MITSUBISHI ELECTRIC RESEARCH LABORATORIES
Cambridge, Massachusetts
High resolution SAR imaging using random pulse timing
Dehong Liu
Joint work with Petros Boufounos.
IGARSS’ 2011
Vancouver, CANADA
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Outline
•
Overview of synthetic aperture radar (SAR)
•
Compressive sensing (CS) and random pulse timing
•
Iterative reconstruction algorithm
•
Imaging results with synthetic data
•
Conclusion and future work
2
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Overview of SAR
3
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Synthetic Aperture Radar (SAR)
v
Reflection duration depends on range length.
azimuth
azimuth
Ground
Range
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Strip-map SAR: uniform pulsing
v
azimuth
azimuth
Ground
Range
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Data acquisition and image formation
• SAR acquisition follows linear model
y =  x, where
y: Received Data,
x: Ground reflectivity,
 : Acquisition function determined by SAR parameters, for example,
pulse shape, PRF, SAR platform trajectory, etc.
•
Image formation: determine
x
given
– Range Doppler Algorithm
– Chirp Scaling Algorithm
• Specific to Chirp Pulses
y
and  .
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SAR imaging resolution
• Range resolution
– Determined by pulse frequency bandwidth
• Azimuth resolution
Range
– Determined by Doppler bandwidth
– Requiring high Pulse Repetition Frequency (PRF)
azimuth
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Trade-off for uniform pulse timing
T
T
T
T
Reflection
Reflection
T
Reflection
Reflection
T
overlapping
T
Reflection
T
Reflection
Low azimuth resolution, large range.
Reflection
High azimuth resolution, small range.
Reflection
High azimuth resolution, large range ?
missing
• Tradeoff between azimuth resolution and range length
– Reflection duration depends on range length
– Increasing PRF reduces the range length we can image
– High azimuth resolution means small range length.
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Ground coverage at high PRF
azimuth
range
•
Issue: missing data always in the same range interval
– Produces black spots in the image
– High resolution means small range coverage
•
Solution: Motivated by compressive sensing, we propose random pulse
timing scheme for high azimuth resolution imaging.
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Compressive sensing and random pulse timing
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Compressive sensing vs. Nyquist sampling
• Nyquist / Shannon sampling theory
– Sample at twice the signal bandwidth
• Compressive sensing
– Sparse / compressible signal
– Sub-Nyquist sampling rate
– Reconstruct using the sparsity model
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Compressive sensing and reconstruction
•
CS measurement
x  W
Φ
sparse
signal
measurements
Non-zeroes
•
Reconstruction
x  arg min
x
•
•
•
1
2
y  x
2
2
 W
1
x
1
Signal model: Provides prior information; allows undersampling;
Randomness: Provides robustness/stability;
Non-linear reconstruction: Incorporates information through computation.
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Connection between CS and SAR imaging
SAR imaging
CS
Data acquisition
Random projection
measurements
y
x
Radar echo
CS measurements
Ground reflectivity
Sparse signal

Acquisition function
determined by SAR
parameters
Random projection
matrix
Image formation
Sparse signal
reconstruction
y=x
x | y, 
Question: Can we apply compressive sensing to SAR imaging?
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Random pulse timing
Randomized timing
mixes missing data
Randomized pulsing interval
azimuth
range
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Iterative reconstruction algorithm
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Iterative reconstruction algorithm
Note: Fast computation of  and  H always speeds up the algorithm.
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Efficient computation
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
Chirp Scaling Algorithm
y
Azimuth FFT
Fa
Chirp Scaling
(differential RCMC)
S-1
Range FFT
Fr

x  F
1
a
H
a
1
1
1
H
P Fr R B Pr Fr S Fa
PrH
Bulk RCMC, RC, SRC
B-1
R-1
Range IFFT
Fr-1
Azimuth Compression/
Phase Correction
PaH
Azimuth IFFT
Fa-1
Computation of  follows reverse path
Computation as efficient as CSA
1
H
1
1
1
H
1
H
xˆ  Fa Pa Fr R B Pr Fr S Fa  y   y
1

H
x
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Imaging results with synthetic data
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Experiment w/ synthetic data
• SAR parameters: RADARSAT-1
• Ground reflectivity: Complex valued image of Vancouver area
• Quasi-random pulsing: Oversample 6 times in azimuth, and
randomly select half samples to transmit pulses, resulting 3
times effective azimuth oversampling.
• Randomization ensures missing data well distributed
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data acquisition
Ground
Forward process
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Radar
Raw Data
Radar
Image
CSA imaging result with full uniformly-sampled data
0.1
0.09
2000
Standard
Algorithm
0
0.08
0.07
4000
0.06
6000
2000
0.05
0.04
8000
0.03
4000
0.02
Azimuth
10000
0.01
6000
Classic Pulsing
12000
low PRF
8000
200
400
600
800
1000
0
Image with low azimuth resolution
Conjugate gradient imaging result with random pulsing (L2 constraint)
0.1
10000
0.09
2000
12000
0
200
400
600
800
Iterative
Algorithm
1000
Range
Simulated Ground
Reflectivity
(high-resolution)
0.08
0.07
4000
0.06
6000
0.05
0.04
8000
0.03
0.02
10000
0.01
12000
Random Pulsing
high PRF + missing data
200
400
600
800
1000
0
Image with high azimuth resolution
Random pulsing, High PRF,
Large Doppler Bandwidth
Uniform pulsing, Small PRF,
Small Doppler Bandwidth
True Ground Reflectivity
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Zoom-in imaging results
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Random pulsing, High PRF,
Large Doppler Bandwidth
Uniform pulsing, Small PRF,
Small Doppler Bandwidth
True Ground Reflectivity
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Zoom-in imaging results
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Conclusion and future work
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Conclusion
• Proposed random pulse timing scheme with high
average PRF for high resolution SAR imaging.
• Utilized iterative non-linear CS reconstruction method
to reconstruct SAR image.
• Achieved high azimuth resolution imaging results
without losing range coverage.
Future work
• Noise and nadir echo interference issues.
• Computational speed.
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