MITSUBISHI ELECTRIC RESEARCH LABORATORIES Cambridge Massachusetts High resolution

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

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

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Overview of SAR 3

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

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

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 – Range Doppler Algorithm – Chirp Scaling Algorithm • Specific to Chirp Pulses y and .

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

MITSUBISHI ELECTRIC RESEARCH LABORATORIES 8 Trade-off for uniform pulse timing T T Reflection T overlapping T Reflection Low azimuth resolution, large range. Reflection High azimuth resolution, small range. Reflection High azimuth resolution, large range ? missing • 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.

MITSUBISHI ELECTRIC RESEARCH LABORATORIES 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.

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Compressive sensing and random pulse timing 10

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

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

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Connection between CS and SAR imaging CS Data acquisition Random projection measurements y x Radar echo CS measurements Ground reflectivity Sparse signal Acquisition function determined by SAR parameters Random projection matrix Image formation Sparse signal reconstruction y= x x | y, Question: Can we apply compressive sensing to SAR imaging? 13

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

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Iterative reconstruction algorithm 15

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

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Efficient computation Chirp Scaling Algorithm y Azimuth FFT Fa Chirp Scaling (differential RCMC) S-1 Range FFT Fr Pr. H Bulk RCMC, RC, SRC B-1 Range IFFT Fr-1 Azimuth Compression/ Phase Correction P a. H Azimuth IFFT Fa-1 Computation of follows reverse path Computation as efficient as CSA 17

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Imaging results with synthetic data 18

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

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

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

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

MITSUBISHI ELECTRIC RESEARCH LABORATORIES Conclusion and future work 23

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. Future work • Noise and nadir echo interference issues. • Computational speed. 24