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High resolution SAR imaging using random pulse timing

High resolution SAR imaging using random pulse timing. Dehong Liu. Joint work with Petros Boufounos.

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High resolution SAR imaging using random pulse timing

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  1. High resolution SAR imaging using random pulse timing Dehong Liu Joint work with Petros Boufounos. IGARSS’ 2011 Vancouver, CANADA

  2. 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. Overview of SAR 3

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

  5. Strip-map SAR: uniform pulsing 5 v azimuth azimuth Ground Range

  6. Data acquisition and image formation 6 • 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. 7 SAR imaging resolution • Range resolution • Determined by pulse frequency bandwidth • Azimuth resolution • Determined by Doppler bandwidth • Requiring high Pulse Repetition Frequency (PRF) azimuth Range

  8. T T T Reflection Reflection Reflection overlapping missing 8 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. Low azimuth resolution, large range. T T Reflection Reflection High azimuth resolution, small range. T T T Reflection Reflection Reflection High azimuth resolution, large range ?

  9. 9 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.

  10. Compressive sensing and random pulse timing 10

  11. 11 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

  12. Φ sparsesignal measurements 12 Compressive sensing and reconstruction • CS measurement • Reconstruction • Signal model: Provides prior information; allows undersampling; • Randomness: Provides robustness/stability; • Non-linear reconstruction: Incorporates information through computation. Φ sparsesignal measurements Non-zeroes

  13. Connection between CS and SAR imaging 13 Question: Can we apply compressive sensing to SAR imaging?

  14. Randomized timing mixes missing data 14 Random pulse timing Randomized pulsing interval azimuth range

  15. Iterative reconstruction algorithm 15

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

  17. 17 Efficient computation  Chirp Scaling Algorithm y Azimuth FFT Fa Chirp Scaling (differential RCMC) S-1 Range FFT Fr PrH B-1 Bulk RCMC, RC, SRC R-1 Range IFFT Fr-1 Azimuth Compression/ Phase Correction PaH Computation of  follows reverse path Computation as efficient as CSA Azimuth IFFT Fa-1

  18. Imaging results with synthetic data 18

  19. 19 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

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

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

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

  23. Conclusion and future work 23

  24. 24 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. Future work

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