Fast Factorized Backprojection
Algorithm for UWB Bistatic
SAR Image Reconstruction
Viet Vu, Thomas Sjögren and Mats Pettersson
Blekinge Institute of Technology, Karlskrona, Sweden.
Outline
• Motivation
• Contribution
• Development from GBP to BiFFBP
– From monostatic GBP to bistatic GBP
– Bistatic FBP development on bistatic GBP
– From bistatic FBP to bistatic FFBP
• Simulation Results and Evaluation
• Conclusion
Motivation
• Algorithms for NB bistatic SAR
– Frequency-domain: Range Doppler (RD), Range
Migration (RM), Chirp Scaling (CS).
– Time-domain: Global Backprojection applied to
bistatic cases (BiGBP).
• Algorithms for UWB monostatic SAR
– Frequency-domain: not recommended [1].
– Time-domain: GBP, Fast Backprojection (FBP), Fast
Factorized Backprojection (FFBP).
[1] V. T. Vu et. al., “A comparison between fast factorized backprojection and
frequency-domain algorithms in UWB low frequency SAR,” in Proc. IEEE
IGARSS’2008, Boston, MA, Jul. 2008, pp. 1293–1296.
Motivation (cont.)
• Algorithms for UWB bistatic SAR
– BiGBP:
• Avaibilable in principal.
• Require huge computational burden.
– BiFBP:
• Shown to work with UWB bistatic SAR data [2].
• Require low computational cost.
– BiFFBP:
• Need to be investigated.
• Supposed to require even lower computational cost.
[2] V. T. Vu et. al., “Fast backprojection algorithm for UWB bistatic SAR,” in Proc.
IEEE RadarCon’2011, Kansas City, MO, May 2011, pp. 431-434.
Contribution
• BiFFBP, a fast time-domain algorithm
– Aim at UWB bistatic SAR systems but available for
NB bistatic SAR systems.
– Inherit time-domain characteristics such as unlimited
scene size, local processing, motion compensation
and so on.
– Tested with different bistatic configurations and
shown to be not limited by any bistatic configuration.
– Low computational cost.
From GBP to BiGBP
• GBP
– Reconstructed either on a slant-range plane or ground
plane.
– Time-domain characteristics.
– Spherical mapping.
– Huge computational burden.
2
2
c,,
i
i
t
t
plnm dtRtvgrxh
From GBP to BiGBP (cont.)
• BiGBP
– Reconstructed only on a ground plane.
– Time-domain chracteristics.
– Ellipsoidal mapping.
– No limitation of bistatic configuration.
– Also huge computational burden.
2
2
c,,,
i
i
t
t
rtnm dtRtvtvgrxh
BiFBP Development on BiGBP
• BiFBP
– Reconstructed only on a ground plane.
– Time-domain chracteristics.
– Ellipsoidal mapping.
– No limitation of bistatic configuration.
– Two processing stages:
• Beam forming.
• Local backprojection
– Low computational cost.
BiFBP Development on BiGBP (cont.)
• Beam forming from radar echoes
– Linear superpositions of radar echoes.
– References for superposition are centers of
• Transmitter subaperture
• Receiver subaperture
• Subimage.
2
2
,
,
c,,
c,,
sl
sl
tt
tt
kllrlt
kllrlt
dtRtvtvg
Rtvtvb
BiFBP Development on BiGBP (cont.)
• Local backprojection from formed beam
– Over elipsoidal mapping.
– Foci determined by centers of subapertures.
– Major axis defined by line connecting foci.
L
l
c
kllrltnm RRtvtvbyxh1
,,,,
From BiFBP to BiFFBP
• BiFFBP
– Reconstructed only on a ground plane.
– Time-domain chracteristics.
– Ellipsoidal mapping.
– No limitation of bistatic configuration.
– More than two processing stages:
• Firtst beam forming.
• ...
• Final beam forming
• Local backprojection
– Lower computational cost than BiFBP.
From BiFBP to BiFFBP (cont.)
• Beam forming from beam previously formed
– Linear superpositions of beam formed in previous
stage. Reconstructed only on a ground plane.
– References for superposition are centers of
• New (longer) transmitter subaperture
• New (longer) receiver subaperture
• New (smaller) subimage.
2
12
2
121
1
1121111
1
1121111
11
,,,1
,,,2
,
,
L
Ll
L
Lll
c
kl
c
klkll
c
kl
c
klkll
RRRtb
RRRtb
From BiFBP to BiFFBP (cont.)
• Mathematical expression for BiFFBP with two
beam forming stages
dtRRRRRtvtvg
yxh
sl
sl
tt
tt
c
kl
c
kl
c
klkllrlt
K
k
K
Kk
K
Kkk
L
l
L
Ll
L
Lll
nm
2
2
,,,,
111
111
2
22
1
11
1
2111
1
1
1
21
1
212
2
2
2
12
2
121
c,,
,
Simulations and Evaluation
Parameter CARABAS-II
(transmitter)
LORA
(receiver)
The maximum frequency 82 MHz
The minimum frequency 22 MHz
Platform speed 𝑣𝑝𝑙 126 m/s 130 m/s
Aperture step 0.9375 m 0.9673 m
Aperture length 3840 m 3950 m
Flight altitude 3700 m 2900 m
Minimum range 𝑟0 5900 m 3000 m
PRF 137 Hz
Bistatic angle 00/00/600
• Simulation parameters
Simulations and Evaluation (cont.)
• Simulated ground scene
– Series of point-like scaterers.
– Equally spaced.
– The same radar cross sections (RCS).
– No noise added.
Simulations and Evaluation (cont.)
• Considered bisatic configurations
– Quasi-monostatic: transmitter and receiver are
mounted on a single platform.
– Azimuth-invariant: transmitter and receiver are
mounted on two different platforms whose flight
tracks are parallel.
– General bistatic: transmitter and receiver are mounted
on two different platforms whose flight tracks are
arbitrary, e.g. 600.
Simulations and Evaluation (cont.)
• Quasi-monostatic:
– Work.
– Similar monostatic
Simulations and Evaluation (cont.)
• Azimuth-invariant:
– Work.
– Beter resolution.
Simulations and Evaluation (cont.)
• General bistatic:
– Work.
– Familiar features
Simulations and Evaluation (cont.)
• Compared to BiGBP
Simulations and Evaluation (cont.)
• Comparison between BiGBP and
– Phase error due to approximations in BiFFBP is
observed.
Phase Error Calculation
• Phase error equation [3]
– Calculate the phase error generated by approximations
in BiFFBP.
– Select subimage and subaperture size.
– Minimize phase error.
[3] V. T. Vu et. al., “Phase error calculation for fast time-domain bistatic SAR
algorithms,” in Proc. IEEE Trans. Aerosp. Electron. Syst., submitted for publication.
Conclusion
• Propose an algorithm BiFFBP.
• Derive BiFFBP analytically.
• Test BiFFBP with simulated UWB bistatic SAR
data.
• Test BiFFBP with different bistatic configurations.
• Compare with BiGBP.
Thanks for your attention!