This document proposes using random pulse timing in synthetic aperture radar (SAR) imaging to achieve high azimuth resolution while maintaining full ground range coverage. It describes how compressive sensing allows for undersampling by mixing missing data through randomization. An iterative reconstruction algorithm is used to incorporate the sparsity prior and reconstruct high-resolution SAR images from randomly sampled radar echo data. Simulation results using synthetic data demonstrate the approach can produce images with improved azimuth resolution compared to uniform pulse timing schemes.

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

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

3. Overview of SAR

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

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

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

9. 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. azimuth range

10. Compressive sensing and random pulse timing

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. 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. measurements sparse signal Non-zeroes Φ measurements sparse signal Φ

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

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

15. Iterative reconstruction algorithm

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

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

18. Imaging results with synthetic data

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. 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)

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

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

23. Conclusion and future work

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