1. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Cambridge, Massachusetts High resolution SAR imaging using random pulse timing Dehong Liu IGARSS’ 2011 Vancouver, CANADA Joint work with Petros Boufounos.

2. 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

3. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Overview of SAR 3

4. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Ground Synthetic Aperture Radar (SAR) 4 Range v azimuth Reflection duration depends on range length.

5. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Ground Strip-map SAR: uniform pulsing 5 azimuth Range azimuth v

6. 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

7. MITSUBISHI ELECTRIC RESEARCH LABORATORIES SAR imaging resolution Range resolution –Determined by pulse frequency bandwidth Azimuth resolution –Determined by Doppler bandwidth –Requiring high Pulse Repetition Frequency (PRF) 7 azimuth Range

8. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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 T T T overlapping missing T Reflection TT 8 Low azimuth resolution, large range. High azimuth resolution, small range. High azimuth resolution, large range ?

9. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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

10. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Compressive sensing and random pulse timing 10

11. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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

12. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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 measurements sparse signal Non-zeroes Φ measurements sparse signal Φ

13. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 13 Connection between CS and SAR imaging SAR imagingCS y =  x Data acquisitionRandom projection measurements y Radar echoCS measurements x Ground reflectivitySparse signal  Acquisition function determined by SAR parameters Random projection matrix x | y,  Image formationSparse signal reconstruction Question: Can we apply compressive sensing to SAR imaging?

14. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Random pulse timing Randomized timing mixes missing data Randomized pulsing interval 14 azimuth range

15. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Iterative reconstruction algorithm 15

16. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Iterative reconstruction algorithm Note: Fast computation of  and  H always speeds up the algorithm. 16

17. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Efficient computation  Azimuth FFT Chirp Scaling (differential RCMC) Range FFT Bulk RCMC, RC, SRC Range IFFT FrFr FaFa S -1 F r -1 PaHPaH F a -1 Azimuth Compression/ Phase Correction Azimuth IFFT PrHPrH B -1 R -1 Chirp Scaling Algorithm Computation of  follows reverse path Computation as efficient as CSA 17 y

18. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Imaging results with synthetic data 18

19. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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

20. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Radar Image Radar Raw Data Ground Classic Pulsing low PRF Random Pulsing high PRF + missing data Image with low azimuth resolution Image with high azimuth resolution Radar data acquisition Forward process Standard Algorithm Iterative Algorithm Simulated Ground Reflectivity (high-resolution) 20

21. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Zoom-in imaging results True Ground Reflectivity Uniform pulsing, Small PRF, Small Doppler Bandwidth Random pulsing, High PRF, Large Doppler Bandwidth 21

22. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Zoom-in imaging results True Ground Reflectivity Uniform pulsing, Small PRF, Small Doppler Bandwidth Random pulsing, High PRF, Large Doppler Bandwidth 22

23. MITSUBISHI ELECTRIC RESEARCH LABORATORIES Conclusion and future work 23

24. MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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