High-ResolutionRadarTargetRecognitionviaInception-Based ... · Conv1–16 Conv5–32 Conv1–96...

Research ArticleHigh-Resolution Radar Target Recognition via Inception-BasedVGG (IVGG) Networks

Wei Wang1 Chengwen Zhang1 Jinge Tian1 Xin Wang1 Jianping Ou2 Jun Zhang 2

and Ji Li 1

1School of Computer and Communication Engineering Changsha University of Science and Technology Changsha 410114 China2ATR Key Laboratory National University of Defense Technology Changsha 410073 China

Correspondence should be addressed to Jun Zhang zhj64068sinacom and Ji Li hangliji163com

Received 13 June 2020 Revised 21 June 2020 Accepted 1 July 2020 Published 18 July 2020

Academic Editor Nian Zhang

Copyright copy 2020 Wei Wang et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Aiming at high-resolution radar target recognition new convolutional neural networks namely Inception-based VGG (IVGG)networks are proposed to classify and recognize different targets in high range resolution profile (HRRP) and synthetic apertureradar (SAR) signals +e IVGG networks have been improved in two aspects One is to adjust the connection mode of the fullconnection layer +e other is to introduce the Inception module into the visual geometry group (VGG) network to make thenetwork structure more suik for radar target recognition After the Inception module we also add a point convolutional layer tostrengthen the nonlinearity of the network Compared with the VGG network IVGG networks are simpler and have fewerparameters +e experiments are compared with GoogLeNet ResNet18 DenseNet121 and VGG on 4 datasets +e experimentalresults show that the IVGG networks have better accuracies than the existing convolutional neural networks

1 Introduction

Radar automatic target recognition (RATR) technology canprovide inherent characteristics of the target such as theattributes categories and models and these characteristicscan provide richer information for battlefield commanddecisions +e high-resolution radar echo signal obtainedfrom the wide bandwidth signal transmitted by the broad-band radar provides more detailed features of the targetwhich makes it possible to identify the target type +ereforemore and more research studies focus on RATR technology

Traditional methods of radar target automatic recognitioninclude k-nearest neighbor classifier (KNN) and support vectormachine learning (SVM) and so on Zhao and Principe [1]applied support vectormachine to automatic target recognitionof SAR image Obozinski et al [2] proposed the Trace-normRegularized multitask learning method (TRACE) to solve theproblem of recovering a set of common covariates related toseveral classification problems at the same time It assumes thatall models share a common low-dimensional subspace but themethod cannot be extended to the nonlinear field well

Regularized multitask learning (RMTL) proposed by Evgeniouand Pontil [3] extends the existing kernel-based learningmethods of single-task learning such as SVM Zhou et al [4]proposed the clustered multitask learning (CMTL) method toreplace multitask learning (MTL) It assumes that multipletasks follow the cluster structure and achieves high recognitionaccuracy of SAR image Zhang and Yeung [5] proposed themultitask relationship learning (MTRL) method which canlearn the correlation between positive and negative tasks au-tonomously and the recognition accuracy is higher than that ofCMTL Cong et al [6] proposed a new classificationmethod byimproving MTRL which can autonomously learn multitaskrelationship and cluster information of different tasks and beeasily expanded to the nonlinear domain He et al [7] used theprincipal component analysis (PCA) method to realize the fasttarget recognition of SAR image

With the development of artificial intelligence more andmore applications based on neural networks are used fortarget recognition [8] In the field of image target recog-nition convolutional neural network (CNN) has achievedgreat success which is widely used in object detection and

HindawiComputational Intelligence and NeuroscienceVolume 2020 Article ID 8893419 11 pageshttpsdoiorg10115520208893419

localization semantic segmentation target recognition andso on [9] Visual geometry group networks (VGGNets) [10]proposed by Simonyan and Zisserman have significantlyimproved image recognition accuracy by deepening thenetwork depth to 19 layers In the same year GoogLeNet[11] proposed by Christian Szegedy used the Inceptionmodule to have several parallel convolution routes forextracting input features which widened the networkstructure horizontally and deepened the network depth to acertain extent while the network parameters are reducedStudies have shown that deeper networks have better per-formance but deepening the network is faced with theproblem of gradient disappearance and the complex net-works also have the risk of overfitting Residual networks(ResNets) [12] and dense convolutional network (DenseNet)[13 14] solve the above problems by using skip connectionsand significantly increase the depth of the network Recentlyproposed highway networks ResNets and DenseNet havedeepened the network structure to more than 100 layers anddemonstrated outstanding performance in the field of imagerecognition

Different from image data radar data are sparse andhave a little amount +erefore the network should be ableto extract multidimensional features and the depth couldnot be too deep So we considered using the Inceptionmodule and VGG network for training VGG networks havelimited depth and been proven to have excellent featureextraction capabilities +e Inception module has multipathconvolution which can extract radar multidimensionalinformation for learning and its internal large-scale con-volution kernels are also more effective to extract the in-formation with sparse characteristics +erefore weproposed a method to fuse the Inception module with theVGG network

+is paper focuses on target recognition based on 1DHRRP and SAR images and proposes the IVGG convolu-tional neural network structure which is most suitable forhigh-resolution radar target recognition +e parameters ofIVGG can also be greatly reduced

2 Target Recognition Model IVGG Networks

21 VGGNets VGGNets [10] adopted the convolution fil-ters with a small local receptive field and proposed 6 differentnetwork configurations In VGGNets the convolution filtersare set to 3times 3 and the max-pooling is 2times 2 with stride 2

+e contribution of the VGGNet is the application of the3times 3 small convolution filters By stacking small convolutionfilters the depth of the network is increased and thenonlinearity of the convolutional layers is strengthened too[15] +erefore the nonlinear function can be better fitted(but the overfitting phenomenon needs to be prevented) andthe parameters of the network are reduced

Before the VGG network was proposed An et al alsoused small convolution filters but the network was not asdeep as VGGNet [16] +e VGGNet has better performancethan other convolutional networks in extracting targetfeatures

In the structure of VGGNet the convolutional layers andpooling layers alternately appear After two to four con-volutional layers a max-pooling layer is followed In order tokeep the computational complexity of the constituentstructures at each feature layer roughly consistent thenumber of convolution kernels at the next layer is doubledwhen the size of the feature map is reduced by half throughthe max-pooling layer VGGNet ends with three fullyconnected layers which are also the classifier for the system

22 e Improved Model IVGG Network Because SARimages and HRRP data are sparse it is difficult to fullyrepresent all the feature information of the targets by usingall 3times 3 convolution filters GoogLeNet proposed byChristian Szegedy [11] uses the Inception modules withlarger convolution filters which can extract radar multidi-mensional information for learning As shown in Figure 1there are several parallel convolutional lines in the Inceptionmodule and the large convolution filters in parallel linesincrease the width and the depth of the network structureSo the Inception module is used to modify the VGGmodule+e new network is specially designed for radar dataanalysis and has a high recognition rate of radar targetmodels +e principle of improvement will be introduced inthe next section

In this paper the ldquoConvrdquo module includes convolutionbatch standardization and activation functions as shown inFigure 2

Based on the above structures we propose 4 new IVGGnetworks In this structure a certain number of Inceptionmodules are used to replace ldquoConv3rdquo module in the originalVGGNets Note that we add a very deep point convolutionallayer after the Inception module and it is important Manytraditional algorithms show poor performance for radartarget recognition is because they cannot effectively fit thenonlinear structure in the radar signal [6] Drawing on thispoint of view we have strengthened the nonlinear capa-bilities of IVGG by adding a point convolutional layerImmediately following the Inception module the layercontains activation function which increases the nonline-arity of the network Further we set the input number ofchannels is same with output In other words the pointconvolutional layer does not compress the output featuremaps It also strengthens the nonlinearity of the networkTable 1 shows the specific configuration of the IVGG net-works where the Inception module and Conv1 modulewhich are used to replace Conv3 modules in the originalnetwork are identified in italics

+e fully connected layers of VGGNets are shown inTable 2 Since there have 3 layers we use ldquo3FCrdquo to refer to thestructure in Table 2

+e classifier of the VGG networks is fully connectedlayers containing most of the parameters of the wholenetwork In order to reduce the parameters we improved theFC layers reducing the 3-layer FC to a single-layer ldquoFC-410rdquo which is represented by ldquo1FCrdquo

In the experiment the network we proposed relates tothe above two classifiers which can be represented by

2 Computational Intelligence and Neuroscience

ldquoIVGGx-1FCrdquo and ldquoIVGGx-3FCrdquo respectively where x isthe network depth

+e IVGG11 network is shown in Figure 3 the structureshows how conv3 modules are replaced and the othernetworks with different depths (IVGG131619) in Table 1also follow this rule

3 Characteristic Analysis of IVGG Networks

31 Relationship between Data Sparsity and NetworkStructure In this section we perform theoretical analysis todemonstrate the sparse characteristics of 3 times 3 filters and 5 times

5 filters It can further explain that the IVGG network canovercome the target recognition difficulties caused by sparseradar data to some extent

Assume that in the convolution layers the weight tensoris s W isin RCintimesCouttimes(k1k2) where Cin is the number of inputchannels Cout is the number of output channels andk1 and k2 are the convolutional kernel size Considering thecalculation process of convolution filters and feature map ineach channel the weight matrix of the filter isWfilter isin Rk1timesk2 We unfold the weight matrix into a vectorw isin Rk1k2 Each local receptive field in the input (consideringa certain channel) is expanded into a vector x and then wTXrepresents the output where the matrixX (x1 x2 xN) and the number of elements in theoutput feature map is represented by N

If the kernel size of a convolution layer is (k1 k2) weighttensor wT (w1 w2 wk1timesk2

)T the output feature mapcan be represented as follows

wTX wTx1wTx2 wTxN1113872 1113873 1113944

k1timesk2

i1wixi1 1113944

k1timesk2

i1wixi2 1113944

k1timesk2

i1wixiN

⎛⎝ ⎞⎠

wTX0 n (1 2 N) | 1113944

k1timesk2

i1wixin ne 0⎛⎝ ⎞⎠

wTX1 1113944N

n11113944

k1timesk2

i1wixin

1113868111386811138681113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868111386811138681113868

(1)

Assume the elements in matrix X are set to zero inprobability P1(P1 lt 1) the weight vector w element valueswi are set to zero in probability P2 that is P wi1113864 1113865 P2 WhenP1⟶ 1 X0⟶ 0foralln (1 2 N) the probabilitywhen the neuron is activated is as follows

limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ limP1⟶1

1 minus 1 minus 1 minus P1( 1113857 1 minus P2( 1113857( 111385725

1113872 1113873

limP1⟶1

1 minus 1 minus 1 minus P1 minus P2 + P1P2( 1113857( 111385725

1113872 1113873

1 minus 1 minus 1 minus P1 minus P2 + P2( 1113857( 111385725

1 minus 1 minus 1 minus P1( 1113857( 111385725

1 minus P251

(2)

Base

Conv1

Conv5

Conv1

Conv3

MaxPool(3)

Conv1

Depth concat

Conv1

Figure 1 +e Inception module where Conv1 means the con-volutional filter is 1times 1 Conv3 means the convolutional filter is3times 3 and Conv5 means the convolutional filter is 5times 5

Convolution

Batchnormalization

ReLUTanh

Figure 2 ldquoConvrdquo module

Table 1 IVGG network configuration

IVGG11 IVGG13 IVGG16 IVGG1911 weightlayers

13 weightlayers

16 weightlayers

19 weightlayers

Input (HRRP OR SAR)

conv3-64 conv3-64 conv3-64 conv3-64conv3-64 conv3-64 conv3-64

MaxPool


MaxPoolInception-256 conv3-256 conv3-256 conv3-256conv1-256 Inception-256 Inception-256 Inception-256conv3-256 conv1-256 conv1-256 conv1-256

conv3-256 conv3-256conv3-256

MaxPoolInception-512 conv3-512 conv3-512 Inception-512conv1-512 conv3-512 Inception-512 conv1-512Inception-512 conv1-512 conv3-512conv1-512 Inception-512 conv3-512

conv1-512 Inception-512conv1-512

MaxPoolconv3-512 Inception-512 conv3-512 conv3-512conv3-512 conv1-512 conv3-512 conv3-512

Inception-512 conv3-512 conv3-512conv1-512 conv3-512

MaxPoolFully connected layersSoft-max

Table 2 +ree fully connected layers (3FC)FC-4096FC-4096FC-410

Computational Intelligence and Neuroscience 3

Input

MaxPool

MaxPoolBase

Conv1ndash16

Conv5ndash32

Conv1ndash96

Conv3ndash128

MaxPool(3)

Conv1ndash32

Conv1ndash64

Depth concat

ReplaceDelete

MaxPool Base

Conv1ndash24

Conv5ndash64

Conv1ndash112

Conv3ndash224

MaxPool(3)

Conv1ndash64

Conv1ndash160

Depth concat

MaxPool

MaxPool Fully connected layers Soft-max

ReplaceDelete

Inception

Deep point conv

Inception

Deep point conv

times2

Conv3ndash64

Conv3ndash128

Conv3ndash256

Conv3ndash256

Conv1ndash256

Conv3ndash512

Conv1ndash512

Conv3ndash512

Conv3ndash512

Conv3ndash512

Figure 3 IVGG11 network architecture


Similarly we can get the following expression

limP1⟶1

P 1113944

3times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ 1 minus P91 (3)

So we can get the following inequality

there4 limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ gt limP1⟶ 1

P 11139443times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭

(4)

When k1 3 k2 3 we use a0 and a1 to denote wTX0and wTX1 When k1 5 k2 5 we use b0 and b1 to denotewTX0 and wTX1 +en

a0 N 1 minus P911113872 1113873

b0 N 1 minus P2511113872 1113873

a0 lt b0

(5)

For the convenience of calculations we assume thatinput feature vectortensor does zero padding BecauseP1⟶ 1 this does not affect the calculation result +en wehave

a1 wTX1 1113944N

n11113944

3times3

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

b1 wTX1 1113944

N

n11113944

5times5

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

(6)

It is easy to prove a1 lt b1 +erefore the large-scaleconvolution kernel can effectively extract the target featuresif the input data are too sparse

+e sparsity of the convolutional layer can bring manybenefits such as better robustness and higher feature ex-traction efficiency However if the input data are excessivesparse feature extraction will become more difficult+erefore after repeated experiments we finally chose theInception module instead of the larger convolution kernelWe just added an appropriate number of Inception moduleto the network and they are not all composed of Inceptionmodules like GoogLeNet In order to improve the networkrsquosability to fit nonlinear structures in radar data (such as SARimages) we add a very deep point convolutional layer be-hind the Inception module It should be noted that the pointconvolutional layer introduces an activation function andthe channels of input and output channels are the samewhich improves the nonlinearity of the new network

32 e Parameter Number of the Networks As shown inFigure 4 our method has about 3 million parameters lessthan the VGG network at the same depth +e number ofparameters of networks connected to the above two clas-sifiers is shown in Table 3 By improving the classifier ournetwork can further reduce the parameter amount by 86ndash92

+e comparisons of floating points of operations(FLOPs) are shown in Figure 5 According to Figure 5 thecomputation cost is most affected by the network depth

IVGG16 and IVGG19 are very computation-intensive It canbe seen from Figure 4 that at the same number of networklayers the FLOPs of IVGG are significantly less than those ofthe VGG networks For example IVGG16-3FC saves 2361FLOPs compared to VGG19 So our methods not only saveparameter storage space but also reduce computation cost

4 Experiment and Results Analysis

41 Dataset +e SAR image dataset used in this paper is apublic dataset released by MSTAR +ere are many researchstudies on radar automatic target recognition based on theMATAR SAR dataset such as references [1ndash4 17ndash20] +eexperimental results in this paper are compared with theabove methods +e MSTAR dataset and the HRRP datasetare used for experiments Published by MSTAR [6 21] theSAR dataset includes ground-based military targets +eacquisition conditions of the MSTAR dataset are classifiedinto standard operating condition (SOC) and extendedoperating condition (EOC) +ere are 10 kinds of targetsunder SOC conditions each of which contains omnidi-rectional SAR image data at 15deg and 17deg pitch angles In theexperiments observation data at 17deg were used for trainingand the observation data at 15deg pitch angle were used fortesting +e optical image of the targets in the MSTAR SARdataset collected under SOC conditions is shown in Figure 6In the EOC-1 dataset there are 4 kinds of ground targets inwhich the targets with a side view angle of 17deg are used forthe training set and the targets with a side view angle of 30degare used for the test set

+e test set and training set are the samemodel targets indifferent pitch angles In fact this is one of the differencesbetween high-resolution radar target recognition and imagerecognition +e purpose of this paper is to accuratelyrecognize the target model through high-resolution radardata In academia there is only a difference in pitch anglebetween the test set and the training set which is feasible andin line with reality [6 21ndash23]

Because SAR images are extremely sensitive to changesin pitch angle it is more difficult to identify the targets underEOC-1 conditions +e pitch angle difference between theSOC training set and the test set is 2deg while the differenceunder the EOC-1 is increased to 13deg +is may lead to a bigdeviation of the same target in SAR images under the sameposture which increases the difficulty of recognition+erefore the experimental conclusions based on the SAR-EOC dataset are more valuable

As shown in Table 4 the two vectors are two samples inthe dataset HRRP-1 which reflects the scattering charac-teristics of the armored transport vehicle and the heavytransport vehicle respectively

+e HRRP-1 dataset [22] is target electromagneticscattering data obtained by high-frequency electromagneticcalculation software HRRP provides the distribution oftarget scattering points along the distance and is an im-portant structural feature of the target HRRP has thecharacteristics of stable resolution easy acquisition andrealization and short imaging period +e simulation da-tabase contains 4 kinds of ground vehicle targets armored


transport vehicles heavy transport vehicles heavy trucksand vans Acting on the stepped frequency echo signal at thesame observation angle of the target Inverse fast Fouriertransform (IFFT) is used to synthesize the HRRP Since theelectromagnetic simulation data are turntable-like data it isnot necessary to translate and align In the experiment thetarget electromagnetic scattering echo under the HH po-larization mode is selected as the basic dataset +e targetswith a pitch angle of 27deg are used for training and the targetswith a pitch angle of 30deg are used for test Both the trainingset and the test set have 14400 samples each of which is a128times1 array with complex data type +e training set is thesame as the test set except for the pitch angle In addition theHRRP data generated by inversion of the MSTAR SARdataset are used as the second HRRP dataset (HRRP-2)

42 Preprocessing and Experimental Setup For the MSTARSAR images each sample is resized to 128times128 and thenthe center cut and random horizontal rotation are

performed After this preprocessing the number of SARimages has been expanded by 3 times which compensatesfor the shortage of SAR images and alleviates the overfittingproblem of the network to some extent

+e phase profile of the complex high-resolution echo ofthe target can be divided into two parts the initial phase thatis sensitive to the distance and the remaining phase reflectingthe scattering characteristics of the target +erefore like theamplitude profiles (real HRRP) phase profiles in thecomplex HRRP also represent a certain information of thescattering point distribution of the target and it should bevaluable in recognition +e complex HRRP contains all thephase information of the target scatter point subecho in-cluding the initial phase and the remaining phase of thescatter point subecho +erefore although the complexHRRP has a sensitivity to the initial phase which is notconducive to HRRP target recognition it retains otherphases information that is helpful for recognition [24] +etraditional RATR uses the amplitude image of HRRP andloses the phase information Phase information is especiallyuseful for target recognition but most convolution networkmodels cannot deal with complex data types At present themain processing method of complex HRRP is modulusoperation which can keep the amplitude information ofrange profile and get relatively high recognition accuracy

Unlike images that can use superresolution method toimprove recognition accuracy [25] HRRP is made up ofone-dimensional data points so we propose a new way topreprocess HRRP data +e real part and the imaginary partof each data are extracted and arranged in an orderly way sothat the length of each sample is expanded from 128 to 256In this way the differential phase information between thedistance units in each HRRP sample can be preserved andthe amount of data in each sample can be expanded

To compare the test results of different models theexperiments are carried out on the same platform and en-vironment as shown in Table 5

Considering that the radar data are sparse the activationfunction Rectified Linear Unit (ReLU) [26] will undoubtedlyincrease this sparseness and reduce the useful information ofthe target which is unfavorable for recognition So weintroduce another activation function Hyperbolic Tangentfunction (Tanh) +e resulting impact will be further ana-lyzed in the experiments

+e learning rate attenuation method is also introducedin the training processing As the number of iterations in-creases the learning rate gradually decreases +is can en-sure that the model does not fluctuate greatly in the laterperiod of training and closer to the optimal solution

We adjust the parameters according to the results ofmany experiments and get the final parameters We useVGGNet pretrained by ImageNet in PyTorch to initialize theparameters of IVGG networks In the training stage thebatch size of the training set is set to 16 and that of the test setis set to 32 For MSTAR SAR dataset recognition the initiallearning rate is set as 001 and 200 epochs are used fortraining+e learning rate decreases by 2 times since the first50 epochs and then decreases by 2 times every 20 epochs+eaverage recognition accuracy of the last 100 epochs was

11 13 16 19VGG 128 128 134 139

IVGG 125 125 1306 136

128 128

134

139

125 125

1306

136

115

120

125

130

135

140

145Pa

ram

eter

s (in

mill

ions

)

Figure 4 +e number of parameters (in millions) of VGG net-works and our methods

Table 3 +e number of parameters (in millions) of our networkswith different classifiers

Network 1FC 3FCIVGG11 719 125IVGG13 596 125IVGG16 1127 1306IVGG19 1767 136

11 13 16 19IVGG-1FC 180574 309409 380984 544795IVGG-3FC 192519 321355 39293 55674VGG 257108 378376 514399 650423

01000200030004000500060007000

FLO

Ps (i

n m

illio

ns)

IVGG-1FCIVGG-3FCVGG

Figure 5 Comparison of floating points of operations (FLOPs)


calculated as the final results For HRRP dataset recognitionthe initial learning rate is set as 01 and 100 epochs are usedfor training +e learning rate decreases by 2 times since thefirst 50 epochs and then decreases by 2 times every 10epochs +e average recognition accuracy of the last 10epochs was calculated as the final results

43 Recognition Results of the MSTAR SAR Dataset +erecognition accuracy on the MSTAR SAR dataset is shownin Table 6 On SAR-SOC the results of IVGG networks andVGG networks are better than those of GoogLeNetResNet18 and DenseNet121 It can be seen from Table 6 thaton the SAR-SOC IVGG networks with both 1FC and 3FChave good recognition performance It shows that ourmethods have better robustness +e recognition rates ofIVGG networks are similar to those of VGGNets but each of

them reduces about 3 million parameters compared with thelatter

GoogLeNet achieves high recognition accuracies onSAR-SOC but its recognition accuracies on SAR-EOC-1 arepoor which are only 9062 and 9019 +is shows that itsgeneralization ability is not so ideal Based on the horizontalcomparison of the recognition accuracies of the activationfunctions Tanh and ReLU in Table 6 we can see the per-formance of Tanh on SAR-EOC-1 is generally strongerindicating that Tanh has a better effect on sparse dataprocessing

On SAR-SOC IVGG16-3FC with ldquoTanhrdquo achieves amaximum accuracy of 9951 On SAR-EOC-1 IVGG19-3FC achieves the highest accuracy of 9927 and IVGG13-31FC also achieves the accuracy of 9922 +e classifi-cation on SAR-EOC is more difficult and it requires thatCNNs have higher performance So we especially focus onanalyzing the experimental results on SAR-EOC

+e accuracy rate of IVGG13 on SAR-EOC is signifi-cantly higher than those of GoogLeNet ResNet18 Dense-Net121 VGG11 and VGG13 It is still 012 higher thanVGG16 and VGG19 But the parameter number of IVGG13is only 445 of VGG16 and 429 of VGG19 and theFLOPs are significantly lower than those of VGG16 andVGG19 Specifically IVGG13-1FC saves 3985 FLOPsthan VGG16 and 5243 than VGG19 +e accuracy rate ofIVGG13-13FC is only 005 lower than that of IVGG19-

Table 4 +e samples of complex HRRP vector

Sample 1 of HRRP Sample 2 of HRRP5947548139439314eminus 04ndash7029982346588466eminus 04i minus0001741710511154 + 0005854695561424i5973508449729275eminus 04ndash7301167648045039eminus 04i minus0001602329272711 + 0005996485005943i5998884995750467eminus 04ndash7586149497061626eminus 04i minus0001459788439038 + 0006143776077643i6023640017197894eminus 04ndash7885879483632503eminus 04i minus0001313674253423 + 0006297298858010i6047727981516010eminus 04ndash8201413412111810eminus 04i minus0001163535049426 + 0006457875798999i

(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)

Figure 6 Images of the MSTAR SAR dataset under SOC

Table 5 Experimental platform configuration

Attribute Configuration informationOS Ubuntu 14045 LTSCPU Intel (R) Xeon (R) CPU E5-2670 v3 230GHzGPU GeForce GTX TITAN XCUDNN CUDNN 6021CUDA CUDA 8061Framework PyTorch


3FC but the parameter of IVGG13-1FC is only 477 of thatof IVGG19-3FC and the FLOPs of IVGG13-13FC are onlyabout 56 of those of IVGG19-3FC

+e experiments show that the IVGG networks canwork well on the SAR image public dataset and have goodrobustness and recognition performance +e importantpoint is that IVGG uses a significantly shallower networkto achieve better accuracy than other CNNs It greatlyimproves the computational efficiency and can save greatparameter space In fact IVGG13-1FC relies on relativelyless parameters and FLPOs to achieve quite good resultsIn contrast although IVGG16 and IVGG19 networks canslightly improve the recognition accuracy they have paida high price (increase in parameters and computationalcost) We further compare the experimental results of theIVGG13-1FC network with other deep learning methodsproposed by Wang et al [17] Pei et al [18] and Chenet al [19] as shown in Table 7 +ese literature studies usethe same SAR image dataset with this paper Wang et al[17] proposed a method for SAR images target recog-nition by combining two-dimensional principal com-ponent analysis (2DPCA) and L2 regularizationconstraint stochastic configuration network (SCN) +eyapplied the 2DPCA method to extract the features of SARimages By combining 2DPCA and SCN (randomlearning model with a single hidden layer) the 2DPCA-SCN algorithm achieved good performance Due to thelimited original SAR images it is difficult to effectivelytrain the neural networks To solve this problem Pei et al[18] proposed a multiview deep neural network+is deepneural network includes a parallel network topology withmultiple inputs which can learn the features of SARimages with different views layer by layer Chen et al [19]used all convolutional neural networks (A-CNNs) [27] tothe target recognition of SAR images Under the standardoperating condition the recognition accuracy on theSAR-SOC image dataset is remarkably high but therecognition accuracy has declined under extended op-erating condition

Although some methods such as A-CNN can achieveaccuracy of 9941 on the SAR-SOC it is difficult toachieve satisfactory results on SAR-EOC-1 data whichhave a greater difference in pitch angles +e 2DPCA-SCN method achieves 9849 accuracy on SAR-EOC-1but only 9580 on SAR-SOC Other methods on theSAR-EOC-1 also achieve lower recognition accuraciesthan our methods It can be found from Table 6 thatIVGG networks achieve exceedingly high accuracies onboth SAR-SOC and SAR-EOC-1 datasets In particularon the SAR-EOC-1 dataset IVGG13 can achieve higheraccuracy and more stable performance which shows thatour network has stronger generalization ability and betterrobustness

IVGG13-1FC is also compared with traditional rec-ognition methods such as KNN SVM and SRC [6 23]and the results are shown in Table 8 +e method pro-posed in reference [6] is a new classification approach ofclustering multitask learning theory (I-CMTL) and SRCis a recognition method based on sparse representation-based classifier (SRC) proposed in 2016 [23] From Ta-ble 8 we can see that our network is better than those ofall the traditional recognition methods

Table 8 shows that some traditional approaches are notso effective such as KNN and SVM methods Althoughmany complex classifiers have been designed they cannotfully utilize the potential correlation between multiple radarcategories On the other hand large-scale and complete SARdatasets are difficult to collect so the samples obtained areusually limited or unbalanced

+e classification algorithm approaches under themultitask framework have higher recognition accuraciessuch as CMTL MTRL and I-MTRL +e multitask re-lational learning (MTRL) method proposed in [6] canautonomously learn the correlation between positive andnegative tasks and it can be easily extended to thenonlinear field +e MTRL is further improved by addinga projection regularization term to the objective function[7] which can independently learn multitask relation-ships and cluster information of different tasks and canalso be easily extended to the nonlinear field Howeverthe Trace-norm Regularized multitask learning (TRACE)which is also under the multitask framework has thelowest recognition accuracy because the TRACE methodlearns the linear prediction function and cannot accu-rately describe the nonlinear structure of SAR imagewhich also proves the importance of extending themultitask learning method to the nonlinear field

+e IVGG networks proposed in this paper canadaptively learn the nonlinear structure of SAR imagesand reduce the difficulty in redesigning the classifierwhen the SAR image conditions change In contrast theartificially designed feature extraction approach iscomplex and sometimes it can only be effective forcertain fixed problems Its generalization ability is not soideal +erefore our networks enhance the feature ex-traction capability of sparse data

Table 6 Accuracy rates () on the MSTAR SAR dataset

MethodSAR-SOC SAR-EOC-1

Tanh ReLU Tanh ReLUGoogLeNet 9887 9865 9062 9019ResNet18 9720 9790 7845 8225DenseNet121 (k 32) 9866 9893 9641 9866VGG11 9931 9932 9861 9760VGG13 9922 9948 9822 9754VGG16 9914 9950 9910 9675VGG19 9926 9921 9910 9791IVGG11-3FC 9921 9898 9797 9805IVGG11-1FC 9923 9913 9702 9773IVGG13-3FC 9904 9931 9922 9804IVGG13-1FC 9934 9914 9922 9824IVGG16-3FC 9951 9934 9884 9870IVGG16-1FC 9942 9919 9762 9768IVGG19-3FC 9942 9923 9927 9771IVGG19-1FC 9923 9937 9715 9847


44 Recognition Result of theHRRPDataset +e recognitionaccuracy rates on the HRRP dataset are shown in Table 9

On the HRRP-1 dataset the optimal recognition accu-racies of GoogLeNet ResNet18 and DenseNet121 are987132 985234 and 987299 respectively and theperformance of the activation function Tanh is slightly betterthan that of ReLU +e best recognition results (accu-racygt 9905) are all obtained by the activation functionTanh +e networks with recognition rate higher than9905 are VGG13 (Tanh) IVGG16-3FC (Tanh) andIVGG19-3FC (Tanh) Among them the recognition rate ofIVGG16-3FC (Tanh) is the highest reaching 9924

In the identification of the HRRP-1 dataset the networkswhich are deeper have better recognition results IVGG16and IVGG19 can achieve better recognition effects

+e network with the best recognition accuracy on theHRRP-2 dataset is IVGG19-3FC (ReLU) +e VGGNet andIVGG-3FC have higher recognition accuracies +e recog-nition results of IVGG networks and VGGNets have noobvious difference among which IVGG19-3FC (ReLU)achieves the best recognition accuracy of 9898

On the HRRP-1 dataset our method is also comparedwith other methods such as SVM Maximum CorrelationCriterion-Template Matching Method (MCC-TMM) [28]Bayesian Compressive Sensing (BCS) [29] Joint SparseRepresentation (JSR) [30] and a CNN method with SVM asits classifier [20] as shown in Table 10

45 Comprehensive Analysis of Results In conclusion wefind that DenseNet121 also has high performance in the SARdataset (still slightly inferior to our method) but its rec-ognition performance for HRRP is obviously reduced In

HRRP recognition ResNet18 has a high performance (stillslightly inferior to our method) but the performance of SARimage recognition is exceptionally low (only 80) Differentfrom the above two methods our method has high recog-nition performance for SAR andHRRP signals whichmeansthat the method in this paper is efficient and stable VGGnetwork achieves good performance for radar target rec-ognition but IVGG reduces the parameters significantly andimproves the computation and recognition efficiency

+e performances of IVGG networks are better thanthose of VGGNets on the HRRP-1 dataset and SAR-EOC-1dataset and better than those of other neural networks andtraditional algorithms on all the experimental datasets

In fact the SAR image dataset used in this paper is apublic dataset published by MSTAR and the HRRPdataset also has been published in other papers +e radar issensitive to the pitch angles and the radar echo data of thesame target at different pitch angles are quite different +isis also the difficulty of radar target recognition On the SAR-EOC dataset the difference of pitch angles between the testset and the training set is greater than that on SAR-SOC andthe recognition accuracy on the SAR-EOC test set is slightlylower than that on SAR-SOC

In addition we also found a problem in the experimentWhen the network comes very deep the recognition algo-rithmmay be invalid For example when we use ResNet50 itwill cause themethod loss efficacy+e reason is that the dataamount of each sample is small (especially HRRP is one-dimensional data) and the downsampling layers in theResNet50 are too many for HRRP +is problem may alsooccur in SAR images But overall SAR images will be slightlybetter Solving this problem has two points one feasiblemethod is to reduce the downsampling layers but it willundoubtedly weaken the robustness of the network whichmay lead to insufficient results and waste in computing costsAnother effective solution is to design shallow convolutionalneural networks for radar target recognition such as theIVGG networks proposed in this paper

For target recognition in radar signals the IVGG net-works and VGGNets perform better than several convolu-tional neural networks recently proposed +e main reasonsare as follows

+e noise of the optical image is usually additive noisewhile the noise of the SAR image is mostly speckled mul-tiplicative noise HRRP data are a one-dimensional arraywhich is the vector sum of projection of the target scatteringpoint echoes in the radar ray direction Neither of them hasobvious edge features and texture information like thetraditional optical image SAR image is sensitive to theazimuth of the target when it is imagedWhen the azimuth isdifferent even for the same target there are still excessivelybig differences in SAR images

+e data amount of HRRP and SAR images is less thanthat of traditional optical images In this paper only 256 dataper HRRP target and 128times12816384 data per SAR imageare sent into the networks However a slightly larger opticalimage can often reach 256 times 256 65536 pixels For thisreason the CNN models for radar target recognition cannotbe too deep Otherwise they may fall into overfitting So

Table 7 Accuracy rates () on theMSTAR SAR dataset of differentCNNs

Method SAR-SOC SAR-EOC-12DPCA-SCN [17] 9580 98492-view DCNNs [18] 9781 93293-view DCNNs [18] 9817 94344-view DCNNs [18] 9852 9461A-CNN [19] 9941 9713IVGG13-1FC 9934 9922

Table 8 Accuracy rates () of different methods on the SARdataset

Method SAR-SOC SAR-EOC-1KNN [1] 9271 9142SVM [1] 9017 8673SRC [23] 8976 mdashTRACE [2] 7504 6742RMTL [3] 9209 9203CMTL [4] 9391 9472MTRL [5] 9584 9546I-CMTL [6] 9734 9824IVGG13-1FC 9934 9922


compared with ResNet and DenseNet IVGG networks andVGGNets with fewer network layers have better recognitionability

In the experiment the activation function Tanh hasexcellent performance on the SAR-EOC-1 and HRRPdatasets +e radar data itself have sparsity which is en-hanced by the activation function ReLU while too sparsedata will weaken the ability of the convolution layer toextract target features Activation function Tanh has betternonlinearity and works better when the feature difference isobvious

5 Conclusion

In this paper we propose the IVGG networks and usethem for target recognition on HRRP data and SARimages +e first improvement in this paper is to proposethe IVGG networks +en we simplify the fully connectedlayers which can significantly reduce parameters Ex-periments show that our methods have the best recog-nition effect At the same time with the improvement ofthe networks there are fewer parameters in the networkswhich can improve the processing efficiency of targetrecognition and make the method more suitable for thereal-time requirements

In addition we also find that for radar target recognitionTanhrsquos performance is generally better than that of ReLUwhich is different from image recognition

Data Availability

All datasets in this article are public datasets and can befound on public websites

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is research was funded by the National Defense Pre-Research Foundation of China under Grant9140A01060314KG01018 National Natural Science Foun-dation of China under Grant 61471370 Equipment Ex-ploration Research Project of China under Grant 71314092Scientific Research Fund of Hunan Provincial EducationDepartment under Grant 17C0043 and Hunan ProvincialNatural Science Fund under Grant 2019JJ80105

References

[1] Q Zhao and J C Principe ldquoSupport vector machines for SARautomatic target recognitionrdquo IEEE Transactions on Aero-space and Electronic Systems vol 37 no 2 pp 643ndash654 2001

[2] G Obozinski B Taskar and M I Jordan ldquoJoint covariateselection and joint subspace selection for multiple classifi-cation problemsrdquo Statistics and Computing vol 20 no 2pp 231ndash252 2010

[3] T Evgeniou and M Pontil ldquoRegularized multi-task learningknowledge discovery and data miningrdquo in Proceedings of the2004 ACM SIGKDD International Conference on KnowledgeDiscovery and Data Mining pp 109ndash117 Seattle WC USA2004

[4] J Zhou J Chen J Ye et al ldquoClustered multi-task learning viaalternating structure optimizationrdquo Neural InformationProcessing Systems vol 2011 pp 702ndash710 2011

Table 9 Accuracy rates () on the HRRP dataset

MethodHRRP-1 HRRP-2

Tanh ReLU Tanh ReLUGoogLeNet 9871 9795 9848 9785ResNet18 9852 9802 9848 9820DenseNet121 9873 9794 9815 9765VGG11 9832 9818 9856 9751VGG13 9905 9889 9876 9879VGG16 9875 9855 9894 9888VGG19 9890 9840 9866 9876IVGG11-3FC 9879 9776 9835 9819IVGG11-1FC 9852 9828 9795 9842IVGG13-3FC 9875 9886 9865 9880IVGG13-1FC 9846 9843 9833 9854IVGG16-3FC 9924 9899 9890 9867IVGG16-1FC 9854 9879 9850 9863IVGG19-3FC 9906 9905 9884 9898IVGG19-1FC 9835 9884 9802 9811

Table 10 Accuracy rates () of different methods on the HRRP-1dataset

Method Accuracy rate ()SVCA+ SVM [28] 9424MCC-TMM [28] 9281BCS [29] 9276JSR [30] 9149CNN+SVM [20] 9645IVGG16-3FC 9924


[5] Y Zhang and D-Y Yeung ldquoA regularization approach tolearning task relationships in multitask learningrdquo ACMTransactions on Knowledge Discovery from Data vol 8 no 3pp 1ndash31 2014

[6] L Cong B Weimin X Luping et al ldquoClustered multi-tasklearning for automatic radar target recognitionrdquo Sensorsvol 17 no 10 p 2218 2017

[7] Z He J Lu and G Kuang ldquoA fast SAR target recognitionapproach using PCA featuresrdquo in Proceedings of the FourthInternational Conference on Image and Graphics (ICIG 2007)IEEE Chengdu China pp 580ndash585 August 2007

[8] D Meng and L Sun ldquoSome new trends of deep learningresearchrdquo Chinese Journal of Electronics vol 28 no 6pp 1087ndash1090 2019

[9] W Wang C Tang X Wang et al ldquoImage object recognitionvia deep feature-based adaptive joint sparse representationrdquoComputational Intelligence and Neuroscience vol 2019 Ar-ticle ID 8258275 9 pages 2019

[10] K Simonyan and A Zisserman ldquoVery deep convolutionalnetworks for large-scale image recognitionrdquo 2014 httpsarxivorgabs14091556

[11] C Szegedy W Liu Y Jia et al ldquoGoing deeper with con-volutionsrdquo in Proceedings of the IEEE Conference ComputerVision and Pattern Recognition pp 1ndash9 Boston MA USA2015

[12] K He X Zhang S Ren et al ldquoDeep residual learning forimage recognitionrdquo in Proceedings of the IEEE Conference onComputer Vision amp Pattern Recognition pp 770ndash778 LasVegas NV USA 2016

[13] G Huang Z Liu V D M Laurens et al ldquoDensely connectedconvolutional networksrdquo in Proceedings of the IEEE Confer-ence Computer Vision and Pattern Recognition pp 2261ndash2269 Honolulu HI USA 2017

[14] W Wang Y Li T Zou et al ldquoA novel image classificationapproach via dense-MobileNet modelsrdquo Mobile InformationSystems vol 2020 Article ID 7602384 18 pages 2020

[15] W Wang Y Yang X Wang et al ldquo+e development ofconvolution neural network and its application in imageclassification a surveyrdquo Optical Engineering vol 58 no 4Article ID 040901 2019

[16] D Ciresan U Meier J Masci et al ldquoFlexible high perfor-mance convolutional neural networks for image classifica-tionrdquo in Proceedings of the International Joint Conference onArtificial Intelligence vol 30 pp 1237ndash1242 Barcelona Spain2011

[17] Y Wang Y Zhang L Yang et al ldquoTarget recognition methodbased on 2DPCA-SCN regularization for SAR imagesrdquoJournal of Signal Processing vol 35 no 5 pp 802ndash808 2019in Chinese

[18] J Pei Y Huang W Huo Y Zhang J Yang and T-S YeoldquoSAR automatic target recognition based on multiview deeplearning frameworkrdquo IEEE Transactions on Geoscience andRemote Sensing vol 56 no 4 pp 2196ndash2210 2018

[19] Y Cheng L Yu and X Xie ldquoSAR image target classificationbased on all congvolutional neural networkrdquo Radar Scienceand Technology vol 16 no 3 pp 242ndash248 2018 in Chinese

[20] S He R Zhang J Ou et al ldquoHigh resolution radar targetrecognition based on convolution neural networkrdquo Journal ofHunan University (Natural Sciences) vol 46 no 8 pp 141ndash148 2019 in Chinese

[21] J C Mossing and T D Ross ldquoAn evaluation of SAR ATRalgorithm performance sensitivity to MSTAR extended op-erating conditionsrdquo in Proceedings of SPIE-e International

Society for Optical Engineering pp 554ndash565 Moscow Russia1998

[22] S Liu R Zhan Q Zhai et al ldquoMulti-view polarization HRRPtarget recognition based on joint sparsityrdquo Journal of Elec-tronics and Information Technology vol 38 no 7 pp 1724ndash1730 2016

[23] H Song K Ji Y Zhang X Xing and H Zou ldquoSparserepresentation-based SAR image target classification on the10-class MSTAR data setrdquo Applied Sciences vol 6 no 1 p 262016

[24] L Du H Liu Z Bao et al ldquoRadar automatic target recog-nition based on complex high range resolution profile featureextractionrdquo Science in China Series F-Information Sciencesvol 39 no 7 pp 731ndash741 2009 in Chinese

[25] W Wang Y Jiang Y Luo et al ldquoAn advanced deep residualdense network (DRDN) approach for image super-resolu-tionrdquo International Journal of Computational IntelligenceSystems vol 12 no 2 pp 1592ndash1601 2019

[26] V Nair and G E Hinton ldquoRectified linear units improverestricted Boltzmann machinesrdquo in Proceedings of the In-ternational Conference on Machine Learning pp 807ndash814Haifa Israel 2010

[27] J T Springenberg A Dosovitskiy T Brox et al ldquoStriving forsimplicity the all convolutional netrdquo 2014 httpsarxivorgabs14126806

[28] A Zyweck and R E Bogner ldquoRadar target classification ofcommercial aircraftrdquo IEEE Transactions on Aerospace andElectronic Systems vol 32 no 2 pp 598ndash606 1996

[29] S Ji Y Xue L Carin et al ldquoBayesian compressive sensingrdquoIEEE Transactions on Signal Processing vol 56 no 6pp 2346ndash2356 2008

[30] S Shekhar V M Patel N M Nasrabadi and R ChellappaldquoJoint sparse representation for robust multimodal biometricsrecognitionrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 36 no 1 pp 113ndash126 2014


localization semantic segmentation target recognition andso on [9] Visual geometry group networks (VGGNets) [10]proposed by Simonyan and Zisserman have significantlyimproved image recognition accuracy by deepening thenetwork depth to 19 layers In the same year GoogLeNet[11] proposed by Christian Szegedy used the Inceptionmodule to have several parallel convolution routes forextracting input features which widened the networkstructure horizontally and deepened the network depth to acertain extent while the network parameters are reducedStudies have shown that deeper networks have better per-formance but deepening the network is faced with theproblem of gradient disappearance and the complex net-works also have the risk of overfitting Residual networks(ResNets) [12] and dense convolutional network (DenseNet)[13 14] solve the above problems by using skip connectionsand significantly increase the depth of the network Recentlyproposed highway networks ResNets and DenseNet havedeepened the network structure to more than 100 layers anddemonstrated outstanding performance in the field of imagerecognition

Different from image data radar data are sparse andhave a little amount +erefore the network should be ableto extract multidimensional features and the depth couldnot be too deep So we considered using the Inceptionmodule and VGG network for training VGG networks havelimited depth and been proven to have excellent featureextraction capabilities +e Inception module has multipathconvolution which can extract radar multidimensionalinformation for learning and its internal large-scale con-volution kernels are also more effective to extract the in-formation with sparse characteristics +erefore weproposed a method to fuse the Inception module with theVGG network

+is paper focuses on target recognition based on 1DHRRP and SAR images and proposes the IVGG convolu-tional neural network structure which is most suitable forhigh-resolution radar target recognition +e parameters ofIVGG can also be greatly reduced

2 Target Recognition Model IVGG Networks

21 VGGNets VGGNets [10] adopted the convolution fil-ters with a small local receptive field and proposed 6 differentnetwork configurations In VGGNets the convolution filtersare set to 3times 3 and the max-pooling is 2times 2 with stride 2

+e contribution of the VGGNet is the application of the3times 3 small convolution filters By stacking small convolutionfilters the depth of the network is increased and thenonlinearity of the convolutional layers is strengthened too[15] +erefore the nonlinear function can be better fitted(but the overfitting phenomenon needs to be prevented) andthe parameters of the network are reduced

Before the VGG network was proposed An et al alsoused small convolution filters but the network was not asdeep as VGGNet [16] +e VGGNet has better performancethan other convolutional networks in extracting targetfeatures

In the structure of VGGNet the convolutional layers andpooling layers alternately appear After two to four con-volutional layers a max-pooling layer is followed In order tokeep the computational complexity of the constituentstructures at each feature layer roughly consistent thenumber of convolution kernels at the next layer is doubledwhen the size of the feature map is reduced by half throughthe max-pooling layer VGGNet ends with three fullyconnected layers which are also the classifier for the system

22 e Improved Model IVGG Network Because SARimages and HRRP data are sparse it is difficult to fullyrepresent all the feature information of the targets by usingall 3times 3 convolution filters GoogLeNet proposed byChristian Szegedy [11] uses the Inception modules withlarger convolution filters which can extract radar multidi-mensional information for learning As shown in Figure 1there are several parallel convolutional lines in the Inceptionmodule and the large convolution filters in parallel linesincrease the width and the depth of the network structureSo the Inception module is used to modify the VGGmodule+e new network is specially designed for radar dataanalysis and has a high recognition rate of radar targetmodels +e principle of improvement will be introduced inthe next section

In this paper the ldquoConvrdquo module includes convolutionbatch standardization and activation functions as shown inFigure 2

Based on the above structures we propose 4 new IVGGnetworks In this structure a certain number of Inceptionmodules are used to replace ldquoConv3rdquo module in the originalVGGNets Note that we add a very deep point convolutionallayer after the Inception module and it is important Manytraditional algorithms show poor performance for radartarget recognition is because they cannot effectively fit thenonlinear structure in the radar signal [6] Drawing on thispoint of view we have strengthened the nonlinear capa-bilities of IVGG by adding a point convolutional layerImmediately following the Inception module the layercontains activation function which increases the nonline-arity of the network Further we set the input number ofchannels is same with output In other words the pointconvolutional layer does not compress the output featuremaps It also strengthens the nonlinearity of the networkTable 1 shows the specific configuration of the IVGG net-works where the Inception module and Conv1 modulewhich are used to replace Conv3 modules in the originalnetwork are identified in italics

+e fully connected layers of VGGNets are shown inTable 2 Since there have 3 layers we use ldquo3FCrdquo to refer to thestructure in Table 2

+e classifier of the VGG networks is fully connectedlayers containing most of the parameters of the wholenetwork In order to reduce the parameters we improved theFC layers reducing the 3-layer FC to a single-layer ldquoFC-410rdquo which is represented by ldquo1FCrdquo

In the experiment the network we proposed relates tothe above two classifiers which can be represented by










wTX wTx1wTx2 wTxN1113872 1113873 1113944

k1timesk2

i1wixi1 1113944

k1timesk2

i1wixi2 1113944

k1timesk2

i1wixiN

⎛⎝ ⎞⎠

wTX0 n (1 2 N) | 1113944

k1timesk2


wTX1 1113944N

n11113944

k1timesk2

i1wixin

1113868111386811138681113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868111386811138681113868

(1)


limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ limP1⟶1


1113872 1113873

limP1⟶1


1113872 1113873



1 minus P251

(2)

Base

Conv1

Conv5

Conv1

Conv3

MaxPool(3)

Conv1

Depth concat

Conv1


Convolution

Batchnormalization

ReLUTanh




13 weightlayers

16 weightlayers

19 weightlayers

Input (HRRP OR SAR)


MaxPool











Input

MaxPool

MaxPoolBase

Conv1ndash16

Conv5ndash32

Conv1ndash96

Conv3ndash128

MaxPool(3)

Conv1ndash32

Conv1ndash64

Depth concat

ReplaceDelete

MaxPool Base

Conv1ndash24

Conv5ndash64

Conv1ndash112

Conv3ndash224

MaxPool(3)

Conv1ndash64

Conv1ndash160

Depth concat

MaxPool


ReplaceDelete

Inception

Deep point conv

Inception

Deep point conv

times2

Conv3ndash64

Conv3ndash128

Conv3ndash256

Conv3ndash256

Conv1ndash256

Conv3ndash512

Conv1ndash512

Conv3ndash512

Conv3ndash512

Conv3ndash512




limP1⟶1

P 1113944

3times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ 1 minus P91 (3)


there4 limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ gt limP1⟶ 1

P 11139443times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭

(4)


a0 N 1 minus P911113872 1113873

b0 N 1 minus P2511113872 1113873

a0 lt b0

(5)


a1 wTX1 1113944N

n11113944

3times3

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

b1 wTX1 1113944

N

n11113944

5times5

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

(6)






















11 13 16 19VGG 128 128 134 139

IVGG 125 125 1306 136

128 128

134

139

125 125

1306

136

115

120

125

130

135

140

145Pa

ram

eter

s (in

mill

ions

)





01000200030004000500060007000

FLO

Ps (i

n m

illio

ns)

IVGG-1FCIVGG-3FCVGG











(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)




































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2









































wTX wTx1wTx2 wTxN1113872 1113873 1113944

k1timesk2

i1wixi1 1113944

k1timesk2

i1wixi2 1113944

k1timesk2

i1wixiN

⎛⎝ ⎞⎠

wTX0 n (1 2 N) | 1113944

k1timesk2


wTX1 1113944N

n11113944

k1timesk2

i1wixin

1113868111386811138681113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868111386811138681113868

(1)


limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ limP1⟶1


1113872 1113873

limP1⟶1


1113872 1113873



1 minus P251

(2)

Base

Conv1

Conv5

Conv1

Conv3

MaxPool(3)

Conv1

Depth concat

Conv1


Convolution

Batchnormalization

ReLUTanh




13 weightlayers

16 weightlayers

19 weightlayers

Input (HRRP OR SAR)


MaxPool











Input

MaxPool

MaxPoolBase

Conv1ndash16

Conv5ndash32

Conv1ndash96

Conv3ndash128

MaxPool(3)

Conv1ndash32

Conv1ndash64

Depth concat

ReplaceDelete

MaxPool Base

Conv1ndash24

Conv5ndash64

Conv1ndash112

Conv3ndash224

MaxPool(3)

Conv1ndash64

Conv1ndash160

Depth concat

MaxPool


ReplaceDelete

Inception

Deep point conv

Inception

Deep point conv

times2

Conv3ndash64

Conv3ndash128

Conv3ndash256

Conv3ndash256

Conv1ndash256

Conv3ndash512

Conv1ndash512

Conv3ndash512

Conv3ndash512

Conv3ndash512




limP1⟶1

P 1113944

3times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ 1 minus P91 (3)


there4 limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ gt limP1⟶ 1

P 11139443times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭

(4)


a0 N 1 minus P911113872 1113873

b0 N 1 minus P2511113872 1113873

a0 lt b0

(5)


a1 wTX1 1113944N

n11113944

3times3

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

b1 wTX1 1113944

N

n11113944

5times5

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

(6)






















11 13 16 19VGG 128 128 134 139

IVGG 125 125 1306 136

128 128

134

139

125 125

1306

136

115

120

125

130

135

140

145Pa

ram

eter

s (in

mill

ions

)





01000200030004000500060007000

FLO

Ps (i

n m

illio

ns)

IVGG-1FCIVGG-3FCVGG











(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)




































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2

































Input

MaxPool

MaxPoolBase

Conv1ndash16

Conv5ndash32

Conv1ndash96

Conv3ndash128

MaxPool(3)

Conv1ndash32

Conv1ndash64

Depth concat

ReplaceDelete

MaxPool Base

Conv1ndash24

Conv5ndash64

Conv1ndash112

Conv3ndash224

MaxPool(3)

Conv1ndash64

Conv1ndash160

Depth concat

MaxPool


ReplaceDelete

Inception

Deep point conv

Inception

Deep point conv

times2

Conv3ndash64

Conv3ndash128

Conv3ndash256

Conv3ndash256

Conv1ndash256

Conv3ndash512

Conv1ndash512

Conv3ndash512

Conv3ndash512

Conv3ndash512




limP1⟶1

P 1113944

3times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ 1 minus P91 (3)


there4 limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ gt limP1⟶ 1

P 11139443times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭

(4)


a0 N 1 minus P911113872 1113873

b0 N 1 minus P2511113872 1113873

a0 lt b0

(5)


a1 wTX1 1113944N

n11113944

3times3

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

b1 wTX1 1113944

N

n11113944

5times5

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

(6)






















11 13 16 19VGG 128 128 134 139

IVGG 125 125 1306 136

128 128

134

139

125 125

1306

136

115

120

125

130

135

140

145Pa

ram

eter

s (in

mill

ions

)





01000200030004000500060007000

FLO

Ps (i

n m

illio

ns)

IVGG-1FCIVGG-3FCVGG











(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)




































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2


































limP1⟶1

P 1113944

3times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ 1 minus P91 (3)


there4 limP1⟶1

P 11139445times5

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭ gt limP1⟶ 1

P 11139443times3

i1wixin ne 0

⎧⎨

⎩

⎫⎬

⎭

(4)


a0 N 1 minus P911113872 1113873

b0 N 1 minus P2511113872 1113873

a0 lt b0

(5)


a1 wTX1 1113944N

n11113944

3times3

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

b1 wTX1 1113944

N

n11113944

5times5

i1wixin

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

(6)






















11 13 16 19VGG 128 128 134 139

IVGG 125 125 1306 136

128 128

134

139

125 125

1306

136

115

120

125

130

135

140

145Pa

ram

eter

s (in

mill

ions

)





01000200030004000500060007000

FLO

Ps (i

n m

illio

ns)

IVGG-1FCIVGG-3FCVGG











(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)




































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2










































11 13 16 19VGG 128 128 134 139

IVGG 125 125 1306 136

128 128

134

139

125 125

1306

136

115

120

125

130

135

140

145Pa

ram

eter

s (in

mill

ions

)





01000200030004000500060007000

FLO

Ps (i

n m

illio

ns)

IVGG-1FCIVGG-3FCVGG











(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)




































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2









































(a) (b) (c) (d) (e)

(f ) (g) (h) (i) (j)




































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2
































































5 Conclusion



Data Availability




Acknowledgments


References






MethodHRRP-1 HRRP-2

































High-ResolutionRadarTargetRecognitionviaInception-Based ... · Conv1–16 Conv5–32 Conv1–96...

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