Long data collecting time is one of the bottlenecks of the stepped-frequency continuous-wave ground penetrating radar (SFCW-GPR). We discuss the applicability of the Compressive Sensing (CS) method to three dimensional buried point-like targets imaging for SFCW-GPR. It is shown that the image of the sparse targets can be reconstructed by solving a constrained convex optimization problem based on l1norm} minimization with only a small number of data from randomly selected frequencies and antenna scan positions, which will reduce the data collecting time. Target localization ability, performance in noise, the effect of frequency bandwidth, and the effect of the wave travel velocity in the soil are demonstrated by simulated data. Numerical results show that the presented CS method can reconstruct the point-like targets in the right position even with 10% additive Gaussian white noise and some wave travel velocity estimation error. p
2. Feng, X. and M. Sato, "Pre-stack migration applied to GPR for landmine detection," Inverse Prob., Vol. 20, 99-115, 2004.
doi:10.1088/0266-5611/20/6/S07
3. Groenenboom, J. and A. Yarovoy, "Data processing and imaging in GPR system dedicated for landmine detection," Subsurf. Sens. Technol. Appl., Vol. 3, No. 4, 387-402, 2002.
doi:10.1023/A:1020321632316
4. Hubbard, S., C. Jinsong, K. Williams, Y. Rubin, and J. Peterson, "Environmental and agricultural applications of GPR," Proc. 3rd Int. Workshop on Adv. Ground Penetrating Radar, 45-49, 2005.
doi:10.1109/AGPR.2005.1487843
5. Daniels, D., Ground Penetrating Radar, 2nd edition, London, UK, 2004.
doi:10.1049/PBRA015E
6. Counts, T., A. C. Gurbuz, W. R. Scott, Jr., J. H. McClellan, and K. Kangwook, "Multistatic ground-penetrating radar experiments," IEEE Trans. Geosci. Remote Sens., Vol. 45, No. 8, 2544-2553, Aug. 2007.
doi:10.1109/TGRS.2007.900677
7. Lopera, O., E. C. Slob, N. Milisavljevic, and S. Lambot, "Filtering soil surface and antenna effects from GPR data to enhance landmine detection," IEEE Trans. Geosci. Remote Sens., Vol. 45, No. 3, 707-717, 2007.
doi:10.1109/TGRS.2006.888136
8. Fang, G.-Y. and M. Sato, "Stepped frequency ground penetrating radar and its application for landmine detection," Acta Electronica Sinica, Vol. 33, No. 3, 436-439, 2005.
9. Gurbuz, A. C., J. H. McClellan, and W. R. Scott, "A compressive sensing data acquisition and imaging method for stepped frequency GPRs," IEEE Transactions on Signal Processing, Vol. 57, No. 7, 2640-2650, 2009.
doi:10.1109/TSP.2009.2016270
10. Donoho, D. L., "Compressive sensing," IEEE Trans. on Information. Theory, Vol. 52, No. 4, 1289-1306, 2006.
doi:10.1109/TIT.2006.871582
11. Baraniuk, R. and P. Steeghs, "Compressive radar imaging," Proc. IEEE Radar Conf., 128-133, 2007.
12. Yu., H.-M. and Y. Fang, "Research on compressive sensing based 3D imaging method applied to ground penetrating radar," Journal of Electronics & Information Technology, Vol. 32, No. 1, 12-16, 2010.
doi:10.3724/SP.J.1146.2009.00040
13. Huang, Q., L. Qu, B. Wu, and G. Fang, "UWB through-wall imaging based on compressive sensing," IEEE Trans. Geosci. Remote Sens., Vol. 48, No. 3, 1408-1415, 2010.
doi:10.1109/TGRS.2009.2030321
14. Wei, S.-J., X.-L. Zhang, J. Shi, and G. Xiang, "Sparse reconstruction for SAR imaging based on compressed sensing," Progress In Electromagnetics Research, Vol. 109, 63-81, 2010.
doi:10.2528/PIER10080805
15. Zhang, L., et al., "Achieving higher resolution ISAR imaging with limited pulses via compressed sampling," IEEE Geoscience and Remote Sensing Letters, Vol. 6, No. 3, 567-571, 2009.
doi:10.1109/LGRS.2009.2021584
16. Candes, E. J. and M. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, 2130, Mar. 2008.
17. Johansson, E. M. and J. E. Mast, "Three dimensional ground penetrating radar imaging using a synthetic aperture time-domain focusing," Proc. SPIE Conf. Adv. Microw. Millimeter Wave Detectors, Vol. 2275, 205-214, 1994.
18. Candes, E. and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n," Ann. Statist., Vol. 35, No. 6, 2313-2351, 2007.
doi:10.1214/009053606000001523
19. Tuncer, M. A. C. and A. C. Gurbuz, "Ground reflection removal in compressive sensing ground penetrating radars," IEEE Geoscience and Remote Sensing Letters, 2011.
20. Picardi, M., "Background subtraction techniques - A review," Proc. IEEE Int. Conf. Syst. Man. Cybern., 3099-3104, Oct. 10-13, 2004.
21. Mayordomo, A. M. and A. Yarovoy, "Optimal background subtraction in GPR for humanitarian demining," Proc. 5th Eur. Radar Conf., 48-51, Oct. 2008.
22. Grant, M. and S. Boyd, , CVX: Matlab Software for Disciplined Convex Programming (Web Page and Software), 2011, Available: http://stanford.edu/ boyd/cvx..
Submit
