A NOVEL APPROACH TO POLARIMETRIC SAR DATA …giorgio-antonino.licciardi/pr_licciardi.pdf · A NOVEL...

Procedia Computer Science 00 (2013) 1–??

ProcediaComputerScience

A NOVEL APPROACH TO POLARIMETRIC SAR DATAPROCESSING BASED ON NONLINEAR PCA

Giorgio Licciardia, Ruggero Giuseppe Avezzanob, Fabio Del Frateb, Giovanni Schiavonb,Jocelyn Chanussota,c

aGIPSA-Lab. Grenoble Institute of Technology, Grenoble, FrancebDICII, Tor Vergata University, Italy

cFaculty of Electrical and Computer Engineering, University of Iceland

Abstract

In remotely sensed Synthetic Aperture Radar (SAR) images, scattering from a target is often the result of a mixture of differentmechanisms. For this reason, detection of targets and classification of SAR images may be very difficult and very differentfrom other sensor imagery. Fully polarimetric data offer the possibility to separate the different mechanisms, interpret them andconsequently identify the geometry of the targets. To achieve this task, several target decomposition techniques have been proposedin the literature to improve the interpretation of this kind of data. Among these, the physical based techniques are the mostconsidered.This paper proposes a novel approach for target decomposition based on the use of Nonlinear Principal Component Analysis.Differently from physical based target decomposition techniques, the proposed method is based on a nonlinear decorrelation of thereceived polarimetric SAR (POLSAR) signal into few elementary components that could be associated to the different scatteringmechanisms present in the image. A comparison of the classification results obtained using different decomposition techniquesdemonstrates that the proposed approach can be an effective alternative to classical physical based methods.

c© 2011 Published by Elsevier Ltd.

Keywords: Nonlinear Principal Component Analysis, SAR polarimetry, polarimetric decomposition, classification.

1. Introduction

The last generations of spaceborne Synthetic Aperture Radar improved the exploitation of the information con-tained into polarization diversity. Over the years, the advantages of polarimetric systems over conventional singlepolarization SAR sensors have been demonstrated. The main property of a multiple polarization radar acquisition liesin the ability of the microwaves to interact with the geometrical and the physical structure of the target. The polariza-tion is an intrinsic property of a wave. It describes the orientation of the electric field and its variations during time.When a polarized plane wave interacts with a dielectric target, the combined effect of the incident electromagneticfield and the target permittivity generates a scattered electromagnetic wave, which is radiated into space and reachesthe sensor. This effect of the presence of the target is described by the scattering matrix S.Being E(i) and E(s) the incident and the scattered field, respectively, they are related as:

E(s) =e− jk0R

RSE(i) (1)

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The two electric fields are expressed using the Jones formalism, so every field is a column vector containing thecomponents of the field with respect to an orthonormal basis. Often, the horizontal and the vertical directions are usedas the basis function. The scattering matrix will account for the relations between the incident and the scattered, andthe horizontal and the vertical components of the electric field [1], as:[

EH(s)

EV(s)

]=

e− jk0R

R

[S HH S HV

S VH S VV

] [EH

(i)

EV(i)

](2)

An important property of the scattering matrix and, as a consequence, of the polarimetric systems that measure it,is that it contains all the information needed to describe the polarimetric behavior of the target [2]. Its elementsare complex quantities and, due to the reciprocity property, only three out of four are independent (S HV = S VH).The whole polarimetric information can then be obtained from five real quantities: three amplitudes and two phasedifferences.

S =

[S HH S HV

S VH S VV

]=

√σHH

0√σHV

0e jφHV−HH√σHV

0e jφHV−HH√σVV

0e jφVV−HH

e jφHH (3)

SAR is an imaging radar and a pixel represents the results of the coherent sum of all the echoes from elementaryscatterers inside it. The scattering matrix, consequently, does not represent the response from a point target, but amixture of responses from elementary scatterers; therefore the target is called distributed. Moreover, the sensitivity tothe different media is much affected by the sensor configuration (i.e., frequency, polarization, and incidence angle),and a wide variability of geometrical and physical properties characterize the various targets [3][4]. In SAR remotesensing literature [5], the principal five scattering mechanisms are recognized as (Fig. 1):

1. backscattering from a rough surface;2. low-order multiple scattering, as occurs from dihedral effects in forest and urban areas;3. single scattering from anisotropic structures such as tree trunks, where the backscatter can be modeled as that

from a rough dielectric cylinder or an other canonical object with polarization anisotropy due to shape anddielectric material structure.

4. surface scattering after propagation through a random medium;5. random volume backscatter from a non-penetrable layer of discrete scatterers;

Although these five mechanisms provide the basis for the interpretation of many remote sensing scattering problems,there are some situations where combinations become important [6][7]. In the α/Entropy analysis devoloped byCloude and Pottier [8], the classification of scattering mechanisms is derived by these two features. The angle αrepresents the kind of scattering process of the average target: values of α close to zero suggest a Bragg scatteringtype, values of α around π/4 identify scattering from a cloud of anisotropic particles, and high values of α are relatedto double-bounce scattering (urban areas experiment such values of α). The Entropy is a measure of the mixture ofdifferent scattering mechanisms: low entropy indicates the presence of only one dominant scattering mechanism, puretarget exhibits zero entropy, high entropy values show high depolarization effects and the limit of H = 1 indicates thepresence of pure noise. Following this rationale, nine different possible mixtures of scattering mechanisms have beenextracted:

1. Bragg surface scattering and specular scattering phenomena, physical surfaces such as water at L and P-Bands,sea-ice at L-Band, as well as very smooth land surfaces, all fall into this category;

2. Isolated dipole scatterers, such as scattering from vegetation with strongly correlated orientation of anisotropicscattering elements;

3. Low entropy double or even bounce scattering events, such as provided by isolated dielectric and metallicdihedral scatterers;

4. Scattering due to a surface cover comprising oblate spheroidal scatterers, such as leafs or discs;5. Scattering from vegetated surfaces with anisotropic scatterers and moderate correlation of scatterer orientations;6. Dihedral scattering with moderate entropy. This occurs for example in forestry applications, where double

bounce mechanisms occur at P and L bands following propagation through a canopy. A second importantprocess in this category is urban areas, where dense packing of localized scattering centers can generate loworder multiple scattering dominant;

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7. High entropy surface scattering;8. High entropy volume scattering, scattering from forest canopies lies in this region, as does the scattering from

some types of vegetated surfaces with random highly anisotropic scattering elements;9. High entropy multiple scattering. Such mechanisms can be observed in forestry applications or in scattering

from vegetation which has a well developed branch and crown structure, as well as in urban environments.

Polarimetry has been demonstrated to be a valuable tool for interpreting and separating different scattering mecha-nisms starting from the knowledge of the scattering matrix or covariance matrix or coherency matrix [9][10][11][12][12].While algorithms based on the scattering matrix are often referred to as coherent decompositions, the use of the secondorder matrices is usually referred to as incoherent decompositions. However, all the classical decomposition methodsare based on the backscattering models that have a limited validity range. This is particularly evident consideringthe effects produced by depolarizing targets. Most of the targets observed by a SAR system can be considered as acombination of different basic targets having lower dimension than the resolution of the SAR system. This is the caseof the forest, where the polarimetric information is supposed to be very rich for this kind of targets, because it containsmany elements oriented and arranged in volume that induce both phenomena of orientation, but also depolarization.These effects increase with the frequency, and then models that present good performances on long wavelengths (C,L bands) tend to loose their validity on shorter wavelengths. Considering the received signal as a mixture of sev-eral principal scattering mechanisms, it is possible to consider the polarimetric decomposition as a problem of BlindSource Separation (BSS). Different techniques exist for the separation of the principal sources from a mixed signalwithout any a-priori knowledge [13][14], mainly based on Principal Component Analysis (PCA), Independent Com-ponent Analysis (ICA) or Non-negative Matrix Factorization(NMF) [15][16][17][18] [19][20][21]. Starting from thisassumption, in this paper, we propose a novel approach for the detection of few elementary components that could beassociated to the different scattering mechanisms present in the image by means of Nonlinear Principal ComponentAnalysis (NLPCA), performed by Autoassociative Neural Networks (AANN).In particular, in [22] it has been demonstrated that NLPCA can be used to effectively decorrelate the informationcontained in a hyperspectral image and then can be used to unmix the original image into few pure spectral signa-tures called endmembers [23]. From this point of view, similarly to the hyperspectral case, NLPCA can be used todecompose the full polarimetric signal into a certain number of principal signals that can be associated to the differentscattering contributions present in the POLSAR image.A qualitative analysis of the obtained NLPCs has been proposed as a comparison with the principal physical basedtarget decomposition theorems that can be found in the literature. Moreover, a comparison of the classification accu-racies obtained using the NLPCA approach with those obtained using classical decomposition approaches has beenperformed by using a Support Vector Machine (SVM) algorithm.The paper is organized as follows: section II briefly describes some of the most popular target decomposition methods,while section III introduces the non-linear Principal Component Analysis. Section IV presents experimental resultsobtained on three different datasets. Finally conclusions are drawn in Section V.

2. Polarimetric target decomposition techniques

The description of a complete generalizing model representing all the possible scattering mechanisms is not a triv-ial task, thus several techniques to separate the different scattering mechanisms have been developed. For this reasonsome approximations become essential when designing polarimetric decompositions able to describe the scatteringproperties of the targets present in a SAR image. In the literature, two main classes of polarimetric decompositionscan be identified: the coherent decompositions, which deal with the expression of the scattering matrix as a superim-position of elementary scattering matrices, and incoherent decomposition, mainly used for identification of distributedscatterers, for which knowledge of the second order moments is required.A fundamental coherent decomposition is based on the Pauli spin matrix group. The Pauli decomposition expressesthe scattering matrix S , in the monostatic case, as the linear combination of three matrices from the classical unitaryPauli matrices group.

S =

[S HH S HV

S VH S VV

]= a[1 00 1

]+ b[1 00 −1

]+ c[0 11 0

](4)

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where a,b,c are complex and equal to:

a = S HH + S VV b = S HH − S VV c = S HV (5)

The resulting components can be associated to elementary scattering mechanisms: single or odd bounce scattering,double or even bounce scattering and diffuse/asymmetric scattering. In this case the elementary scattering matricesare mutually orthogonal, but alternatives in which the elementary matrices are not expressions of specific targetcharacteristics have been proposed [24].Decompositions of the complex scattering matrix are particularly suited for coherent processing and cases where thescattering is due to a few dominating scattering centers. When the resolution cell is bigger than the wavelength,in natural terrain surfaces there will be many spatially distributed scattering centers. In this second case, severalincoherent decompositions have been developed, based on the analysis of the covariance and coherency matrices.Although these two matrices express the polarimetric information in a form that is closer to system measurables(covariance) or target responses (coherency), they are mutually related. Different approaches have been proposed forthis class of decomposition. The most important and diffused ones are the eigenvalues/eigenvectors analysis of thecoherency matrix proposed by Cloude [25] and the model based approach developed by Freeman and Durden [26]and improved by Yamaguchi [27]. In the latter case, the covariance matrix is expressed as a sum of contributionsfrom three scattering mechanisms: canopy scatter from a cloud of randomly oriented dipoles (volume scattering PV ),even-bounce or double-bounce scattering from pairs of orthogonal surfaces with different dielectric constants (P2B),and Bragg scattering from a moderately rough surface (odd bounce or surface scattering PS ). The total power fromeach resolution pixel can be expressed as the sum of these three contributions:

PTOT = PS + P2B + PV (6)

This approach is based on the physics of radar scattering and can be used to derive the dominant scattering mech-anisms, although the reflection symmetry property does not hold sometimes, leading to wrong interpretations. Toovercome the symmetry problem found in Freeman/Durden Decomposition, Yamaguchi added helix scattering power(PH) as the fourth component of the decomposition. It was shown that an helix scatterer returns a circular polarizationstate for every incident linear polarization. It is relevant for describing man-made targets in urban area scattering. Thereceived power is decomposed as:

PTOT = PS + P2B + PV + PH (7)

As can be noted, all of these methods are based on the decomposition of the received signal into three main com-ponents, representing different scattering mechanisms, except for the Yamaguchi method, that introduces a fourthelement. However, even if three or four components could be sufficient to characterize the different scattering re-sponses in each resolution cell, they are sometimes not able to represent all the scattering mechanisms characterizingdifferent targets in the scene. For instance, all the presented methods are able to extract a component that can berelated to the double bounce mechanism. In all the methods the double bounce component presents good responseson those targets that are facing directly the sensor. On the other hand, targets having different orientations, even if theycan produce a double bounce response having a lower intensity, are not completely detected by the classical methods.This effect is particularly clear on Fig. 2, where the Sinclair RGB composition (R=HH, G=HV and B=VV) obtainedfrom a RADARSAT-2 full polarimetric image acquired over the San Francisco area is depicted. In particular, it can benoted that almost all the buildings are oriented facing the sensor except for the business district, where the buildingshave a different orientation. In both areas, however, double bounce should be the dominant effect, but as it can beseen none of the presented components was able to detect it on the business district, leading to an incorrect result. Inparticular, for both methods, the business district presents the same response as the forest area on the left part of theimage. In order to resolve this oblique urban problem, methods based on the rotation of the coherency matrix, therotation angle, and the decomposition scheme using the rotated coherency matrix have been proposed in the literature[28][29][30].As the frequency increase and consequently the resolution cell becomes smaller, the incoherent part of the scatteringproduced by different targets tends to become dominant. This effect results in an increase of the volume scatteringmechanisms, that while in low frequencies is produced mainly by vegetation, at higher frequency tends to be producedby most of the targets present in the scene. From this point of view, the physical based approaches tend to loose their

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validity and are no more reliable to effectively separate the different scattering mechanisms in the image. To dealwith this problem it is possible to look at it from another point of view. In particular it is possible to consider thereceived signal as a mixture of several principal scattering mechanisms. In this way the polarimetric decompositioncan be considered as a Blind Source Separation problem. Different approaches have been proposed in the literatureto decompose the received signal based on linear transformations, such as Principal Component Analysis (PCA), In-dependent Component Analysis (ICA) or Non-negative Matrix Factorization (NMF). The application of PCA in thedomain of polarimetric SAR images has been investigated in the literature thanks to its ability to decorrelate signals[31][32][33]. Blind source separation by ICA has received attention because of its potential applications in variousdomains. What distinguishes ICA from other methods is that it looks for components that are both statistically inde-pendent and non-Gaussian by using some form of higher-order statistics, which means information not contained inthe covariance matrix [34][35][36][37]. In [38], the use of the NMF has been proposed for the fusion of POLSARimages. However, being based on linear transformations, these methods are not able to properly manage SAR data,where the noise is not only additive but also multiplicative. From this point of view, nonlinear based methods, such asNLPCA are able to overcome the limitations of linear approaches.

3. Nonlinear Principal Component Analysis

Trying to overcome the limitations introduced by the approximations in the definition of the traditional physical-based methods, in this paper, we propose a novel polarimetric decomposition approach based on the nonlinear-decorrelation of the received signals. In particular, we propose the use of nonlinear principal component analysis(NLPCA), commonly referred to as nonlinear generalization of standard principal component analysis. NLPCA isbased on Autoassociative Neural Networks (AANN) or as auto-encoder networks [39][40].

3.1. Autoassociative Neural NetworkAn AANN is a conventional multi-layer perceptrons (MLP) feedforward neural network, having nonlinear activa-

tion functions in each node, among which the Logistic function is the most popular:

σ(x) =1

1 + e−x (8)

where σ(x)→ 1 as x→ +∞ and σ(x)→ 0 as x→ −∞.The training of AANN is performed by backpropagation or similar algorithms. In particular, in this work we choosea training approach based on the Standard Conjugated Gradient SCG [41].The peculiarity of an AANN relies on a symmetrical network architecture, where the number of nodes in the inputlayer coincide with the number of nodes in the output layer. Differently from the standard NN topology, a nonlinearAANN sees the use of three hidden layers, including an internal bottleneck layer of smaller dimension than eitherinput or output. In particular, the AANN is trained to perform identity mapping (the input X has to be equal to theoutput Y), in order to minimize the sum-of-squares error of the form:

MS E =12

N∑n=1

d∑k=1

{yk(xn) − xn

k

}2(9)

Where X = {x1, x2, ..., xk} and Y = {y1, y2, ..., yk} are the input and output vectors, respectively. This means that if thetraining phase finds an acceptable solution, i.e., a solution that gives an error below a predefined threshold, a goodcompressed representation of the input must exist in the bottleneck layer. The presence of two more hidden layersforces the bottleneck layer to represent significant features in the data.The AANN can be viewed as two successive functional mappings. The first part represents the encoding, or extractionfunction:

T = F(X) (10)

that projects the original k-dimensional data X onto a feature space defined by the activations of the units in the centralhidden layer (bottleneck). In a similar way, the second half of the network defines an arbitrary functional mapping:

Y = G(T ) (11)5


that projects from the feature space back into the original k-dimensional space (Fig. 3). If we consider the two sub-networks separately, for the subnetwork representing F, we know the input X while the desired output T is unknown.On the other hand, for the network representing G, the desired output Y is known, while the input T is not. From thispoint of view, a supervised training of these networks is not possible since input or output are unknown. However, itis possible to observe that T is at the same time output of F and input of G.

Y = G(F(X)) (12)

This allows us to combine the two networks so that the NN performing F feeds directly the NN performing G, asdepicted in Fig. 4. In this case both input and output of the combined NN are known and a supervised training to learnidentity mapping is now possible [42].It is important to note that in order to perform an effective nonlinear decomposition, an AANN requires exactlythree hidden layers. This can be easily understood considering AANN as a combination of two NNs performing twononlinear functions F and G. The ability of each of these NNs to fit arbitrarily nonlinear functions depends on thepresence of a hidden layer with nonlinear nodes between input and output. Without the hidden layer the network isonly capable of producing linear combinations of the inputs, given linear nodes in the output layer. A network lackinga hidden layer but including sigmoidal nonlinearities in the output layer is only capable of generating multivariablesigmoidal functions, i.e., linear functions compressed into the range (0, 1) by the nonlinear activation function. Forthese reasons, in order to be nonlinear, each individual function requires one hidden layer with nonlinear activationfunctions. In fact, if we consider an AANN where the mapping and demapping layers have been eliminated, we willhave a combined network with only one hidden layer. If the nodes in the hidden layer are linear, this would correspondexactly to the linear PCA. Even if we use nonlinear activation functions in the hidden layer we will have only linearcombinations of the inputs compressed by the sigmoid into the range (0, 1) [43]. This leads to the conclusion thatthree hidden layers are necessary in order to obtain an optimal nonlinear feature extraction.It has to be noted that, as the output has to simply replicate the input, no independent target data are provided, andthere is no need to have an a priori knowledge for the implementation of the learning phase. This implies that theAANN training can be performed in a fully automatic way and that all pixels in the image can be considered for thistask, which actually is the technique adopted in this paper.

3.2. AANN tuning

One of the main difficulties in designing the AANN is the selection of the number of nodes in the three hiddenlayers and, in particular, in the bottleneck layer that minimizes the loss of information of the entire network. Usually,this problem can be solved by using a simple grid-search algorithm that varies recursively the number of nodes ofthe hidden layers and evaluates the respective MSE. The NN presenting the lowest error is then selected. However,we observed the existence of strong correlations among different NLPCs when a too high number of nodes wasused. This means that, since the scope of this work is to find nonlinear principal components that should representbasic scattering mechanisms, a grid search algorithm based on the training error can be useful only to determine thedimension of the coding and decoding layers. To solve this problem, before detecting the best dimension for thecoding/decoding layers, it is possible to perform a further grid-search algorithm, that iteratively varies the number ofnodes in the bottleneck layer and evaluates the correlation between NLPCs.However, without a starting point, this approach can be extremely time consuming and a different solution should befound. Analyzing the structure of the AANN, it can be found that the number of adjustable parameters in this kind ofnetworks is:

(M1 + M2)(m + f + 1) + m + f (13)

where M1 and M2 are the numbers of nodes in the mapping and demapping layers, respectively, m and f are thenumber of nodes of the input/output layers and in the bottleneck layer, respectively. Eq. 13 implies the followinginequality:

M1 + M2 � m(n − f )

(m + f + 1)(14)

where n is the number of training samples. Eq. 14 greatly reduces the number of different AANN configurations tobe tested. In a POLSAR image, the number of basic scattering mechanisms that can be effectively detected can be

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considered as much lower than the number of training pixels:

f � n (15)

Once determined the number of nodes in bottleneck layer f , Eq. 14 leads to:

M1 + M2 � n (16)

Assuming a balanced structure of the AANN, M1 and M2 should have the same dimensions (M1 = M2 = M), and Eq.16 can be simplified as:

2M � n (17)

Eq. 17 is effective only if the number of mapping/demapping nodes M is greater then the number of nodes in thebottleneck layer f , otherwise there will not be enough data to effectively extract f nonlinear components.In the literature, the use of NLPCA has been proposed as an effective decorrelation method to extract intrinsic informa-tion from different types of data, such as ozone profiles measurements [44], and hyperspectral imagery [45][46][22].The advantage of NLPCA over other linear approaches lies in the two following main features:

• while linear approaches such as PCA ICA or MNF [47][16][48], are based on linear correlations among inputbands, NLPCA permits to detect both linear and nonlinear correlations. This allows the NLPCA to representintrinsic information content in fewer components than linear approaches;

• Differently from other decorrelation approaches, NLPCA projects the data into a fixed-dimension feature space,and the relative components are not ranked in terms of decreasing variance or increasing noise [49].

In addition to these general features, the use of nonlinear approaches applied to SAR images is preferable among targetdecomposition approaches also because of the multiplicative nature of noise in SAR images[50]. For this reason wepropose to decorrelate the POLSAR signal by means of NLPCA in order to extract the most relevant polarimetriccharacteristics of the different targets in the scene.

3.3. NLPCA-based decompositionThe main idea of this paper is to project the POLSAR image into a feature space that better highlights the different

scattering mechanisms that characterize the targets in the image. Entering in more details, we can define the inputdataset X as composed by m features (HH, HV, VV polarizations and the two phases’ differences VV-HH and HV-HH). The function F projects the input dataset X into the nonlinear feature space. The first step of the approach is todetect the number of nodes f , in the bottleneck layer, that are necessary to project the input dataset X into the featurespace. This can be achieved by setting the number of nodes in the coding/decoding layers to an arbitrary value (higherthan the number of input/output nodes) and the number of nodes in the bottleneck layer to be equal to the nodesin the input/output layers. All the pixels in the dataset are then used to train the AANN. After training the AANN,the correlation between components is performed and if one or more components present high correlation with othercomponents, the number of nodes in the bottleneck layer is reduced by one and another training is performed. Thisprocedure is repeated iteratively until no correlation is present between the different components. In a similar way itis possible to perform a grid-search algorithm in order to find the number of nodes M1 = M2, in the coding/decodinglayers, that minimizes the MS E in eq. 9. Once the best topology for the AANN is determined. Eq. 10 is thenexploited to obtain the set of f NLPCs called NLPC = [nlpc1, . . . ,nlpc f ].The complete processing for the selection of the best AANN topology is resumed in Algorithm 1.

4. Experiments

To evaluate the effectiveness of the proposed method to decompose the received signal and enhance the infor-mation related to the different scattering mechanisms, we used three images acquired over the same location withdifferent frequencies and spatial resolutions. In particular, we used images acquired over the San Francisco area in L-band by ALOS-PalSAR, in C-band by RADARSAT-2 and in X-band by TERRASAR-X, respectively. In general, thesame approach has been followed in each experiment. For each image a different AANN has been trained according

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Algorithm 1 NLPCA-based decompositionNLPC = F(X)

- Set the initial parameters M = M1 = M2 >m and q = f = m.f lag = 0while f lag = 0 do

- Train the AANN using M1 = M2 = M and f = q.- Use eq. (10) to get NLPC = [nlpc1, . . . ,nlpc f ].- Compute the correlation ρ between nlpci and nlpcj to get ρi j = ρ(nlpci,nlpc j) with i , j ∈ f .if ρi j ≥ θ then

q = q − 1else

f lag = 1.end if

end while- Set the lowest error MS E0 to a starting value (i.e. MS E0 = 100).for M = 1→ m do

- Train the AANN using M1 = M2 =M and f = q.- Use eq. (9) to get Mean Square Error MS E.- Determine if the present MS E is lower than MS E0.if MS E ≤ MS E0 then

MS E0 = MS E.M1 = M2 = M.

end ifend for- Train the AANN using M1 = M2 and f = q.- Use eq. (10) to get f NLPC = [nlpc1, . . . ,nlpc f ].

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to Algorithm 1. The extracted NLPCs have been then qualitatively evaluated by comparison with the most populardecomposition methods. Typically, the activation level of each nodes in the bottleneck layer lies on a scale from 0to 1 which represents the variation from extremely low to extremely high strength of membership to the associatedcomponent of each investigated pixel. However, since the output of the bottleneck layer is distinctly non-linear, adirect quantitative comparison with other approaches wouldn’t be reliable. For this reason, in order to demonstratethat the NLPCA is able to highlight the most relevant scattering mechanisms in the image, we performed a compari-son in terms of accuracies of land-cover classification of the results obtained with the proposed method and the mostpopular physical based decomposition techniques. In particular, the classification is carried out by means of a SupportVector Machine (SVM) algorithm. Since the three images have been acquired over the same area, and in order to havean inter-experiment comparison, the same land cover classes have been selected for the whole experiments [51]. Inparticular, based on the different scattering mechanisms that can characterize different land cover types, four classeswere selected: buildings (high multiple bounce scattering), trees and forests (high volume scattering), low vegetationsurfaces (medium volume and surface scatterings) and water surfaces (surface scattering). The ground truth has beenobtained by visual inspections, and the selected samples have been divided into three datasets (training, test and val-idation sets, respectively). The classification of SAR images has been always influenced by the speckle noise [52].Table 1 reports the average speckle noise associate to each image expressed as Equivalent Number of Looks (ENL)defined as the square of the mean pixel intensity divided by the variance of a uniform region. For sake of comparisonfor each image the ENL has been evaluated over the same area.

Table 1. Characteristics of the three images used

Band Central Frequency Cell resolution ENLHH HV VV

ALOS L band 1270MHz 24 to 89m 0.4533 0.4950 0.3662RADARSAT-2 C-band 5,405GHz 24x28m 0.7212 0.4115 1.1662TerraSAR-X X-band 9,65GHz 10m 2.665 4.2464 2.2311

4.1. ALOS PalSAR datasetOn a first experiment, the proposed method has been applied to a full polarization ALOS PALSAR image ac-

quired in 2009 over the San Francisco area. The PALSAR sensor operates in L-band, and in different polarimetricconfigurations. In particular the selected image was acquired in Quad-Pol mode, meaning that HH, HV, VV and VHpolarizations compose the dataset. The image has been radiometrically calibrated and terrain corrected, resulting ina pixel spatial resolution of about 24m. The scene presents urban areas with both high and low densities, sparsevegetation and water surfaces. According to Algorithm 1, the input dataset was composed by HH, VV, HV and thephases’ differences VV-HH and HV-HH. A preprocessing phase in which the image has been normalized in order toobtain zero mean and unitary variance has been carried out. This procedure is necessary to avoid that most of thedata could fall in the tails of the Logistic function. After the grid search phase five different NLPCs have been found,and the complete topology for the AANN that minimizes the MSE has been found to be 5-8-5-8-5. In Fig. 6, the 5obtained NLPCs are reported. In order to detect the scattering mechanisms associated to each NLPCs, an analysisof the responses over some well known reference targets has been carried out. In particular, Fig. 6 also highlights adense urban area, a forest and the airport runways used as references for the volumes, surface and multiple scatteringmechanisms, respectively. On an immediate analysis it can be noted that components 1 and 3 can be both associatedto multiple scattering mechanisms, but while component 1 presents the highest values only over the dense urban area,component 3 has high values also over other areas than water surfaces. This permits to associate component 1 to evenmultiple bounces effects, while component 3 corresponds to odd multiple bounces. Component 5 presents high valuesonly over flat surfaces, allowing us to associate this component with surface scattering. On the contrary, component 2presents the lowest values over the areas characterized by forests. In this case component 2 tends to be associated tothe inverse of volume scattering. Finally, component 4 does not seem to be associated to any basic scattering mecha-nism, but on a deeper analysis, it could be associated to Bragg scattering mechanisms.

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Fig. 7 shows the RGB images, obtained combining the volume, surface and multiple scattering bands obtained withthe Pauli, Freeman and H/A/α techniques and the components 1, 2 and 5 obtained from the NLPCA approach. It isinteresting to highlight that differently from physical based approaches, NLPCA method is able to quantify the con-tribution of the basic elements associated to the different components, based only on the decorrelation of the receivedsignal. This is particularly visible in Fig. 8, where, while physical based methods are only able to detect high scatter-ing values for the mechanisms associated to objects that are oriented perpendicularly to the sensor (double bounces),component 1, presents good performances also on those buildings that are not perfectly facing the sensor.Being the NLPCA the nonlinear characterization of the classical PCA, it would be interesting to analyze the decom-position obtained through the most used linear decorrelation methods. Fig. 9 reports the first 3 components obtainedprojecting the input dataset into the feature space by means of PCA, MNF and ICA, and the components 1, 2 and5 obtained from the NLPCA approach, respectively. As expected the three linear methods, except for the first PC,presents components that are influenced by noise and not as well defined as the NLPCs.A quantitative comparison of the proposed method with the physical based ones is not possible due to the nonlinearrepresentation of the information in the NLPCs. For this reason, in order to quantify the effectiveness of the NLPCAmethod a further assessment has been exploited in terms of classification accuracy. In particular, the classificationwas performed by means of a Support Vector Machines (SVM) algorithm based on the Libsvm Matlab code 1 [53].The SVM has been trained using a Radial Basis Function (RBF) kernel type while Cost and Gamma parameters havebeen optimized by a grid search routine. The search was composed by many iterations each with a finer step size.According to the different scattering mechanisms that can be effectively detected, the classification has been based onabout 200.000 samples representing four land cover classes: water, buildings, low vegetation and trees.Table 2 reports the classification results in terms of overall accuracy (OA) and per class accuracies, while Fig. 10reports the classification maps obtained with the different methods. On a qualitative inspection of the classificationmaps, NLPCA and Freeman approaches obtain similar results, while the other two methods were not able to correctlyclassify wide areas of water and buildings. This is also confirmed by analyzing the overall accuracies inTable 2. On amore accurate analysis, the main differences in the four classification can be found in three main areas characterizedby low density urban area, high density urban area with buildings not perfectly facing the sensor and very calm watersurfaces, respectively. These three areas are composed by mixed pixels characterized by different scattering mecha-nisms. For instance, in the low density urban areas, the pixels are characterized by a mixture of multiple bounce andvolume scattering mechanisms, while in high density urban areas, the multiple bounce mechanism is dominant. Thesemixed pixels have been correctly classified by Freeman and NLPCA approaches, while H/A/α and Pauli failed.

Table 2. Producer accuracies for the classifications of the ALOS image obtained with an SVM applied to the different decompositions

Class H/A/α Freeman Pauli NLPCAWater (%) 85.42 86.44 88.53 90.5173316 pixels (62630) (63374) (64905) (69724)Buildings (%) 45.74 65.43 49.84 89.0738720 pixels (17709) (25336) (19298) (34488)Low vegetation (%) 29.44 61.15 69.53 46.744466 pixels (1315) (2731) (3105) (2087)Trees (%) 89.87 90.28 64.26 62.0720246 pixels (19431) (18279) (13011) (12567)Overall Accuracy (%) 73.92 80.23 73.36 86.98136748 pixels (101085) (109720) (100319) (118866)

4.2. Radarsat-2 datasetOn a second experiment, we evaluated the proposed technique on a Radarsat-2 image acquired in Fine Quad

Polarization, meaning that the dataset was composed by HH, VV, VH and HV polarizations in C-band. The date of

1www.csie.ntu.edu.tw/cjlin/libsvm/

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acquisition was 9 april 2008. The dataset has been calibrated, and geo-referenced, resulting in a final image havinga pixel size of about 10 m. The area covered by the image is the same as in the previous experiment, so that wecan assume the same reference targets. However, being the data acquired at a higher frequency than in the previousexperiment, incoherent scattering mechanisms tend to be produced not only by depolarizing targets usually associatedwith volume scattering, but also by other types of targets. Similarly to the first experiment, a grid search algorithmhas been exploited in order to detect the AANN topology, and the best configuration has been found to be 5-8-5-8-5,meaning that 5 different NLPCs have been detected. It is important to highlight how the topology of this AANNcoincide with the topology found in the previous experiment. This suggests that the NLPCA handled in the same waythe information retained by the two datasets.Analyzing the five NLPCs in Fig. 11, it can be seen that components 3 and 4 (Fig. 11-c and 11-d) clearly retaininformation about even multiple scattering and surface scattering mechanisms, respectively. Components 1, on theother hand, can be associated to the volume scattering. Component 2 (Fig. 11-b) presents characteristics that letus associate it to second order multiple scattering mechanisms. Finally, as for component 5 (Fig. 11-e), presentingthe higher values over the forest areas, it is possible to associate it to volume scattering mechanisms produced byvegetated surfaces with random highly anisotropic scattering elements.A further assessment can be carried out by comparing the obtained results with other approaches. In particular,in Fig.12 are reported RGB composites obtained using Freeman, Pauli, H/A/α and NLPCA approaches. From thesepictures it can be noted that the NLPCA approach is able to separate the different scattering contribution in the originaldata, and represents them in a more clear way. Another important feature is that differently from the physical basedtechniques, the proposed approach does not present great differences in the multiple scattering components betweenbuildings having different orientations.Following the same approach as in the previous experiments, the quantitative assessment is performed by classifyingthe 5 NLPCs obtained from the proposed method. The obtained results have been compared to those obtained by theclassification of the Freeman, Pauli and H/A/α decompositions. Over 100.000 samples have been accurately chosento build up a ground truth from which training, test and validation sets have been used to train the SVM and to validatethe accuracy. As for the previous experiment four land cover classes have been selected (water surfaces, buildings,low vegetation and trees).In Table 3 the values for overall and per class accuracies are reported for the four approaches, while in Fig. 13the classification maps are depicted. Based on visual inspection of the classification maps and on the quantitativeanalysis of the classification accuracies, the best results have been obtained by the H/A/α and NLPCA methods.On a more detailed analysis, it can be noted that incoherent scattering effects, mainly generated by targets that arenot associable to volume scattering, influenced negatively the classifications. This is particularly evident on theclassification maps of Pauli and Freeman decompositions, where the waves on the sea surface due to the wind producescattering responses that are more associable to the volume scattering than to the surface one. Another interestinganalysis regards the classification of buildings in low density urban areas. In particular, the classification of theNLPCA permitted to correctly identify the alternation of vegetation and buildings, while the classifications of thephysical based decompositions in most cases were not able to identify the buildings.

4.3. TerraSAR-X datasetA third and final experiment has been carried out by decomposing a PolSAR image acquired in X-band. In

particular, in this experiment we considered a TerraSAR-X image acquired in full polarization mode over the city ofSan Francisco. In this case the PolSAR image is particularly challenging due to the very high spatial resolution. Inparticular, almost all objects in the scene act in part as a depolarizing targets, resulting in a diffuse noise associable tovolume scattering along the entire image, as it can be also noted in Fig. 14.Following the processing steps described in the previous section, two grid-search algorithms have been exploited inorder to detect the best AANN topology, resulting to be 5-6-4-6-5. On a visual analysis of the NLPCs depicted in Fig.15 it is possible to note that component 1 presents information that can be associated to multiple scattering scatteringmechanisms, while component 2 can be associate to surface scattering due to the presence of very high values oververy flat areas. On the other hand, component 3 presents characteristics that let us associate it to second order multiplescattering mechanisms. Finally, component 4 can be associated to volume scattering. On a comparison with theprevious experiment, it can be noted that only four components have been detected. In this case second order volumescattering, that can be associated to depolarizing targets, has not been detected by the NLPCA. This can be explained

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Table 3. Producer accuracies for the classifications of the RS-2 image obtained with an SVM applied to the different decompositions


by considering that this kind of scattering mechanism acts as a noise and is not identified by the NLPCA as a basicscattering signal.Fig. 16 presents a comparison of the NLPCA method with the physical-based approaches. Also in this case, theproposed approach does not present great differences in the multiple scattering component between buildings havingdifferent orientations. Moreover, on a comparison with the decomposition obtained with the RS-2 dataset (Fig. 12) itcan be noted that, while physical based approaches change their information content with the frequency, the NLPCAapproach presents similar characteristics in both images.A quantitative assessment of the proposed method is performed by classifying the 4 NLPCs and the three physicalbased decomposition by means of a SVM algorithm. More than 200.000 samples have been chosen to build up aground truth representing the same four land cover classes of the previous experiments. Table 4 and Fig. 17 reportthe classification accuracies and the classification maps, respectively. In this case the NLPCA approach obtain thebest overall accuracy, while Freeman and H/A/α obtain also good results but with lower accuracies. In particular,for the three physical-based approaches, part of the negative result is greatly influenced by the misclassification ofthe water surfaces, that have been confused with vegetation or trees. Moreover, while the classification of Freemanand H/A/α decompositions present results that are similar to the classification of the NLPCA, the classification of thePauli decomposition was not able to detect most of the buildings present in the scene.

Table 4. Producer accuracies for the classifications of the RS-2 image obtained with an SVM applied to the different decompositions


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5. Conclusions

In this paper we have presented a novel approach based on the use of Nonlinear Principal Component Analysisfor the decomposition of the different scattering mechanisms. Differently from classical physical-based target decom-position techniques, the proposed method is based on the decorrelation of the received polarimetric SAR signal. Inparticular, the received signal is considered as a mixture of different basic scattering signals. The use of the NLPCApermits to separate these contributions in order to exploit the PolSAR images in a more interpretable way.The proposed method has been tested on three different full polarization SAR images acquired in C, L and X-bands.From a qualitative point of view, the obtained results allowed us to affirm that the NLPCA based method effectivelydecorrelates the information carried out by a SAR image, producing nonlinear principal components that can be effec-tively associated to the different scattering mechanisms present in the images. Another important result that emergedfrom the experimental analysis is that the proposed method is able to decorrelate the full polarimetric signal into 5main scattering mechanisms independently from the used frequency.A quantitative analysis was carried out by comparing the classification results obtained using the NLPCA and threemodel based approaches, namely Pauli, Freeman and H/A/α. In particular, the classification was performed by meansof a SVM classifier based on four land cover classes exploiting different scattering mechanisms. The obtained re-sults allow us to affirm that the NLPCA approach could be an effective alternative to the most popular decompositionmethods.

6. Acknowledgement

RADARSAT-2 dataset were provided within the Science and Operational Application Research for RADARSAT-2program SOAR Project 1488 and SOAR-EU Project 6795 2.TerraSAR-X (TS-X) Dual Receive Antenna (DRA) quad-pol data are provided by DLR through the AO proposal LAN1390.

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Figure 1. Basic scattering mechanisms in radar remote sensing representing 1) backscattering from a rough surface; 2) low-ordermultiple scattering; 3) single scattering from anisotropic structures; 4) surface scattering after propagation through a randommedium; 5) random volume backscatter from a non-penetrable layer of discrete scatterers.

Figure 2. Original RGB image of the area of San Francisco (left) and a false color image obtained using VV, HH and VH for the R,G and B channels, respectively (right).

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Figure 3. Networks implementing mapping (left) and demapping functions (right)..

Figure 4. Auto-associative neural networks scheme used for feature reduction.

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Figure 5. AANN subnet performing the encode function.

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Figure 6. a) RGB composite obtained using VV, HH and HV for R, G and B channels of the ALOS Palsar image, respectively and the5 components obtained using NLPCA transformation. The red, green and yellow circles indicate airport runways, a dense urbanarea and a forest, respectively, where the surface, multiple scattering and volume mechanisms are dominant.

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Figure 7. ALOS dataset (From left to right): RGB images obtained combining multiple scattering, volume and surface componentsderived from Pauli, Freeman and H/A/α decompositions, respectively, and using components 1, 3 and 4 of the NLPCA.

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Figure 8. ALOS dataset: Highlight over a dense urban area presenting buildings with different angles with respect to the sensor.

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Figure 9. ALOS dataset: Comparison of the five components obtained by transforming amplitude and phases inputs with PCA, MNFand ICA.

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Figure 10. ALOS dataset: Classification maps obtained with the SVM classifier applied to the Pauli, Freeman and H/A/α decompo-sitions and the 5 NLPCs. Color code is as follows: red=buildings; green=low vegetation; sea green=trees and forests; blue=watersurfaces

Figure 11. RS-2 dataset: The five nonlinear components extracted using the NLPCA approach.

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Figure 12. RS-2 dataset (from left to right): RGB images obtained combining HH, HV and VV amplitudes of the original dataset,multiple scattering, volume and surface components derived from Pauli, Freeman and H/A/α decompositions, respectively, andusing components 3, 1 and 4 of the NLPCA.

Figure 13. RS-2 dataset: Classification maps obtained with the SVM classifier applied to the Pauli, Freeman and H/A/α decomposi-tions and the 5 NLPCs. Color code is as follows: red=buildings; green=low vegetation; sea green=trees and forests; blue=watersurfaces

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Figure 14. TerraSAR-X dataset: RGB image obtained combining HH, HV and VV amplitudes of the original dataset.

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Figure 15. TerraSAR-X dataset: The four nonlinear components extracted using the NLPCA approach.

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Figure 16. TerraSAR-X dataset (from left to right): RGB images obtained combining HH, HV and VV amplitudes of the originaldataset, multiple scattering, volume and surface components derived from H/A/α Pauli and Freeman decompositions, respectively,and using components 3, 1 and 2 of the NLPCA.

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Figure 17. TerraSAR-X dataset: Classification maps obtained with the SVM classifier applied to the Pauli, Freeman and H/A/αdecompositions and the 4 NLPCs. Color code is as follows: red=buildings; green=low vegetation; sea green=trees and forests;blue=water surfaces

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