volume | PIER Journals

Abstract

Sparse microwave imaging is the combination of microwave imaging and sparse signal processing, which aims to extract physical and geometry information of sparse or transformed sparse scene from least number of radar measurements. As a primary investigation on its performance, this paper focuses on the performance guarantee for a one-dimensional radar, which detects delays of several point targets located at a sparse scene via randomly sub-sampling of radar returns. Based on the Lasso framework, the quantity relationship among three important factors is discussed, including the sub-sampling ratio ρ_M, sparse ratio ρ_K and signal-to-noise ratio (SNR), where ρ_M is the ratio of number of random sub-sampling to that of Nyquist's sampling, and ρ_K is the ratio of sparsity to the number of unknowns. In particular, to ensure correct delay detection and accurate back scattering coefficient reconstruction for each target, one needs ρ_M to be greater than C(ρ_K)ρ_KlogN and the input SNR be of order logN, where N is the number of range cells in scene.

1. The Institute of Electronics, Chinese Academy of Sciences, "Statement tasks and project plan of 973 program: Studies on theory, system, and methodology of sparse microwave imaging," , 2009.
doi:10.1109/TIT.2006.871582 Google Scholar

2. Donoho, D. L., "Compressive sensing," IEEE Transactions on Information Theory, Vol. 52, No. 4, 1289-1306, 2006.
doi:10.1109/MSP.2007.914731 Google Scholar

3. Candes, E. J. and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 21-30, 2008. Google Scholar

4. Wu, Y., B. Zhang, and W. Hong, "Sparse microwave imaging: Principles and applications," China Science (F), Vol. 55, 1722-1754, 2012. Google Scholar

5. Baraniuk, R. and P. Steeghs, "Compressive radar imaging," IEEE Radar Conference, 128-133, Waltham, Massachusetts, 2007.
doi:10.2528/PIER10080805 Google Scholar

6. Wei, S. J., X.-L. Zhang, J. Shi, and G. Xiang, "Sparse reconstruction for SAR imaging based on compressive sensing," Progress In Electromagnetics Research, Vol. 109, 63-81, 2010.
doi:10.2528/PIERB11121212 Google Scholar

7. Ren, X. Z., Y. F. Li, and R. Yang, "Four-dimensional SAR imaging scheme based on compressive sensing," Progress In Electromagnetics Research B, Vol. 39, 225-239, 2012. Google Scholar

8. Luo, Y., Q. Zhang, Y.-Q. Bai, and Y.-L. Duan, "High-resolution ISAR imaging with sparse-spectrum OFDM-LFM waveform," PIERS Proceedings, 230-234, Kuala Lumpur, Malaysia, Mar. 27-30, 2012. Google Scholar

9. Liu, J., X. Li, S. Xu, and Z. Zhuang, "ISAR imaging of non-uniform rotation targets with limited pulse via compressed sensing," Progress In Electromagnetics Research B, Vol. 41, 285-305, 2012.
doi:10.1016/j.sigpro.2009.03.030 Google Scholar

10. Gurbuz, A., J. McClellan, and W. Scott, Jr., "Compressive sensing for subsurface imaging using ground penetrating radar," Signal Processing, Vol. 89, No. 10, 1959-1972, 2009. Google Scholar

11. Stojanovic, I., M. Cetin, and W. Karl, "Joint space aspect reconstruction of wide-angle sar exploiting sparsity," SPIE, Vol. 6970, 2008.
doi:10.1109/ACSSC.2008.5074356 Google Scholar

12. Chen "Compressive sensing in MIMO radar," 2008 42nd Asilomar Conference on Signals, Systems and Computers, 41-44, IEEE, 2008.
doi:10.1016/j.sigpro.2009.11.009 Google Scholar

13. Ender, J., "On compressive sensing applied to radar," Signal Processing, Vol. 90, No. 5, 1402-1414, 2010.
doi:10.1109/JSTSP.2009.2039181 Google Scholar

14. Patel, V., G. Easley, D. Healy, and R. Chellappa, "Compressed synthetic aperture radar," IEEE Journal of Selected Topics, in Signal Processing, Vol. 4, No. 2, 244-254, 2010.
doi:10.1109/TSP.2010.2052460 Google Scholar

15. Ben-Haim, Z., Y. Eldar, and M. Elad, "Coherence-based performance guarantees for estimating a sparse vector under random noise," IEEE Trans. on Signal Processing, Vol. 58, No. 10, 5030-5043, 2010.
doi:10.1002/cpa.20124 Google Scholar

16. Candes, E., J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Communications on Pure and Applied Mathematics, Vol. 59, No. 8, 1207-1223, 2006.
doi:10.1109/TIT.2005.858979 Google Scholar

17. Candes, E. and T. Tao, "Decoding by linear programming," IEEE Trans. on Information Theory, Vol. 51, No. 12, 4203-4215, 2005.
doi:10.1109/TIT.2004.834793 Google Scholar

18. Tropp, J., "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. on Information Theory, Vol. 50, No. 10, 2231-2242, 2004. Google Scholar

19. Candes, E. J. and C. Fernandez-Granda, "Towards a mathematical theory of super-resolution," Communications on Pure and Applied Mathematics, 2013. Google Scholar

20. Eaves, J. L. and E. K. Reedy, Principles of Modern Radar, Van Nostrand Reinhold Company, New York, 1987.
doi:10.1109/TIT.2005.858979

21. Candes, E. J. and T. Tao, "Decoding by linear programming," IEEE Trans. on Information Theory, Vol. 51, No. 13, 4203-4215, 2005. Google Scholar

22. Golub, G. H. and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1996.

23. Mackey, L., M. I. Jordan, R. Y. Chen, B. Farrell, and J. A. Tropp, "Matrix concentration inequalities via the method of exchangeable Pairs," , 29 pages, 2012. Google Scholar

25. Bioucas-Dias, J. and M. Figueiredo, "Two-step algorithms for linear inverse problems with non-quadratic regularization," IEEE International Conference on Image Processing, ICIP 2007, Vol. 1, I-105-I-108, IEEE, 2007. Google Scholar

Dr. Yin Xiang

Dr. Bingchen Zhang

Dr. Wen Hong