. Fusion of Multistatic Synthetic Aperture Radar Data to obtain a Superresolution Image Ali Mohammad-Djafari1 , Sha Zhu1 , Franck Daout1 and Philippe Fargette3 1 Laboratoire des Signaux et Syst` emes (UMR 8506 CNRS - SUPELEC - Univ Paris Sud 11) Sup´ elec, Plateau de Moulon, 91192 Gif-sur-Yvette, FRANCE. {djafari,zhu}@lss.supelec.fr 2
SATIE, ENS Cachan, Universit´ e Paris 10, France
[email protected] 3
DEMR, ONERA, Palaiseau, France
[email protected]
WIO 2009, 19-24 July, 2009, Paris, France 1 / 28
Summary ◮
Introduction to SAR imaging
◮
Monostatic, Bistatic and Multistatic SAR imaging
◮
Forward modeling as a Fourier Synthesis inverse problem
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Classical inversion methods ◮ ◮ ◮
Inverse Fourier Transform Gerchberg-Papoulis Least square and deterministic regularization
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Bayesian estimation approach
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Proposed method of joint data fusion and super-resolution reconstruction
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Simulation and experimental data results
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Conclusions and Discussions 2 / 28
Synthetic Aperture Radar (SAR) imaging ◮
Point sources: s(t) =
XX m
◮
Continuous case: s(t) =
◮
f (m, n) p(t − τm,n )
n
ZZ
f (x, y) p(t − τ (x, y)) dx dy
SAR imaging with a set of transmitter/receivers along the axis u: ZZ s(t, u) = f (x, y) p(t − τ (x, y, u)) dx dy k=
kx ky
=
s(ω, u, θ(u)) = P (ω)
ZZ
k cos(θ) k sin(θ)
|k| = k = ω/c
f (x, y) exp {−jωτ (x, y, θ(u))} dx dy 3 / 28
Monostatic, Bistatic and Multstatic cases Mono-static case (same transmitter-receivers) ZZ s(t, u(θ)) = f (x, y) p(t − τ (x, y, u(θ))) dx dy
2p 2 2 x + (y − u)2 = (kx x + ky (y − u)) c ω
τ (x, y, u(θ)) =
S(u,v)
−70 −65 −60 −55
kx = k cos(θ) ky = k sin(θ)
−50
v (rad/m)
◮
−45 −40 −35 −30 −25 −20 15
20
25
30
35 40 u (rad/m)
s(ω, u, θ(u)) = P (ω) = P (ω)
45
50
ZZ
ZZ
55
f (x, y) exp {−jωτ (x, y, θ(u))} dx dy f (x, y) exp {−j(kx x + ky y)} dx dy 4 / 28
Bistatic and Multstatic cases ◮
Bistatic case (one transmitter, many receivers)
◮
Multistatic case (one transmitter, many receivers) ZZ s(t, u) = f (x, y) p(t − τtc (x, y) − τrc (x, y, u(θ))) dx dy τtc + τcr =
2 (kx x + ky (y − u)) ω
S(u,v) −70
−60
−50
kx = k (cos(θtc ) + cos(θcr ) ky = k (sin(θtc ) + sin(θcr )
v (rad/m)
−40
−30
−20
−10
0
10 10
15
20
25
30 35 u (rad/m)
40
45
50
s(ω, u, θ(u)) = P (ω)
55
ZZ
f (x, y) exp {−j(kx x + ky y)} dx dy 5 / 28
Monostatic, Bistatic and Multstatic cases s(ω, u, θ(u)) = P (ω)
ZZ
f (x, y) exp {−j(kx x + ky y)} dx dy S(u,v)
−70 −65
3 −60
2
−55 −50
0
v (rad/m)
1
Tx
5
−45 −40
4 3
−35
2 −30
1 0 5
−1
−25
4 −2
3
−20
2
−3 −4
1 0
15
20
25
30
35 40 u (rad/m)
45
50
55
Results on experimental data (2 bands fusion) Reconstruction by backpropagation
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y (m)
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BF1 band
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y (m)
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fh(x,y)
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0
fh(x,y)
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fh(x,y)
0
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fh(x,y)
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y (m)
0 x (m)
fh(x,y)
y (m)
y (m)
fh(x,y)
BF1 & BF2
0
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BF2 band
Reconstruction by backpropagation
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y (m)
y (m)
Reconstruction by backpropagation −0.6
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27 / 28
Conclusions and Perspectives
◮
Bayesian estimation framework is an appropriate one for handeling inverse problems and in particular Fusion and inversion of SAR imaging data
◮
Proposed method shows good results both on simulated and experimental data
◮
For experimental data, we still need to account for polarisation information
◮
Present forward modeling assumes a scene with point sources
◮
More accurate forward models are needed for accounting for real sources
28 / 28
