neighborhood test sample collection, p-th
First prediction label of neighborhood test sample isIt is assumed thatThe probability for belonging to c class isThen multi-faceted neighborhood is thrown
Ticket rule are as follows:
Work as satisfaction
Then i-th of test sampleThe second prediction label beWherein,For intermediate parameters, P is neighborhood test specimens
This concentration neighborhood test sample number.
Preferably, specifically comprise the following steps: in step (7)
I-th of test sampleThe prediction obtained under Gabor transformation feature, PCA feature and Wavelet Transform Feature mode
Label is respectivelyWithIt is assumed that the recognition accuracy under these three feature modes is respectively PGabor, PPCAAnd PWavelet,
The radar target to be measured for belonging to c class under Gabor characteristic mode is predicted to beThe confidence level of class can be by as follows
Bayesian criterion is calculated:
Wherein, P (c) represents i-th of test sampleBelong to the probability of c class,It indicates in Gabor characteristic
I-th of test sample of c class under modeIt is predicted asThe probability of class；
The confidence level under PCA feature and Wavelet Transform Feature mode can similarly be obtainedWith
To each test sample, the available confidence level under every kind of feature mode, mutually similar confidence level is by three kinds
The product of confidence level under feature mode determines that the classification with maximum confidence is then as the final class label exported, that is,
Bayesian Decision fusion can be expressed as following formula:
Wherein, R is final class label, c*For the classification of maximum confidence,For the product of the confidence level under three kinds of mutually similar feature modes,
In conclusion the invention discloses a kind of SAR target identification methods based on the fusion of multiple features low-rank representation, including
Following steps: (1) the known radar target different for N class acquires the SAR figure in multiple orientation of every class known radar target
Picture, using the SAR image of each known radar target as a training sample, using the set of all training samples as training sample
This collection extracts the Gabor transformation feature, PCA feature and Wavelet Transform Feature of each training sample respectively；(2) it is directed to thunder to be measured
Up to target, the SAR image in multiple orientation of radar target to be measured is acquired, using each SAR image as a test sample, by institute
Have the set of test sample as test sample collection, extract respectively the Gabor transformation feature of each test sample, PCA feature and
Wavelet Transform Feature；(3) the Gabor transformation feature based on training sample set, PCA feature and Wavelet Transform Feature obtain tagged word
Allusion quotation；(4) Gabor transformation feature, PCA feature and Wavelet Transform Feature based on training sample set and test sample collection seek test specimens
The low-rank representation coefficient matrix of this collection；(5) the low-rank representation coefficient matrix based on characteristics dictionary and test sample collection acquires test
First prediction label of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature in sample set；(6) to survey
It is more that sample originally concentrates the first prediction label of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature to carry out
Orientation neighborhood votes to obtain test sample and concentrates the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature
Second prediction label；(7) the Gabor transformation feature, PCA feature and Wavelet Transform Feature of each test sample are concentrated to test sample
The second prediction label carry out Bayesian Fusion, obtain the final class label of test sample collection, realize to radar target to be measured
Identification.Low-rank representation model is applied in the target identification problem under SAR configuration by the present invention, is joined using multiple features low-rank representation
Identification SAR target is closed, accuracy of identification is improved, in addition, the invention also provides a kind of new two-graded fusion strategy, this fusion
Strategy has sufficiently excavated the contribution of the multi-faceted correlation and multiple features of SAR image to identification, and two stage decision is integrated into one
Step improves the robustness of proposed method.
Detailed description of the invention
In order to keep the purposes, technical schemes and advantages of application clearer, the present invention is made into one below in conjunction with attached drawing
The detailed description of step, in which:
Fig. 1 is a kind of flow chart of SAR target identification method based on the fusion of multiple features low-rank representation disclosed by the invention.
Fig. 2 is low-rank representation coefficient matrix of the training sample set under characteristics dictionary under Gabor characteristic model.
Fig. 3 is low-rank representation coefficient matrix of the training sample set under characteristics dictionary under PCA characteristic model.
Fig. 4 is low-rank representation coefficient matrix of the training sample set under characteristics dictionary under wavelet character model.
Fig. 5 is low-rank representation coefficient matrix of the test sample collection under characteristics dictionary under Gabor characteristic model.
Fig. 6 is low-rank representation coefficient matrix of the test sample collection under characteristics dictionary under PCA characteristic model.
Fig. 7 is low-rank representation coefficient matrix of the test sample collection under characteristics dictionary under wavelet character model.
Fig. 8 is that recognition performance of six kinds of methods under different characteristic dimension compares.
Specific embodiment
The present invention is described in further detail with reference to the accompanying drawing.
As shown in Figure 1, the invention discloses a kind of SAR target identification method based on the fusion of multiple features low-rank representation, packet
Include following steps:
(1) the known radar target different for N class, acquires the SAR image in multiple orientation of every class known radar target,
Using the SAR image of each known radar target as a training sample, using the set of all training samples as training sample
Collection, extracts the Gabor transformation feature, PCA feature and Wavelet Transform Feature of each training sample respectively；
(2) it is directed to radar target to be measured, the SAR image in multiple orientation of radar target to be measured is acquired, by each SAR image
As a test sample, using the set of all test samples as test sample collection, each test sample is extracted respectively
Gabor transformation feature, PCA feature and Wavelet Transform Feature；
Most of traditional SAR Target Recognition Algorithms only use original SAR image, however the higher-dimension of original image is special
Property will affect subsequent classifier performance.Here, we extract the feature of the three types of SAR target image, i.e. Gabor transformation
Feature, PCA feature and Wavelet Transform Feature.Low-rank representation is carried out respectively to these three features, rather than directly to SAR original graph
As carrying out low-rank representation, the above problem can be effectively avoided.
(3) the Gabor transformation feature based on training sample set, PCA feature and Wavelet Transform Feature obtain characteristics dictionary；
(4) Gabor transformation feature, PCA feature and Wavelet Transform Feature based on training sample set and test sample collection are asked
The low-rank representation coefficient matrix of test sample collection；
(5) the low-rank representation coefficient matrix based on characteristics dictionary and test sample collection acquires test sample and concentrates each test specimens
First prediction label of Gabor transformation feature originally, PCA feature and Wavelet Transform Feature；
(6) the of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature is concentrated to test sample
One prediction label, which carries out multi-faceted neighborhood, votes to obtain test sample and concentrates the Gabor transformation feature of each test sample, PCA feature
And the second prediction label of Wavelet Transform Feature；
(7) the of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature is concentrated to test sample
Two prediction labels carry out Bayesian Fusion, obtain the final class label of test sample collection, realize the identification to radar target to be measured.
For in the multi-faceted multi-configuration identification of SAR target, the class inherited between target is small and difference is big in class, causes to calculate
The not high problem of the accuracy of identification and robustness of method, the present invention propose a kind of SAR target based on the fusion of multiple features low-rank representation
Recognition methods.Compared to the prior art, method proposed by the present invention has the advantage that low-rank representation model is applied to by (1)
In target identification problem under SAR configuration, combines identification SAR target using multiple features low-rank representation, improves accuracy of identification,
(2) a kind of new two-graded fusion strategy is proposed, this convergence strategy has sufficiently excavated the multi-faceted correlation of SAR image and more
Contribution of the feature to identification, and two stage decision fusion further improves the robustness of proposed method.
When it is implemented, in step (3):
Characteristics dictionary is Xk, XkIndicate corresponding k-th of the eigenmatrix of N class training sample, whereinK is characterized types index, k=1, and 2,3, k-th of eigenmatrix of c class sample be
When it is implemented, in step (4):
Based on formulaSeek the low-rank table of test sample collection
Show coefficient matrix Wk(y), wherein α and β is respectively noise term coefficient and regularization term coefficient, | | | |FRepresenting matrix
Frobenius norm,C class training sample relative toLow-rank representation coefficient matrix,Refer to and eliminates
Corresponding k-th of the eigenmatrix of N class training sample of c class training sample, 1≤c≤N, EkIt is noise matrix, AkIt indicates to include instruction
Practice the eigenmatrix of sample set and test sample collection, Ak=[Xk,Yk], YkIndicate corresponding k-th of feature square of all test samples
Battle array, wherein characteristics dictionary Xk, XkIndicate corresponding k-th of the eigenmatrix of N class training sample, whereinK is characterized types index, k=1, and 2,3, the low-rank representation coefficient matrix of kth kind feature is Wk,
Middle Wk=[Wk(x),Wk(y)]。
Most of traditional SAR Target Recognition Algorithms only use original SAR image, however the higher-dimension of original image is special
Property will affect subsequent classifier performance.Here, we extract the feature of the three types of SAR target image, i.e. Gabor transformation
Feature, PCA feature and Wavelet Transform Feature.Low-rank representation is carried out respectively to these three features, rather than directly to SAR original graph
As carrying out low-rank representation, the above problem can be effectively avoided.
Based on the unique image-forming mechanism of SAR, SAR image is sensitive to imaging azimuth, and which results in same class SAR targets
Between due to different angles, result in class and differ greatly；Furthermore in the configuration model (mesh of same major class for introducing target
Have different configuration models under mark) after, difference configures the target between model, and class inherited is smaller.To difference in this kind
Greatly, the target identification problem in the small situation of class inherited, the introducing of low-rank representation model can reach preferable recognition effect.
Firstly, we carry out Gabor, PCA and Wavelet three classes feature extraction to original SAR image respectively.Indicate corresponding three eigenmatrixes of N class training sample.Each eigenmatrix
It is that classification based on training sample and azimuth are tactic, whereinIt indicates by ncA dimension is the training of m
K-th of eigenmatrix of the c class sample of sample composition (c represents classification).Indicate all tests
Corresponding k-th of the eigenmatrix of sample, each column indicate a test sample in the matrix.Ak=[Xk,Yk] indicate to include training
The eigenmatrix of data set and test data set.AkIn each sample can pass through characteristics dictionary XkLinear group of middle atom
It closes to indicate.
Ak=XkWk
Wherein, Wk=[Wk(x),Wk(y)], Wk(x)It is the low-rank representation coefficient matrix of training sample set, Wk(y)It is test sample
The low-rank representation coefficient matrix of collection.
Low-rank degree reflects the degree that low dimensional structures are excavated from high dimensional data.Compared to rarefaction representation, low-rank representation pair
It is more reasonable in the degree of rarefication of Description Matrix data.In the case where considering noise, low-rank representation can be solved by following formula.
s.t.Ak=XkWk+Ek
Wherein EkIt is corresponding noise matrix.Due to the discreteness and nonconvex property of rank function, the solution of above formula is usually one
A NP-hard problem.Nuclear norm is the optimal convex approximation of rank function, can substitute rank function well with nuclear norm, can will be upper
Formula non-convex optimization problem is converted into following convex optimization problem.
s.t.Ak=XkWk+Ek
Wherein | | Wk||*It is WkNuclear norm, i.e. WkThe sum of singular value.With the eigenmatrix X of training sample setkAs spy
Levy dictionary.In this way, each training sample should be reconstructed by mutually similar atom corresponding in characteristics dictionary.Therefore in training sample
Low-rank representation coefficient matrix Wk(x)In, the non-zero of each training sample indicates that coefficient only concentrates on corresponding mutually similar atom
On.In order to obtain this structure, we introduce regularization termThe purpose for introducing the regularization term is different in order to make
The expression coefficient of class atom is minimum, i.e., constraint is so that the expression coefficient of similar atom is maximum.We have obtained finally low in this way
The objective function that order indicates,
s.t.Ak=XkWk+Ek
Above formula solves the method for Lagrange multipliers that can use augmentation.
Based on WkCharacteristic with low-rank and structure regularization is carried out to it, if the azimuth of test sample is also to press
Ascending is tactic, then test sample passes through low-rank representation coefficient matrix Wk(y)It should be with the low-rank representation of training sample
Coefficient matrix Wk(x)With similar structure.In order to verify this inference, we learn three kinds of features corresponding to it respectively
Low-rank representation matrix Wk, as shown in Figures 2 to 7.It can be seen that the low-rank representation for any feature in from Fig. 2 to Fig. 7
Coefficient matrix Wk, Wk(y)And Wk(x)A kind of diagonal arrangement is all presented, i.e. the maximum value of expression coefficient is generally concentrated on the diagonal.
For Wk(y), these maximum expression coefficient values correspond to and test sample has close azimuthal atom.Based on above point
Analysis, to each feature, it is proposed that the target identification decision-making technique of the low-rank representation coefficient based on test sample.
Fig. 2 to Fig. 4 refers respectively to Gabor, and under PCA and wavelet character mode, training sample set is low under characteristics dictionary
Order indicates coefficient matrix.As can be seen that since regularization term is block diagonal form, low-rank representation of the training sample under dictionary
Coefficient concentrates on the atom of its respective class, i.e., image is only indicated by the base of respective class.Obtained expression coefficient matrix is presented
A kind of diagonal arrangement, further demonstrates this point.It can also be seen that the test sample collection for learning to obtain is in spy from Fig. 5 to Fig. 7
Levying the low rank sparse matrix approximation under dictionary is in diagonal arrangement, it is contemplated that for test sample, be should also be by the base of corresponding class
It indicates, i.e. the otherness of the distribution of coefficient reflects the difference of test sample classification, therefore this structure has stronger mirror
Other ability, my classification are also based on the low-rank representation coefficient matrix of each class testing collection feature
When it is implemented, in step (5) the first prediction label of k-th of feature of i-th of test sample the side of seeking
Method is as follows:
Wi k(y)The low-rank representation coefficient matrix W of test sample collection under k-th of featurek(y)In i-th column, indicate i-th
Test sampleIn characteristics dictionary XkUnder expression coefficient vector, according to Wi k(y)Maximum coefficient value set coefficient threshold ρ, to the
I test sampleWith the azimuth of its corresponding training sample of low-rank representation coefficient maximum valueCentered on, and orientation is set
Angular neighborhood range V obtains azimuth in all kinds of training samples and is inSubset in sectionIt finds each
Training sample subsetIn Wi k(y)In corresponding coefficient subsetWhereinIt represents
C class training sample subsetCorresponding coefficient subset,
Work as satisfactionThen determine i-th of test sampleThe first prediction label be rk；
Wherein, AndFor intermediate parameters, 1≤q≤Q.
There is close azimuthal atom with test sample since maximum expression coefficient value corresponds to.Therefore in mechanism
On, the non-zero of test sample indicates that coefficient should concentrate on having on certain close azimuthal class atom with test sample, and statistics is every
Atom corresponding coefficient in a kind of neighbour azimuth is greater than the quantity of threshold value, theoretically only has and test sample belongs to of a sort original
Son is just with the coefficient number for being at most more than threshold value.The strong of adjacent orientation angle training sample is utilized in our recognition strategy
Correlation.According to this method, corresponding first prediction label of three kinds of features is obtained.
When it is implemented, the acquiring method of the second prediction label in k-th of feature of i-th of the test sample of step (6)
It is as follows:
Wi k(y)It is the low-rank representation coefficient matrix W of the test sample collection under k-th of featurek(y)In the i-th column vector, indicate
I-th of test sampleIn characteristics dictionary XkUnder expression coefficient vector, with the azimuth of the test sampleCentered on set
One orientation neighborhoodQ is field angle, obtains the neighborhood test sample collection for being in the neighborhood, and p-th adjacent
First prediction label of domain test sample isIt is assumed thatThe probability for belonging to c class isThen multi-faceted neighborhood ballot rule
Then are as follows:
Work as satisfaction
Then i-th of test sampleThe second prediction label beWherein,For intermediate parameters, P is neighborhood test specimens
This concentration neighborhood test sample number.
The output of second prediction label of current test sample is surveyed based on the neighborhood in the test sample orientation angular neighborhood
Obtained from the label of sample sheet is voted.In this step, we have excavated test sample and its neighborhood test sample
Strong correlation；For theoretically, test sample and its neighborhood test sample should class label having the same, in this way using in many ways
The method of multiple sample ballot fusions, greatly reduces the erroneous judgement to target type in the neighborhood of position.It is worth noting that: this melts
Conjunction is still to complete under single feature, therefore what is merged by this level-one is still three the second prediction labels.
When it is implemented, specifically comprising the following steps: in step (7)
I-th of test sampleThe prediction obtained under Gabor transformation feature, PCA feature and Wavelet Transform Feature mode
Label is respectivelyWithIt is assumed that the recognition accuracy under these three feature modes is respectively PGabor, PPCAAnd PWavelet,
The radar target to be measured for belonging to c class under Gabor characteristic mode is predicted to beThe confidence level of class can be by as follows
Bayesian criterion is calculated:
Wherein, P (c) represents i-th of test sampleBelong to the probability of c class,It indicates in Gabor characteristic
I-th of test sample of c class under modeIt is predicted asThe probability of class；
The confidence level under PCA feature and Wavelet Transform Feature mode can similarly be obtainedWith
To each test sample, the available confidence level under every kind of feature mode, mutually similar confidence level is by three kinds
The product of confidence level under feature mode determines that the classification with maximum confidence is then as the final class label exported, that is,
Bayesian Decision fusion can be expressed as following formula:
Wherein, R is final class label, c*For the classification of maximum confidence,
For the product of the confidence level under three kinds of mutually similar feature modes,
In order to prove the validity of proposed two-stage multiple features low-rank representation blending algorithm (TFMFLRR), we
Itself and other five kinds of algorithms are compared.This five kinds of algorithms include: the low-rank representation learning algorithm (LRR based on Gabor characteristic
(Gabor)), the low-rank representation learning algorithm based on PCA feature (LRR (PCA)), the low-rank representation based on wavelet character learn to calculate
Method (LRR (Wavelet)), multiple features low-rank representation vote blending algorithm (VFMFLRR, the method for corresponding step (6) of the present invention)
And multiple features low-rank representation Bayesian Fusion algorithm (BFMFLRR, the method for corresponding step (7) of the present invention).We are further
Recognition performance of six kinds of methods under different intrinsic dimensionalities is compared, as shown in Figure 8.From figure 8, it is seen that for based on single
The low-rank representation learning algorithm of one feature, such as LRR (Gabor), LRR (PCA) and LRR (Wavelet), with intrinsic dimensionality
Increase, discrimination also significantly rises.When dimension is more than 600, the discrimination of these three algorithms is more than 90%.In addition, right
In blending algorithm, with the increase of intrinsic dimensionality, VFMFLRR and BFMFLRR can improve the identity of LRR to a certain extent
Can, but TFMFLRR is below on Arbitrary Dimensions.This is primarily due to the ballot of first order test sample orientation angular neighborhood can be effective
The error sample under every kind of feature mode is reduced, while the Bayesian Fusion of the second level can make full use of the first order obtained three
The probability density characteristics of kind decision.The mechanism merged using this two stage decision, can effectively improve the recognition performance of LRR.
Finally, it is stated that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting, although passing through ginseng
According to the preferred embodiment of the present invention, invention has been described, it should be appreciated by those of ordinary skill in the art that can
To make various changes to it in the form and details, without departing from the present invention defined by the appended claims
Spirit and scope.
Claims (6)
1. a kind of SAR target identification method based on the fusion of multiple features low-rank representation, which comprises the steps of:
(1) the known radar target different for N class, acquires the SAR image in multiple orientation of every class known radar target, will be every
The SAR image of a known radar target is divided as a training sample using the set of all training samples as training sample set
Indescribably take the Gabor transformation feature, PCA feature and Wavelet Transform Feature of each training sample；
(2) be directed to radar target to be measured, acquire the SAR image in multiple orientation of radar target to be measured, using each SAR image as
One test sample, using the set of all test samples as test sample collection, the Gabor for extracting each test sample respectively becomes
Change feature, PCA feature and Wavelet Transform Feature；
(3) the Gabor transformation feature based on training sample set, PCA feature and Wavelet Transform Feature obtain characteristics dictionary；
(4) Gabor transformation feature, PCA feature and Wavelet Transform Feature based on training sample set and test sample collection ask test
The low-rank representation coefficient matrix of sample set；
(5) the low-rank representation coefficient matrix based on characteristics dictionary and test sample collection acquires test sample and concentrates each test sample
First prediction label of Gabor transformation feature, PCA feature and Wavelet Transform Feature；
(6) the first pre- of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature is concentrated to test sample
Mark label, which carry out multi-faceted neighborhood, votes to obtain test sample and concentrates the Gabor transformation feature of each test sample, PCA feature and small
Second prediction label of wave conversion feature；
(7) the second pre- of the Gabor transformation feature of each test sample, PCA feature and Wavelet Transform Feature is concentrated to test sample
Mark label carry out Bayesian Fusion, obtain the final class label of test sample collection, realize the identification to radar target to be measured.
2. the SAR target identification method as described in claim 1 based on the fusion of multiple features low-rank representation, which is characterized in that
In step (3):
Characteristics dictionary is Xk, and Xk indicates corresponding k-th of the eigenmatrix of N class training sample, whereink
It is characterized types index, k=1,2,3, k-th of eigenmatrix of c class sample be
3. the SAR target identification method as described in claim 1 based on the fusion of multiple features low-rank representation, which is characterized in that
In step (4):
Based on formulaSeek the low-rank representation system of test sample collection
Matrix number Wk(y), wherein α and β is respectively noise term coefficient and regularization term coefficient, | | | |FThe Frobenius of representing matrix
Norm,C class training sample relative toLow-rank representation coefficient matrix,Refer to and eliminates c class training sample
This corresponding k-th of the eigenmatrix of N class training sample, 1≤c≤N, EkIt is noise matrix, AkIndicate include training sample set and
The eigenmatrix of test sample collection, Ak=[Xk,Yk], YkIndicate corresponding k-th of the eigenmatrix of all test samples, wherein special
Sign dictionary is Xk, XkIndicate corresponding k-th of the eigenmatrix of N class training sample, whereinK is characterized
Types index, k=1,2,3, the low-rank representation coefficient matrix of kth kind feature is Wk, wherein Wk=[Wk(x),Wk(y)]。
4. the SAR target identification method as described in claim 1 based on the fusion of multiple features low-rank representation, which is characterized in that
The acquiring method of the first prediction label of k-th of feature of i-th of test sample is as follows in step (5):
Wi k(y)The low-rank representation coefficient matrix W of test sample collection under k-th of featurek(y)In i-th column, indicate i-th test
SampleIn characteristics dictionary XkUnder expression coefficient vector, according to Wi k(y)Maximum coefficient value set coefficient threshold ρ, to i-th
Test sampleWith the azimuth of its corresponding training sample of low-rank representation coefficient maximum valueCentered on, and azimuth is set
Contiguous range V obtains azimuth in all kinds of training samples and is inSubset in sectionFind each instruction
Practice sample setIn Wi k(y)In corresponding coefficient subsetWhereinRepresent c
Class training sample subsetCorresponding coefficient subset,
Work as satisfactionThen determine i-th of test sampleThe first prediction label be rk；
Wherein, AndFor intermediate parameters, 1≤q≤Q.
5. the SAR target identification method as described in claim 1 based on the fusion of multiple features low-rank representation, which is characterized in that
The acquiring method of second prediction label of k-th of feature of i-th of the test sample of step (6) is as follows:
Wi k(y)It is the low-rank representation coefficient matrix W of the test sample collection under k-th of featurek(y)In the i-th column vector, indicate i-th
A test sampleIn characteristics dictionary XkUnder expression coefficient vector, with the azimuth of the test sampleCentered on set one
Orientation neighborhoodQ is field angle, obtains the neighborhood test sample collection for being in the neighborhood, and p-th of neighborhood is surveyed
First prediction label of sample sheet isIt is assumed thatThe probability for belonging to c class isThen multi-faceted neighborhood voting rule
Are as follows:
Work as satisfaction
Then i-th of test sampleThe second prediction label beWherein,For intermediate parameters, P is neighborhood test sample concentration
Neighborhood test sample number.
6. the SAR target identification method as described in claim 1 based on the fusion of multiple features low-rank representation, which is characterized in that
Step (7) specifically comprises the following steps:
I-th of test sampleThe prediction label obtained under Gabor transformation feature, PCA feature and Wavelet Transform Feature mode
RespectivelyWithIt is assumed that the recognition accuracy under these three feature modes is respectively PGabor, PPCAAnd PWavelet,
The radar target to be measured for belonging to c class under Gabor characteristic mode is predicted to beThe confidence level of class can be by as follows
Bayesian criterion is calculated:
Wherein, P (c) represents i-th of test sampleBelong to the probability of c class,It indicates in Gabor characteristic mode
Lower i-th of test sample of c classIt is predicted asThe probability of class；
The confidence level under PCA feature and Wavelet Transform Feature mode can similarly be obtainedWith
To each test sample, the available confidence level under every kind of feature mode, mutually similar confidence level is by three kinds of features
The product of confidence level under mode determines that the classification with maximum confidence is then as the final class label exported, that is,
Bayesian Decision fusion can be expressed as following formula:
Wherein, R is final class label, c*For the classification of maximum confidence,For the product of the confidence level under three kinds of mutually similar feature modes,
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