remote sensing

Article Exploiting Multi-View SAR Images for Robust Target Recognition

Baiyuan Ding * and Gongjian Wen Science and Technology on Automatic Target Recognition Laboratory, National University of Defense Technology, Changsha 410073, China; [email protected] * Correspondence: [email protected]; Tel.: +86-177-5562-0119

Academic Editor: Qi Wang Received: 19 September 2017; Accepted: 7 November 2017; Published: 9 November 2017

Abstract: The exploitation of multi-view synthetic aperture radar (SAR) images can effectively improve the performance of target recognition. However, due to the various extended operating conditions (EOCs) in practical applications, some of the collected views may not be discriminative enough for target recognition. Therefore, each of the input views should be examined before being passed through to multi-view recognition. This paper proposes a novel structure for multi-view SAR target recognition. The multi-view images are first classified by sparse representation-based classification (SRC). Based on the output residuals, a reliability level is calculated to evaluate the effectiveness of a certain view for multi-view recognition. Meanwhile, the support samples for each view selected by SRC collaborate to construct an enhanced local dictionary. Then, the selected views are classified by joint sparse representation (JSR) based on the enhanced local dictionary for target recognition. The proposed method can eliminate invalid views for target recognition while enhancing the representation capability of JSR. Therefore, the individual discriminability of each valid view as well as the inner correlation among all of the selected views can be exploited for robust target recognition. Experiments are conducted on the moving and stationary target acquisition recognition (MSTAR) dataset to demonstrate the validity of the proposed method.

Keywords: synthetic aperture radar (SAR); multi-view recognition; sparse representation-based classification (SRC); enhanced local dictionary; joint sparse representation (JSR); MSTAR

1. Introduction Automatic target recognition (ATR) from synthetic aperture radar (SAR) images has important meanings for its pervasive applications in both the military and civil fields [1]. All these years, researchers have tried to find or design proper feature extraction methods and classification schemes for SAR ATR. Principal component analysis (PCA) and linear discriminant analysis (LDA) [2] are usually used for feature extraction from SAR images. Other features, such as geometrical descriptors [3], attributed scattering centers [4,5], and monogenic spectrums [6], are also applied to SAR target recognition. As for the decision engines, various classifiers, including support vector machines (SVM) [7], sparse representation-based classification (SRC) [8,9], and convolutional neural networks (CNN) [10] are employed for target recognition and have achieved delectable results. Despite great effort, SAR target recognition under extended operating conditions (EOCs) [1] is still a difficult problem. Most of the previous SAR ATR methods make use of single view SAR image. The single view image is compared with the training samples to find its nearest neighbor in the manifolds spanned by individual training classes. Due to the unique mechanism of SAR imaging, an SAR image is very sensitive to the view angle [11]. Hence, the usage of multi-view SAR images may help in the interpretation of SAR images. Actually, multi-view SAR exploitation has been successfully applied to SAR image registration [12]. As for SAR target recognition, it is predictable that the classification

Remote Sens. 2017, 9, 1150; doi:10.3390/rs9111150 www.mdpi.com/journal/remotesensing Remote Sens. 2017, 9, 1150 2 of 18 performance may vary with the view angle and the usage of multi-view images will probably improve the effectiveness and robustness of SAR ATR systems. As in the case of remote sensing data fusion [13], the benefits of using multi-view SAR images can be analyzed from two aspects. On the one hand, the images from different views can provide complementary descriptions for the target. On the other hand, the inner correlation among different views is also discriminative to target recognition. Therefore, the exploitation of multiple incoherent views of a target should provide a more robust classification performance than single view classification. Several ATR algorithms based on multi-view SAR images have been proposed, which can be generally divided into three categories. The first category uses parallel decision fusion for multi-view SAR images based on the assumption that the multiple views are independent. Brendel et al. [14] analyze the fundamental benefits of aspect diversity for SAR ATR based on the experimental results of a minimum-square-error (MSE) classifier. A Bayesian multi-view classifier [15] is proposed by Brown for target classification. The results demonstrate that use of multiple SAR images can significantly improve the ATR algorithm’s performance even with only two or three SAR views. Bhanu et al. [16] employ scatterer locations as the basis to describe the azimuthal variance with application to SAR target recognition. The experimental results demonstrated that the correlation of SAR images can be only maintained in a small azimuth interval. Model-based approaches [17] are developed by Ettinger and Snyder by fusing multiple images of a certain target at different view angles, namely decision-level and hypothesis-level fusion. Vespe et al. [18] propose a multi-perspective target classification method, which uses function neural networks to combine multiple views of a target collected at different locations. Huan et al. [19] propose a parallel decision fusion strategy for SAR target recognition using multi-aspect SAR images based on SVM. The second category uses a data fusion strategy. Methods of this category first fuse the multi-view images to generate a new input, which is assumed to contain the discriminability of individual views as well as the inner correlation of these views. Then, the fused data is employed for target recognition. Two data fusion methods for multi-view SAR images are proposed by Huan et al., i.e., the PCA method and the discrete wavelet transform (DWT) fusion method [19]. The third category uses joint decision fusion. Rather than classifying multi-view images respectively and then fusing the outputs, the joint decision strategy puts all the views in a unified decision framework by exploiting their inner correlation. Zhang et al. [20] apply joint sparse representation (JSR) to multi-view SAR ATR, which can exploit the inner correlations among different views. The superiority of multiple views over a single view is quantitatively demonstrated in their experiments. In comparison, the first category neglects the inner correlation among multi-view images. Although the data fusion methods consider both individuality and inner correlation, it is hard to evaluate the discriminability loss during the fusion process. The third category considers the inner correlation in the decision process, but the strategy may not work well when the multi-view images are not closely related. In the above literatures, multi-view recognition has been demonstrated to be much more effective than single view recognition. However, some practical restrictions on multi-view recognition are neglected. Due to the EOCs in real scenarios, some of the collected views may be severely contaminated. Then, it is unwise to use these views during multi-view recognition. In this paper, a novel structure for multi-view recognition is proposed. The multiple views of a target are first classified by SRC. Based on the reconstruction residuals, a principle is designed to judge whether a certain view is discriminative enough for multi-view recognition. Then, JSR is employed to classify the selected views. However, when the input views are not closely related, the joint representation over the global dictionary is not optimal due to an incorrect correlation constraint. As a remedy, in this paper, the selected atoms of each of the input views by SRC are combined to construct an enhanced local dictionary. The selected atoms and their neighboring ones (those sharing approaching azimuths) are used to construct the enhanced local dictionary, which inherits the representation capability of the global dictionary for the selected views. Meanwhile, it constrains the atoms for representation, thus avoiding the incorrect atom selections occurring in the global dictionary, especially when the multiple views are not closely related. By performing JSR on the enhanced local dictionary, both the correlated views and the unrelated views Remote Sens. 2017, 9, 1150 3 of 18 Remote Sens. 2017, 9, 1150 3 of 18 enhanced local dictionary, both the correlated views and the unrelated views can be represented properly. Finally, the target label will be decided according to the residuals of JSR based on the canminimum be represented residual properly.principle. Finally, the target label will be decided according to the residuals of JSR basedIn on the the following, minimum residualwe first principle.introduce the practical restrictions on multi-view recognition in SectionIn the2. Then, following, in Section we first 3, introducethe proposed the practicalstructure restrictionsfor multi-view on multi-viewrecognition recognition is presented. in SectionExtensive2. Then, experiments in Section are3, theconducted proposed on structure the moving for multi-view and stationary recognition target isacquisition presented. recognition Extensive experiments(MSTAR) dataset areconducted in Section 4, on and the finally, moving conclusions and stationary are drawn target in acquisition Section 5. recognition (MSTAR) dataset in Section4, and finally, conclusions are drawn in Section5. 2. Practical Restrictions on Multi-View Target Recognition 2. Practical Restrictions on Multi-View Target Recognition With the development of space-borne and air-borne SAR systems, the multi-view SAR images of a targetWith theare developmentbecoming accessible. of space-borne However, and due air-borne to the EOCs SAR systems,in real scenarios, the multi-view some views SAR imagesare not ofdiscriminative a target are becoming enough for accessible. target recognition. However, due Th toen, the it EOCs is preferable in real scenarios, to discard some these views views are not in discriminativemulti-view recognition. enough for The target following recognition. depicts Then, some it is preferabletypical practical to discard restrictions these views on in multi-view multi-view recognition. The following depicts some typical practical restrictions on multi-view recognition. 2.1. Target Variation 2.1. Target Variation The target itself may have some variations due to configuration diversity or wreckage. Figure1 The target itself may have some variations due to configuration diversity or wreckage. Figure 1 shows two serial numbers of the T72 tank, i.e., A04 and A05. A04 is equipped with fuel drums shows two serial numbers of the T72 tank, i.e., A04 and A05. A04 is equipped with fuel drums while while A05 has no fuel drums. When we want to classify A04 as a T72 with the training source A05 has no fuel drums. When we want to classify A04 as a T72 with the training source of A05 of A05 samples, it is possible that the views which present the characteristics of fuel drums cause samples, it is possible that the views which present the characteristics of fuel drums cause much much discordance with the A05 samples. In this case, these views should be discarded in multi-view discordance with the A05 samples. In this case, these views should be discarded in multi-view recognition. Generally speaking, for a target with local variations, the views which remarkably manifest recognition. Generally speaking, for a target with local variations, the views which remarkably the properties of the discordance may probably impair the multi-view recognition’s performance. manifest the properties of the discordance may probably impair the multi-view recognition’s Therefore, such views should be cautiously passed through to multi-view recognition. performance. Therefore, such views should be cautiously passed through to multi-view recognition.

(a) (b)

Figure 1. Two configurationsconfigurations of the T72 tank: (aa)) A04;A04; andand ((bb)) A05.A05.

2.2. Environment Variation The targettarget may may stand stand on differenton different backgrounds, backgrou suchnds, as meadowssuch as ormeadows cement roads.or cement Furthermore, roads. itFurthermore, may be occluded it may by be trees occluded or manmade by trees buildings or manmade as shown buildings in Figure as shown2. Figure in Figure2a,b shows 2. Figure two T722a,b tanksshows occluded two T72 tanks by trees occluded and a manmade by trees and wall, a manma respectively.de wall, Figure respectively.2b,c presents Figure two 2b,c views presents of a T72two tankviews occluded of a T72 by tank a manmade occluded wall.by a Asmanmade for target wall. recognition, As for target it is preferablerecognition, that it theis preferable view in Figure that the2b shouldview in be Figure used, as2b mostshould of thebe used, target’s as characteristics most of the target’s can be observed.characteristics For the can view be observed. angle in Figure For the2c, aview large angle proportion in Figure of 2c, the a targetlarge pr isoportion occluded. of Thus,the target the imageis occluded at this. Thus, view the can image provide at this very view limited can discriminabilityprovide very limited for target discriminability recognition. for target recognition.

(a) (b)(c)

Figure 2. Examples of environment variation: (a) Target occluded by trees; (b) Target occluded by a wall; and (c) Target occluded by a wall from another view. Remote Sens. 2017, 9, 1150 4 of 18

RemoteFigure Sens. 2017 2. ,Examples9, 1150 of environment variation: (a) Target occluded by trees; (b) Target occluded by 4a of 18 wall; and (c) Target occluded by a wall from another view.

2.3.2.3. SensorSensor VariationVariation Actually,Actually, thethe multi-viewmulti-view imagesimages ofof aa certaincertain targettarget maymaycome come from from different different sensors. sensors. FigureFigure3 3 showsshows three typical typical situations situations during during the the collection collection of multi-view of multi-view SAR images. SAR images. In Figure In 3a, Figure multiple3a, multipleimages are images captured are captured by the same by the airborne same airborne sensor at sensor consecutive at consecutive azimuths. azimuths. The collected The collected multiple multipleviews in Figure views 3b in are Figure from3b different are from airborne different sens airborneors at quite sensors different at quite view differentangles. Figure view 3c angles. shows Figurethe multiple3c shows views the acquired multiple by views both acquired the airborne by both and thesatellite-based airborne and platforms. satellite-based Consequently, platforms. the Consequently,images may have the quite images different may have view quite angles. different Furthermore, view angles. due to Furthermore,the sensor variety, due tothey the may sensor also variety,have different they may resolutions also have and different signal-to-noise resolutions rati andos (SNR). signal-to-noise As the training ratios (SNR). samples As are the probably training samplescollected are at several probably fixed collected resolutions at several and SNRs, fixed resolutionsthe multi-view and images SNRs, thewith multi-view different resolutions images with or differentSNRs will resolutions provide disproportionate or SNRs will provide discriminability disproportionate for target discriminability recognition. Then, for targetthe views recognition. with low Then,discriminability the views with should low not discriminability be used for multi-view should not recognition. be used for multi-view recognition.

(a) (b)(c)

Figure 3. Illustration of the collection of multi-view synthetic aperture radar (SAR) images: (a) Figure 3. Illustration of the collection of multi-view synthetic aperture radar (SAR) images: (aConsecutive) Consecutive views views by the by sensor; the sensor; (b) Views (b) Views with different with different azimuths azimuths from different from different sensors; sensors; and (c) andViews (c) Viewsfrom air-borne from air-borne and satellite-based and satellite-based sensors. sensors.

Actually,Actually, therethere areare manymany moremore EOCs EOCs in in practical practical applications. applications. Consequently,Consequently, asas wewe analyzeanalyze above,above, images images from from different different views views provide provide unequal uneq discriminabilityual discriminability to target to target recognition recognition under EOCs.under Therefore,EOCs. Therefore, for robust for target robust recognition, target recognition, the validity the of validity the input of views the input for multi-view views for recognitionmulti-view shouldrecognition be examined should be beforehand. examined beforehand.

3.3. ProposedProposed StructureStructure ofof Multi-ViewMulti-View SAR SAR Target Target Recognition Recognition

3.1.3.1. SparseSparse Representation-BasedRepresentation-Based ClassificationClassification (SRC) (SRC) WithWith thethe developmentdevelopment ofof compressivecompressive sensingsensing (CS)(CS) theory,theory, sparsesparse signalsignal processingprocessing overover aa redundantredundant dictionarydictionary hashas drawndrawn pervasivepervasive attention.attention. ByBy enforcingenforcing aa sparsitysparsity constraintconstraint onon thethe representationrepresentation coefficients, coefficients, the the decision decision is is made made by by evaluating evaluating which which class class of samples of samples can recovercan recover the testthe sampletest sample with with the minimum the minimum error. error. 1 2 C d×N DenoteDenote the dictionarythe dictionary constructed constructed by training samplesby training from C classes samples as A =from [A ,A , ···C , Aclasses] ∈ R as, d×N i i ´ dN´ whereAAAA=Î[,A12∈ ,,]RR CdN(i = 1,,2, ···where, C) isA i aÎ= class-dictionaryR i (1,2,,)iC formed is a by class-dictionary individual classes, formedd is theby C dimensionalityindividual classes, of the d atom,is the anddimensionalityN is the total of the number atom, of and all theN trainingis the total samples: numberN of= all∑ Nthei. C i=1 = i y Basedtraining on samples: the assumption NNå thati a. Based test sample on they fromassumption class lies that in a the test same sample subspace from with class the trainingi lies in samples from the same class,i=1 SRC assumes that y can be recovered from its sparse representation with respectthe same to globalsubspace dictionary with theA =training [A1, A2 ,sample··· , ACs ]fromas follows: the same class, SRC assumes that y can be recovered from its sparse representation with respect to global dictionary AAAA= [,12 ,,] C as

follows: ˆx = argminkxk0

2 s.t.xxˆk=yargmin− Axk ≤ ε (1) 2 0 where x is the sparse coefficient vector, and ε is the allowed error tolerance. The non-convex `0-norm objective in Equation (1) is an NP-hard problem. Typical approaches for solving the problem are either

Remote Sens. 2017, 9, 1150 5 of 18

approximating the original problem with `1-norm based convex relaxation [9] or resorting to greedy schemes, such as orthogonal matching pursuit (OMP) [8]. After solving the optimal representation ˆx, SRC decides the identity of the test sample by evaluating which class of samples could result in the minimum reconstruction error.

i 2 r(i) = ky − Aδ (ˆx)k2(i = 1, 2, ··· , C)

identity (y) = argmin(r(i)) (2) i where the operation δi(·) extracts the coefficients corresponding to class i and r(i)(i = 1, 2, ··· , C) denotes the reconstruction error of each class.

3.2. Joint Sparse Representation (JSR) for Classification Assume there are M views of the same target, then the M sparse representation problems can be jointly formulated as: M 2 {ˆxi}i=1 = argminkyi − Axik2 {xi}

s.t. kxik0 ≤ K∀1 ≤ i ≤ M. (3)

Denote X = [x1, x2, ··· , xM], Y = [y1, y2, ··· , yM], then Equation (3) can be rewritten as

ˆ 2 X = argminkY − AXkF

s.t. kXk0 ≤ K . (4)

In Equation (4), k · kF represents the Frobenius norm and kXk0 denotes the number of non-zero elements in X. However, the inner correlation among multiple views is not fully considered due to the fact that kXk0 is decomposable over each column (view). To overcome this defect, it is assumed that the multiple views of the same target share a similar sparse pattern over the same dictionary while the values of the coefficients corresponding to the same atom may be different for each input view. This can be achieved by solving the following optimization problem with `0\`2 mixed-norm regularization as ˆ 2 X = argminkY − AXkF X s.t. kXk ≤ K (5) `0\`2 where kXk is the mixed-norm of matrix X obtained by first applying the ` norm on each row of X `0\`2 2 and then applying the `0 norm on the resulting vector. To solve the problem in Equation (5), the simultaneous orthogonal matching pursuit (SOMP) [21,22] method can be used. After solving the coefficient matrix Xˆ , the target label is determined by the minimum reconstruction error, which is the same as SRC. JSR incorporates the inner correlation of multiple views in the joint decision framework. However, when the multiple views are not closely related due to a large azimuth difference, environmental variations, etc., the correlation constraint in JSR may result in incorrect atom selections. Then, the classification performance will degrade.

3.3. Structure for Multi-View Target Recognition Due to the EOCs in real scenarios, some of the collected multiple views may provide little discriminability for target recognition. In order to build a robust multi-view recognition framework, each of the input views is first examined by SRC. Based on the residuals of individual classes, a reliability level is calculated, which indicates the effectiveness of a certain view for multi-view Remote Sens. 2017, 9, 1150 6 of 18 recognition. The reliability level is evaluated by the ratio of the minimum residual r(k) and the second minimum residual as Equation (6).

r(k) S = (j 6= k). (6) min(r(j))

It is obvious that S ranges from 0 to 1, while a lower S indicates higher reliability. By presetting a threshold T on S, only the views with higher reliability than T will be passed through to multi-view recognition. A lower T means a stricter criterion for selecting a valid view. Then, the selected views are classified by JSR to exploit their possible inner correlation for target recognition. As indicated in the JSR model, when the multiple inputs are not closely related (for example they are acquired at quite different azimuths), the resulting coefficients by JSR may not be optimal. In order to overcome this situation, an enhanced local dictionary is built based on the selected atoms of the selected views by SRC. The selected atoms by each view are combined to form a local dictionary which only contains a few atoms. To further enhance the representation capability of the local dictionary, the samples in the original dictionary A, which are closely related to these atoms, are added to the local dictionary. The detailed process for constructing the enhanced local dictionary is described in Algorithm 1. In our ◦ practical application, Tθ is set to be 5 , assuming that SAR images keep highly correlated in such an azimuth interval. On the one hand, the enhanced local dictionary inherits the representation capability of the global dictionary for the selected views. On the other hand, it can avoid the incorrect atom selection of JSR over the global dictionary to make more robust decisions. The framework of the proposed method is shown in Figure4. The threshold judgment based on the reliability level can effectively eliminate those views with low discriminability. The enhanced local dictionary will promote the representation capability of JSR; thus, it can still work robustly when the multiple views are not closely related. Therefore, the proposed method can improve the performance of multi-view recognition, especially when the input views contain some corrupted samples due to EOCs. In the implementation of the proposed method, OMP and SOMP are employed in SRC and JSR, respectively, for their high efficiency.

Algorithm 1. Construction of enhanced local dictionary

1. Input: The selected atom of K views of SAR images: C = {C1, C2, ··· , CK}. K 2. Calculate the union of C to obtain a local dictionary D = ∪ Ck. k=1 3. for i = 1: length(D) if (Azi(Ai) − Azi(Di) < Tθ) DE = D ∪ Ai end end 4. Output: The enhanced local dictionary DE. Remote Sens. 2017, 9, 1150 7 of 18 Remote Sens. 2017, 9, 1150 7 of 18

Remote Sens. 2017, 9, 1150 7 of 18

Figure 4. The framework of the proposed method. SRC: sparse representation-based classification; FigureFigure 4. The 4. frameworkThe framework of the of the proposed proposed method. method. SRC: SRC: sparse sparse representation-based representation-based classification;classification; JSR: JSR: joint sparse representation. joint sparseJSR: joint representation. sparse representation.

4. Experiment4. Experiment

4.1. MSTAR4.1. MSTAR DatasetDataset Dataset To testtestTo thethetest proposedproposedthe proposed method,method, method, thethe the MSTAR MSTAR dataset datasetdataset isis employed, employed,employed, which whichwhich is the isis thethe benchmark benchmark for SAR for SAR ATR.ATR. TheThe SARTheSAR SAR imagesimages images areare are collectedcollected collected byby by X-bandX-band X-band sensors sensors withwith a a a0.3 0.30.3 m mm × ×0.3× 0.30.3 m mresolution.m resolution.resolution. The TheThedataset datasetdataset includesincludesincludes tenten classes tenclasses classes of of military ofmilitary military targets: targets: targets: BMP2, BMP2,BMP2, BTR70, BTR70, T72, T72, T62,T72, T62, BRDM2,T62, BRDM2, BRDM2, BTR60, BTR60, BTR60, ZSU23/4, ZSU23/4, ZSU23/4, D7, D7, ZIL131, D7, ZIL131, and 2S1. The corresponding optical images of these targets are shown in Figure 5. SAR andZIL131, 2S1. and The 2S1. corresponding The corresponding optical images optical of theseimages targets of these are showntargetsin are Figure shown5. SAR in Figure images 5. at SAR the images at the depression angles of 15° and 17° are listed in Table 1, which cover full aspect angles depressionimages at the angles depression of 15◦ and angles 17◦ areof 15° listed and in 17° Table are1 ,listed which in cover Table full 1, aspectwhich anglescover full from aspect 0–360 angles◦. from 0–360°. fromIn 0–360°. orderIn order to quantitativelyto quantitatively evaluate evaluate the the proposed proposed method, method, several several state-of-the-art state-of-the-art algorithms algorithms are are usedInused order asas the theto references,quantitativelyreferences, includingincluding evaluate single single the proposedview view methods methods method, and and severalmulti-view multi-view state-of-the-art methods. methods. The algorithms Thedetailed detailed are descriptionsused descriptionsas the ofreferences, these of these methods includingmethods are presented are single presented inview Table inmethods 2Table. SVM 2. and andSVM SRC multi-viewand are SRC employed are methods. employed for the classificationThe for detailedthe ofdescriptions singleclassification view of SAR theseof single images. methods view The SAR are MSRC, images. presented DSRC, The MS andin RC,Table joint DSRC, sparse2. SVMand representation-basedjoint and sparse SRC representation-based are employed classification for the (JSRC)classificationclassification methods of aresingle (JSRC) used viewmethods for multi-view SAR are images. used recognition. for The multi-view MSRC, For recognition. DSRC, a fair comparison, and For joint a fair sparse all comparison, of these representation-based methods all of these employ Gaussianclassificationmethods random (JSRC)employ projection methodsGaussian for randomare feature used projection extractionfor multi-view for with feature therecognition. dimensionextraction Forwith of 1024.a thefair dimension Incomparison, the rest of of 1024. thisall of section,In these wemethods firstthe performrest employ of this theGaussian section, proposed we random first method perform projection under the proposed standardfor feature method operating extraction under conditionsstandard with the operating dimension (SOC), conditions i.e., of a 10-class1024. In (SOC), i.e., a 10-class recognition problem. Afterwards, the performance is evaluated under several recognitionthe rest of this problem. section, Afterwards, we first perform the performance the proposed is method evaluated under under standard several operating extended conditions operating extended operating conditions (EOCs), namely, configuration variance, noise corruption, partial conditions(SOC), i.e., (EOCs),a 10-class namely, recognition configuration problem. variance, Afterwards, noise the corruption, performance partial is occlusion,evaluated andunder resolution several occlusion, and resolution variance. At last, we examine the proposed method under different variance.extendedthresholds Atoperating last, of wereliability examineconditions level. the (EOCs), proposed namely, method co undernfiguration different variance, thresholds noise of reliabilitycorruption, level. partial occlusion, and resolution variance. At last, we examine the proposed method under different thresholds of reliability level.

(1) BMP2 (2) BTR70 (3) T72 (4) T62 (5) BRDM2

(1) BMP2 (2) BTR70 (3) T72 (4) T62 (5) BRDM2

(6)BTR60 (7) ZSU23/4 (8) D7 (9) ZIL131 (10) 2S1

Figure 5. Optical images of the ten military targets. Figure 5. Optical images of the ten military targets. (6)BTR60 (7) ZSU23/4 (8) D7 (9) ZIL131 (10) 2S1

Figure 5. Optical images of the ten military targets.

Remote Sens. 2017, 9, 1150 8 of 18

Table 1. Training and test sets in the experiments.

Depr. BMP2 BTR70 T72 T62 BDRM2 BTR60 ZSU23/4 D7 ZIL131 2S1 233(Sn_9563) 232(Sn_132) 17◦ 232(Sn_9566)233 231(Sn_812) 299 298 256 299 299 299 299 233(Sn_c21) 228(Sn_s7) 195(Sn_9563) 196(Sn_132) 15◦ 196(Sn_9566)196 195(Sn_812) 273 274 195 274 274 274 274 196(Sn_c21) 191(Sn_s7)

Table 2. The reference methods used in this paper.

Abbre. Description Ref. SVM Kernel support vector machine [7] Single View SRC Sparse representation-based classification [8] PSRC Parallel decision fusion for multi-view images based on SRC [19] Multi-view DSRC SRC for fused data of multi-view images by PCA [19] JSRC Joint sparse representation for multi-view images [20]

4.2. Recognition under SOC

4.2.1. Preliminary Performance Verification We first test the proposed method under SOC. Images at a 17◦ depression angle are used for training and images at a 15◦ depression angle are tested. For BMP2 and T72 with three different serial numbers, only the standard ones (Sn_9563 for BMP2 and Sn_132 for T72) are used for training (see Table1). For each test sample, we choose M − 1 other samples at an azimuth interval of ∆θ and then the M samples are put together for multi-view recognition. The reliability level threshold is set at T = 0.96, M = 3, and ∆θ = 12◦, and the recognition results of the proposed method are displayed as the confusion matrix in Table3. All of the 10 targets can be recognized with a percentage of correct classification (PCC) over 97% and an overall PCC of 98.94%. The proposed method is compared with the reference methods in Table4. It is clear that all the multi-view methods achieve a disproportionate improvement over the single view methods. Among the multi-view methods, the proposed method has the highest PCC. DSRC has the lowest PCC, probably due to the discriminability loss during the data fusion. MSRC achieves a slightly higher PCC than JSRC at the sacrifice of computation efficiency. The results demonstrate the significant superiority of the multi-view methods over the single view algorithms and the high effectiveness of the proposed method under SOC. Table 3. Confusion matrix of the proposed method under standard operating conditions (SOC).

Class BMP2 BTR70 T72 T62 BDRM2 BTR60 ZSU23/4 D7 ZIL131 2S1 PCC (%) BMP2 574 1 6 0 0 0 1 0 4 0 97.95 BTR70 0 196 0 0 0 0 0 0 0 0 100 T72 4 1 572 0 0 0 4 0 0 0 98.45 T62 0 0 0 274 0 0 0 0 0 0 100 BDRM2 0 0 0 0 272 1 1 0 0 0 99.27 BTR60 0 1 0 2 0 192 0 0 0 0 98.97 ZSU23/4 0 0 0 0 2 0 271 1 0 0 98.91 D7 0 0 0 1 1 0 0 272 0 0 99.27 ZIL131 0 1 0 0 0 0 1 0 272 0 99.27 2S1 0 0 0 0 0 0 0 0 0 274 100 Average 98.94 PCC: percentage of correct classification. Remote Sens. 2017, 9, 1150 9 of 18

Table 4. Comparison with reference methods.

Method SVM SRC MSRC DSRC JSRC Proposed PCC (%) 94.22 93.66 98.07 95.12 97.71 98.94

4.2.2. Performance at Different View Numbers In this part, we evaluate the effects of view numbers on the proposed method. The azimuth interval is set as ∆θ = 1◦, and Table5 summarizes the performance of all of the multi-view recognition methods at different view numbers.

Table 5. PCCs of multi-view methods at different view numbers (%).

View Number 2 3 4 5 6 7 8 9 10 MSRC 95.69 96.72 97.10 97.60 98.03 98.41 98.72 98.97 99.03 DSRC 93.54 94.67 95.47 95.50 94.69 93.35 91.66 89.13 88.04 JSRC 95.78 96.69 97.00 97.41 97.75 97.88 98.06 98.09 98.63 Proposed 96.35 97.10 97.44 97.97 98.16 98.71 98.92 99.05 99.12

Except for DSRC, the other multi-view methods gain improvement with the increase of the view number and they share approaching PCCs, while the proposed method achieves the highest one. It is reasonable that more views could provide more information for target recognition, thus improving the performance. As for DSRC, the fused result of too many samples by PCA may hardly find a best match in the dictionary. This is probably the reason for its performance degradation when the view number is more than 5.

4.2.3. Robustness to Azimuthal Variation In previous works, the researchers assumed a fixed azimuth separation between the multi-view images. With the view number set as M = 3, the performance of the multi-view recognition algorithms at different fixed view steps are shown in Figure6. The proposed method achieves the best performance, and DSRC has the lowest PCC at each view step. By comparing MSRC and JSRC, JSRC performs better when the view step is less than 15. This is mainly because the views with a smaller azimuth interval share a higher inner correlation. When the view step continues to increase, the performance of JSRC becomes worse than that of MSRC due to the weak correlation between different views. For DSRC, the fused results of multiple views with a large azimuth interval may hardly resemble the training samples of the same class. Therefore, its performance may even be inferior to that of single view methods at large view steps. Actually, the collected views may probably have unstable azimuth separations. Therefore, a further experiment is carried out on the random selected views. For each test sample, we randomly selected two other samples from the same class. Then, the three samples are passed through to multi-view recognition. We repeated the test 10 times, and the average PCCs of the multi-view methods are presented in Table6. The proposed method outperforms the others. Also, JRSC has a lower PCC than MSRC due to the unstable inner correlation among the views with random azimuths. Remote Sens. 2017, 9, 1150 10 of 18 Remote Sens. 2017, 9, 1150 10 of 18

FigureFigure 6. 6. TheThe PCCs PCCs of of multi-view multi-view methods methods at at fixed fixed view view steps. steps.

TableTable 6. 6. PCCsPCCs of of multi-view multi-view methods methods under under unstable unstable azimuth azimuth separations. separations.

MethodMethod MSRCMSRC DSRC DSRCJSRC JSRC Proposed Proposed PCCPCC (%) (%) 97.85 97.85 94.56 94.56 97.25 97.25 98.37 98.37

4.3. Recognition under EOCs 4.3. Recognition under EOCs In the following, the proposed method is tested under several EOCs, i.e., configuration In the following, the proposed method is tested under several EOCs, i.e., configuration variance, variance, noise corruption, partial occlusion, and resolution variance. According to the experimental noise corruption, partial occlusion, and resolution variance. According to the experimental results results in Section 4.2, we set M = 3 and Δθ = 12 as a tradeoff between the view number and in Section 4.2, we set M = 3 and ∆θ = 12◦ as a tradeoff between the view number and recognition performance. recognition performance.

4.3.1.4.3.1. Configuration Configuration Variance Variance InIn real real scenarios, scenarios, a aspecial special target target class class may may include include several several variants. variants. Therefore, Therefore, it is it necessary is necessary to testto test the theATR ATR methods methods under under configuration configuration variance variance as the as training the training samples samples may may not cover not cover all the all possiblethe possible configurations. configurations. Table Table 7 describes7 describes the the training training and and test test sets sets for for the the experiment underunder configurationconfiguration variation. The trainingtraining setset is is composed composed of of four four targets, targets, BMP2, BMP2, BRDM2, BRDM2, BTR70, BTR70, and and T72, T72,and and the testthe settest consistsset consists of only of only BMP2 BMP2 and and T72. T72. For For BMP2 BMP2 and and T72, T72, the the configurations configurations available available for fortesting testing are notare containednot contained in the in training the training set. Table set.8 Tablepresents 8 presents the confusion the confusion matrix of matrix the proposed of the proposedmethod under method configuration under configuration variance. variance. Table9 compares Table 9 compar the proposedes the proposed method with method the referencewith the referencemethods. methods. It is clear It thatis clear the that multi-view the multi-view methods methods perform perform much much better better than thethan single the single view view ones. ones.With With the highest the highest PCC, PCC, the proposed the proposed method method is the is most the robustmost robust under under configuration configuration variance. variance.

TableTable 7. 7. DatasetDataset for for configuration configuration variance variance test. test. BMP2 BDRM2 BTR70 T72 BMP2 BDRM2 BTR70 T72 Training set (17°) 233(Sn_9563) 298 233 232(Sn_132) ◦ Training set (17 ) 233(Sn_9563) 298 233426(Sn_812) 232(Sn_132) 573(Sn_A04)426(Sn_812) Test set (15°, 17°) 428(Sn_9566) 429(Sn_c21) 0 0 573(Sn_A05)573(Sn_A04) Test set (15◦, 17◦) 428(Sn_9566) 429(Sn_c21) 0 0 573(Sn_A05) 573(Sn_A07)573(Sn_A07) 567(Sn_A10)567(Sn_A10)

Remote Sens. 2017, 9, 1150 11 of 18 Remote Sens. 2017, 9, 1150 11 of 18

Table 8. Confusion matrix of the proposed methodmethod underunder configurationconfiguration variance.variance.

Class Class Serial No. Serial No. BMP2 BMP2 BRDM2 BRDM2 BTR-70 BTR-70 T-72 T-72 PCC (%) PCC (%) Sn_9566 Sn_9566420 420 3 3 4 4 1 1 98.13 98.13 BMP2 BMP2 Sn_c21 Sn_c21417 417 5 5 4 4 3 3 97.20 97.20 Sn_812 Sn_81226 26 1 1 1 1 398 398 93.43 93.43 Sn_A04 Sn_A0415 15 8 8 0 0 550 550 95.99 95.99 T72 T72Sn_A05 Sn_A0512 12 2 2 2 2 557 557 97.21 97.21 Sn_A07 Sn_A078 8 2 2 1 1 562 562 98.08 98.08 Sn_A10 12 5 0 550 97.00 Sn_A10 12 5 0 550 97.00 Average Average 96.78 96.78

Table 9. PCCs of different methodsmethods underunder configurationconfiguration variance.variance.

MethodMethod Proposed Proposed SVM SVM SRC MSRC MSRC DSRC DSRCJSRC JSRC PCC (%)PCC (%) 96.78 96.78 86.12 86.12 8484.65.65 96.11 96.11 91.16 91.16 93.86 93.86

4.3.2. Noise Corruption 4.3.2. Noise Corruption The measured SAR images may be corrupted by noises from the background and radar system. The measured SAR images may be corrupted by noises from the background and radar system. Therefore, it is crucial that the ATR method can keep robust under noise corruption. Actually, there Therefore, it is crucial that the ATR method can keep robust under noise corruption. Actually, there are are many types of noises in SAR images. In this paper, additive complex Gaussian noise is employed many types of noises in SAR images. In this paper, additive complex Gaussian noise is employed as the representative, which is also used in several relevant researches [23,24]. Since it is impossible as the representative, which is also used in several relevant researches [23,24]. Since it is impossible to perfectly eliminate all of the noises in the original SAR images, the original MSTAR images are to perfectly eliminate all of the noises in the original SAR images, the original MSTAR images are assumed to be noise free and different amounts of Gaussian noises are added according to the SNR assumed to be noise free and different amounts of Gaussian noises are added according to the SNR level defined as Equation (7). level defined as Equation (7). IL 2 I L ril(,) åå 2 (7) SNR()10log dB = il∑==11∑ |r(i, l)| 10 i= l= 2 SNR(dB) = 10 log 1 IL1σ (7) 10 ILσ2 where ril(,) is the complex frequency data of MSTAR images, and σ 2 is the variance of Gaussian ( ) 2 wherenoise. r i, l is the complex frequency data of MSTAR images, and σ is the variance of Gaussian noise. Figure7 7 illustrates illustrates thethe procedureprocedure ofof transformingtransforming thethe originaloriginal MSTARMSTAR imagesimages toto thethe frequencyfrequency domain. By By transforming transforming the the original original image image using using a two-dimensional (2D) inverse fast Fourier transform (FFT) (FFT) and and removing removing the the zero zero padding padding and and window window during during the theimaging imaging process, process, the the frequency data is separated as a I × L matrix. Then, the Gaussian noises are added to the frequency frequency data is separated as a IL´ matrix. Then, the Gaussian noises are added to the frequency data according to the preset SNRs and thethe noise-corruptednoise-corrupted images are obtainedobtained by transforming the noised frequencyfrequency data data back back to the to image the domain.image domain. Figure8 givesFigure some 8 examplesgives some of the examples noise-corrupted of the imagesnoise-corrupted of a BMP2 images image of (chip a BMP2 number image “HB03341.000”) (chip number at“HB03341.000”) different SNRs. at different SNRs.

Figure 7.7.ProcedureProcedure of of transforming transforming SAR SAR images images to theto the frequency frequency domain. domain. 2D: two-dimensional;2D: two-dimensional; FFT: fastFFT: Fourier fast Fourier transform. transform.

Remote Sens. 2017, 9, 1150 12 of 18 RemoteRemote Sens.Sens. 20172017,, 99,, 11501150 1212 ofof 1818

((aa)) OriginalOriginal ((bb))−−1010 dB dB ((cc)) −−55 dBdB

((dd)) 00 dBdB ((ee)) 55 dB dB ((ff)) 1010 dBdB

FigureFigure 8.8. NoiseNoise corruptedcorrupted imagesimages atat differedifferentnt signal-to-noisesignal-to-noise ratiosratios (SNRs).(SNRs). Figure 8. Noise corrupted images at different signal-to-noise ratios (SNRs). The details of the implementation of this experiment are as follows. For the multi-view The detailsdetails ofof the the implementation implementation of thisof this experiment experiment are as are follows. as follows. For the multi-viewFor the multi-view methods, methods, two of the three views are corrupted by noise. For the single view methods, we randomly methods,two of the two three of viewsthe three are corruptedviews are bycorrupted noise. For by thenoise. single For view the single methods, view we methods, randomly we corrupt randomly 2/3 corrupt 2/3 of the test samples for a fair comparison. Figure 9 shows the performance of all the corruptof the test 2/3 samples of the test for asamples fair comparison. for a fair Figurecomparison.9 shows Figure the performance 9 shows the of performance all the methods of all under the methods under different noise levels. It is clear that the multi-view methods achieve much better methodsdifferent noiseunder levels. different It is noise clear levels. that the It multi-view is clear that methods the multi-view achieve muchmethods better achieve performance much better than performance than the single view methods. It is also noticeable that DRSC performs better than performancethe single view than methods. the single It is alsoview noticeable methods. that It is DRSC also performsnoticeable better that thanDRSC MSRC performs and JSRC better at SNRsthan MSRC and JSRC at SNRs lower than 0 dB. This is mainly because the PCA process in the data fusion MSRClower thanand JSRC 0 dB. at This SNRs is mainly lower than because 0 dB. the This PCA is mainly process because in the data the PCA fusion process eliminates in the some data noises.fusion eliminates some noises. With the highest PCC at each SNR, the proposed method is demonstrated to eliminatesWith the highest some noises. PCC at With each the SNR, highest the proposedPCC at ea methodch SNR, isthe demonstrated proposed meth tood be is the demonstrated most effective to be the most effective and robust. beand the robust. most effective and robust.

FigureFigure 9.9. TheThe PCCsPCCs ofof differentdifferent method methodsmethodss under under different different noise noise levels. levels.

Remote Sens. 2017, 9, 1150 13 of 18

Remote Sens. 2017, 9, 1150 13 of 18 4.3.3. Partial Occlusion 4.3.3.The targetPartial mayOcclusion be occluded by obstacles, so it is meaningful to test the ATR algorithms under partial occlusion.The target Asmay there be occluded are no by accepted obstacles, empirical so it is meaningful models of to objecttest the occlusion ATR algorithms in SAR under imagery, we considerpartial occlusion. the occlusion As there to occurare no possiblyaccepted empirical from eight models different of object directions occlusion as inin Ref.SAR [imagery,25]. To simulatewe the occludedconsider the target, occlusion the targetto occur region possibly is from first eight segmented different using directions the algorithmas in Ref. [25]. in Ref.To simulate [26]. Then, differentthe occluded levels of target, partial the occlusion target region are simulatedis first segmented by occluding using the different algorithm proportions in Ref. [26]. of Then, the target regiondifferent from the levels eight of directions.partial occlusion Figure are 10 simulated shows 20 by percent occluding occluded different images proportions from eightof the directions. target region from the eight directions. Figure 10 shows 20 percent occluded images from eight directions. The experimental implementation in this part is similar to the former one except that the noise The experimental implementation in this part is similar to the former one except that the noise corruption is replaced by partial occlusion. Figures 11–14 show the results of different methods at corruption is replaced by partial occlusion. Figures 11–14 show the results of different methods at directionsdirections 1, 3, 1, 5, 3, and 5, and 7 (due 7 (due to to the the symmetry, symmetry, the other directions directions are are not not presented). presented). In each In eachfigure, figure, subfiguresubfigure (a) compares(a) compares the the performance performance ofof allall of the methods methods and and subfigure subfigure (b) (b)presents presents a detailed a detailed comparisoncomparison of the of multi-view the multi-view methods. methods. Clearly, Clearly, the multi-view the multi-view methods methods gain significant gain significant improvement overimprovement the single view over methods the single and view the methods proposed and methodthe proposed achieves method the achieves best performance the best performance under partial occlusion.under partial Specifically, occlusion. with Specifically, the degradation with the degradation of partial occlusion,of partial occlusion, the superiority the superiority of the of proposed the methodproposed becomes method more becomes and more more significant. and more significant. When the When SAR the image SAR image is severely is severely occluded, occluded, it actually it losesactually the discriminability loses the discriminability required for required target recognition;for target recognition; thus, it is thus, preferable it is preferable to discard to discard it in multi-view it in multi-view recognition. It also can be observed from the results under noise corruption and partial recognition. It also can be observed from the results under noise corruption and partial occlusion that occlusion that SRC achieves better performance than SVM, which is consistent with the conclusions SRCin achieves Ref. [9]. better performance than SVM, which is consistent with the conclusions in Ref. [9].

(a) Original (b) direction 1 (c) direction 2

(d) direction 3 (e) direction 4 (f) direction 5

(g) direction 6 (h) direction 7 (i) direction 8

Figure 10. Twenty percent (20%) occluded images from eight directions. Figure 10. Twenty percent (20%) occluded images from eight directions.

Remote Sens. 2017, 9, 1150 14 of 18 Remote Sens. 20172017,, 99,, 11501150 1414 ofof 1818

((a)) ((b))

FigureFigure 11. 11.Performance PerformancePerformance underunderunder partialpartial ococ occlusionclusionclusion fromfrom from directiondirection direction 1.1. ((a) 1.) SingleSingle (a) Singleviewview methods;methods; view methods; ((b)) (b) Multi-viewMulti-view methods.methods

((a)) ((b))

FigureFigure 12. 12.Performance PerformancePerformance underunderunder partialpartial ococ occlusionclusionclusion fromfrom from directiondirection direction 3.3. ((a) 3.) SingleSingle (a) Singleviewview methods;methods; view methods; ((b)) (b) Multi-viewMulti-view methods.methods

Remote Sens. 2017, 9, 1150 15 of 18

((a)) ((b))

FigureFigure 13. 13.Performance PerformancePerformance underunderunder partialpartial ococ occlusionclusionclusion fromfrom from directiondirection direction 5.5. ((a) 5.) SingleSingle (a) Singleviewview methods;methods; view methods; ((b))

(b) Multi-viewMulti-view methods.methods

(a) (b) Figure 14. Performance under partial occlusion from direction 7. (a) Single view methods; (b) Figure 14. Performance under partial occlusion from direction 7. (a) Single view methods; Multi-view methods (b) Multi-view methods. 4.3.4. Resolution Variance Due to the variation of SAR sensors, it is possible that multi-view SAR images may have some different resolutions. Figure 15 shows the SAR images of the same target at different resolutions from 0.3 m to 0.7 m.

(a) 0.3 m (b)0.4m (c) 0.5 m

(d) 0.6 m (e)0.7m

Figure 15. Images at different resolutions.

With a similar experimental setup to the former two experiments, the results of different methods are plotted in Figure 16. Compared with EOCs such as noise corruption and partial occlusion, the resolution variance causes less degradation to the ATR method’s performance. It is also noticeable that SRC has a much greater PCC than SVM. With the highest PCC, the proposed method enjoys the best effectiveness and robustness among all the methods.

Remote Sens. 2017, 9, 1150 15 of 18

(a) (b)

RemoteFigure Sens. 2017 14., 9Performance, 1150 under partial occlusion from direction 7. (a) Single view methods; (b15) of 18 Multi-view methods

4.3.4.4.3.4. Resolution Resolution Variance Variance DueDue to to the the variation variation of of SAR SAR sensors, sensors, it it is is possible that that multi-view multi-view SAR SAR images images may may have have some some differentdifferent resolutions. FigureFigure 1515 shows shows the the SAR SAR images images of theof the same same target target at different at different resolutions resolutions from from0.3 m 0.3 to m 0.7 to m. 0.7 m.

(a) 0.3 m (b)0.4m (c) 0.5 m

(d) 0.6 m (e)0.7m

FigureFigure 15. 15. ImagesImages at at different different resolutions. resolutions.

WithWith aa similarsimilar experimental experimental setup setup to theto formerthe form twoer experiments,two experiments, the results the ofresults different of different methods methodsare plotted are in plotted Figure in16 .Figure Compared 16. Compared with EOCs with such EOCs as noisesuch corruptionas noise corruption and partial and occlusion, partial occlusion,the resolution the varianceresolution causes variance less degradationcauses less degradation to the ATR method’s to the ATR performance. method’s Itperformance. is also noticeable It is alsothat noticeable SRC has a muchthat SRC greater has PCCa much than greater SVM. WithPCC thethan highest SVM. PCC,With thethe proposedhighest PCC, method the enjoysproposed the Remotemethodbest effectiveness Sens. enjoys 2017, 9 the, 1150 andbest robustness effectiveness among and robustness all the methods. among all the methods. 16 of 18

FigureFigure 16. 16. PCCsPCCs of of different different methods methods under under different different resolutions. resolutions.

4.4. Recognition under Different Thresholds One of the key parameters in the proposed method is the reliability level threshold. Actually, it is a nuisance problem that is used to determine the threshold. In order to provide some insights into the threshold’s determination, we test the proposed method at different thresholds. As shown in Figure 17, the performance under SOC improves with the increase of the threshold. Actually, most of the samples under SOC are discriminative for target recognition. Therefore, it is preferable that all the views are used for recognition. For EOC recognition, the highest PCCs are achieved at different thresholds for different EOCs. Specially, for the MSTAR dataset, a proper threshold is 0.96 for performance under all conditions, which is relatively high.

Figure 17. Performance of the proposed method at different thresholds

5. Conclusions This paper proposes an SAR target recognition method by exploiting the information contained in multi-view SAR images. Each of the input multi-view SAR images is first examined by SRC to

Remote Sens. 2017, 9, 1150 16 of 18

Remote Sens. 2017, 9, 1150 16 of 18 Figure 16. PCCs of different methods under different resolutions.

4.4.4.4. Recognition Recognition under under Different Different Thresholds Thresholds OneOne of the key parameters inin thethe proposedproposed methodmethod is is the the reliability reliability level level threshold. threshold. Actually, Actually, it it is isa nuisancea nuisance problem problem that that is usedis used to to determine determine the the threshold. threshold. In orderIn order to provideto provide some some insights insights into into the thethreshold’s threshold’s determination, determination, we test we the test proposed the propos methoded method at different at different thresholds. thresholds. As shown As in shown Figure 17in , Figurethe performance 17, the performance under SOC under improves SOC with improves the increase with ofthe the increase threshold. of the Actually, threshold. most Actually, of the samples most ofunder the samples SOC are under discriminative SOC are discriminative for target recognition. for target Therefore, recognition. it is Therefore, preferable it that is preferable all the views that areall theused views for recognition. are used for For recognition. EOC recognition, For EOC the recognit highestion, PCCs the highest are achieved PCCsat are different achieved thresholds at different for thresholdsdifferent EOCs. for different Specially, EOCs. for the Specially, MSTAR dataset, for the a properMSTAR threshold dataset, isa 0.96proper for performancethreshold is under0.96 for all performanceconditions, which under is all relatively conditions, high. which is relatively high.

Figure 17. PerformancePerformance of of the proposed me methodthod at different thresholds thresholds.

5.5. Conclusions Conclusions ThisThis paper paper proposes proposes an an SAR SAR targ targetet recognition recognition method method by by exploiting exploiting the the information information contained contained inin multi-view multi-view SAR SAR images. images. Each Each of of the the input input mult multi-viewi-view SAR SAR images images is is first first examined examined by by SRC SRC to to evaluate its validity for multi-view recognition. Then, the selected views are jointly recognized using JSR. To improve the adaptability of JSR, an enhanced local dictionary is constructed based on the selected atoms by SRC. Extensive experiments are conducted on the MSTAR dataset under SOC and various EOCs, and a comparison is made with several state-of-the-art methods including SVM, SRC, MSRC, DSRC, and JSRC. Based on the experimental results, conclusions can be drawn as follows: (1) the multi-view methods can significantly improve the ATR method’s performance compared with single view methods; (2) the proposed method can better exploit multi-view SAR images to improve the ATR method’s performance under SOC; and (3) the proposed method can significantly enhance the robustness of an ATR system to various EOCs.

Acknowledgments: This work was supported by the Program for New Century Excellent Talents in University of China under Grant No. NCET-11-0866. Author Contributions: Baiyuan Ding proposed the general idea of the method and performed the experiments. Gongjian Wen reviewed the idea and provided many suggestive advices. This manuscript was written by Baiyuan Ding. Conflicts of Interest: The authors declare no conflict of interest. Remote Sens. 2017, 9, 1150 17 of 18

References

1. El-Darymli, K.; Gill, E.W.; McGuire, P.; Power, D.; Moloney, C. Automatic Target Recognition in Synthetic Aperture Radar Imagery: A State-of-the-Art Review. IEEE Access 2016, 4, 6014–6058. [CrossRef] 2. Mishra, A.K. Validation of PCA and LDA for SAR ATR. In Proceedings of the 2008 IEEE Region 10 Conference, Hyderabad, India, 19–21 November; pp. 1–6. 3. Ding, B.Y.; Wen, G.J.; Ma, C.H.; Yang, X.L. Decision fusion based on physically relevant features for SAR ATR. IET Radar Sonar Navig. 2017, 11, 682–690. [CrossRef] 4. Ding, B.Y.; Wen, G.J.; Zhong, J.R.; Ma, C.H. A robust similarity measure for attributed scattering center sets with application to SAR ATR. Neurocomputing 2017, 219, 130–143. [CrossRef] 5. Ding, B.Y.; Wen, G.J.; Huang, X.H.; Ma, C.H.; Yang, X.L. Target recognition in synthetic aperture radar images via matching of attributed scattering centers. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2017, 10, 3334–3347. [CrossRef] 6. Dong, G.G.; Kuang, G.Y.; Wang, N.; Zhao, L.J.; Lu, J. SAR target recognition via joint sparse representation of monogenic signal. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2015, 8, 3316–3328. [CrossRef] 7. Zhao, Q.; Principe, J.C. Support Vector Machines for Synthetic Radar Automatic Target Recognition. IEEE Trans. Aerosp. Electron. Syst. 2001, 37, 643–654. [CrossRef] 8. Thiagarajan, J.; Ramamurthy, K.; Knee, P.P.; Spanias, A.; Berisha, V. Sparse representation for automatic target classification in SAR images. In Proceedings of the 2010 4th Communications, Control and Signal Processing (ISCCSP), Limassol, Cyprus, 3–5 March 2010. 9. Wright, J.; Yang, A.; Ganesh, A.; Sastry, S.; Ma, Y. Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 2009, 31, 210–227. [CrossRef][PubMed] 10. Chen, S.Z.; Wang, H.P.; Xu, F.; Jin, Y.Q. Target classification using the deep convolutional networks for SAR images. IEEE Trans. Geosci. Remote Sens. 2016, 47, 1685–1697. [CrossRef] 11. Ding, B.Y.; Wen, G.J.; Huang, X.H.; Ma, C.H.; Yang, X.L. Target recognition in SAR images by exploiting the azimuth sensitivity. Remote Sens. Lett. 2017, 8, 821–830. [CrossRef] 12. Schmitt, M.; Maksymiuk, O.; Magnard, C.; Stilla, U. Radargrammetric registration of airborne multi-aspect SAR data of urban areas. ISPRS J. Photogramm. Remote Sens. 2013, 86, 11–20. [CrossRef] 13. Schmitt, M.; Zhu, X.X. Data fusion and remote sensing: An ever-growing relationship. IEEE Geosci. Remote Sens. Mag. 2016, 4, 6–23. [CrossRef] 14. Brendel, G.; Horowitz, L. Benefits of aspect diversity for SAR ATR: Fundamental and experimental results. In Proceedings of the SPIE, Orlando, FL, USA, 24 August 2000; pp. 567–578. 15. Brown, M.Z. Analysis of multiple-view Bayesian classification for SAR ATR. In Proceedings of the SPIE, Orlando, FL, USA, 12 September 2003; pp. 265–274. 16. Bhanu, B.; Jones, G. Exploiting azimuthal variance of scatterers for multiple look SAR recognition. In Proceedings of the SPIE, Riverside, CA, USA, 1 August 2003; pp. 290–298. 17. Ettinger, G.; Snyder, W. Model-based fusion of multi-look SAR for ATR. In Proceedings of the SPIE, Orlando, FL, USA, 1 August 2002; pp. 277–289. 18. Vespe, M.; Baker, C.J.; Griffiths, H.D. Aspect dependent drivers for multi-perspective target classification. In Proceedings of the IEEE Conference on Radar, Verona, NY, USA, 24–27 April 2006; pp. 256–260. 19. Huan, R.H.; Pan, Y. Target recognition of multi-aspect SAR images with fusion strategies. Prog. Electromagn. Res. 2013, 134, 267–288. [CrossRef] 20. Zhang, H.C.; Nasrabadi, N.M.; Zhang, Y.N.; Huang, T.S. Multi-view automatic target recognition using joint sparse representation. IEEE Trans. Aerosp. Electron. Syst. 2012, 48, 2481–2497. [CrossRef] 21. Tropp, J.A.; Gilbert, A.C.; Strauss, M.J. Algorithms for simultaneous sparse approximation. EURASIP J. Adv. Appl. Signal Process. 2006, 589–602. 22. Rakotomamonjy, A. Surveying and comparing simultaneous sparse approximation (or group lasso) algorithms. Signal Process. 2011, 91, 1505–1526. [CrossRef] 23. Doo, S.; Smith, G.; Baker, C. Target Classification Performance as a Function of Measurement Uncertainty. In Proceedings of the 5th Asia-Pacific Conference on Synthetic Aperture Radar (APSAR), Singapore, 1–4 September 2015. 24. Zhou, J.X.; Shi, Z.G.; Cheng, X.; Fu, Q. Automatic target recognition of SAR images based on global scattering center model. IEEE Trans. Geosci. Remote Sens. 2011, 10, 3713–3729. Remote Sens. 2017, 9, 1150 18 of 18

25. Jones, G.; Bhanu, B. Recognition of articulated and occluded objects. IEEE Trans. Pattern Anal. Mach. Intell. 1999, 21, 603–613. [CrossRef] 26. Sun, Y.J.; Liu, Z.P.; Todorovic, S.; Li, J. Adaptive boosting for SAR automatic target recognition. IEEE Trans. Aerosp. Electron. Syst. 2007, 43, 112–125. [CrossRef]

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).