Scatterer Characterisation Using Polarimetric SAR Tomography

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focussing, which is performed using standard high resolution methods such as Fourier, Capon, and MUSIC [5]. A tomographic data acquisition system is constitued by K sensors, or interferometric paths. The signals xk received by each sensor k provided by D scatterers localised at height {zd} D d=1 are arranged in the K × 1 vector �x: �x =[A]�s + �n (1) where �s represents the backscattered power of the D scatterers and �n denotes a vector formed by scalar nk representing a circular Gaussian white noise. The [A] matrix, with dimension K × D, contains the phase response due to the sensor geometry only. This matrix is made up various vectors �a(zd) representing the steering vector, which corresponds to the d-th scatterer: �a(zd) =[e iφ1(zd) iφK(zd) T ···e ] (2) where φk(zd) = − 4π λ each term is define by Fig. 2. zs H0 √ (H0−zd+zs) 2 +(ygr+ys+ z d tan θ )2, where ys θ Ck ygr z tan θ θ z Fig. 2. Geometric parameters used during tomographic data processing. All high resolution methods are based on a covariance matrix formulation defined as: [R] =〈�x�x † 〉 which is estimated by [ ˆ N� R]= (3) n=1 �xn�x † n where N > K represents the number of sample used, necessary to obtain a non-singular matrix [ ˆ R]. To focus tomographic SAR data, two approaches based on high resolution methods are existing: classical- and subspacebased. Classical methods are the famous Fourier- and Caponbased approaches. The main idea is to focus the system on a certain height, corresponding to the height of a scatterer. To do that, the range of valid heights is scanned in order to find the maximum of power. The estimated powers given by Fourier- and Capon-based, ˆ PF (z) and ˆ PC(z) respectively, beamforming approaches are function of the height z: ˆPF (z) = �a(z)† [ ˆ R]�a(z) K2 and ˆ 1 PC(z) = �a(z) † [ ˆ R] −1 (4) �a(z) where �a(z) represents the steering vector given by Eq. 2. The second category is based on the principle of subspace estimation. It gives an estimation of the scatterer height with an infinite resolution, independently of the signal-to-noise ratio (SNR). The must known subspace methods are MUSIC, ESPRIT, WSF [5]. In the case of tomographic SAR data processing, the MUSIC method has been used. The pseudobeamforming of MUSIC, ˆ PM(z), is given by: ˆPM(z) = 1 �a † ([ ÊN ][ ÊN ] † )�a where [ ÊN ] represents the noise subspace obtained after an eigendecomposition of the observed covariance matrix, [ ˆ R]= [ Ê][ˆ Λ][ Ê]† [5]. The term pseudo-beamforming is employed here because the position of the retrieved power is using only to localise the target height. The different methods presented above have been applied to a L-band data set of the E-SAR. The data were acquired in May 1998 on the test site of Oberpfaffenhofen/Germany. During the campaign fully polarimetric data sets were recorded from K =14 parallel flight tracks with a respective distance of approximatively 20 meters. The airplane used by the E- SAR is equipped with a high-precision positioning system, which allows an absolute estimation of the antenna tracks with an accuracy of few centimetres. With this data the errors arising from the aircraft movements are compensated by a new approach of motion compensation during SAR processing [6]. Additionally, a very precise velocity and range delay variation compensation have been carried out. To minimise small errors in the absolute positioning of the aircraft, also a calibration of the image phases, based on the response of a single corner reflectors is performed. height (m) height (m) 660 650 640 630 Fourier - HH street forest building corner reflector surface 620 0 surface 100 200 300 400 500 azimuth position (pixels) MUSIC (1) - HH 660 street 650 640 630 forest building corner reflector surface 620 0 surface 100 200 300 400 500 azimuth position (pixels) height (m) height (m) 660 650 640 630 CAPON - HH street forest building corner reflector surface (5) 620 0 surface 100 200 300 400 500 azimuth position (pixels) MUSIC (5) - HH 660 street 650 640 630 forest building corner reflector surface 620 0 surface 100 200 300 400 500 azimuth position (pixels) Fig. 3. Fourier-, Capon-, MUSIC 1-, MUSIC 5-based height/azimuth slice tomograms. Fig. 3 represent height/azimuth slices of tomograms obtained using Fourier, Capon, and MUSIC approaches, respectively. The left part of the scene is constituted by a dense spruce forest with a height of 15 to 20 meters [1]. Then, the azimuth slice crosses a street, some bushes and a building. The right part of the scene consists of nearly flat grass land with a corner reflector. The Capon-based approach makes it possible to reduce the sidelobes, particularly strong in case of the building and the corner reflector. The ground under the forest is better visible with Capon-based approach. Indeed, the reflectivity of the
grass land is less visible than the ground under the forest. This indicates that the scattering mechanisms detected under the forest canopy and the grass land are different. Like the grass land possesses a surface reflection, the scattering mechanism under the forest canopy corresponds essentially to a doublebounce ground-trunk, which gives the ground location. The same holds for the canopy density. It is also possible to determinate a height of about 20 meters for the trees. In the MUSIC-based approach, on the one hand, only one scatterer was assumed, on the other hand, 5 scatterers where considered in the processing. The shape of the building is better visualised, as well as the ground of the grass field, when only one scatterer is assumed. It is also possible to estimate the height of the corner reflector. Over the forest, ground and canopy reflection can be expected. These results are better when using 5 scatterers, but make no sense for the building and specially for the grass area. The result interpretation is possible thanks to a precise knowledge of the ground-truth of the area under study. Otherwise, the used high resolution methods give any information about the physical nature of the detected object. In order to be able to characterise the nature of the detected objects, it is necessary to use polarimetric SAR data. Indeed SAR polarimetry studies the behaviour of the electromagnetic scattering from the observed scene. This provides physical information on scatterers in terms of separation and identification of scattering mechanisms inside a resolution cell [7]. III. POLARIMETRIC SAR TOMOGRAPHY To visualise the importance of the polarisation in the SAR tomography field, the Capon-based approach has been applied to SAR data with different polarisation. The Capon-based approach is selected because it is sensitive to the power of the detected backscatterer and reduce the sidelobes. height (m) 660 650 640 630 CAPON - HH street forest building corner reflector surface height (m) 620 0 surface 100 200 300 400 500 620 0 surface 100 200 300 400 500 azimuth position (pixels) azimuth position (pixels) CAPON - HV 660 street 650 640 630 forest building corner reflector surface height (m) 660 650 640 630 620 0 surface 100 200 300 400 500 azimuth position (pixels) CAPON - VV street forest building corner reflector surface Fig. 4. Capon-based height/azimuth slice tomograms using SAR data with different polarisation. Fig. 4 shows the results obtained using the Capon-based approach with different polarisation data. They are different according to the selected polarisation. Over the forest, it can be observed that the ground is less visible using a vertical polarisation (VV) and disappear in the cross-polarisation data (HV). On the contrary, the canopy density becomes more explicit by using HV data. The corner reflector misses in the HV data, which is one of the principal characteristic of the HV data. on the other hand, the reflection over the building is the strongest with VV data. This first result interpretation using data with diverse polarisations shows that the nature of the observed scattering mechanisms can be estimated. But, like previously, this interpretation is valid only if the ground-truth is known. Like the Capon-based obtained data are not coherent, it is not possible to apply simple polarimetric decomposition, like Pauli-based decomposition, which can inform about the physical nature of the detected scatterer. Thereby, the tomographic SAR approach is extended to the use of the vectorial properties of electromagnetic waves as a logical extension to the tomographic DATA processing. An extension of the MUSIC algorithm [8] allows to retrieve the polarisation information associate to dominant scatterers [3]. This approach is based on the use of Jones-vector formulation. The polarisation state of an electromagnetic wave is defined by its Jones-vector, � E, which contains complete information about amplitudes and phases of electromagnetic field components. The Jones-vector can be written using two polarisation angles: γ and δ, and the polarisation ratio ρ � E : �E def = E � cos γ sin γe iδ � � 1 = E cos γ with ρ � E = tan γe iδ . Using a similar form than Eq. 2, let �y, �s, and �n denote the received signal, the source amplitude, and the noise vectors. Then, �y has the following form: ρ � E � (6) �y =[A]�s + �n (7) where the 2K × D matrix [A] is the steering matrix with columns �ad as the steering vectors: �ad =[ � E T d e iφA(zd) ··· � E T d e iφK(zd) ] T where { � Ed = [cos γd sin γdeiδd T D ] } d=1 and φk(zd) is given by Eq. 2. In [8], a polarisation estimation method using the noise subspace eigenvectors of [ ˆ R] is described. It can be shown that each steering vector �ad may be written as the linear combination of two direction vectors �b1(zd) and �b2(zd), which are associated to the scattering height zd and two arbitrary orthogonal polarisations. The steering vector �ad can be written as: �ad =[Bd] � fd (9) where {[Bd] =[ � b1(zd) � b2(zd)]} D d=1 and � fd represents a 2×1 vector consisting of the linear combination coefficients. For the sake of simplicity, { � b1(zd)} D d=1 and {� b2(zd)} D d=1 are normalised: � b ′ 1(zd) = � b1(zd) � � b1(zd)� and � b ′ 2(zd) = � b2(zd) � � b2(zd)� (8) (10)
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Scatterer Characterisation Using Polarimetric SAR Tomography

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