CN109063750B - SAR target classification method based on CNN and SVM decision fusion - Google Patents

SAR target classification method based on CNN and SVM decision fusion Download PDF

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CN109063750B
CN109063750B CN201810781174.4A CN201810781174A CN109063750B CN 109063750 B CN109063750 B CN 109063750B CN 201810781174 A CN201810781174 A CN 201810781174A CN 109063750 B CN109063750 B CN 109063750B
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张磊
李青伟
刘宏伟
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Xidian University
Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Xian Cetc Xidian University Radar Technology Collaborative Innovation Research Institute Co Ltd
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Abstract

The invention discloses an SAR target classification method based on decision fusion of CNN and SVM, which has the following thinking: determining an SAR image, wherein the SAR image comprises a lambda target, and dividing the lambda target to obtain a training set and a test set; then, the test set is standardized and sub-set divided to obtain a first test sub-set testx1, a second test sub-set testx2 and a third test sub-set testx 3; then obtaining a normalized feature matrix tranndata of the tranix, a normalized feature matrix testdata1 of the testx1, a normalized feature matrix testdata2 of the testx2 and a normalized feature matrix testdata3 of the testx3, and then respectively obtaining a parameter matrix W and an offset vector bb; determining a first column vector C1, a second column vector C2, and a third column vector C3; further obtaining a final prediction category column vector; v is obtained by calculation2Class is identified as v1Probability of class
Figure DDA0001732599970000011
And the SAR target classification result based on CNN and SVM decision fusion is recorded later.

Description

SAR target classification method based on CNN and SVM decision fusion
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an SAR target classification method based on decision fusion of CNN and SVM, which is suitable for identifying and classifying radar targets.
Background
The Support Vector Machine (SVM) is a common machine learning classification model and has good effect on the classification and identification of small samples, non-linear and high-dimensional targets; the SVM is a supervised classifier which finds a hyperplane by learning training data, completely separates different types of targets, and simultaneously maximizes the sum of the distances from two points on two sides of the plane closest to the plane; if the target is linear inseparable, the target can be mapped from a low-dimensional space to a high-dimensional space by adding a proper kernel function, and then a hyperplane is found to correctly classify the target; by introducing a relaxation variable, a small number of sample classification errors are allowed while the interval is maximized, classification for practical tasks can be better performed, and the influence of overfitting is reduced.
The convolutional neural network CNN is a feedforward neural network, which generally comprises an input layer, a convolutional layer, an excitation layer, a pooling layer, a full-link layer and an output layer; the CNN has achieved great success in the field of image processing, avoids complex preprocessing of images, can directly input original images, and has a good final recognition effect. When a general network processes images, the images are regarded as one or more two-dimensional vectors, and all layers of feature maps are connected, so that the number of parameters to be determined in the training process of the network is very large, the time required for training the network is very long, and even the training fails, and the problem is solved by the CNN through a local connection and weight sharing strategy. The CNN extracts various characteristics of the image through the convolutional layer and samples input data through the pooling layer, so that parameters required by a training model are reduced, and the overfitting degree of the network is reduced. And extracting a part of the image from the convolutional layer through a sliding window, carrying out convolution on the part of the image and the convolution kernel, and adding the obtained corresponding pixel point results to obtain a final convolutional layer output result.
When the SVM is used for classification, the characteristic extraction of the data has great influence on the final classification result. If a proper feature extraction method can be found, the data is subjected to feature extraction, so that the classification accuracy can be greatly improved; conversely, if the feature extraction method is inappropriate, the classification accuracy may be deteriorated.
When the SAR target image is classified by the SVM, the two targets may be similar at certain angles, so that the recognition effect of the targets is not ideal near the angles.
Disclosure of Invention
The invention aims to provide a method for classifying SAR targets based on decision fusion of CNN and SVM, so as to improve the recognition rate of SAR images and enable different types of target images to be classified correctly.
The main ideas of the invention are as follows: taking out a part of the SAR image data set as a training set and taking a part of the SAR image data set as a test set, and standardizing the size of each picture of the training set and the test set; inputting standardized training data into an untrained CNN network for training, and carrying out fine adjustment through a BP algorithm; and inputting the standardized test set into the trained CNN network, inputting the output of the CNN into the SVM for decision fusion classification, and finally obtaining the prediction category of the target.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
A SAR target classification method based on CNN and SVM decision fusion comprises the following steps:
step 1, determining an SAR image, wherein the SAR image comprises a lambda target, and dividing the lambda target to obtain a training set and a test set; then, the test set is standardized and sub-set divided to obtain a first test sub-set testx1, a second test sub-set testx2 and a third test sub-set testx 3; wherein lambda is more than or equal to 2;
step 2, setting a CNN network and training to obtain a trained CNN network;
step 3, obtaining a standardized feature matrix trandinata of the standardized training set, a standardized feature matrix testdata1 of the first testing subset testx1, a standardized feature matrix testdata2 of the second testing subset testx2 and a standardized feature matrix testdata3 of the third testing subset testx3 according to the first testing subset testx1, the second testing subset testx2, the third testing subset testx3 and the training set;
step 4, training a standardized feature matrix tranndata of a standardized training set tranix by using a traditional SVM classification algorithm to respectively obtain a parameter matrix W and an offset vector bb;
step 5, calculating prediction category column vectors of the first test subset testx1, the second test subset testx2 and the third test subset testx3 according to results obtained in the step 3 and the step 4, and respectively marking the prediction category column vectors as a first column vector C1, a second column vector C2 and a third column vector C3;
step 6, obtaining a final prediction category column vector according to the first column vector C1, the second column vector C2 and the third column vector C3;
step 7, obtaining v according to the final prediction category column vector2Class is identified as v1Probability of class
Figure BDA0001732599950000021
1≤v1≤m，1≤v2M is not less than m, m is not less than 2 and not more than lambda; v is2Class is identified as v1Probability of class
Figure BDA0001732599950000022
The method is an SAR target classification result based on CNN and SVM decision fusion.
The invention has the following advantages
Firstly, the invention uses the CNN network when extracting the characteristics of the data, can well extract the characteristics of the data and reduce the interference of noise and the like on classification.
Secondly, the method has good effect on the classification and identification of the small samples due to the use of the SVM classifier.
Thirdly, the final classification effect is further improved by performing decision fusion on the prediction results of the same target at different azimuth angles.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of an SAR target classification method based on decision fusion of CNN and SVM in the present invention;
FIG. 2 is a graph of the results of object classification using the method of the present invention.
Detailed Description
Referring to fig. 1, it is a flowchart of a decision fusion classification method based on SVM and CNN of the present invention; the decision fusion classification method based on the SVM and the CNN comprises the following steps:
step 1: and (6) initializing data.
1.1) the invention is directed to target identification of radar SAR images, for each SAR image its target class is known; determining an SAR image, wherein the SAR image comprises lambda targets, lambda is more than or equal to 2, each target corresponds to a label, and then obtaining a label y corresponding to the lambda targetstr1、ytr2、…、ytrλEach type of target at least comprises one target, and the azimuth angle and the pitch angle of all targets in each type of target are the same.
For the lambda class targets at pitch angles from sigma1To sigma2Interval σ3Azimuth angle from xi1To xi2Interval xi3SAR imaging is carried out to obtain
Figure BDA0001732599950000031
A SAR image with 0 degree or less sigma1≤90°，0°≤σ2≤90°，σ1≤σ2，σ3>0，0°≤ξ1≤360°，0°≤ξ2≤360°，ξ1≤ξ2，ξ3>0, each SAR image comprises a target, the size of each SAR image is c x t, c is larger than or equal to a, and t is larger than or equal to a.
In the above-mentioned
Figure BDA0001732599950000032
Selecting a pitch angle theta from the SAR image1Azimuth angle from xi1To xi2Azimuthal interval ofIs xi4Obtaining the SAR images of the m types of targets
Figure BDA0001732599950000033
A SAR image, wherein the label corresponding to the m-type target is ytr1、ytr2、…、ytrmWill be
Figure BDA0001732599950000034
Taking the SAR image and the label corresponding to the m-type target as a training set, wherein sigma1≤θ1≤σ2，0<ξ4≤ξ3，2≤m≤λ。
In the above-mentioned
Figure BDA0001732599950000041
Selecting a pitch angle theta from the SAR image2Azimuth angle from xi1To xi2Azimuth interval xi4Obtaining the SAR image of the m' type target
Figure BDA0001732599950000042
A SAR image, wherein the label corresponding to the m' class target is ytr1、ytr2、…、ytrm'Will be
Figure BDA0001732599950000043
Taking the SAR image and a label corresponding to the m' type target as a test set, wherein sigma1≤θ2≤σ2，θ1≠θ2And m' has the same value as m.
Importing a training set and a testing set into commercial software MATLAB, and standardizing the size of each SAR image in the training set and the testing set to a x a to obtain a standardized training set tranix and a standardized testing set testx, wherein the standardized training set tranix comprises
Figure BDA0001732599950000044
A label corresponding to the normalized SAR image and the m-type target, wherein the normalized test set testx comprises
Figure BDA0001732599950000045
And (4) obtaining a normalized SAR image and a label corresponding to the m' type target.
1.2) dividing the standardized test set testx into three test subsets, namely a first test subset testx1, a second test subset testx2 and a third test subset testx3, according to the difference of the azimuth angle of each standardized SAR image in the standardized test set testx, wherein the first test subset testx1 comprises m1' Label corresponding to class target, and is marked as label column vector y corresponding to first test subset testx1te1(ii) a The second test subset testx2 comprises m2' Label corresponding to class target, and is marked as label column vector y corresponding to second test subset testx2te2(ii) a The third test subset testx3 comprises m3' Label corresponding to class target, and is marked as label column vector y corresponding to third test subset testx3te3。
The first test subset testx1 corresponds to an azimuth of
Figure BDA0001732599950000046
The second test subset testx2 corresponds to an azimuth of
Figure BDA0001732599950000047
The third test subset testx3 corresponds to an azimuth of
Figure BDA0001732599950000048
Wherein
Figure BDA0001732599950000049
For the azimuthal interval of each normalized SAR image in the first test subset testx1,
Figure BDA00017325999500000410
j is the number of each normalized SAR image in the normalized test set testx,
Figure BDA00017325999500000411
label column vector y corresponding to the first test subset testx1te1And the label column vector y corresponding to the second test subset testx2te2The label column vector y corresponding to the third test subset testx3te3Are respectively as
Figure BDA00017325999500000412
And (5) maintaining.
Step 2: the CNN network is initialized.
2.1) setting a CNN network to totally comprise n +1 layers, wherein n is a positive integer more than 3; let layer 0 type0For input layer, i layer typeiWherein i is more than or equal to 1 and less than or equal to n-2, the ith layer typeiOptional convolutional and pooling layers, layer n-1 typen-1Being a fully-connected hierarchy, the nth typenThe total number of characteristic graphs of the ith layer is p as an output layeri，piIs a positive integer greater than 0, piSimilarly to n, it can be arbitrarily set.
Wherein the total number of the characteristic graphs of the 0 th layer is p0Total number p of characteristic diagrams of n-1 th layern-11, total number p of characteristic diagrams of the n-th layernIs 1; the total number of the characteristic diagrams of the pooling layer is the same as the value of the total number of the characteristic diagrams of the layer above the pooling layer; the size of each feature map in the ith layer is di×di，diA ≦ a, and each feature size in layer n-1 is (d)n-2·dn-2·pn-2) X1, and each feature size in the nth layer is λ x 1.
If the i-th layer typeiThe layer i is connected with the layer i-1 through convolution kernels, all the convolution kernels in the CNN network have the same size, and the sizes of the convolution kernels are k x k, diThe distance of each sliding of the convolution kernel is q, and q is more than or equal to 1 and less than or equal to k; setting learning rate to alpha, alpha>0。
If the i-th layer typeiDetermining the sampling interval of the pooling layer as sc, and d is more than or equal to 0 and less than or equal to sci-1，di-1×di-1Representing the size of each feature map in the i-1 th layer, and the sampling intervals of all pooling layers are the same, di-1A is less than or equal to a; each time the magnitude b of the normalized SAR image is input, wherein b is
Figure BDA0001732599950000051
The divisor of (a) is greater than (b),
Figure BDA0001732599950000052
for the azimuthal interval of each normalized SAR image in the first test subset testx1,
Figure BDA0001732599950000053
initialization: setting the h-th layer of the i-1 th layer after the l-th update1Characteristic diagram and h-th layer in i-th layer2The initial value of the convolution kernel of the characteristic diagram is
Figure BDA0001732599950000054
And is
Figure BDA0001732599950000055
Is a k x k matrix, where 0 ≦ h1≤pi-1，0≤h2≤pi，pi-1Indicates the total number of profiles, p, of the i-1 th layeriIndicates the total number of characteristic diagrams of the i-th layer
Figure BDA0001732599950000056
The values of k × k elements in the total are-HiAnd HiRandom number between, HiThe formula is calculated as follows:
Figure BDA0001732599950000057
where k × k denotes the convolution kernel size.
2.2) according to the i-th layer typeiAnd the size d of each feature map in the i-1 th layeri-1Calculating the size d of each feature map in the ith layeri×di，1≤i≤n-2。
If the i-th layer typeiAs a convolutional layer, then:
di＝di-1-k+1
if the i-th layer typeiFor the pooling layer, then:
Figure BDA0001732599950000061
layer 0 type0Is an input layer, and type of layer 11For convolutional layers, the input layer is connected to the convolutional layer by a convolutional kernel, then d1＝a。
2.3) initialization: full connection matrix initial value ffw between layer n-1 and layer n0And an initial value ffb of an offset vector between the n-1 th layer and the n-th layer0。
Full connection matrix initial value ffw between layer n-1 and layer n0Is one (d)n×(dn-1·dn-1·pn-1) ) of the n-1 th layer and the n-th layer, an initial value ffw of the full connection matrix between the n-1 th layer and the n-th layer0Each element value is a random number between-HH and HH, and HH is calculated as follows:
Figure BDA0001732599950000062
initial value ffb of offset vector between layer n-1 and layer n0Is a dnX b matrix, initial value of offset vector between layer n-1 and layer n ffb0Each element value is 0.
Initialization: l represents the first update, the initial value of l is 0, and the maximum value of l is
Figure BDA0001732599950000063
And step 3: CNN network forward input
B standardized SAR images are randomly selected in the first time in a standardized training set trainx to form a data set B after the first time of updatinglAnd updating the data set B for the first timelDeleting the data from the standardized training set trainx, and updating the data set B for the first timelInputting the data into the CNN network set in the step 2, carrying out forward propagation to obtain values of each layer of neural network, and finally obtaining the first time of updatingOutput o of new CNN networkl。
3.1) if the i-th layer typeiFor convolutional layer, the value of each feature map in the i-th layer is di×diLet p in the ith layermThe value of each feature map is di×diOf (2) matrix
Figure BDA0001732599950000071
P-th in the i-1 th layernThe value of each feature map is di-1×di-1Of (2) matrix
Figure BDA0001732599950000072
Wherein 1 is not more than pm≤pi，1≤pn≤pi-1。
Is provided with
Figure BDA0001732599950000073
Is a k × k matrix, represents
Figure BDA0001732599950000074
Middle (alpha)1-1). q line to (α)1Line (α) 1) q + k2-1). q columns to (α)2-1) q + k columns, wherein
Figure BDA0001732599950000075
di>k，q>0, then
Figure BDA0001732599950000076
Middle alpha1Line, alpha2Initial value of column
Figure BDA0001732599950000077
The calculation formula of (a) is as follows:
Figure BDA0001732599950000078
Figure BDA0001732599950000079
wherein, the size of each characteristic diagram in the convolution layer is the same,
Figure BDA00017325999500000710
representing a convolution operation.
3.2) if the i-th layer typeiFor the pooling layer, the value of each feature map in the i-th layer is di×diLet p in the ith layermThe value of each feature map is di×diOf (2) matrix
Figure BDA00017325999500000711
Let p in the i-1 st layermThe value of each feature map is di-1×di-1Of (2) matrix
Figure BDA00017325999500000712
1≤pm≤pi。
Is provided with
Figure BDA00017325999500000713
To represent
Figure BDA00017325999500000714
Middle alpha3Line, alpha4The value of the column element(s),
Figure BDA00017325999500000715
to represent
Figure BDA00017325999500000716
Middle 2. alpha3Line 1, 2. alpha4-1 value of column element, wherein 1 ≦ α3≤di/2，1≤α4≤di/2，
Figure BDA00017325999500000717
The calculation formula of (a) is as follows:
Figure BDA00017325999500000718
wherein, the size of each characteristic diagram in the pooling layer is the same.
3.3) setting the second layer in the n-2 th layer
Figure BDA00017325999500000719
The value of each feature map is dn-2×dn-2Of (2) matrix
Figure BDA00017325999500000720
The total number of the characteristic diagrams of the n-2 th layer is pn-2The size of each feature map in the n-2 th layer is dn-2×dn-2I.e. by
Figure BDA00017325999500000721
P in the n-2 th layern-2The feature map is developed into a vector fv according to the following formula and the vector is stored in p of the n-1 th layern-1In the feature map, the (p) th in the vector fvm-1)·(dn-2)2+((r-1)·dn-2) Element to (p)m-1)·(dn-2)2+(r·dn-2) Each element is respectively connected with
Figure BDA00017325999500000722
Middle (r) th column 1 st element to dn-2The elements are in one-to-one correspondence and equal in value, and the corresponding expression is as follows:
Figure BDA0001732599950000081
wherein the content of the first and second substances,
Figure BDA0001732599950000082
represents the second in the vector fv
Figure BDA0001732599950000083
Element to (p)m-1)·(dn-2)2+(r·dn-2) The number of the elements is one,
Figure BDA0001732599950000084
to represent
Figure BDA0001732599950000085
From the 1 st element in the r-th column to the d-th element in the r-th columnn-2R is more than or equal to 1 and less than or equal to dn-2(ii) a Vector fv is pn-1-1-dimensional column vectors.
3.4) initial value ffw based on the full connection matrix between n-1 and n-th layers0And an initial value ffb of an offset vector between the n-1 th layer and the n-th layer0To obtain the final output matrix initial value o0The expression is as follows:
o0＝ffw0·fv+ffb0
and 4, step 4: fine-tuning the CNN network parameters according to the parameters in the step 3 and the labels of the training data, wherein the fine-tuning comprises the following substeps:
4.1) determining the data set B after the first updatelThe b standard SAR images correspondingly comprise b targets, the b targets are set to belong to eta targets, and labels y corresponding to the eta targetstr1、ytr2、…、ytrηForm the column vector y of the tag set after the ith updateηWherein eta is more than or equal to 1 and less than or equal to b.
Setting a zero matrix of lambda x b if the column vector y of the tag set after the ith updateηThe value of the element in the ddth column is yη(dd) ≦ dd ≦ b, then change the values of the σ -th row and η -th column elements in the λ × b zero matrix to 1, while the values of all other elements are still 0, and then obtain the tag matrix y of the η -class target after the first updateηl。
Wherein 1< σ < λ.
4.2) final output matrix o after the first updatinglAnd the label matrix y of the eta class target after the first updatingηlCalculating the error matrix e after the first updatel：
el＝ol-yηl
4.3) according to the error matrix e after the first updatelRespectively calculating the cost function after the first updateLlResidual error matrix od of nth layer after the first updatinglAnd residual matrix fvd of the n-1 th layer after the ith updatelThe calculation expressions are respectively:
Figure BDA0001732599950000091
odl＝el·(ol·(1-ol))
fvdl＝ffwl T·odl
wherein e isl(mu, rho) represents the error matrix e after the first updatelThe values of the elements in the middle mu row and the rho column are more than or equal to 1 mu and less than or equal to lambda, and are more than or equal to 1 rho and less than or equal to b, ffwl TRepresentation ffwlTranspose of (2), ffwlRepresenting the full connection matrix between the n-1 th layer and the n-th layer after the ith update.
4.4) calculating the p-th layer in the i-th layer according to the parametersmSensitivity matrix of individual characteristic diagram
Figure BDA0001732599950000092
Set to the (n-1) th layer
Figure BDA0001732599950000093
The sensitivity matrix of the individual characteristic map is
Figure BDA0001732599950000094
Length dn-1Residual matrix fvd of n-1 th layer after the ith updatelConversion to dn-1×dn-1Of the matrix, sensitivity matrix
Figure BDA0001732599950000095
Is as column (ss) of
Figure BDA0001732599950000096
Figure BDA0001732599950000097
Wherein the content of the first and second substances,
Figure BDA0001732599950000098
pn-1the total number of characteristic diagrams of the (n-1) th layer is shown,
Figure BDA0001732599950000099
to represent
Figure BDA00017325999500000910
Ss th column dn-1Element, fvdl((ss-1)·dn-1:(ss·dn-1) Residual matrix fvd representing the n-1 th layer after the l-th updatelMiddle (ss-1) dn-1Line elements to ss dn-1Line elements, ss is more than or equal to 1 and less than or equal to dn-1。
If it is the ith1Layer type
Figure BDA00017325999500000911
Is a pooling layer because of layer 0 type0For input layer, n layer typenIs an output layer, so1N-1, n-2, …,2,1, then the ith1In a layer of
Figure BDA00017325999500000912
Sensitivity matrix of individual characteristic diagram
Figure BDA00017325999500000913
Comprises the following steps:
Figure BDA00017325999500000914
wherein the content of the first and second substances,
Figure BDA00017325999500000915
Figure BDA00017325999500000916
denotes the ith1The total number of the characteristic diagrams of +1 layer,
Figure BDA00017325999500000917
denotes the ith1The sensitivity matrix of the kth signature in layer +1,
Figure BDA00017325999500000918
indicating that the ith update is connected1H in the layer1A feature map and the ith1H in +1 layer2A convolution kernel of the feature map; fp denotes a first setting function which satisfies:
let D1＝fp(D)，
Figure BDA00017325999500000919
Is a k × k matrix, then:
D1(xx,yy)＝D(k-xx+1,k-yy+1)，
wherein D is1(xx, yy) represents a matrix D1The (k-xx +1, k-yy +1) represents the (k-xx +1) th row and the (k-yy +1) th column of the matrix D.
If it is the ith1Layer type
Figure BDA0001732599950000101
Is a convolutional layer, then i1In a layer of
Figure BDA0001732599950000102
Sensitivity matrix of individual characteristic diagram
Figure BDA0001732599950000103
Comprises the following steps:
Figure BDA0001732599950000104
wherein, let i1In a layer of
Figure BDA0001732599950000105
The value of each feature map is one
Figure BDA0001732599950000106
Of (2) matrix
Figure BDA0001732599950000107
Denotes the ith1+1 layer of the first
Figure BDA0001732599950000108
A sensitivity matrix of the individual signature; ex represents a second setting function, which satisfies:
Figure BDA0001732599950000109
wherein the content of the first and second substances,
Figure BDA00017325999500001010
l1and l2Are respectively as
Figure BDA00017325999500001011
The total number of rows and the total number of columns,
Figure BDA00017325999500001012
denotes c1×c2The matrix of all 1 s of (a) is,
Figure BDA00017325999500001013
4.5) calculating the h in the i-1 th layer after the l time of updating according to the parameters1Characteristic diagram and h-th layer in i-th layer2Convolution kernel gradient matrix of individual feature map
Figure BDA00017325999500001014
Fully connected matrix gradient dffw after ith updatelAnd the full connection offset dffb after the first updatelThe calculation expressions are respectively:
Figure BDA00017325999500001015
Figure BDA00017325999500001016
Figure BDA00017325999500001017
wherein, when l and i take the same value and h1And h2When the values are different, the h-th layer in the i-1 th layer is connected after each update1Characteristic diagram and h-th layer in i-th layer2The convolution kernel gradient matrices of the individual feature maps are all identical; b represents the total number of normalized SAR images included in each updated data set, fvTRepresenting transpose of fv, odl(pp) denotes odlAll elements, od, of the pp-th column of the matrixlRepresenting the residual matrix of the nth layer after the ith update.
Step 5, adding 1 to the value of l, calculating the h in the i-1 layer after the l time of updating1Characteristic diagram and h-th layer in i-th layer2Convolution kernel of individual feature map
Figure BDA00017325999500001018
Convolution layer bias after the first update blFull connection matrix ffw between layer n-1 and layer n after the first updatelAnd an offset vector ffb between layer n-1 and layer n after the ith updatelThe calculation expressions are respectively:
Figure BDA0001732599950000111
bl＝bl-1-α·dbl-1
ffwl＝ffwl-1-α·dffwl-1
ffbl＝ffbl-1-α·dffbl-1
wherein the content of the first and second substances,
Figure BDA0001732599950000112
indicates that the h in the i-1 th layer is connected after the l-1 th update1A feature map andh in the i-th layer2A convolution kernel gradient matrix of the feature map; let p in the i-1 st layernThe value of each feature map is di-1×di-1Of (2) matrix
Figure BDA0001732599950000113
1≤i≤n-2，
Figure BDA0001732599950000114
Denotes the p-th in the i-th layermSensitivity matrix of individual characteristic map, bl-1Denotes the convolution layer offset after the first-1 update, b0＝0，α>0；
Figure BDA0001732599950000115
Indicates that the h-th layer in the i-1 th layer is connected after the l-1 th update1Characteristic diagram and h-th layer in i-th layer2The convolution kernel of the individual feature maps,
Figure BDA0001732599950000116
indicates that the h-th layer in the i-1 th layer is connected after the l-th update1Characteristic diagram and h-th layer in i-th layer2Initial values of convolution kernels of the feature maps; dbl-1Representing the gradient of the offset vector after the l-1 th update,
Figure BDA0001732599950000117
b represents the total number of normalized SAR images included in each updated data set.
Then returning to the step 3; until it is calculated to be
Figure BDA0001732599950000118
Connecting h in the i-1 th layer after secondary updating1Characteristic diagram and h-th layer in i-th layer2Convolution kernel of individual feature map
Figure BDA0001732599950000119
First, the
Figure BDA00017325999500001110
Post-update convolutional layer biasing
Figure BDA00017325999500001111
First, the
Figure BDA00017325999500001112
Fully connected matrix between n-1 th layer and n-th layer after secondary updating
Figure BDA0001732599950000121
And a first
Figure BDA0001732599950000122
Offset vector between n-1 th layer and n-th layer after sub-update
Figure BDA0001732599950000123
For the first
Figure BDA0001732599950000124
Connecting h in the i-1 th layer after secondary updating1Characteristic diagram and h-th layer in i-th layer2Convolution kernel of individual feature map
Figure BDA0001732599950000125
Let i equal 1,2, …, n-2, and then get the second
Figure BDA0001732599950000126
After secondary update, connect h in layer 01Characteristic diagram and h in layer 12Convolution kernel of individual feature map
Figure BDA0001732599950000127
To the first
Figure BDA0001732599950000128
After the second update, connecting the h-th layer in the n-3 th layer1A characteristic diagram and h in the n-2 th layer2Convolution kernel of individual feature map
Figure BDA0001732599950000129
And the initial value b of the bias of the convolution layer obtained at this time0To the first
Figure BDA00017325999500001210
Post-update convolutional layer biasing
Figure BDA00017325999500001211
Full connection matrix initial value ffw between layer n-1 and layer n0To the first
Figure BDA00017325999500001212
Fully connected matrix between n-1 th layer and n-th layer after secondary updating
Figure BDA00017325999500001213
And an initial value ffb of an offset vector between the n-1 th layer and the n-th layer0To the first
Figure BDA00017325999500001214
Offset vector between n-1 th layer and n-th layer after sub-update
Figure BDA00017325999500001215
And the set CNN network is indicated to be trained and recorded as the trained CNN network.
Step 6: and extracting the feature matrix of the training data and the test data by using the CNN network.
6.1) the normalized training set trainx, and the first test subset testx1, the second test subset testx2 and the third test subset testx3 are trained using the trained CNN network to obtain the feature matrix trainx _ new of the normalized training set trainx, the feature matrix testx1_ new of the first test subset testx1, the feature matrix testx2_ new of the second test subset testx2 and the feature matrix testx3_ new of the third test subset testx3, respectively.
6.2) using a data normalization algorithm to normalize the eigen matrix train _ new of the normalized training set train x, the eigen matrix testx1_ new of the first test subset testx1, the eigen matrix testx2_ new of the second test subset testx2 and the eigen matrix testx3_ new of the third test subset testx3, respectively, resulting in a normalized eigen matrix trandinata of the normalized training set train x, the normalized eigen matrix testdata1 of the first test subset testx1, the normalized eigen matrix testdata2 of the second test subset testx2 and the normalized eigen matrix testdata3 of the third test subset testx3, respectively, which are calculated as:
Figure BDA0001732599950000131
Figure BDA0001732599950000132
Figure BDA0001732599950000133
Figure BDA0001732599950000134
wherein, the mean function represents the column mean value of the matrix, and the SID function represents the column standard deviation of the matrix.
Step 7, training the normalized feature matrix traindata of the normalized training set trainx by using a traditional SVM (support vector machine) classification algorithm to respectively obtain a parameter matrix W and an offset vector bb, wherein the parameter matrix W is pn-1X m matrix, offset vector bb is pn-1A row vector of x 1; p is a radical ofnIndicates the total number of characteristic diagrams of the n-th layer, pn-1The total number of profiles of the (n-1) th layer is shown.
Step 8, calculating prediction category column vectors of the first test subset testx1, the second test subset testx2 and the third test subset testx3, respectively as a first column vector C1, a second column vector C2 and a third column vector C3 according to the feature matrix testdata1 of the first test subset testx1, the feature matrix testdata2 of the second test subset testx2 and the feature matrix testdata3 of the third test subset testx3, as well as the parameter matrix W and the offset vector bb, and obtaining the following steps: "
fen1＝testdata1·WT+repmat(bb,[size(testdata1,1),1])
fen2＝testdata2·WT+repmat(bb,[size(testdata2,1),1])
fen3＝testdata3·WT+repmat(bb,[size(testdata3,1),1])
Where size (testdata1,1) represents the number of rows, repmat (bb, [ size (testdata1,1) of matrix testdata1]) Represents a size (testdata1,1) line pn-1Matrix of columns, the size (testdata1,1) row pn-1Each row of the matrix of columns is an offset vector bb; fen1 is a size (testdata1,1) xpn-1Matrix of (2), size (testdata1,1) × pn-1Each row of the matrix has only one element with a value of 1 and the remaining elements of each row have values of 0, respectively; if the number of columns where value 1 of the element in row # 1 of fen1 is Δ 1, C1(ψ 1) is Δ 1, where 1 ≦ ψ 1 ≦ size (testdata1), and 1 ≦ Δ 1 ≦ pn-1C1(ψ 1) denotes the value of the ψ 1-th element of the first column vector C1; let ψ 1 be 1,2, …, size (testdata1), and then get a first column vector C1, which first column vector C1 includes size (testdata1) elements.
Where size (testdata2,1) represents the number of rows, repmat (bb, [ size (testdata2,1),1, of matrix testdata2]) Represents a size (testdata2,1) line pn-1Matrix of columns, the size (testdata2,1) row pn-1Each row of the matrix of columns is an offset vector bb; fen2 is a size (testdata2,1) xpn-1Matrix of (2), size (testdata2,1) × pn-1Each row of the matrix has only one element with a value of 1 and the remaining elements of each row have values of 0, respectively; if the number of columns where value 1 of element in row # 2 of fen2 is Δ 2, C2(ψ 2) is Δ 2, where 1 ≦ ψ 2 ≦ size (testdata2), and 1 ≦ Δ 2 ≦ pn-1C2(ψ 2) denotes the value of the ψ 2-th element of the second column vector C2; let ψ 2 be 1,2, …, size (testdata2), resulting in a second column vector C2, said second column vector C2 comprising size (testdata2) elements.
Where size (testdata3,1) represents the number of rows, repmat (bb, [ size (testdata3,1),1, of matrix testdata3]) Represents a size (testdata3,1) line pn-1Matrix of columns, the size (testdata3,1) row pn-1Each row of the matrix of columns is an offset vector bb; fen3 is a size (testdata3,1) xpn-1Matrix of (2), size (testdata3,1) × pn-1Each row of the matrix has only one element with a value of 1 and the remaining elements of each row have values of 0, respectively; if the number of columns in which value 1 of element in row # 3 of fen3 is Δ 3, C3(ψ 3) is Δ 3, where 1 ≦ ψ 3 ≦ size (testdata3), and 1 ≦ Δ 3 ≦ pn-1C3(ψ 3) denotes the value of the ψ 3 th element of the third column vector C3; let ψ 3 be 1,2, …, size (testdata3), which results in a third column vector C3, which third column vector C3 comprises size (testdata3) elements.
Step 9, decision fusion classification
Each row of the first column vector C1, the second column vector C2, and the third column vector C3 is decided, and the final prediction class column vector is obtained.
Taking the values of the delta-th row element of the first column vector C1, the second column vector C2 and the third column vector C3 respectively, and marking as the value C1 (delta) of the delta-th row element of the first column vector C1, the value C2 (delta) of the delta-th row element of the second column vector C2 and the value C3 (delta) of the delta-th row element of the third column vector C3 respectively, wherein 1 is larger than or equal to delta and smaller than or equal to S, and S is the total column number of the first column vector C1; setting the S-dimensional column vector as C, the procedure of obtaining the value C (δ) of the δ -th row element of the S-dimensional column vector C is:
if C1(δ) is C2(δ) or C1(δ) is C3(δ), then:
C(δ)＝C1(δ)。
if C2(δ) is C3(δ), then:
C(δ)＝C2(δ)。
if two of C1 (delta), C2 (delta) and C3 (delta) are different, any value of C1 (delta), C2 (delta) and C3 (delta) is randomly selected as the value C (delta) of the delta-th row element of the S-dimensional column vector C.
Let δ be 1,2, …, S, and further obtain the values C (1) of the 1 st row element of the S-dimensional column vector C to the values C (S) of the S-th row element of the S-dimensional column vector C, respectively, and record them as a final prediction type column vector, which is the S-dimensional column vector.
Step 10, calculating v according to the prediction result obtained in step 92Class is given as v1Number of classes
Figure BDA0001732599950000151
Calculating v2Class is identified as v1Probability of class
Figure BDA0001732599950000152
If the value of the phi 4 th row element of the final prediction class column vector is v1And the label column vector y to which the first test subset testx1 correspondste1Has a value v of the element of row # 42Counting the value of the element in S elements in the final prediction category column vector as v1Total number of rows of elements, denoted as S1，S1<S, then counting S1The rows correspond to the label column vector yte1The value of the middle element is v2Total number of (2), denoted as v2Class is identified as v1Number of classes
Figure BDA0001732599950000153
Wherein
Figure BDA0001732599950000154
V is then2Class is identified as v1Probability of class
Figure BDA0001732599950000155
Comprises the following steps:
Figure BDA0001732599950000161
wherein v is not less than 11≤m，1≤v2≤m。
The invention is further illustrated below by means of a simulation example:
1) setting CNN network parameters and SVM classifier parameters:
the number n of layers of the CNN network is set to 7, the first layer is an input layer and includes a 32 × 32 feature map, the second layer is a convolutional layer and includes 6 28 × 28 feature maps, the third layer is a pooling layer and includes 6 14 × 14 feature maps, the sampling interval sc is 2, the fourth layer is a convolutional layer and includes 12 10 × 10 feature maps, the fifth layer is a pooling layer and includes 12 5 × 5 feature maps, the sampling interval sc is 2, the sixth layer is a vector expansion layer and includes 300 1 × 1 feature maps, the seventh layer is an output layer, the size of a convolutional kernel is 5 × 5, the distance of each sliding of the convolutional kernel is 1, the learning rate is 1, and the number of input pictures per time is 18.
SVM parameter is set, learning rate is 1.5, and regularization coefficient is 101.5The kernel function adopts a change function.
2) Training set and test set
Three types of tanks with training sets of T95, BT-7 and IS-4 have a pitch angle of 50 degrees, an azimuth angle of 0-360 degrees and intervals
Figure BDA0001732599950000162
The SAR image IS 10 degrees, and three types of tanks with test sets of T95, BT-7 and IS-4 have a pitch angle of 60 degrees, an azimuth angle of 0-360 degrees and intervals
Figure BDA0001732599950000163
SAR image at 10 °.
3) Emulation content
Decision fusion classification is carried out on the training set and the test set by using the method of the invention, and the classification result is shown in figure 2, and figure 2 is a target classification result graph obtained by using the method of the invention.
Some of the experimental data of the present invention are shown in Table 3, and the experimental result data of the present invention are shown in Table 4.
TABLE 3
Figure BDA0001732599950000164
TABLE 4
Figure BDA0001732599950000171
As can be seen from tables 3 and 4, the method can accurately identify and classify the SAR target, and the accuracy of classification is greatly improved compared with the method that only CNN is used for feature extraction and then SVM is used for classification.
The foregoing description is only an example of the present invention and is not intended to limit the invention, so that it will be apparent to those skilled in the art that various modifications and variations in form and detail can be made therein without departing from the spirit and scope of the invention.

Claims (6)

1. A SAR target classification method based on CNN and SVM decision fusion is characterized by comprising the following steps:
step 1, determining an SAR image, wherein the SAR image comprises a lambda target, and dividing the lambda target to obtain a training set and a test set; then, the test set is standardized and sub-set divided to obtain a first test sub-set testx1, a second test sub-set testx2 and a third test sub-set testx 3; wherein lambda is more than or equal to 2;
in step 1, the training set and the test set are obtained by the following steps:
the SAR image comprises lambda targets, lambda is larger than or equal to 2, each target corresponds to a label, and then a label y corresponding to the lambda targets is obtainedtr1、ytr2、…、ytrλEach type of target at least comprises one target, and the azimuth angle and the pitch angle of all targets in each type of target are the same;
for the lambda class targets at pitch angles from sigma1To σ2Interval σ3Azimuth angle from xi1To xi2Interval xi3SAR imaging is carried out to obtain
Figure FDA0003538379460000011
A SAR image with 0-sigma1≤90°，0°≤σ2≤90°，σ1≤σ2，σ3>0，0°≤ξ1≤360°，0°≤ξ2≤360°，ξ1≤ξ2，ξ3>0, each SAR image comprises a target, the size of each SAR image is c x t, c is more than or equal to a, and t is more than or equal to a;
in the above-mentioned
Figure FDA0003538379460000012
Selecting a pitch angle theta from the SAR image1Azimuth angle from xi1To xi2Azimuthal angle interval of xi4Obtaining the SAR images of the m types of targets
Figure FDA0003538379460000013
A SAR image, wherein the label corresponding to the m-type target is ytr1、ytr2、…、ytrmWill be
Figure FDA0003538379460000014
Taking the SAR image and the label corresponding to the m-type target as a training set, wherein sigma1≤θ1≤σ2，0<ξ4≤ξ3，2≤m≤λ；
In the above-mentioned
Figure FDA0003538379460000015
Selecting a pitch angle theta from the SAR image2Azimuth angle from xi1To xi2Azimuthal angle interval of xi4Obtaining the SAR image of the m' type target
Figure FDA0003538379460000016
A SAR image, wherein the label corresponding to the m' class target is ytr1、ytr2、…、ytrm'Will be
Figure FDA0003538379460000017
Taking the SAR image and a label corresponding to the m' type target as a test set, wherein sigma1≤θ2≤σ2，θ1≠θ2M' has the same value as m;
the first test subset testx1, the second test subset testx2 and the third test subset testx3 are obtained by the following steps:
normalizing the size of each SAR image in the training set and the test set to a x a to obtain a normalized training set tranix and a normalized test set testx, wherein the normalized training set tranix comprises
Figure FDA0003538379460000021
A label corresponding to the normalized SAR image and the m-type target, wherein the normalized test set testx comprises
Figure FDA0003538379460000022
The method comprises the steps of obtaining a standard SAR image and a label corresponding to an m' type target;
the standardized test set testx is divided into three test subsets, a first test subset testx1, a second test subset testx2 and a third test subset testx3, according to the difference of the azimuth angle of each standardized SAR image in the standardized test set testx, wherein the first test subset testx1 comprises m1' Label corresponding to class target, and is marked as label column vector y corresponding to first test subset testx1te1(ii) a The second test subset testx2 comprises m2' Label corresponding to class target, and is marked as label column vector y corresponding to second test subset testx2te2(ii) a The third test subset testx3 comprises m3' Label corresponding to class target, and is marked as label column vector y corresponding to third test subset testx3te3；
Step 2, setting a CNN network and training to obtain a trained CNN network;
step 3, obtaining a normalized feature matrix trandinata of the normalized training set, a normalized feature matrix testdata1 of the first testing subset testx1, a normalized feature matrix testdata2 of the second testing subset testx2 and a normalized feature matrix testdata3 of the third testing subset testx3 according to the first testing subset testx1, the second testing subset testx2, the third testing subset testx3 and the training set;
step 4, training a standardized feature matrix tranndata of a standardized training set tranix by using a traditional SVM classification algorithm to respectively obtain a parameter matrix W and an offset vector bb;
step 5, calculating prediction category column vectors of the first test subset testx1, the second test subset testx2 and the third test subset testx3 according to results obtained in the step 3 and the step 4, and respectively marking the prediction category column vectors as a first column vector C1, a second column vector C2 and a third column vector C3;
step 6, obtaining a final prediction category column vector according to the first column vector C1, the second column vector C2 and the third column vector C3;
step 7, obtaining v according to the final prediction category column vector2Class is identified as v1Probability of class
Figure FDA0003538379460000023
1≤v2M is not less than m, m is not less than 2 and not more than lambda; v is2Class is identified as v1Probability of class
Figure FDA0003538379460000024
The method is an SAR target classification result based on CNN and SVM decision fusion.
2. The SAR target classification method based on CNN and SVM decision fusion as claimed in claim 1, characterized in that in step 2, the trained CNN network is obtained by the following processes:
2.1) setting a CNN network to totally comprise n +1 layers, wherein n is a positive integer more than 3; let layer 0 type0For input layer, i layer typeiWherein i is more than or equal to 1 and less than or equal to n-2, the ith layer typeiTaking convolutional and pooling layers, layer n-1 typen-1Being a fully-connected hierarchy, the nth typenThe total number of characteristic graphs of the ith layer is p as an output layeri，piIs a positive integer greater than 0;
initialization: setting the h-th layer of the i-1 th layer after the l-th update1Characteristic diagram and h-th layer in i-th layer2The initial value of the convolution kernel of the characteristic diagram is
Figure FDA0003538379460000031
And is
Figure FDA0003538379460000032
Is a matrix of k x k, and,
Figure FDA0003538379460000033
the values of k × k elements in the total are-HiAnd HiRandom number between, HiThe formula is calculated as follows:
Figure FDA0003538379460000034
wherein k × k represents the convolution kernel size, 0 ≦ h1≤pi-1，0≤h2≤pi，pi-1Indicates the total number of profiles, p, of the i-1 th layeriThe total number of the characteristic graphs of the ith layer is shown;
full connection matrix initial value ffw between layer n-1 and layer n0Is one (d)n×(dn-1·dn-1·pn-1) A matrix of full connection matrix initial values ffw between the n-1 th layer and the n-th layer0Each element value is a random number between-HH and HH, and HH is calculated as follows:
Figure FDA0003538379460000035
initial value ffb of offset vector between layer n-1 and layer n0Is a dnX b matrix, initial value of offset vector between layer n-1 and layer n ffb0Each element value is 0; final output matrix initial value o0＝ffw0·fv+ffb0Fv is pn-1The (p) th of the 1-dimensional column vector, fvm-1)·(dn-2)2+((r-1)·dn-2) Element to (p)m-1)·(dn-2)2+(r·dn-2) Each element is respectively connected with
Figure FDA0003538379460000036
Middle (r) th column 1 st element to dn-2The elements are in one-to-one correspondence and equal in value,
Figure FDA0003538379460000037
denotes the second in the n-2 th layer
Figure FDA0003538379460000038
The value of each feature map is dn-2×dn-2The matrix of (a) is,
Figure FDA0003538379460000039
pn-2the total number of the characteristic diagrams of the n-2 th layer is shown; 1 is not more than pm≤piLet di×diRepresenting the size of each characteristic diagram in the ith layer, wherein i is more than or equal to 1 and less than or equal to n-2; dn-1·dn-1Denotes the size of each feature map in the n-1 th layer, dn·dnRepresenting the size of each feature map in the nth layer;
initialization: l represents the first update, the initial value of l is 0, and the maximum value of l is
Figure FDA0003538379460000041
2.2) determining the data set B after the first updatelThe b standard SAR images correspondingly comprise b targets, the b targets are set to belong to eta targets, and labels y corresponding to the eta targetstr1、ytr2、…、ytrηForm the column vector y of the tag set after the first updateηWherein eta is more than or equal to 1 and less than or equal to b;
setting a zero matrix of lambda x b if the column vector y of the tag set after the ith updateηThe value of the element in the ddth column is yη(dd) ≦ dd ≦ b, then change the values of the σ -th row and η -th column elements in the λ × b zero matrix to 1, while the values of all other elements are still 0, and then obtain the tag matrix y of the η -class target after the first updateηl；
Wherein 1< σ < λ;
according to the final output matrix o after the first updatinglAnd the label matrix y of the eta class target after the first updatingηlCalculating the error matrix e after the first updatel：
el＝ol-yηl；
2.3) according to the error matrix e after the first updatelRespectively calculating the cost function L after the first updatelResidual error matrix od of nth layer after the first updatinglAnd residual matrix fvd of the n-1 th layer after the ith updatelThe calculation expressions are respectively:
Figure FDA0003538379460000042
odl＝el·(ol·(1-ol))
fvdl＝ffwl T·odl
wherein e isl(mu, rho) represents the error matrix e after the first updatelThe values of the elements in the middle mu row and the rho column are more than or equal to 1 mu and less than or equal to lambda, and are more than or equal to 1 rho and less than or equal to b, ffwl TRepresentation ffwlTranspose of (2), ffwlRepresenting a full connection matrix between the (n-1) th layer and the nth layer after the ith update;
2.4) calculating the h-th in the i-1 th layer after the first update1Characteristic diagram and h-th layer in i-th layer2Convolution kernel gradient matrix of individual feature map
Figure FDA0003538379460000051
Fully connected matrix gradient dffw after ith updatelAnd the full connection offset dffb after the first updatelThe calculation expressions are respectively:
Figure FDA0003538379460000052
Figure FDA0003538379460000053
Figure FDA0003538379460000054
wherein, when l and i take the same value and h1And h2When the values are different, the h-th layer in the i-1 th layer is connected after each update1Characteristic diagram and h-th layer in i-th layer2The convolution kernel gradient matrices of the individual feature maps are all identical; b represents the total number of normalized SAR images included in each updated data set, fvTRepresenting transpose of fv, odl(pp) denotes odlAll elements, od, of the pp-th column of the matrixlRepresenting a residual error matrix of the nth layer after the ith update;
2.5) adding 1 to the value of l, calculating the h in the i-1 th layer after the l time of updating1Characteristic diagram and h-th layer in i-th layer2Convolution kernel of individual feature map
Figure FDA0003538379460000055
Convolution layer bias after the first update blFull connection matrix ffw between layer n-1 and layer n after the first updatelAnd an offset vector ffb between layer n-1 and layer n after the ith updatelThe calculation expressions are respectively:
Figure FDA0003538379460000056
bl＝bl-1-α·dbl-1
ffwl＝ffwl-1-α·dffwl-1
ffbl＝ffbl-1-α·dffbl-1
wherein the content of the first and second substances,
Figure FDA0003538379460000057
indicates that the h-th layer in the i-1 th layer is connected after the l-1 th update1Characteristic diagram and h-th layer in i-th layer2A convolution kernel gradient matrix of the feature map; let p in the i-1 st layernThe value of each feature map is di-1×di-1Of (2) matrix
Figure FDA0003538379460000058
Figure FDA0003538379460000059
Denotes the p-th in the i-th layermSensitivity matrix of individual characteristic map, bl-1Denotes the convolution layer offset after the first-1 update, b0＝0，α>0；
Figure FDA00035383794600000510
Indicates that the h-th layer in the i-1 th layer is connected after the l-1 th update1Characteristic diagram and h-th layer in i-th layer2The convolution kernel of the individual feature maps,
Figure FDA0003538379460000061
indicates that the h-th layer in the i-1 th layer is connected after the l-th update1Characteristic diagram and h in i layer2Initial values of convolution kernels of the feature maps; dbl-1Representing the gradient of the offset vector after the l-1 th update,
Figure FDA0003538379460000062
b represents the total number of the standardized SAR images included in the data set after each update;
then returning to the step 2.2); until it is calculated to be
Figure FDA0003538379460000063
Connecting h in the i-1 th layer after secondary updating1Characteristic diagram and h-th layer in i-th layer2Convolution kernel of individual feature map
Figure FDA0003538379460000064
First, the
Figure FDA0003538379460000065
Post-update convolutional layer biasing
Figure FDA0003538379460000066
First, the
Figure FDA0003538379460000067
Fully connected matrix between n-1 th layer and n-th layer after secondary updating
Figure FDA0003538379460000068
And a first
Figure FDA0003538379460000069
Offset vector between n-1 th layer and n-th layer after sub-update
Figure FDA00035383794600000610
For the first
Figure FDA00035383794600000611
Connecting h in the i-1 th layer after secondary updating1Characteristic diagram and h-th layer in i-th layer2Convolution kernel of individual feature map
Figure FDA00035383794600000612
Let i equal 1,2, …, n-2, and then get the second
Figure FDA00035383794600000613
After secondary update, connect h in layer 01Characteristic diagram and h in layer 12Convolution kernel of individual feature map
Figure FDA00035383794600000614
To the first
Figure FDA00035383794600000615
After the second update, connecting the h-th layer in the n-3 th layer1A characteristic diagram and h in the n-2 th layer2Convolution kernel of individual feature map
Figure FDA0003538379460000071
And the initial value b of the bias of the convolution layer obtained at this time0To the first
Figure FDA0003538379460000072
Post-update convolutional layer biasing
Figure FDA0003538379460000073
Full connection matrix initial value ffw between layer n-1 and layer n0To the first
Figure FDA0003538379460000074
Fully connected matrix between n-1 th layer and n-th layer after secondary updating
Figure FDA0003538379460000075
And an initial value ffb of an offset vector between the n-1 th layer and the n-th layer0To the first
Figure FDA0003538379460000076
Offset vector between n-1 th layer and n-th layer after sub-update
Figure FDA0003538379460000077
And the set CNN network is indicated to be trained and recorded as the trained CNN network.
3. A CNN and SVM decision fusion based SAR target classification method according to claim 2, characterized in that in step 3, the normalized feature matrix tranndata of the normalized training set tranix, the normalized feature matrix testdata1 of the first test subset testx1, the normalized feature matrix testdata2 of the second test subset testx2 and the normalized feature matrix testdata3 of the third test subset testx3 are obtained by:
3.1) training the normalized training set trainx, the first test subset testx1, the second test subset testx2 and the third test subset testx3 respectively by using the trained CNN network to obtain a feature matrix trainx _ new of the normalized training set trainx, a feature matrix testx1_ new of the first test subset testx1, a feature matrix testx2_ new of the second test subset testx2 and a feature matrix testx3_ new of the third test subset testx3 respectively;
3.2) normalizing the feature matrix trainx _ new of the normalized training set trainx, the feature matrix testx1_ new of the first test subset testx1, the feature matrix testx2_ new of the second test subset testx2 and the feature matrix testx3_ new of the third test subset testx3, respectively, using a data normalization algorithm, resulting in a normalized feature matrix traindata of the normalized training set trainx, a normalized feature matrix testdata1 of the first test subset testx1, a normalized feature matrix testdata2 of the second test subset testx2 and a normalized feature matrix testdata3 of the third test subset testx3, respectively, which are calculated as:
Figure FDA0003538379460000081
Figure FDA0003538379460000082
Figure FDA0003538379460000083
Figure FDA0003538379460000084
wherein, the mean function represents the column mean value of the matrix, and the SID function represents the column standard deviation of the matrix.
4. The method for classifying SAR targets based on CNN and SVM decision fusion as claimed in claim 3, wherein in step 5, the first column vector C1, the second column vector C2 and the third column vector C3 are obtained by:
according to the feature matrix testdata1 of the first test subset testx1, the feature matrix testdata2 of the second test subset testx2 and the feature matrix testdata3 of the third test subset testx3, as well as the parameter matrix W and the offset vector bb, the column vectors of prediction categories for the first test subset testx1, the second test subset testx2 and the third test subset testx3, which are respectively denoted as a first column vector C1, a second column vector C2 and a third column vector C3, are calculated as follows: "
fen1＝testdata1·WT+repmat(bb,[size(testdata1,1),1])
fen2＝testdata2·WT+repmat(bb,[size(testdata2,1),1])
fen3＝testdata3·WT+repmat(bb,[size(testdata3,1),1])
Where size (testdata1,1) represents the number of rows, repmat (bb, [ size (testdata1,1) of matrix testdata1]) Represents a size (testdata1,1) line pn-1Matrix of columns, size (testdata1,1) line pn-1Each row of the matrix of columns is an offset vector bb; fen1 is a size (testdata1,1) xpn-1Matrix of (2), size (testdata1,1) × pn-1Each row of the matrix has only one element with a value of 1 and the remaining elements of each row have values of 0, respectively; if the number of columns where value 1 of the element in row # 1 of fen1 is Δ 1, C1(ψ 1) is Δ 1, where 1 ≦ ψ 1 ≦ size (testdata1), and 1 ≦ Δ 1 ≦ pn-1C1(ψ 1) denotes the value of the ψ 1-th element of the first column vector C1; let ψ 1 be 1,2, …, size (testdata1), and then get a first column vector C1, the first column vector C1 including size (testdata1) elements;
where size (testdata2,1) represents the number of rows, repmat (bb, [ size (testdata2,1),1, of matrix testdata2]) Represents a size (testdata2,1) line pn-1Matrix of columns, the size (testdata2,1) row pn-1Each row of the matrix of columns is an offset vector bb; fen2 is a size (testdata2,1) xpn-1Matrix of (2), size (testdata2,1) × pn-1Each row of the matrix has only one element with a value of 1 and the remaining elements of each row have values of 0, respectively; if the number of columns where value 1 of element in row # 2 of fen2 is Δ 2, C2(ψ 2) is Δ 2, where 1 ≦ ψ 2 ≦ size (testdata2), and 1 ≦ Δ 2 ≦ pn-1C2(ψ 2) denotes the value of the ψ 2 th element of the second column vector C2; let ψ 2 be 1,2, …, size (testdata2), and then get a second column vector C2, said second column vector C2 comprising size (testdata2) elements;
where size (testdata3,1) represents the number of rows, repmat (bb, [ size (testdata3,1),1, of matrix testdata3]) Represents a size (testdata3,1) line pn-1Matrix of columns, the size (testdata3,1) row pn-1Each row of the matrix of columns is an offset vector bb; fen3 is a size (testdata3,1) xpn-1Matrix of (2), size (testdata3,1) × pn-1Each row of the matrix has only one element with a value of 1 and the remaining elements of each row have values of 0, respectively; if the number of columns in which value 1 of element in row # 3 of fen3 is Δ 3, C3(ψ 3) is Δ 3, where 1 ≦ ψ 3 ≦ size (testdata3), and 1 ≦ Δ 3 ≦ pn-1C3(ψ 3) denotes the value of the ψ 3 th element of the third column vector C3; let ψ 3 be 1,2, …, size (testdata3), which results in a third column vector C3, which third column vector C3 comprises size (testdata3) elements.
5. The method for classifying SAR target based on CNN and SVM decision fusion as claimed in claim 4, wherein in step 6, the final prediction class column vector is obtained by:
making a decision on each row of the first column vector C1, the second column vector C2 and the third column vector C3 to obtain a final prediction type column vector;
taking the values of the delta-th row element of the first column vector C1, the second column vector C2 and the third column vector C3 respectively, and marking as the value C1 (delta) of the delta-th row element of the first column vector C1, the value C2 (delta) of the delta-th row element of the second column vector C2 and the value C3 (delta) of the delta-th row element of the third column vector C3 respectively, wherein 1 is larger than or equal to delta and smaller than or equal to S, and S is the total column number of the first column vector C1; setting the S-dimensional column vector as C, the procedure of obtaining the value C (δ) of the δ -th row element of the S-dimensional column vector C is:
if C1(δ) is C2(δ) or C1(δ) is C3(δ), then:
C(δ)＝C1(δ)；
if C2(δ) is C3(δ), then:
C(δ)＝C2(δ)；
if two of C1 (delta), C2 (delta) and C3 (delta) are different, randomly selecting any one value of C1 (delta), C2 (delta) and C3 (delta) as a value C (delta) of a delta-th row element of the S-dimensional column vector C;
let δ be 1,2, …, S, and further obtain the values C (1) of the 1 st row element of the S-dimensional column vector C to the values C (S) of the S-th row element of the S-dimensional column vector C, respectively, and record them as a final prediction type column vector, which is the S-dimensional column vector.
6. The SAR target classification method based on CNN and SVM decision fusion as claimed in claim 5, characterized in that in step 7, the v2Class is identified as v1Probability of class kv1v2The obtaining process is as follows:
if the value of the phi 4 th row element of the final prediction class column vector is v1And the label column vector y to which the first test subset testx1 correspondste1Has a value v of the element of row # 42Counting the value of the element in S elements in the final prediction category column vector as v1Total number of rows of elements, denoted as S1，S1<S, then counting S1The rows correspond to a label column vector yte1The value of the middle element is v2Total number of (2), denoted as v2Class is identified as v1Number of classes
Figure FDA0003538379460000101
Wherein
Figure FDA0003538379460000102
V is then2Class is identified as v1Probability of class
Figure FDA0003538379460000103
Comprises the following steps:
Figure FDA0003538379460000104
wherein v is not less than 11≤m，1≤v2≤m。
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