High resolution SAR imaging using random pulse timing

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.

MITSUBISHI ELECTRIC RESEARCH LABORATORIES

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


Overview of SAR

3


Ground

Synthetic Aperture Radar (SAR)

4

RangeRange

v

azimuthazimuth

azimuthazimuth

Reflection duration depends on range length.


Ground

Strip-map SAR: uniform pulsing

5

azimuthazimuth

RangeRange

azimuthazimuth

v

MITSUBISHI ELECTRIC RESEARCH LABORATORIES 6

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


SAR imaging resolution

• Range resolution– Determined by pulse frequency bandwidth

• Azimuth resolution– Determined by Doppler bandwidth– Requiring high Pulse Repetition Frequency (PRF)

7

azimuthazimuth

RangeRange


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

8

Low azimuth resolution, large range.

High azimuth resolution, small range.

High azimuth resolution, large range ?


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.

9

azimuth

range


Compressive sensing and random pulse timing

10


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

11


• 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

12

1

12

22

1minarg xWxyxx

measurementssparsesignal

Non-zeroes

ΦWx

measurementssparsesignal

ΦWx

MITSUBISHI ELECTRIC RESEARCH LABORATORIES 13

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?


Random pulse timing

Randomized timing mixes missing data

Randomized pulsing intervalRandomized pulsing interval

14

azimuth

range


Iterative reconstruction algorithm

15


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.

16


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

17

y

yyFSFPBRFPFx Har

Hrr

Haa 11111ˆ

xFSFPBRFPFxH

arH

rrH

aa11111


Imaging results with synthetic data

18


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

19


Radar Image

Radar Raw Data

Ground

CSA imaging result with full uniformly-sampled data

200 400 600 800 1000

2000

4000

6000

8000

10000

12000 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

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)

200 400 600 800 1000

2000

4000

6000

8000

10000

12000 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Radar data acquisition

Forward process

Standard Algorithm

Iterative AlgorithmSimulated Ground

Reflectivity(high-resolution)

Range

Azi

mut

h

0 200 400 600 800 1000

0

2000

4000

6000

8000

10000

12000

20


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

21


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

22


Conclusion and future work

23


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.

24

Future work

High resolution SAR imaging using random pulse timing

Documents

Transcript of High resolution SAR imaging using random pulse timing