POLARIMETRIC INTERFEROMETRIC SAR DATA ANALYSIS … · POLARIMETRIC INTERFEROMETRIC SAR DATA...

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POLARIMETRIC INTERFEROMETRIC SAR DATA ANALYSIS BASED ON ESPRIT/MUSIC METHODS Stéphane Guillaso (1) , Laurent Ferro-Famil (1) , Andreas Reigber (2) , and Eric Pottier (1) (1) IETR (Institute of Electronic and Telecommunication of Rennes), UMR CNRS 6164, “Radar Imaging, Remote Sensing and Polarimetric Team”, Campus de Beaulieu, Bat 11C, 263 Av. du Général Leclerc, CS 74205, F – 35042 Rennex Cedex, France. Email: [email protected], [email protected], [email protected] (2) Technical University of Berlin, Photogrammetry and Cartography Strasse des 17. Juni 135, EB9 D – 10623 Berlin, Germany Email: [email protected] ABSTRACT/RESUME This paper presents a polarimetric interferometric SAR data analysis based on high-resolution methods such as ES- PRIT. The ESPRIT algorithm is used in order to separate and to retrieve the interferometric phase centre of local domi- nant scatterer. In a second part, an extension of the ESPRIT algorithm is presented that allows to retrieve the polarisa- tion information retrieval. 1 INTRODUCTION Interferometric SAR provides a two-dimensional image of elevation angles related to the scatterer height. By construc- tion, SAR imaging is a projection of a volume response onto a plane. The retrieval of the scatterer height assumes that only one scattering mechanism occurs in each resolution cell. This assumption is invalid in the sense that multiple scat- terers, with distinct elevation angles, arise in a single resolution cell. This effect introduces artefacts during the projec- tion under the form of a phase centre bias. To improve the interferometric phase estimation over man-made or volumet- ric targets, it is thus necessary to discriminate the different scattering mechanisms arising. Recently, many approaches have been proposed to estimate the interferometric phase over forested areas using po- larimetric data [1], [2]. One of them is based on the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithm, often employed for Direction-Of-Arrival estimation using antenna arrays [2]. For volumetric targets, this algorithm can directly retrieve the interferometric phase of the ground and the canopy. For man-made tar- gets the interferometric phase estimation becomes complex due to the varying nature of highly spatially concentrated targets like buildings, houses, vegetated areas and infrastructures (roads, bridges…). This paper addresses a polarimetric interferometric SAR data analysis based on ESPRIT/MUSIC algorithm, using inter- ferometric fully polarimetric SAR images. In the first part, interferometric phase centres of scatterers (over forested or man-made areas) are separated and estimated using an interferometric signal model adapted to the ESPRIT algorithm. In the second part, the estimation of the polarisation states of one dominant scatterer is introduced. In a third part, the efficiency of this polarimetric interferometric SAR data analysis is demonstrated using fully polarimetric SAR images, obtained from DLR-ESAR airborne sensor in L-band repeat-pass mode. 2 PHASE ESTIMATION SAR backscattered waves results from the sum of different contributions corresponding to different scattering mecha- nisms. Depending on the nature of the observed medium, the value of the resulting interferometric phase may varying in

Transcript of POLARIMETRIC INTERFEROMETRIC SAR DATA ANALYSIS … · POLARIMETRIC INTERFEROMETRIC SAR DATA...

POLARIMETRIC INTERFEROMETRIC SAR DATA ANALYSIS BASED ONESPRIT/MUSIC METHODS

Stéphane Guillaso(1), Laurent Ferro-Famil(1), Andreas Reigber(2), and Eric Pottier(1)

(1) IETR (Institute of Electronic and Telecommunication of Rennes), UMR CNRS 6164, “Radar Imaging, Remote Sensing and Polarimetric Team”,

Campus de Beaulieu, Bat 11C, 263 Av. du Général Leclerc, CS 74205, F – 35042 Rennex Cedex, France.Email: [email protected], [email protected], [email protected]

(2) Technical University of Berlin, Photogrammetry and CartographyStrasse des 17. Juni 135, EB9 D – 10623 Berlin, Germany

Email: [email protected]

ABSTRACT/RESUME

This paper presents a polarimetric interferometric SAR data analysis based on high-resolution methods such as ES-

PRIT. The ESPRIT algorithm is used in order to separate and to retrieve the interferometric phase centre of local domi-

nant scatterer. In a second part, an extension of the ESPRIT algorithm is presented that allows to retrieve the polarisa-

tion information retrieval.

1 INTRODUCTION

Interferometric SAR provides a two-dimensional image of elevation angles related to the scatterer height. By construc-

tion, SAR imaging is a projection of a volume response onto a plane. The retrieval of the scatterer height assumes that

only one scattering mechanism occurs in each resolution cell. This assumption is invalid in the sense that multiple scat-

terers, with distinct elevation angles, arise in a single resolution cell. This effect introduces artefacts during the projec-

tion under the form of a phase centre bias. To improve the interferometric phase estimation over man-made or volumet-

ric targets, it is thus necessary to discriminate the different scattering mechanisms arising.

Recently, many approaches have been proposed to estimate the interferometric phase over forested areas using po-

larimetric data [1], [2]. One of them is based on the ESPRIT (Estimation of Signal Parameters via Rotational Invariance

Techniques) algorithm, often employed for Direction-Of-Arrival estimation using antenna arrays [2]. For volumetric

targets, this algorithm can directly retrieve the interferometric phase of the ground and the canopy. For man-made tar-

gets the interferometric phase estimation becomes complex due to the varying nature of highly spatially concentrated

targets like buildings, houses, vegetated areas and infrastructures (roads, bridges…).

This paper addresses a polarimetric interferometric SAR data analysis based on ESPRIT/MUSIC algorithm, using inter-

ferometric fully polarimetric SAR images. In the first part, interferometric phase centres of scatterers (over forested or

man-made areas) are separated and estimated using an interferometric signal model adapted to the ESPRIT algorithm.

In the second part, the estimation of the polarisation states of one dominant scatterer is introduced. In a third part, the

efficiency of this polarimetric interferometric SAR data analysis is demonstrated using fully polarimetric SAR images,

obtained from DLR-ESAR airborne sensor in L-band repeat-pass mode.

2 PHASE ESTIMATION

SAR backscattered waves results from the sum of different contributions corresponding to different scattering mecha-

nisms. Depending on the nature of the observed medium, the value of the resulting interferometric phase may varying in

a significant way. The use of the ESPRIT technique permits to separate the different scattering mechanisms and to esti-

mate the main interferometric phase.

2.1 Interferometric signal model

The signals acquired during an interferometric measurement, S1 and S2, may be written as:

s1pq = s mz m

pq ⋅ ei 4 p

lR

m=1

d

 + n1pq and

s2pq = ¢ s m ¢ z m

pq ⋅ ei 4 p

lR+DRm( )

m=1

d

 + n2pq (1)

where pq denotes the polarisation channels (HH, HV, VV, VH). They consist into a sum of d different elementary scat-

tering contributions represented by

z mkl and

¢ z mkl denoting the normalised backscattering coefficient of the m-th local

scatterer in the pq polarisation, and

s m and

¢ s m denoting the intensity of the m-th local scatterer. R is the slant range

distance from the master orbit. DRm is the range difference of the m-th scatterer between master and slave tracks. Finally

nmkl denotes additive Gaussian noise in the pq polarization channel. Using matrix and vector notation, Eq. 1 may be

written as:

r s 1 = A r s +

r n 1 and

r s 2 = ¢ A ¢ r s +

r n 2 , with

r s 1,2 = s1,2HH s1,2

HV s1,2VH s1,2

VV[ ]T

(2)

In the case of sufficiently small baselines, scattering coefficient of each local scatterer for both interferometric acquisi-

tions are assumed to be remain identical:

z mkl ª ¢ z m

kl , s m ª ¢ s m . Then,

r s 2 may be simplified as follows:

r s 2 ª AFr

s +r n 2 with

F = diag e if1 ,e if2 ,L,e ifd{ } (3)

The form of Eqs. 2-3 are adapted to the TLS-ESPRIT algorithm. Thus, the interferometric phase of each dominant

scatterers can be estimated from F.

2.2 ESPRIT Algorithm

The TLS-ESPRIT algorithm is based on a covariance matrices formulation, gathering the different scattering coeffi-

cient, RXX defined as:

RXX =r k r k † with

r k = s1

HH ,s1HV ,s1

VH ,s1VV ,s2

HH ,s2HV ,s2

VH ,s2VV[ ]

T(4)

the 8x8 matrix, RXX, is then decomposed into an eigenvector basis as follows:

RXX = ELE† = lmRmm=1

8

 (5)

where L = diag{l1,…,l8}, l1≥ … ≥ l8 and E = [

r e 1 | … |

r e 8 ] represent the eigenvalue and eigenvector matrices respec-

tively. The number of dominant local scatterers, d, is determined by a polarimetric technique based on an eigenvalue

spectral analysis [3] (d is assumed to be inferior to the total number of polarisation channels, in this case, d £ 3).

The eigenvectors corresponding to the d dominant eigenvalues can be decomposed into two (n¥n) matrices EX and EY:

ES = l1 e1,L, ld ed[ ] fiEX

EY

È

Î Í

˘

˚ ˙ (6)

Applying a second eigendecomposition leads to:

EXY* EXY =

def EX* T

EY*T

È

Î Í

˘

˚ ˙ EX EY[ ] = ELE*T (7)

E is partitioned into d ¥ d submatrices:

E =E11 E12

E21 E22

È

Î Í

˘

˚ ˙ (8)

Roy and Kailath [4] show that the eigenvalues

¢ l m , of

Y = -E12E22-1 , correspond to the diagonal elements of F. Then the

interferometric phase of each local scatterer, fm, can be estimated by:

fm = arg ¢ l m( ) (9)

This approach permits the segmentation and the estimation of the interferometric phase centre of dominant scatterers, it

does not give any information about the nature of the scattering mechanism.

3 POLARISATION ESTIMATION USING ESPRIT ALGORITHM

An extension of the ESPRIT algorithm, [5], allows to retrieve the polarisation information associate to a dominant

scatterer. The coherent scattering matrix called Sinclair matrix S containing polarimetric information is used:

r E S = S

r E i =

SHH SHV

SVH SVV

È

Î Í

˘

˚ ˙ r E i (10)

where

r E s and

r E i are the Jones vectors of the received and emitted signals (respectively). The scattering matrix may be

decomposzed into two Jones vectors (subscripts 1 or 2 indicate the interferometric track):

r E 1,2

H = S1,210

È

Î Í

˘

˚ ˙ =

SHH1,2

SVH1,2

È

Î Í

˘

˚ ˙ and

r E 1,2

V = S1,201

È

Î Í

˘

˚ ˙ =

SHV1,2

SVV1,2

È

Î Í

˘

˚ ˙ . (11)

The Jones vectors may be reformulated using the gH,V and hH,V polarisation angle:

r E =

Exeidx

Eyeidy

È

Î Í Í

˘

˚ ˙ ˙

=def

Ecosg

singeih

È

Î Í

˘

˚ ˙ then

r E 1

H ,V = E1cosg H ,V

sing H ,VeihH ,V

È

Î Í

˘

˚ ˙ and

r E 2

H ,V = E2cosg H ,V

sing H ,VeihH ,V

È

Î Í

˘

˚ ˙ , with

E2 = E1eiDf (12)

E1 and E2 are normalised, Df is the interferometric phase difference. Introducing the ratio

rH ,V = cosg H ,V /sing H ,VeihH ,V ,

Jones vectors of Eq. 12 become:

r E 1

H ,V = E sing HVeihH ,VrH ,V

Î Í

˘

˚ ˙ and

r E 2

H ,V = E sing HVeihH ,V eiDf rH ,V

Î Í

˘

˚ ˙ (13)

Finally, vectors

r E 1

H ,V and

r E 2

H ,V , are combined in order to separate element containing the polarisation ratio rH,L from

the rest, and a formulation similar to Eqs. 2-3 appears:

E r = E sing HVeihH ,V

rH ,V

rH ,VeiDf

1eiDf

È

Î

Í Í Í Í

˘

˚

˙ ˙ ˙ ˙

= E sing HVeihH ,V ˜ f H ,VrH ,V

Î Í

˘

˚ ˙ , thus

E r =¢ A R¢ A

È

Î Í

˘

˚ ˙ +

r ¢ n 1

r ¢ n 2

È

Î Í

˘

˚ ˙ (14)

From Eq. 14, it is possible to retrieve section the polarisation angles gl and hl, contained into the ration

ˆ r H ,V , corre-

sponding to the dominant scattering mechanism:

g H ,V = tan-1 1rH ,V

Ê

Ë Á Á

ˆ

¯ ˜ ˜ ,

hH ,V = arg 1rH ,V

Ê

Ë Á

ˆ

¯ ˜ (15)

from angles given by Eq. 15, a new normalised Sinclair matrix is formed:

Snew =

SHHnew =

cosg H cosgV

cos2 gV + sin2 g H

SHVnew =

sing H coshH cosgV + i ⋅sing H sinhH cosgV

cos2 gV + sin2 g H

SVHnew = SHV

new SVVnew =

sing H cos hH + hV( )singV + i ⋅sing H sin hH + hV( ) cosgV

cos2 gV + sin2 g H

È

Î

Í Í Í Í Í

˘

˚

˙ ˙ ˙ ˙ ˙

(16)

thus, it is possible to form the anew parameter:

anew = cos-1SHH

new + SVVnew

2

Ê

Ë

Á Á

ˆ

¯

˜ ˜

(17)

4 APPLICATION TO POL-IN-SAR DATA

The analysis methods mentioned above are applied to experimental polarimetric SAR images data of the Oberpfaffen-

hofen test site, acquired at L-band, in repeat-pass mode, by the DLR E-SAR sensor.

4.1 Interferometric phase estimation using ESPRIT algorithm

The interferometric phase (f1, f2, f3) of each local scatterer is calculated by ESPRIT algorithm using Eq. 9.

• Over forest area

Fig 1 gives the interferometric phase profile over a forest zone. The ESPRIT algorithm leads two optimum interfer-

ometric phases. One corresponds to the ground contribution (green) and the second to the canopy contribution (red).

Between these two optima are plotted classic interferometric phases obtained from the Pauli decomposition. Variations

of the ground contribution are due to varying underlying topography but also to a low interferometric coherence in-

volved by decorrelation in the overlying random volume.

Fig 1: Interferometric phase over forest part (rad) (fopt-max – red, fopt-min – orange, fHH+VV – green dashed, fHH-VV – blue,dashed, f2HV – black)

• Over built-up area

u v

w x

Fig 2: interferometric phase over man-made area using ESPRIT algorithm.

In Fig 2 are drawn interferometric phases over built-up rea with a scene schematic description. This complex scene is

composed of vegetation, building, road, … The phase result for building 1 indicates that the three interferometric ES-

PRIT phases converge to the same value which corresponds to the top of the building. It is also the case for buildings 3

and 4. Phase peaks are due to low backscattering power due to electromagnetic shadow or reflection on road. On the top

of building 3 and 4 are installed some antennas which corrupt the ESPRIT phase estimation.

4.2 Polarisation estimation using ESPRIT algorithm

Fig 3: top - a parameter (blue – single image, red – using ESPRIT), bottom – interferometric phase (blue and black –using method described on section [3] , red and green – using ESPRIT algorithm from section 2).

The approach presented in section 0 is applied to fully polarimetric single baseline interferometric SAR data. The inter-

ferometric phase, and the polarisation parameters are extracted and a new Sinclair matrix, corresponding to the main

scattering mechanism is generated and, in order to compare with single pass polarimetric characterisation, the

ˆ a angle

is calculated from the new target vector.

Results drawn in Fig 3 show a better estimation of the a parameter, especially for slightly vegetated surfaces neigh-

bouring some buildings, where anew indicates a single bounce mechanism (anew ‡ 0), and over the building, where the

single bounce to double bounce variations of anew describes the building shape in a better way the a parameter com-

puted from single image.

5 CONCLUSION

This paper presents two complementary approaches based on the ESPRIT algorithm, applied on fully polarimetric inter-

ferometric SAR data. The first approach describes an adapted interferometric signal model to the ESPRIT principle in

order to retrieve interferometric phase centre of dominant scattering mechanism. The application domain is extended

from forested area to man-made area. The principle applied on real SAR data provides two extreme interferometric

phases corresponding to dominant scattering mechanisms. The second approach permits to retrieve the polarisation state

of a main scatterer over different media, based on an interferometric Jones vector model. This model is adjusted to

ESPRIT algorithm. A new scattering matrix and polarisation parameters of a dominant scatterering contributor are cal-

culated. The results show an improvement of the polarimetric parameter descriptivety compared to those computed

using single polarimetric SAR image.

6 REFERENCES

[1] Papathanassiou K and Cloude S, Single-baseline polarimetric SAR interferometry, IEEE trans. Geosci. RemoteSensing, Vol 39, pp. 2352-2363, 2001

[2] Yamada H. et al., Polarimetric SAR interferometry for forest analysis based on the ESPRIT algorithm, IEICETrans. Electron., Vol E84 – C, pp. 1917-1924, 2001

[3] Ferro-Famil L. Pottier E. and Lee J. S., Classification and Interpretation of Polarimetric Interferometric SARdata, IEEE IGARSS’02, Toronto, 2002

[4] Roy R. and Kailath T., ESPRIT – Estimation of Signal Parameters via Rotational Invariance Techniques, IEEETrans. Acous. Speech Signal Processing, Vol. 37, pp. 984-995, 1989

[5] Li J. and Compton R. T., Angle and Polarization Estimation using ESPRIT with a polarization sensitive array,IEEE Trans. Antennas Propagat., Vol 39, pp. 1376-1383, 1991