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Building height estimation using multibaselineL-band SAR data and polarimetric weighted
subspace fitting methods
Yue Huang, Laurent Ferro-Famil
SAPHIR team, IETRUniversity of Rennes 1, France
Jan 2009
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Objectives of urban area analysis
I Estimate height locations ofscatterers
I Extract physical features ofscatterers
MB-PolinSAR approach
I MB-InSAR: heights, layover sources
I PolinSAR: physical features
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
MB-PolinSAR methods and limitations
I Classical methods (Capon, Beamforming): low resolution
I High Resolution methods (MUSIC, Det-ML, Stoch-ML)I Adapted to responses with specific statistical properties:
coherence, correlation, . . .I Irregularly sampled baseline: spurious sidelobes.
Proposed method
PolWSF: polarimetric weighted subspace fitting
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Distributed Scatterer: Unconditional ModelCoherent Scatterer: Conditional Model
General array signal model (m sensors)
y = A(θ)x + n ∈ Cm
I y ∈ Cm: observed noisy data
I x ∈ Cd : source (reflected) signals (d elements)
I n ∈ Cm: additive noise
I m × d steering matrix
A(θ) = [a(θ1), . . . , a(θd)]
I a(θi ) m-element steering vector
I a(θi ) = a(zi ) with height zi
a(zi ) = [1, exp{jkz2zi}, exp{jkzmzi}]T
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Distributed Scatterer: Unconditional ModelCoherent Scatterer: Conditional Model
Unconditional MB-PolinSAR signal model
yu =d∑
i=1
√σixui � a(zi ) + n
I Valid for Distributed Scatterers with speckle affected responsesI Stochastic source signal
xi =√σixui with xui ∼ N (0, I)
I yu ∼ N (0,Ry)I σi , zi estimated from Ry
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Distributed Scatterer: Unconditional ModelCoherent Scatterer: Conditional Model
Conditional MB-PolinSAR signal model
yc =d∑
i=1
√σixcia(zi ) + n
I Valid for coherent scatterers: frequently encountered over urbanareas
I x =√σixci is deterministic (frozen) over N observations (looks)
I yc ∼ N (Ax, σ2nI )
I σi , zi estimated from Ax
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Distributed Scatterer: Unconditional ModelCoherent Scatterer: Conditional Model
Hybrid SAR signal model
I Mixture of coherent and distributed scattering contributions * (Saueret al: 2007)
y = yc + yu
=Pd1
i=1
√σi xci a(zi ) +
Pd2i=1
√σi xui � a(zi ) + n
I MUSIC: degraded performance for coherent scatterers
I Det-ML and Stoch-ML: partially sub-optimal techniques
Model adaptive method⇒ Weighted Subspace Fitting (WSF)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Characteristics of WSF
I Applicable to arbitary array structure
I Multi-dimensional optimization (MUSIC: 1-D optimization)
I Statistically efficient for correlated signals compared to MUSIC
I Optimal for coherent and distributed scatterersI Coherent scatterers
I CWSF (error) ≤ CDet−ML(error)I Asymptotically CWSF (error)→ CRLB
I Distributed scatterersI CWSF (error) = CStoch−ML(error)I CWSF (error)→ CRLB
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
WSF principle * (M. Viberg et al: 1991)
Subspace fitting problem
z, T = arg min ‖EsW1/2 − AT‖
2
F
I T: fitting matrix; W: weighting matrix; A: steering matrix;Es : signal subspace; En: noise subspace
I Objective: determine T that fits the steering matrix space to signalsubspace
I Subspace fitting cost function ‖EsW1/2 − AT‖2
F
Total Least-Square Solution
T = (AHA)−1AHEsW1/2
z = arg min tr{AH EnEHn AW}
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
WSF principle * (M. Viberg et al: 1991)
Various weighting matrix choices
I W = I → MUSIC
I W = Λs − σ2I = Λ→ Det-ML for coherent scatterers
Optimal weighting matrix: WSF
I Wopt = (AH EsΛsW−1S EH
s A)−1
I Estimation error covariance C(Wopt) ≤ C(W)
I C(Wopt) = C(Wstoch−ML) for distributed scatterers
⇒ WSF is optimally model adaptive
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Extension to the fully polarimetric case
(z, Φ) = arg min tr{AH(z,Φ)EnEHn A(z,Φ)W}
Wopt = (AH(z,Φ)Es(Λs − σ2I)−2Λs EHs A(z,Φ))−1
Polarimetric steering vector and matrix
I a(z ,φ) = a1(z)φ1 + a2(z)φ2 + a3(z)φ3
I φ = [φ1, φ2, φ3]T : unitary target vector (4 parameters)
I For d sources, A(z,Φ) = [a(z1,φ1), . . . , a(zd ,φd)]
Optimization of POL-WSF estimation
I Originally search dimension = 5× d
I Analytic optimization solution over polarization space (see paper)Optimization algorithm maintained to 1× d search dimension
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Simulations of distributed and coherent models
Distributed model Coherent model
SNR= 20dBDistributed model Coherent model
Source height (m) 0.0 15.0 0.0 15.0MUSIC 0.0 14.97 -27.9 -5.37WSF -0.1 14.96 0.06 14.85
MUSIC cannot localize coherent scatterers or too closely spacedcontributions
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Urban zone in SAR image
I Acquired by E-SAR (DLR)
I L-Band (1.3 GHz)
I Resolution: 0.5 m × 2.5 m
I Fully polarimetric
I Dual-baseline InSARI Small baseline of 10 m
height of ambiguity: 55 m to 73 mI Large baseline of 40 m
height of ambiguity: 14 m to 18 m
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Coherent and Distributed scatterers in SAR image*( L. Ferro-Famil et al: 2007)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-MUSIC vs SP-WSF tomograms (Model order=1)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-MUSIC vs SP-WSF tomograms (Model order=1)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-WSF tomograms (Model order=1)
Tomogram in slant range Tomogram in ground range
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-WSF tomograms (Model order=1)
Tomogram in slant range Tomogram in ground range
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-MUSIC vs SP-WSF tomograms (Model order=2)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-MUSIC vs SP-WSF tomograms (Model order=2)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-WSF tomograms (Model order=2)
Tomogram in slant range Tomogram in ground range
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
SP-WSF tomograms (Model order=2)
Tomogram in slant range Tomogram in ground range
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
FP-MUSIC vs FP-WSF tomograms (Model order=1)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
FP-MUSIC vs FP-WSF tomograms (Model order=1)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
FP-WSF tomogram (Model order=1)
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Scattering mechanism α-FP-WSF (order=1)
α in slant range
α in ground range
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Scattering mechanism α FP-WSF (order=2)
α in slant range α in ground range
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods
Urban area MB-PolinSAR Signal modelsModel Adaptive HR Height Estimator: WSF
Weighted Subspace FittingPolarimetric WSF estimatorExperimental Results
Conclusion
I Building characterization using Polarimetric MB-inSAR methods:I Source discrimination, physical characterizationI Common HR estimation methods may reach serious limitations
I Proposed approach: Weighted Subspace FittingI Model adaptive : coherent and distributed scatterersI Compared to MUSIC
- WSF has no or very low sidelobes- WSF has a better resolution- WSF performs well on coherent signals
I Extension to the fully polarimetric caseI Analytical polarimetric optimizationI Computation cost equal to the single polarization caseI Refined characterization of building height and scattering
mechanisms
Yue Huang, Laurent Ferro-Famil Building height estimation using multibaseline L-band SAR data and polarimetric weighted subspace fitting methods