,*

1.Department of Electronic Engineering,Tsinghua University,Beijing 100084,China;2.Beijing Institute of Radio Measurement,Beijing 100854,China;3.Xi’an Research Institute of Hi-Technology,Xi’an 710025,China

Novel supervised classificatio approach for multifrequency polarimetric SAR data

Biao You1,Bin Xu1,Jian Yang1,*,Chunmao Yeh2,and Jianshe Song3

1.Department of Electronic Engineering,Tsinghua University,Beijing 100084,China;
2.Beijing Institute of Radio Measurement,Beijing 100854,China;
3.Xi’an Research Institute of Hi-Technology,Xi’an 710025,China

A novel method is proposed for the supervised classificatio of multifrequency polarimetric synthetic aperture radar (PolSAR)images.The coherency matrices in P-,L-,and C-bands are mapped onto a 9×9 matrixΩbased on the eigenvalue decomposition of the coherency matrix of each band.A boxcar filte is then performed on the matrixΩ.The filtere data are put into a complex Wishart classifie.Finally,the effectiveness of the proposed method is demonstrated with JPL/AIRSAR multifrequency PolSAR data acquired over the Flevoland area.

synthetic aperture radar(SAR),polarimetry,classifi cation,multifrequency.

1.Introduction

Multifrequency polarimetric synthetic aperture radar(Pol-SAR)sensors provide more information than traditional monofrequencyPolSAR.A P-band SAR can detect targets beneath the foliage whereas the X-band SAR can retrieve more detailed scenes[1].Such information is often complementary in classification For example,L-and P-bands are suitablefordiscriminationbetweenthe classes oftown, forest,water,agricultural cover whereas X-and C-bands are suitable for agricultural landuse classes discrimination [2].

Many methods have been proposed for multifrequency PolSAR data classification Lee et al.derived a distance based on complex Wishart distribution for multilook SAR data.The complex Wishart classifie can be easily extended to the multifrequency case,provided that the data are uncorrelated between each pair of frequency band[3–5].However,in Section 3,we will show that correlations between different bands sometimes exist. Lardeux et al.[6]applied the support vector machine (SVM)in tropical vegetation classification The SVM algorithm can perform much better than the Wishart approach when the radar data do not satisfy the Wishart distribution.Yang et al.[7]classifie different band data independently through the maximum likelihood method. Theresults were mergedaccordingto the Dempster-Shafer theory of evidence.Therefore,it is essential for the classifie to have enough prior test suite knowledge.Frery et al.[8]developed an iterative conditional mode classifie by using more accurate probability density functions and adding spatial contextual information.However,too many parameters must be set before classification

In this paper,a new method is proposed for fusion classificatio of multifrequency PolSAR images.The method comprises two main stages:(i)The P-,L-,and C-bands coherency matricesTare mapped onto a new 9×9 matrixΩby eigenvector decomposition.A 5×5 boxcar filte is then implemented,and(ii)supervised classificatio is performed on theΩ9matrix.

2.The study site and data set

The experimental data were acquired over Flevoland by JPL/AIRSAR during the SIR-C campaign in June 1991. The data are shown in Fig.1 with red for P-band power, green for L-band power,and blue for C-band power.The experimental area is enclosed by red lines with 14 terrain coversin the scene:potato,beet,wheat,maize,grass,fruit, barley,beans,flax lucerne,oats,onions,peas,and rapeseed[9].Some bright pixels with very high power,known as corner reflectors are excluded from classification A total of 286 455 pixels are used in the experiment.

Fig.1 Test site power image

3.Classificatio methodology

3.1Lee’s Wishart classifie

Single-look PolSAR data may be represented in the form of a Pauli vector:

The coherency matrixTis obtained by the following multi-look processing:

whereNis the number of looks.The Pauli vectorkis assumed to follow complex Gaussian distribution:

In this case,the coherency matrixThas the complex Wishart distribution[10].The probability density function ofTis

where Tr(·)denotes the trace function and

In[3],a distance was derived for maximum likelihood classifie based on the Wishart distribution in supervised classificatio as follows:

whereωmis the set of pixels that belong to themth class; andTmis computedusing pixels within a selected training area.The pixelZis assigned to the class with the minimum Wishart distance.

If the frequencies are well separated,the correlations between different frequency bands are considerably fewer than those within bands,the matricesTP,TLandTCcan be placed on the diagonal elements of one 9×9 matrixT9, and the off-diagonal elements can be set to a zero matrix [3]:

The distance in(6)can then be easily extended to the multifrequencycase:

3.2Decomposition of the coherency matrix

In[11],the coherency matrixTis decomposed into the sum of three matrices,each of which is represented by a single scattering mechanism:

whereθis an arbitrary angle.To eliminate ambiguity,the nuisance phaseθis chosen such that the third element of each eigenvector is positive.

3.3Hypothesis test for independence between different bands

Testing whether the matricesTP,TLandTCare uncorrelated is very difficult For simplicity,only the diagonal termsT11,T22,andT33in the three matrices are tested. Hypothesistestingisconductedwiththefollowingnulland alternative hypothesis.

H0:The elementT11in matricesTPandTLare independent.

H1:Otherwise.

Theotherelementsandbandsaretestedsimilarly.Pixels in each class are used for testing.The level of significancαis set to 0.05.The testing results are shown in Table 1, where the symbol“√”means“accept hypothesis”andthe symbol“×”means“reject hypothesis”.For example, the firs symbol“×”means that the random variableT11in matricesTPandTLis not independent for the potato class.The other symbol in the table has a similar meaning.

Table 1 shows thatT11,T22andT33inTPandTL,TPandTC,TLandTCare all not always independent. From this perspective,the matricesTP,TLandTCare indeed correlated,although the correlation coefficient may be small compared with within bands.

Table 1 Hypothesis test results for independence between different bands in different land classes

3.4Proposed method for multifrequency

classificatio

Table 1 indicates that the correlations between different bands sometimes exist.Classificatio performance may be improved if the correlations are well estimated.Based on this idea,we defin a new matrix as follows: and the vectorseP1,eL1andeC1are the firs eigenvectors ofTP,TLandTC,respectively.In(12),the correlations are estimated by the outer products of the firs eigenvectors.Thereafter,a 5×5 boxcar filte is performed onΩ:

TheoremThe matrixΩ9is positive-definite

ProofIt is sufficien to provethat the matrixΩdefine in(12)is positive-definite

The three terms in the last equation are all positivedefinite Hence,the matrixΩis positive-definite

As mentionedpreviously,thethirdelementsofeP1,eL1andeC1are positive.Hence,the(3,6),(3,9),(6,3),(6,9), (9,3),(9,6)elementsinΩ9arealsopositive.Strictlyspeaking,the matrixΩ9does not follow the Wishart distribution,but has many properties similar to the coherency matrixT.For example,they are both Hermitian and positivedefinite Therefore,we defin a quasi-Wishart distance for matrixΩ9:

whereCmis the center of classωm.With the above matrixΩ9,supervised classificatio may be performed afterwards.The pixel is assigned to the class with the minimum quasi-Wishart distance.

4.Experimental results

4.1One band classificatio

This section presents the classificatio results on the experiment data.The wavelengths of P-,L-,and C-bands are 68 cm,24 cm,and 5.7 cm,respectively.Since the backscattering characteristics of the target heavily depend on the wavelength,the classificatio result differs signifi cantly with different bands.The overall accuracy(OA)of P-,L-,andC-bandsare61.00%,75.36%,and61.19%with the Wishart classifie.The fruit class is poorly classifie in the C-band(25.13%)and well classifie in the P-band (90.73%).However,the rapeseed class is well classifie in the C-band(96.6%)and poorly classifie in the P-band (69.7%).

4.2Two bands classificatio

The multifrequency data contain more reliable and complementary information than the monofrequencydata.The OAs of Lee’s Wishart classificatio and of the proposed method when only two bands are used are shown in Table 2.The proposed method achieves three OAs.Each OA is greater than 95%,which is extremely high.

Table 2 The OAs of two bands classificatioresult of two methods

4.3Three bands classificatio

The ground truth of the test site is shown in Fig.2(a).The wheat class,colored green,has a maximum pixel number of 84 401.The onion class,colored pink,has a minimumpixelnumberof289.Theclassifie imageisshownin Fig.2(b).Lee’s Wishart multifrequency classifie achieves an OA of 94.20%,and the proposed method achieves 98.20%.The confusion matrix is listed in Table 3 and Table 4.

Fig.2 Experiment results of the proposed algorithm

Almost all the class accuracies of the proposed method are higher than those of the traditional multifrequency Wishart classifie except for that of the beans class(with accuracies of 88.92%and 93.79%,respectively).The maizeclass is classifie poorlyin anysingleband(41.84%, 33.22%,and 16.49%for the P-,L-and C-bands,respectively).A combination of the three bands yields the accuracy of 87.30%.This result suggests that the correlation betweendifferentbandsmay help to improveclassificatio performance.

Table 3 Confusion matrix for Lee’s multifrequency Wishart classifie %

Table 4 Confusion matrix for the proposed method %

4.4The KHAT statistic

Cohen’s Kappa coefficien is a measure of agreement or accuracy.The KHAT statistic is an estimate of Cohen’s Kappa coefficient The KHAT statistic is computed as follows[12]:

whereris the number of categories;xijis the number of observations that classify theith class into thejth class;xi+andx+iare the marginal totals of rowiand columni; andMis the total number of observations.This statistic reaches 0.98,which is remarkably high,suggesting that the classificatio result is very good.

5.Summary

In this paper,a new method has been proposed for classificatio of multifrequency PolSAR data.The correlations betweendifferentbandsareestimatedandused forclassifi cation.The proposedmethod is simple and has a high classificatio accuracy.The classificatio algorithm is demonstrated to be effective by JPL/AIRSAR data.Being lack of enough ground-truth multifrquency data,the universality of the proposed method needs to be further validated.

[1]X.Liu,W.Chang,Y.Chang.A multi-band SAR target detec-tion method based on decision fusion.Modern Radar,2007, 29(2):22–25.(in Chinese)

[2]T.Wever,J.Henkel,B.Hafner.Crop identificatio using multifrequency and polarimetric SAR data.Proc.of Geoscience and Remote Sensing Symposium,1995,2:1213–1215.

[3]J.S.Lee,M.R.Grunes,R.Kwok.Classificatio of multilook polarimetric SAR imagery based on complex Wishart distribution.International Journal of Remote Sensing,1994,15(11): 2299–2311.

[4]J.S.Lee,E.Pottier.Polarimetric radar imaging:from basics to applications.Boca Raton,FL:CRC Press,2009.

[5]J.S.Lee,M.R.Grunes,E.Pottier.Quantitative comparison of classificatio capability:fully polarimetric versus dual-and single-polarization SAR.IEEE Trans.on Geoscience and Remote Sensing,2001,39(11):2343–2351.

[6]C.Lardeux,P.L.Frison,C.Tison,et al.Support vector machine for multifrequency SAR polarimetric data classifica tion.IEEE Trans.on Geoscience and Remote Sensing,2009, 47(12):4143–4152.

[7]M.S.Yang,W.M.Moon.Decision level fusion of multifrequency polarimetric SAR and optical data with dempstershafer evidence theory.Proc.of Geoscience and Remote Sensing Symposium,2003,6:3668–3670.

[8]A.C.Frery,A.H.Correia,C.C.Freitas.Classifying multifrequency fullypolarimetric imagery withmultiplesources ofstatistical evidence and contextual information.IEEE Trans.on Geoscience and Remote Sensing,2007,45(10):3098–3109.

[9]D.H.Hoekman,M.A.M.Vissers.A new polarimetric classificatio approach evaluated for agricultural crops.IEEE Trans. on Geoscience and Remote Sensing,2003,41(12):2881–2889.

[10]N.R.Goodman.Statistical analysis based on a certain multivariate complex Gaussian distribution(an introduction).Annals of Mathematical Statistics,1963,34(1):152–177.

[11]S.R.Cloude,E.Pottier.An entropy based classificatio scheme for landapplications ofpolarimetric SAR.IEEETrans. on Geoscience and Remote Sensing,1997,35(1):68–78.

[12]R.G.Congalton.A review of assessing the accuracy of classificatio of remotely sensed data.Remote Sensing of Environment,1991,37:35–46.

Biographies

Biao Youwas born in1976.He received his B.S. and M.S.degrees from Zhengzhou Information Science and Technology Institute,Henan,China, in 1996 and 2001,respectively.He is currently working toward his Ph.D.degree in the Department of Electronic Engineering,Tsinghua University.His research work focuses on polarimetric SAR image interpretation.

E-mail:youb200601@163.com

Bin Xuwas born in 1991.He received his B.S. degree from Tsinghua University,Beijing,China, in 2011,where he is currently working toward his Ph.D.degree in the Department of Electronic Engineering.His research work focuses on SAR image processing and polarimetric SAR image processing.

E-mail:xubin07161@gmail.com

Jian Yangwas born in 1965.He received his B.S. and M.S.degrees from Northwestern Polytechnical University,Xi’an,China,in 1985 and 1990,respectively,and Ph.D.degree from Niigata University, Niigata,Japan,in 1999.In 1985,he joined the Department of Applied Mathematics,Polytechnical University.From 1999 to 2000,he was an assistant professor with Niigata University.In April 2000,he joined the Department of Electronic Engineering,Tsinghua University, Beijing,China,where he is now a professor.His interests include radar polarimetry,remote sensing,mathematical modeling,optimization in engineering,and fuzzy theory.Dr.Yang is the chairman of IEICE in Beijing area and the vice-chairman of IEEE AES in Beijing chapter.

E-mail:yangjian ee@tsinghua.edu.cn

Chunmao Yehwas born in 1981.He received his M.S.degree in 2005 from Harbin Institute of Technology,and Ph.D.degree in 2009 from Tsinghua University in Beijing.He is now a senior engineer serving for Beijing Institute of Radio Measurement. His research interests include signal processing and automatic target recognition.

E-mail:chunmaoyeh@gmail.com

Jianshe Songreceived his B.S.degree from Shanxi Normal University in 1982,and M.S.and Ph.D. degrees from Xidian University in 1989 and 2001, respectively.He is now a professor of Xi’an Research Institute of Hi-Technology.He has finishe many projects and received more than ten awards from Chinese government.He has published fve books and more than 150 papers.His interests include radar theory,signal processing and optimization in engineering.

E-mail:Songjianshe09@126.com

10.1109/JSEE.2015.00133

Manuscript received November 25,2014.

*Corresponding author.

This work was supported in part by the National Natural Science Fundation of China(41171317;61132008;61490693)and Aeronautical Science Foundation of China(20132058003).