MITSUBISHI ELECTRIC RESEARCH LABORATORIES Cambridge, Massachusetts
High resolution SAR imaging using random pulse timing
Dehong Liu
IGARSS’ 2011 Vancouver, CANADA IGARSS’ 2011 Vancouver, CANADA
Joint work with Petros Boufounos.
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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
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Overview of SAR
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Ground
Synthetic Aperture Radar (SAR)
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RangeRange
v
azimuthazimuth
azimuthazimuth
Reflection duration depends on range length.
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Ground
Strip-map SAR: uniform pulsing
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azimuthazimuth
RangeRange
azimuthazimuth
v
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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 y and .
– Range Doppler Algorithm
– Chirp Scaling Algorithm
• Specific to Chirp Pulses
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SAR imaging resolution
• Range resolution– Determined by pulse frequency bandwidth
• Azimuth resolution– Determined by Doppler bandwidth– Requiring high Pulse Repetition Frequency (PRF)
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azimuthazimuth
RangeRange
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Trade-off for uniform pulse timing
• 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.
T Reflection T Reflection
T ReflectionT ReflectionT Reflection
overlappingoverlapping missingmissing
T Reflection TT Reflection Reflection
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Low azimuth resolution, large range.
High azimuth resolution, small range.
High azimuth resolution, large range ?
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Ground coverage at high PRF
• 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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azimuth
range
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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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• CS measurement
• Reconstruction
• Signal model: Provides prior information; allows undersampling;
• Randomness: Provides robustness/stability;
• Non-linear reconstruction: Incorporates information through computation.
Compressive sensing and reconstruction
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1
12
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1minarg xWxyxx
measurementssparsesignal
Non-zeroes
ΦWx
measurementssparsesignal
ΦWx
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Connection between CS and SAR imaging
SAR imaging CS
y = x Data acquisition Random projection
measurements
y Radar echo CS measurements
x Ground reflectivity Sparse signal
Acquisition function determined by SAR parameters
Random projection matrix
x | y, Image formation Sparse signal reconstruction
Question: Can we apply compressive sensing to SAR imaging? Question: Can we apply compressive sensing to SAR imaging?
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Random pulse timing
Randomized timing mixes missing data
Randomized pulsing intervalRandomized pulsing interval
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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.Note: Fast computation of and H always speeds up the algorithm.
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Efficient computation
Azimuth FFT
Chirp Scaling(differential RCMC)
Range FFT
Bulk RCMC, RC, SRC
Range IFFT
Fr
Fa
S-1
Fr-1
PaH
Fa-1
Azimuth Compression/Phase Correction
Azimuth IFFT
PrH
B-1
R-1
Chirp Scaling Algorithm
Computation of follows reverse pathComputation as efficient as CSA
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y
yyFSFPBRFPFx Har
Hrr
Haa 11111ˆ
xFSFPBRFPFxH
arH
rrH
aa11111
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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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Radar Image
Radar Raw Data
Ground
CSA imaging result with full uniformly-sampled data
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Classic Pulsinglow PRF
Random Pulsinghigh PRF + missing data
Image with low azimuth resolution
Image with high azimuth resolution
Conjugate gradient imaging result with random pulsing (L2 constraint)
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Radar data acquisition
Forward process
Standard Algorithm
Iterative AlgorithmSimulated Ground
Reflectivity(high-resolution)
Range
Azi
mut
h
0 200 400 600 800 1000
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Zoom-in imaging resultsT
rue
Gro
und
Ref
lect
ivity
Uni
form
pul
sin
g, S
mal
l PR
F,
Sm
all D
opp
ler
Ban
dwid
th
Ran
dom
pul
sing
, H
igh
PR
F,
Larg
e D
opp
ler
Ban
dwid
th
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Zoom-in imaging resultsT
rue
Gro
und
Ref
lect
ivity
Uni
form
pul
sin
g, S
mal
l PR
F,
Sm
all D
opp
ler
Ban
dwid
th
Ran
dom
pul
sing
, H
igh
PR
F,
Larg
e D
opp
ler
Ban
dwid
th
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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.
• Noise and nadir echo interference issues. • Computational speed.
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Future work