The document presents new SAR subspace processors based on signal and interference subspace models. It introduces SAR subspace models that represent targets and interference as belonging to low-rank subspaces. It describes three SAR processors: SSDSAR uses only the signal subspace, OISDSAR removes interference in the orthogonal interference subspace, and OSISDSAR jointly uses both subspaces to better detect targets while reducing false alarms from interference. The models and processors are demonstrated on simulated forest penetration data, showing improved detection over conventional SAR and reduced false alarms compared to SSDSAR. Future work is outlined on theoretical analysis and evaluating performance on real data.

1. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
New Polarimetric SAR Processors Based on
Signal and Interference Subspace Models 1
F.Brigui1 , L.Thirion-Lefevre1 , G.Ginolhac2 and P.Forster2
1 SONDRA/SUPELEC
2 SATIE, Ens Cachan
1
Funded by the DGA
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2. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Introduction: Context
Main idea
DETECTION OF TARGET IN COMPLEX ENVIRONMENT
◮ Deterministic Target in noise
◮ Others Deterministic Scatterers (Interferences)
FOPEN Application:
Detection of Man Made Target (MMT) in Forest using SAR
u200
z
y
u100
u2
m 10 m
0.5
u1 0
u0
-10 m
x
95 m 115 m
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3. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Introduction: Radar System
SAR System
Antenna moving along a linear trajectory
◮ uN positions of the antenna
◮ Emitted signal e: chirp with frequency bandwidth B of
central frequency f0
◮ Polarimetric Channels: HH, VV
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4. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Introduction: New SAR Processors
Objective
To develop new SAR processors including a priori physical information on the
scatterers:
◮ Aspect angles
◮ Frequencies
◮ Polarisations
1. Prior-knowledge on the target scattering to increase its detection
2. Prior-knowledge on the interferences scattering to decrease false
alarms
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5. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Outline
SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
IGARSS 2010 July 2010

6. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Outline
SAR Subspace Models
SAR Data
Subspace Models
SAR Received Signal
SAR Subspace Processors
Applications to FoPen Data
Conclusion
IGARSS 2010 July 2010

7. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
SAR Data Configuration
◮ N positions ui of acquisitions
◮ K frequencies
◮ Polarization: Co-Polarization (HH and VV)
SAR Received Signal
Co-Polarization
Received signal z ∈ C2NK
 HH 
z1
 . 
 . 
 . 
 HH 
 z
z= N 

 zVV 
1
 . 
 
 . 
.
zVV
N
IGARSS 2010 July 2010

8. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Modeling of zMMT
Canonical Element
MMT can be seen as a set of Perfectly Conducting (PC) Plates
with unknown orientations (α, β) whose scattering is computed
with Physical Optics.
z z
z’ z’
α z"
β
y"=y’
y’
O α β
O y
y
α
β
x (b) x’ (c)
(a) x=x’
x"
zMMT = axy yxy (α, β)
◮ axy = complex attenuation coefficient
◮ yxy (α, β) = the response of a PC plate at the position (x, y ) with
orientation (α, β)
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9. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Modeling of zMMT
Orientation (α, β) unknown!
Hypothesis: yxy (α, β) belongs to a low rank target subspace
Hxy
∀(α, β) ∈ [αmin , αmax ] × [βmin , βmax ] yxy (α, β) ∈ Hxy
Modeling of zMMT
zMMT = Hxy λxy
◮ Hxy ∈ C2NK ×DH = an orthonormal basis of Hxy of rank DH
◮ λxy ∈ CDH ×1 = an unknown coordinate vector.
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10. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Modeling of zTrunk
Canonical Element
Trunk can be seen as a dielectric cylinder with unknown
orientations (γ, δ) whose scattering is computed with
Asymptotic Method.
z’=z
z z" γ
δ
O y’ O y"=y’
O δ γ
y γ
δ
x x’ x"
(a) (b) (c)
zTrunk = bxy ixy (γ, δ)
◮ bxy = complex attenuation coefficient
◮ ixy (γ, δ) = the response of a dielectric cylinder at the position (x, y ) with
orientation (γ, δ)
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11. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Modeling of zTrunk
Orientation (γ, δ) unknown!
Hypothesis: ixy (γ, β) belongs to a low rank interference
subspace Jxy
∀(γ, δ) ∈ [γmin , γmax ] × [δmin , δmax ] ixy (γ, δ) ∈ Jxy
Modeling of zTrunk
zTrunk = Jxy µxy
◮ Jxy ∈ C2NK ×DJ = an orthonormal basis of Jxy of rank DJ
◮ µxy ∈ CDJ ×1 = an unknown coordinate vector.
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12. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Received Signal Modeling
z = Hxy λxy + Jxy µxy + n
◮ n ∈ C2NK = white Gaussian noise vector of variance σ 2
◮ Computations of Hxy and Jxy : SVD of the matrices containing the
responses of the canonical elements for all their possible orientations.
( Ginolhac, Thirion-Lefevre, Durand and Forster, SAR Processors based on Signal or Interference
Subspace Detector, IEEE Trans. on Aero.and Elect. Syst., April 2010.
Brigui, Thirion-Lefevre, Ginolhac and P. Forster, New Polarimetric Signal Subspace Detectors for SAR
Processors, CR-Physique Propagation and remote sensing, vol. 11, n◦ 1, pp.104 - 113, January 2010.)
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13. SAR Subspace Models
SAR Data Configuration
SAR Subspace Processors
Subspace Models
Applications to FoPen Data
SAR Received Signal
Conclusion
Alternative Writing
Decomposition of Jxy in 2 parts:
◮ part belonging to Hxy
◮ ⊥
part belonging to Hxy
z = Hxy λxy + (PHxy Jxy )µxy + (P⊥xy Jxy )µ⊥ + n
H xy
PHxy = Hxy H† and P⊥xy = I − PHxy
xy H
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14. SAR Subspace Models
SSDSAR
SAR Subspace Processors
OISDSAR
Applications to FoPen Data
OSISDSAR
Conclusion
Outline
SAR Subspace Models
SAR Subspace Processors
SSDSAR Processor
OISDAR Processor
OSISDSAR Processor
Applications to FoPen Data
Conclusion
IGARSS 2010 July 2010

15. SAR Subspace Models
SSDSAR
SAR Subspace Processors
OISDSAR
Applications to FoPen Data
OSISDSAR
Conclusion
SSDSAR Processor (Signal Subspace Detector Processor )
Modeling of z z
PHz
z = Hxy λxy + n <H>
Estimation of λxy
λxy = H† z
ˆ xy
<J>
SSDSAR Image
H† z
xy
2 z† PHxy z
IS (x, y) = =
σ2 σ2
where PHxy = Hxy H† is the orthogonal projector onto Hxy .
xy
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16. SAR Subspace Models
SSDSAR
SAR Subspace Processors
OISDSAR
Applications to FoPen Data
OSISDSAR
Conclusion
OISDSAR Processor
(Orthogonal Interference Subspace Detector Processor )
Modeling of z
z
z = Hxy λxy +(PHxy Jxy )µxy +(P⊥xy Jxy )µ⊥ +n
H xy
<H>
T
J P Hz
Estimation of µ⊥
xy
µ⊥ = J′† z
ˆ xy xy
<J>
J′† = (J† P⊥xy Jxy )−1 J† P⊥xy
xy xy H xy H
OISDSAR Image
J′† z
xy
2 z† P⊥xy Jxy (J† P⊥xy Jxy )−1 J† P⊥xy z
H xy H xy H
II⊥ (x, y ) = =
σ2 σ2
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17. SAR Subspace Models
SSDSAR
SAR Subspace Processors
OISDSAR
Applications to FoPen Data
OSISDSAR
Conclusion
OSISDSAR Processor
(Orthogonal Signal and Interference Subspace SAR Processor)
Goal: To reduce false alarms due to the trunks without loss of
detection of the MMT
Definition
Normalized Intensities
IS (x, y) II⊥ (x, y)
ISI⊥ (x, y) = −
(x,y ) IS (x, y) (x,y ) II⊥ (x, y)
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18. SAR Subspace Models
SAR Subspace Processors Configuration
Applications to FoPen Data Images
Conclusion
Outline
SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Configuration
Images
Conclusion
IGARSS 2010 July 2010

19. SAR Subspace Models
SAR Subspace Processors Configuration
Applications to FoPen Data Images
Conclusion
Configuration
Radar Parameters
u200
◮ 200 positions ui
z ◮ chirp with a central frequency
y f0 = 400MHz with a bandwidth
u100 B = 100Mhz
◮ scene in in [90, 140]m for x-axis
and [−25, 20]m for y-axis
u2
m 10 m
5
0.
u1 0
u0 Target and
-10 m
Interference
FOPEN application: target in a forest
x ◮ target is a metallic box of 2m x
95 m 115 m 1.5m x 1m simulated by Feko
◮ interferences are dielectric trunks
simulated by COSMO
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20. SAR Subspace Models
SAR Subspace Processors Configuration
Applications to FoPen Data Images
Conclusion
Images
Classical SAR SSDSAR Co-Pol OSISDSAR Co-Pol
Image Image Image
X Target: Not detected Target: Detected Target: Detected
X False alarms: High X False alarms: High False alarms: Low
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21. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Outline
SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
IGARSS 2010 July 2010

22. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Conclusion
◮ Development of new SAR processors to suppress false
alarms due to interferences:
◮ OSISDSAR: Use of orthogonal interference subspace
◮ Application to simulated data
◮ Robustness of the subspace models based on canonical
element scattering to describe complex scatterers
◮ Great Reduction of the interference responses using the
OSISDSAR in Co-Polarization
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23. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Future Work
◮ Theoretical Study:
◮ Formulation of the OSISDSAR processor as detection
problem.
◮ Subspace Models: extension of the SAR processors based
on subspace models to the cross-polarization (HV, VH).
◮ Performances: derivation and computation of
performances of detection of the OSISDSAR by using
Monte Carlo simulations.
◮ Applications
◮ Application to FoPen real data
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24. SAR Subspace Models
SAR Subspace Processors
Applications to FoPen Data
Conclusion
Thank you for your attention!
Questions?
IGARSS 2010 July 2010