CN102902979A - Method for automatic target recognition of synthetic aperture radar (SAR) - Google Patents

Abstract

The invention discloses a method for automatic target recognition of an SAR. The automatic target recognition of the SAR mainly comprises three steps such as SAR image preprocessing, feature extraction and target classification, and the method is applicable to feature extraction and target classification of the automatic target recognition of the SAR and solves the problem that effective identification information can not be extracted from high-dimensional SAR images. According to the method for the automatic target recognition of the SAR, a manifold structure theory is introduced, and the method is based on a neighborhood identification embedding criterion. The method comprises the steps of A, initializing; B, constructing a similarity matrix and a difference matrix; C, calculating a target matrix on the basis of a maximum margin criterion; D, calculating a projection matrix; E, conducting feature extraction on training samples according to the projection matrix to obtain training sample features; E, conducting feature extraction on SAR images to be classified to obtain test sample features; and F, classifying SAR images to be tested according to a nearest neighbor classifier, wherein Step A-Step E belong to the feature extraction phase, and Step F belongs to the target classification phase. By the aid of the method, the probability of correct identification of targets can be improved.

Description

A kind of method of synthetic-aperture radar automatic target identification

Technical field:

(Synthetic Aperture Radar, be called for short: SAR) field, it is particularly related to, and the SAR Characteristic of Image extracts and the target classification field in the automatic target identification (Automatic Target Recognition, ATR) to the invention belongs to synthetic-aperture radar.

Background technology:

Many weeks, the identification of SAR automatic target is an important application facet of SAR imaging, it combines modern signal processing technology and pattern recognition theory, utilize computing machine that the information that gathers is carried out automatic analysis, finish discovery, location, identification target, thereby so that the ATR technology can provide the information such as objective attribute target attribute, classification.By SAR ATR technology, can remove interfere information in the SAR image and the redundant information of target, extract the diagnostic characteristics of target, both improved the recognition capability to unknown object, shortened again the classification time.

SAR ATR mainly comprises three steps, the i.e. pre-service of SAR image, feature extraction and target classification.Wherein feature extraction is the key issue of SAR ATR, and it directly affects the effect of classification.The purpose of feature extraction is to utilize various converter techniques to improve the distributed architecture of raw data in feature space, removes redundant information, thereby has improved the identifiability of data, reduces operand.In document " Efficient and Robust Feature Extraction by Maximum Margin Criterion ", proposed a kind ofly (to see " Haifeng Li; Tao Jiang; Keshu Zhang; Efficient and robust feature extraction by maximum margin criterion.IEEE Transactions on Neural Networks; Vol 17; No.1 for details based on maximal margin criterion (MMC) feature extracting method, January 2006, pages:157-165. "); the overall linear distributed architecture of the method based on data is theoretical; merged the classification information of training sample; be intended to seek projection matrix, so that the distance between the similar sample is close to each other after the mapping of sample process projection matrix, the distance between foreign peoples's sample away from each other.

In order to make things convenient for treatment S AR view data, usually two-dimensional SAR image is converted to one-dimensional vector, this will produce the data set of one group of higher-dimension, the distribution of high dimensional data in the space is nonlinear organization and be not overall linear structure, therefore the MMC method that proposes based on overall linear structure can not well be described the distributed architecture of SAR image in the space, will certainly affect recognition performance.

Summary of the invention:

In order to solve the problem that can't extract the characteristic information that is conducive to identify in the feature extraction of SAR ATR in high dimensional data, the present invention proposes a kind of synthetic aperture radar automatic target recognition method based on theory of manifolds.The method is theoretical based on manifold learning, utilizes the maximal margin criterion to extract the characteristic information of data, can so that foreign peoples's sample away from each other, similar sample is close to each other, thereby improves the evident characteristics of feature.The present invention has the characteristics of more reasonable, the high robustness of data space structure distribution, high recognition performance.

Content of the present invention for convenience of description, at first make following term definition:

Definition 1, stream shape

If M is the Hausdorff space, if any point x is belonged to M, the neighborhood U homeomorphism of x in M arranged in m dimension Euclidean space R ^mAn opener, claim that then M is m dimension stream shape.See for details document " Chen Shengshen. the infinitesimal geometry teaching materials. the BJ University Press ".

Definition 2, maximal margin criterion

The maximal margin criterion is a kind of criterion of feature extracting method, see document " Haifeng Li; Tao Jiang; Keshu Zhang.Efficient and robust feature extraction by maximum margin criterion.I EEE Transactions on Neural Networks; Vol 17; No.1, and January 2006 " for details.

Definition 3, eigenwert and proper vector

If A is n rank square formations, if exist number λ and n dimension non-vanishing vector α to make A α=λ α, claim that then λ is the eigenwert of square formation A, α is that square formation A is corresponding to a proper vector of eigenvalue λ.See for details document " Huang Tingzhu, Cheng Xiaoyu. linear algebra and space analytic geometry (second edition). Higher Education Publishing House, 2003 ".

Definition 4, Euclidean distance

Euclidean distance is to measure that a kind of of distance measures between two vectors, establishes vector x and y, and the Euclidean distance between them is || x-y|| ₂See for details document " Huang Tingzhu, Zhong Shouming, Li Zhengliang. matrix theory. the .2003 of Higher Education Publishing House ".

Definition 5, vectorial 2 norms

If column vector x=is (x ₁, x ₂... x _n) ^T∈ R ⁿ, wherein T is transpose of a matrix, then || || ₂Vectorial 2 norms,

See for details document " Huang Tingzhu, Zhong Shouming, Li Zhengliang. matrix theory. Higher Education Publishing House, 2003 ".

Definition 6, diagonal matrix

If square formation A=is (a _Ij) _{N * n}First a _Ij=0 (i ≠ j), claim that then A is diagonal matrix, is denoted as A=diag (a ₁₁, a ₂₂..., a _Nn).See for details document " Huang Tingzhu, Cheng Xiaoyu. linear algebra and space analytic geometry (second edition). Higher Education Publishing House, 2003 "

Definition 7, minimum distance classifier

Be provided with L the sample T=[t that classification is known ₁, t ₂... t _L], each sample t _iClassification be ω _i, i=1,2 ..., L.Existing one sample s to be identified calculates respectively s and each sample t _iEuclidean distance d (s, t _i), then s should belong to and its that class apart from the sample representative of minimum, if that is: Then differentiate s ∈ ω _iSee document " Cover.T.Estimati on by the Nearest Neighbor Rule.IEEE Transactions on Information Theory, Vol 14, No.1, January 1968 " for details.

The present invention proposes the method based on a kind of synthetic-aperture radar automatic target identification of theory of manifolds, and it may further comprise the steps:

Step 1, initialization

Read the SAR image, the SAR image that reads is spliced by row, obtain column vector.The training set that definition contains N width of cloth SAR image is expressed as matrix X=(x ₁, x ₂..., x _i..., x _N) ∈ R ^{M * N}, wherein, N represents the number of samples in this group training sample set, N is positive integer, x ₁First training sample, x ₂Second training sample, x _iI training sample, x _NN training sample, i ∈ 1,2 ..., N}.The dimension of each training sample is m * 1 dimension, and m represents the number of pixels of SAR image, and R represents real number set.The category label set expression of definition training sample is matrix Y=(y ₁, y ₂..., y _i..., y _N), y wherein ₁Training sample x ₁Category label, y ₂Training sample x ₂Category label, y _iTraining sample x _iCategory label, y _NTraining sample x _NCategory label, i ∈ 1,2 ..., N}.Definition SAR image measurement sample set is expressed as matrix X'=(x ₁', x ' ₂..., x _t' ..., x ' _{N '}) ∈ R ^{M * N}', x wherein ₁' be first test sample book, x ₂' be second test sample book, x _t' be t test sample book, x ' _NN test sample book, the number of this group test sample book of N ' expression.Each test sample book x _t' dimension be m * 1 dimension, t ∈ 1,2 ..., N ' }, t is the label of test sample book.

Step 2, structure similarity matrix W ^(w)With the otherness matrix W ^(b)

Step 2 comprises step 2.1, step 2.2, step 2.3:

The training sample set X that step 2.1 obtains according to step 1, employing formula (1) is constructed the Euclidean distance matrix G between all training samples:

G=(g _ij) _NxN，i,j∈{1,2,…,N} （1）

Wherein, the element g of Euclidean distance matrix G _Ij=| x _i-x _j|| ₂Training sample x among the expression training sample set X _iAnd x _jBetween Euclidean distance, || || ₂Be vectorial 2 norms, N represents the number of samples in this group training sample set, and N is positive integer.

The category label set Y of the training sample that step 2.2 obtains according to step 1 and the Euclidean distance matrix G that step 2.1 obtains adopt formula (2) to construct similarity matrix W between all samples ^(w):

$W^{\left(w\right)}={\left(w_{\mathrm{ij}}^{\left(w\right)}\right)}_{N\×N},i,j\∈\{\mathrm{1,2},\·\·\·,N\}---\left(2\right)$

Similarity matrix W wherein ^(w)In element

Training sample x among the expression training sample set X _iAnd x _jBetween the similarity factor of influence:

$w_{\mathrm{ij}}^{\left(w\right)}=\left\{\begin{array}{c}\exp \left({-g}_{\mathrm{ij}}\right),\mathrm{if}(g_{\mathrm{ij}}\≤{\mathrm{\ϵ}}_1\∩y_i=y_j)\\ 0,\mathrm{others}\end{array}\right.---\left(3\right)$

Wherein, ∩ presentation logic symbol " with ", y _iAnd y _jRespectively sample x _iAnd x _jCategory label, ε ₁The adjacent region threshold that represents similar sample, the empirical value that adopts emulation to determine in the reality.

The category label set Y of the training sample that step 2.3 obtains according to step 1 and the Euclidean distance matrix G that step 2.1 obtains adopt the otherness matrix W between formula (4) the structure sample ^(b):

$W^{\left(b\right)}={\left(w_{\mathrm{ij}}^{\left(b\right)}\right)}_{N\×N},i,j\∈\{\mathrm{1,2},\·\·\·,N\}---\left(4\right)$

Otherness matrix W wherein ^(b)In element

Training sample x among the expression training sample set X _iAnd x _jBetween the otherness factor of influence:

$w_{\mathrm{ij}}^{\left(b\right)}=\left\{\begin{array}{c}\exp \left({-g}_{\mathrm{ij}}\right),\mathrm{if}(g_{\mathrm{ij}}\≤{\mathrm{\ϵ}}_2\∩y_i\≠y_j)\\ 0,\mathrm{others}\end{array}\right.---\left(5\right)$

Wherein, ∩ presentation logic symbol " with ", y _iAnd y _jRespectively sample x _iAnd x _jCategory label, ε ₂The adjacent region threshold of expression foreign peoples sample, the empirical value that adopts emulation to determine in the reality.

Step 3, calculate objective matrix J based on the maximal margin criterion

The training sample set X that step 1 is obtained, the similarity matrix W that step 2.2 obtains ^(w)The otherness matrix W that obtains with step 2.3 ^(b), adopt formula (6) to calculate objective matrix J:

J＝X(D ^(w)-D ^(b))X ^T-X(W ^(w)-W ^(b))X ^T （6）

Wherein, X represents the training sample set, and w is similarity matrix W ^(w)Subscript, the expression similarity, b is the otherness matrix W ^(b)Subscript, the expression otherness, D ^(w)Be diagonal matrix, be expressed as $D^{\left(w\right)}=\mathrm{diag}(d_1^{\left(w\right)},d_2^{\left(w\right)},\·\·\·,d_i^{\left(w\right)},\·\·\·,d_N^{\left(w\right)})\∈R^{N\×N},$ Wherein,

Diagonal matrix D ^(w)First element, be expressed as

Diagonal matrix D ^(w)Second element, be expressed as

Diagonal matrix D ^(w)I element, be expressed as

Diagonal matrix D ^(w)N element, be expressed as

D ^(b)Be diagonal matrix, be expressed as $D^{\left(b\right)}=\mathrm{diag}(d_1^{\left(b\right)},d_2^{\left(b\right)},\·\·\·,d_i^{\left(b\right)},\·\·\·,d_N^{\left(b\right)})\∈R^{N\×N},$ Wherein,

Diagonal matrix D ^(b)First element, be expressed as

Diagonal matrix D ^(b)Second element, be expressed as Diagonal matrix D ^(b)I element, be expressed as

Diagonal matrix D ^(b)N element, be expressed as

X ^TIt is the transposition of matrix X.

Step 4, calculating projection matrix V

Adopt projection matrix V that training sample set is carried out dimensionality reduction.

According to the objective matrix J that step 3 obtains, calculate m stack features value and the proper vector of objective matrix J

Wherein, λ _iI the eigenwert of objective matrix J, v _iλ _iThe characteristic of correspondence vector, R represents real number set, sample dimension m is positive integer.

After m eigenwert sorted from big to small, be expressed as λ ₁〉=λ ₂〉=... λ _i〉=... 〉=λ _mWherein, λ ₁The 1st eigenwert after objective matrix J sorts from big to small, λ ₂The 2nd eigenwert after objective matrix J sorts from big to small, λ _iI eigenwert after objective matrix J sorts from big to small, λ _mM eigenwert after objective matrix J sorts from big to small.

Choose λ ₁~ λ _mIn before K eigenvalue of maximum λ ₁~ λ _KThe characteristic of correspondence vector v ₁~ v _KForm projection matrix V, wherein λ _KK the eigenwert of objective matrix J, v ₁λ ₁The characteristic of correspondence vector, v _Kλ _KCharacteristic of correspondence vector, K are the dimensions that extracts feature, and K chooses the arbitrary integer between 1 to sample dimension m.

Step 5, feature extraction

The projection matrix V that obtains according to step 4, all the training sample x among the training sample set X that step 1 is obtained _i, i={1,2 ..., N} is according to formula (7), calculation training sample x _iFeature z _i,

z _i=V ^Tx _i,i∈{1,2,…,N} （7）

Obtain the training sample characteristic set, be expressed as matrix Z _Train=(z ₁, z ₂..., z _i..., z _N), z wherein ₁Expression training sample x ₁Feature, z ₂Expression training sample x ₂Feature, z _iExpression training sample x _iFeature, z _NExpression training sample x _NFeature.V ^TIt is the transposition of matrix V.

All test sample book x among the projection matrix V that obtains according to step 4, the test sample book that step 1 the obtains set X ' _t', t ∈ 1,2 ..., N ' }, according to formula (8), calculate test sample book x _t' feature z _t',

z _t′＝V ^Tx _t′,i∈{1,2,…,N′} （8）

Obtain the test sample book characteristic set and be expressed as matrix Z _Test=(z ₁', z ' ₂..., z _t' ..., z ' _{N '}), z wherein ₁' expression test sample book x ₁Feature, z ₂' expression test sample book x ₂Feature, z _t' expression test sample book x _tFeature, z ' _{N '}Expression test sample book x _{N '}Feature, t is the label of test sample book, N ' is the number of test sample book.

Step 6, target classification

The training sample characteristic set Z that obtains according to step 5 _TrainWith test sample book characteristic set Z _Test, adopt traditional minimum distance classifier to test sample book characteristic set Z _TestIn the feature z of each test sample book _t' classify, obtain the category label y of test sample book _t', t ∈ 1,2 ..., N ' }.

The category label set expression of all test sample books is matrix Y '=(y ₁', y ₂' ..., y _t' ..., y ' _{N '}), wherein, y' ₁Expression test sample book x ₁Category label, y ₂' expression test sample book x ₂Category label, y _t' expression test sample book x _tCategory label, y ' _{N '}Expression test sample book x _{N '}Category label.Test sample book x _tCategory label y _t' be exactly the unknown object kind that synthetic-aperture radar is surveyed.

Through above step, realize synthetic aperture radar target identification.

Need to prove: step 1～5th, the SAR image is carried out feature extraction, obtain the feature that is easy to classify; Step 3 is to adopt the maximal margin criterion to calculate objective matrix J, and similar sample is assembled, foreign peoples's sample away from; The purpose of step 6 target classification is by the feature that compares training sample and the feature of test sample book, determines the classification of test sample book according to feature.

The present invention need not manual intervention, automatically finishes from reading the SAR image to exporting other process of target class the SAR image, reaches the purpose of SAR automatic target identification.

Essence of the present invention and innovative point:

The present invention utilizes manifold learning theoretical, has effectively extracted the feature that is easy to classify in the higher-dimension SAR data.Innovation is the problem that can not effectively extract higher-dimension SAR data characteristics for overall linear structure, and it is theoretical to introduce manifold learning, utilizes the maximal margin criterion, extracts the validity feature that is easy to classify when reducing SAR characteristics of image dimension.

Advantage of the present invention:

1: the data space structure distribution is more reasonable: this method meets the nonlinear Distribution structure of higher-dimension SAR image in the space based on theory of manifolds.Adopt theory of manifolds from higher-dimension SAR view data, to recover its low dimensional manifold structure, not only reduced intrinsic dimensionality, can also obtain the characteristic information that is easy to classify.

2: robustness increases: this method adopts the maximal margin criterion, and the dimension disaster problem that has faced when having avoided processing high dimensional data has improved the sane performance of the method.

3: recognition performance increases: with compare based on maximal margin criterion feature extracting method, adopt the feature of the high dimensional data that this method extracts to be easier to classification.

Description of drawings

Fig. 1 is workflow block diagram of the present invention

Fig. 2 is the training sample that uses of the present invention and type and the sample size of test sample book

Fig. 3 is for adopting the object recognition rate of the inventive method

Wherein horizontal ordinate represents the intrinsic dimensionality that extracts, and ordinate represents the discrimination that target is correctly validated.

Fig. 4 is for adopting the optimal identification rate of all kinds of targets of the present invention.

Embodiment

Such as Fig. 1, implementation step of the present invention is as follows:

Step 1, initialization

If the set of SAR image training sample is expressed as matrix X=(x ₁, x ₂..., x _N) ∈ R ^{M * N}, wherein N=698 represents the number of this group training sample, each training sample x _iDimension be m * 1 dimension, m=3721, m get the number of pixels of SAR image, i ∈ 1,2 ..., 698}, R represents real number set.In this simultaneously, the category label set expression of supposing training sample is matrix Y=(y ₁, y ₂..., y ₆₉₈), y wherein _iTraining sample x _iCategory label, i ∈ 1,2 ..., 698}.If SAR image measurement sample set is expressed as matrix X '=(x ₁', x ₂' ..., x ' _{N '}) ∈ R ^{M * N}', wherein N'=1365 represents the number of this group test sample book, each test sample book x' _tDimension be m * 1 dimension, t ∈ 1,2 ..., 1365}, t are the labels of test sample book.

Step 2, structure similarity matrix W ^(w)With the otherness matrix W ^(b)

This step is divided into following 3 little steps:

Step 2.1 obtains training sample set X according to step 1, and employing formula (1) is constructed the Euclidean distance matrix G between all training samples:

G=(g _ij) _698×698，i,j∈{1,2,…,698} （1）

Wherein, the element g of Euclidean distance matrix G _Ij=| x _i-x _j|| ₂Sample x among the expression training sample set X _iAnd x _jBetween Euclidean distance, || || ₂Vectorial 2 norms.

The category label set Y of the training sample that step 2.2 obtains according to step 1 and the Euclidean distance matrix G that step 2.1 obtains adopt formula (2) to construct similarity matrix W between all samples ^(w):

$W^{\left(w\right)}={\left(w_{\mathrm{ij}}^{\left(w\right)}\right)}_{698\×698},i,j\∈\{\mathrm{1,2},\·\·\·,698\}---\left(2\right)$

Similarity matrix W wherein ^(w)Element

Training sample x among the expression training sample set X _iAnd x _jBetween the similarity factor of influence:

$w_{\mathrm{ij}}^{\left(w\right)}=\left\{\begin{array}{c}\exp \left({-g}_{\mathrm{ij}}\right),\mathrm{if}(g_{\mathrm{ij}}\≤{\mathrm{\ϵ}}_1\∩y_i=y_j)\\ 0,\mathrm{others}\end{array}\right.---\left(3\right)$

Wherein, ∩ presentation logic symbol " with ".y _iAnd y _jRespectively sample x _iAnd x _jCategory label.ε ₁The=4.5th, the upper limit of Euclidean distance between the restriction similarity sample of being determined by emulation.

The category label set Y of the training sample that step 2.3 obtains according to step 1 and the Euclidean distance matrix G that step 2.1 obtains adopt the otherness matrix W between formula (4) the structure sample ^(b):

$W^{\left(b\right)}={\left(w_{\mathrm{ij}}^{\left(b\right)}\right)}_{698\×698},i,j\∈[\mathrm{1,2},\·\·\·,698]---\left(4\right)$

Otherness matrix W wherein ^(b)Element

Training sample x among the expression training sample set X _iAnd x _jBetween the otherness factor of influence:

$w_{\mathrm{ij}}^{\left(b\right)}=\left\{\begin{array}{c}\exp \left({-g}_{\mathrm{ij}}\right),\mathrm{if}(g_{\mathrm{ij}}\≤{\mathrm{\ϵ}}_2\∩y_i\≠y_j)\\ 0,\mathrm{others}\end{array}\right.---\left(5\right)$

Wherein, ∩ presentation logic symbol " with ".y _iAnd y _jRespectively sample x _iAnd x _jCategory label.ε ₂The=5th, the upper limit of Euclidean distance between the restriction otherness sample of being determined by emulation.

Step 3, calculate objective matrix J based on the maximal margin criterion

To the training sample set X that step 1 obtains, the similarity matrix W that step 2.2 obtains ^(w)The otherness matrix W that obtains with step 2.3 ^(b), adopt formula (6) to calculate objective matrix J:

J＝X(D ^(w)-D ^(b))X ^T-X(W ^(w)-W ^(b))X ^T （6）

Wherein $D^{\left(w\right)}=\mathrm{diag}(d_1^{\left(w\right)},d_2^{\left(w\right)},\·\·\·,d_i^{\left(w\right)},\·\·\·,d_{698}^{\left(w\right)})\∈R^{698\×698},$ $d_1^{\left(w\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{1j}^{\left(w\right)},$ $d_2^{\left(w\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{2j}^{\left(w\right)},$ $d_i^{\left(w\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}^{\left(w\right)},$ $d_{698}^{\left(w\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{698j}^{\left(w\right)},$ $D^{\left(b\right)}=\mathrm{diag}(d_1^{\left(b\right)},d_2^{\left(b\right)},\·\·\·,d_i^{\left(b\right)},\·\·\·,d_{698}^{\left(b\right)})\∈R^{698\×698},$ $d_1^{\left(b\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{1j}^{\left(b\right)},$ $d_2^{\left(b\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{2j}^{\left(b\right)},$ $d_i^{\left(b\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}^{\left(b\right)},$ $d_{698}^{\left(b\right)}=\underset{j=1}{\overset{698}{\mathrm{\Σ}}}{w}_{698j}^{\left(b\right)},$ I ∈ 1,2 ..., 698}, X ^TIt is the transposition of matrix X.

Step 4, calculating projection matrix V

According to the objective matrix J that step 3 obtains, calculate 3721 stack features value and the proper vectors of objective matrix J

After 3721 stack features values are sorted from big to small, be expressed as λ ₁〉=λ ₂〉=... 〉=λ ₃₇₂₁Choose front K eigenvalue of maximum λ ₁~ λ _KThe characteristic of correspondence vector v ₁~ v _K, form projection matrix V=(v ₁, v ₂..., v _K), V ∈ R ^{3721 * K}, wherein K is the dimension of the feature of extraction, K chooses 1 to the arbitrary integer between the sample dimension 3721.

Step 5, feature extraction

The projection matrix V that obtains according to step 4, all the training sample x among the training sample set X that step 1 is obtained _i, i ∈ 1,2 ..., 698} calculates its feature z according to formula (7) _i,

z _i=V ^Tx _i,i∈{1,2,…,698} （7）

Wherein, V ^TIt is the transposition of matrix V.

Obtain the training sample characteristic set and be expressed as matrix Z _Train=(z ₁, z ₂..., z ₆₉₈);

The projection matrix V that obtains according to step 4, all the test sample book x among the test sample book set X ' that step 1 is obtained _t', t ∈ 1,2 ..., 1365}, t are the labels of test sample book.According to formula (8), calculate its feature z _t',

z _t′＝V ^Tx _t′,i∈{1,2,…,1365} （8）

Obtain the test sample book characteristic set and be expressed as matrix Z _Test=(z ₁', z ₂' ..., z ' ₁₃₆₅).

Step 6, target classification

The training sample characteristic set Z that obtains according to step 5 _TrainWith test sample book characteristic set Z _Test, adopt minimum distance classifier to test sample book characteristic set Z _TestIn each test sample book z _t' classify, obtain the category label y of this test sample book _t', t ∈ 1,2 ..., 1365}.

The category label set expression that finally obtains test sample book is matrix Y '=(y ₁', y ₂' ..., y _t' ..., y ' ₁₃₆₅).Through above-mentioned steps, can finish the identification to test sample book.

Claims (1)

1. synthetic aperture radar automatic target recognition method is characterized in that it may further comprise the steps:

Step 1, initialization

Read the SAR image, the SAR image that reads is spliced by row, obtain column vector; The training set that definition contains N width of cloth SAR image is expressed as matrix X=(x ₁, x ₂..., x _i..., x _N) ∈ R ^{M * N}, wherein, N represents the number of samples in this group training sample set, N is positive integer, x ₁First training sample, x ₂Second training sample, x _iI training sample, x _NN training sample, i ∈ 1,2 ..., N}; The dimension of each training sample is m * 1 dimension, and m represents the number of pixels of SAR image, and R represents real number set; The category label set expression of definition training sample is matrix Y=(y ₁, y ₂..., y _i..., y _N), y wherein ₁Training sample x ₁Category label, y ₂Training sample x ₂Category label, y _iTraining sample x _iCategory label, y _NTraining sample x _NCategory label, i ∈ 1,2 ..., N}; Definition SAR image measurement sample set is expressed as matrix X'=(x ₁', x ' ₂..., x _t' ..., x ' _{N '}) ∈ R ^{M * N}', x wherein ₁' be first test sample book, x ₂' be second test sample book, x _t' be t test sample book, x ' _NN test sample book, the number of this group test sample book of N ' expression; Each test sample book x _t' dimension be m * 1 dimension, t ∈ 1,2 ..., N ' }, t is the label of test sample book;

Step 2, structure similarity matrix W ^(w)With the otherness matrix W ^(b)

Step 2 comprises step 2.1, step 2.2, step 2.3:

The training sample set X that step 2.1 obtains according to step 1, employing formula (1) is constructed the Euclidean distance matrix G between all training samples:

G=(g _ij) _N×N，i,j∈{1,2,…,N} （1）

Wherein, the element g of Euclidean distance matrix G _Ij=| x _i-x _j|| ₂Training sample x among the expression training sample set X _iAnd x _jBetween Euclidean distance, || || ₂Be vectorial 2 norms, N represents the number of samples in this group training sample set, and N is positive integer;

The category label set Y of the training sample that step 2.2 obtains according to step 1 and the Euclidean distance matrix G that step 2.1 obtains adopt formula (2) to construct similarity matrix W between all samples ^(w):

$W^{\left(w\right)}={\left(w_{\mathrm{ij}}^{\left(w\right)}\right)}_{N\×N},i,j\∈\{\mathrm{1,2},\·\·\·,N\}---\left(2\right)$

Similarity matrix W wherein ^(w)In element

Training sample x among the expression training sample set X _iAnd x _jBetween the similarity factor of influence:

$w_{\mathrm{ij}}^{\left(w\right)}=\left\{\begin{array}{c}\exp \left({-g}_{\mathrm{ij}}\right),\mathrm{if}(g_{\mathrm{ij}}\≤{\mathrm{\ϵ}}_1\∩y_i=y_j)\\ 0,\mathrm{others}\end{array}\right.---\left(3\right)$

Wherein, ∩ presentation logic symbol " with ", y _iAnd y _jRespectively sample x _iAnd x _jCategory label, ε ₁The adjacent region threshold that represents similar sample, the empirical value that adopts emulation to determine in the reality;

The category label set Y of the training sample that step 2.3 obtains according to step 1 and the Euclidean distance matrix G that step 2.1 obtains adopt the otherness matrix W between formula (4) the structure sample ^(b):

$W^{\left(b\right)}={\left(w_{\mathrm{ij}}^{\left(b\right)}\right)}_{N\×N},i,j\∈\{\mathrm{1,2},\·\·\·,N\}---\left(4\right)$

Otherness matrix W wherein ^(b)In element

Training sample x among the expression training sample set X _iAnd x _jBetween the otherness factor of influence:

$w_{\mathrm{ij}}^{\left(b\right)}=\left\{\begin{array}{c}\exp \left({-g}_{\mathrm{ij}}\right),\mathrm{if}(g_{\mathrm{ij}}\≤{\mathrm{\ϵ}}_2\∩y_i\≠y_j)\\ 0,\mathrm{others}\end{array}\right.---\left(5\right)$

Wherein, ∩ presentation logic symbol " with ", y _iAnd y _jRespectively sample x _iAnd x _jCategory label, ε ₂The adjacent region threshold of expression foreign peoples sample, the empirical value that adopts emulation to determine in the reality;

Step 3, calculate objective matrix J based on the maximal margin criterion

The training sample set X that step 1 is obtained, the similarity matrix W that step 2.2 obtains ^(w)The otherness matrix W that obtains with step 2.3 ^(b), adopt formula (6) to calculate objective matrix J:

J＝X(D ^(w)-D ^(b))X ^T-X(W ^(w)-W ^(b))X ^T （6）

Wherein, X represents the training sample set, and w is similarity matrix W ^(w)Subscript, the expression similarity, b is the otherness matrix W ^(b)Subscript, the expression otherness, D ^(w)Be diagonal matrix, be expressed as $D^{\left(w\right)}=\mathrm{diag}(d_1^{\left(w\right)},d_2^{\left(w\right)},\·\·\·,d_i^{\left(w\right)},\·\·\·,d_N^{\left(w\right)})\∈R^{N\×N},$ Wherein,

Diagonal matrix D ^(w)First element, be expressed as

Diagonal matrix D ^(w)Second element, be expressed as

Diagonal matrix D ^(w)I element, be expressed as

Diagonal matrix D ^(w)N element, be expressed as

D ^(b)Be diagonal matrix, be expressed as $D^{\left(b\right)}=\mathrm{diag}(d_1^{\left(b\right)},d_2^{\left(b\right)},\·\·\·,d_i^{\left(b\right)},\·\·\·,d_N^{\left(b\right)})\∈R^{N\×N},$ Wherein, Diagonal matrix D ^(b)First element, be expressed as

Diagonal matrix D ^(b)Second element, be expressed as

Diagonal matrix D ^(b)I element, be expressed as

Diagonal matrix D ^(b)N element, be expressed as

X ^TIt is the transposition of matrix X;

Step 4, calculating projection matrix V

Adopt projection matrix V that training sample set is carried out dimensionality reduction;

According to the objective matrix J that step 3 obtains, calculate m stack features value and the proper vector of objective matrix J

Wherein, λ _iI the eigenwert of objective matrix J, v _iλ _iThe characteristic of correspondence vector, R represents real number set, sample dimension m is positive integer;

After m eigenwert sorted from big to small, be expressed as λ ₁〉=λ ₂〉=... λ _i〉=... 〉=λ _mWherein, λ ₁The 1st eigenwert of objective matrix J, λ ₂The 2nd eigenwert of objective matrix J, λ _iI the eigenwert of objective matrix J, λ _mM the eigenwert of objective matrix J;

Choose λ ₁~ λ _mIn before K eigenvalue of maximum λ ₁~ λ _KThe characteristic of correspondence vector v ₁~ v _KForm projection matrix V, wherein λ _KK the eigenwert of objective matrix J, v ₁λ ₁The characteristic of correspondence vector, v _Kλ _KCharacteristic of correspondence vector, K are the dimensions that extracts feature, and K chooses the arbitrary integer between 1 to sample dimension m;

Step 5, feature extraction

The projection matrix V that obtains according to step 4, all the training sample x among the training sample set X that step 1 is obtained _i, i={1,2 ..., N} is according to formula (7), calculation training sample x _iFeature z _i,

z _i=V ^Tx _i,i∈{1,2,…,N} （7）

Obtain the training sample characteristic set, be expressed as matrix Z _Train=(z ₁, z ₂..., z _i..., z _N), z wherein ₁Expression training sample x ₁Feature, z ₂Expression training sample x ₂Feature, z _iExpression training sample x _iFeature, z _NExpression training sample x _NFeature; V ^TIt is the transposition of matrix V;

All test sample book x among the projection matrix V that obtains according to step 4, the test sample book that step 1 the obtains set X ' _t', t ∈ 1,2 ..., N ' }, according to formula (8), calculate test sample book x _t' feature z _t',

z _t′＝V ^Tx _t′,i∈{1,2,…,N′} （8）

Obtain the test sample book characteristic set and be expressed as matrix Z _Test=(z ₁', z ' ₂..., z _t' ..., z ' _{N '}), z wherein ₁' expression test sample book x ₁Feature, z ₂' expression test sample book x ₂Feature, z _t' expression test sample book x _tFeature, z ' _{N '}Expression test sample book x _{N '}Feature, t is the label of test sample book, N ' is the number of test sample book;

Step 6, target classification

The training sample characteristic set Z that obtains according to step 5 _TrainWith test sample book characteristic set Z _Test, adopt traditional minimum distance classifier to test sample book characteristic set Z _TestIn the feature z of each test sample book _t' classify, obtain the category label y of test sample book _t', t ∈ 1,2 ..., N ' };

The category label set expression of all test sample books be matrix Y'=(y ' ₁, y ₂' ..., y _t' ..., y ' _{N '}), wherein, y' ₁Expression test sample book x ₁Category label, y ₂' expression test sample book x ₂Category label, y _t' expression test sample book x _tCategory label, y ' _{N '}Expression test sample book x _{N '}Category label; Test sample book x _tCategory label y _t' be exactly the unknown object kind that synthetic-aperture radar is surveyed;

Through above step, realize synthetic aperture radar target identification.

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