volume | PIER Journals

Abstract

Linear array synthetic aperture radar (LASAR) is a promising radar 3-D imaging technique. In this paper, we address the problem of sparse recovery of LASAR image from under-sampled and phase errors interrupted echo data. It is shown that the unknown LASAR image and the nuisance phase errors can be constructed as a bilinear measurement model, and then the under-sampled LASAR imaging with phase errors can be mathematically transferred into sparse signal recovery by solving an ill-conditioned constant modulus linear program (ICCMLP) problem. Exploiting the prior sparse spatial feature of the observed targets, a new super-resolution sparse autofocus recovery algorithm is proposed for under-sampled LASAR 3-D imaging. The algorithm is an iterative minimize estimation procedure, wherein it converts the ICCMLP into two independent convex optimal problems, and joints l₁-norm reweights least square regularization and semi-definite relax to find the optimal solutions. Simulated and experimental results confirm that the proposed method outperforms the classical autofocus techniques in under-sampled LASAR imaging.

1. Klare, J., A. Brenner, and J. Ender, "A new airborne radar for 3D imaging-image formation using the ARTINO principle," 6th European Conference on Synthetic Aperture Radar, 1-4, 2006.

2. Weiβ, B. M., O. Peters, and J. Ender, "First flight trials with ARTINO," 7th European Conference on Synthetic Aperture Radar, Vol. 4, 187-190, 2008.

3. Weiβ, M. and M. Gilles, "Initial ARTINO radar experiments," 8th European Conference on Synthetic Aperture Radar, 7-10, 2010.

4. Shi, J., X.-L. Zhang, et al. "APC trajectory design for `one-active' linear-array three-dimensional imaging SAR," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 3, 1470-1486, 2010.
doi:10.1109/TGRS.2009.2031430

5. Peng, X., W. Tan, Y. Wang, W. Hong, and Y. Wu, "Convolution back-projection imaging algorithm for downward-looking sparse linear array three dimensional synthetic aperture radar," Progress In Electromagnetics Research, Vol. 129, 287-313, 2012.

6. Wu, J., J. Yang, Y. Huang, Z. Liu, and H. Yang, "A new look at the point target reference spectrum for bistatic SAR," Progress In Electromagnetics Research, Vol. 119, 363-379, 2011.
doi:10.2528/PIER11050704

7. Xu, H., J. Gao, and J. Li, "A variable PRF imaging method for high squint diving SAR," Progress In Electromagnetics Research, Vol. 135, 215-229, 2013.

8. Mahafza, B. R. and M. Sajjadi, "Three-dimensional SAR imaging using linear array in transverse motion," IEEE Trans. Aerospace and Electronic Systems, Vol. 32, No. 1, 499-510, Jan. 1996.
doi:10.1109/7.481296

9. Ender, J. H. G. and J. Klare, "System architectures and algorithms for radar imaging by MIMO-SAR," IEEE Radar Conference, 1-6, 2009.

10. Huang, Y., P. V. Brennan, D. Patrick, I. Weller, P. Roberts, and K. Hughes, "FMCW based MIMO imaging radar for maritime navigation," Progress In Electromagnetics Research, Vol. 115, 327-342, 2011.

11. Zhou, W., J.-T. Wang, H. W. Chen, and X. Li, "Signal model and moving target detection based on MIMO synthetic aperture radar," Progress In Electromagnetics Research, Vol. 131, 311-329, 2012.

12. Shi, J., X. L. Zhang, J. Yang, and K. Liao, "Experiment results on one-active LASAR," IEEE Radar Conference, 1-4, 2009.

13. Shi, J., K.-F. Liao, and X.-L. Zhang, "Three-dimensional SAR with fixed transmitter and its scattering explanation," Progress In Electromagnetics Research, Vol. 133, 285-307, 2013.

14. Wei, S.-J., X.-L. Zhang, J. Shi, and K.-F. Liao, "Sparse array microwave 3-D imaging: Compressed sensing recovery and experimental study," Progress In Electromagnetics Research, Vol. 135, 161-181, 2013.

15. Herman, M. and A. Strohmer, "High-resolution radar via compressed sensing," IEEE Transactions on Signal Processing, Vol. 57, No. 6, 2275-2284, 2009.
doi:10.1109/TSP.2009.2014277

16. Migliore, M. D., "A compressed sensing approach for array diagnosis from a small set of near-field measurements," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 6, 2127-2133, 2011.
doi:10.1109/TAP.2011.2144556

17. Liu, Z., X. Wei, and X. Li, "Adaptive clutter suppression for airborne random pulse repetition interval radar based on compressed sensing," Progress In Electromagnetics Research, Vol. 128, 291-311, 2012.

18. Poli, L., G. Oliveri, and A. Massa, "Microwave imaging within the first-order born approximation by means of the contrast-field bayesian compressive sensing," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 6, 2865-2879, 2012.
doi:10.1109/TAP.2012.2194676

19. Wang, Y., Q. Song, T. Jin, Y. Shi, and X.-T. Huang, "Sparse time-frequency representation based feature extraction method for landmine discrimination," Progress In Electromagnetics Research, Vol. 133, 459-475, 2013.

20. Patel, V. M., G. R. Easley, and D. M. Healy, "Compressed synthetic aperture radar," IEEE Journal of Selected Topics in Signal Processing, Vol. 4, No. 2, 244-254, 2010.
doi:10.1109/JSTSP.2009.2039181

21. 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

22. Roberts, W., J. Li, and P. Stoica, "Sparse learning via iterative minimization with application to MIMO radar imaging," IEEE Transactions on Signal Processing, Vol. 59, No. 3, 1088-1101, 2011.
doi:10.1109/TSP.2010.2096218

23. Zhu, X.-X. and R. Bamler, "Tomographic SAR inversion by l₁-norm regularization the compressive sensing approach," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 10, 3839-3846, 2010.
doi:10.1109/TGRS.2010.2048117

24. Chen, J., J. Gao, Y. Zhu, W. Yang, and P. Wang, "A novel image formation algorithm for high-resolution wide-swath spaceborne SAR using compressed sensing on azimuth displacement phase center antenna ," Progress In Electromagnetics Research, Vol. 125, 527-543, 2012.
doi:10.2528/PIER11121101

25. Wei, S.-J., X.-L. Zhang, and J. Shi, "Linear array SAR imaging via compressed sensing," Progress In Electromagnetics Research, Vol. 117, 299-319, 2011.

26. Wahl, D. E., P. H. Eichel, D. C. Ghiglia, et al. "Phase gradient autofocus --- A robust tool for high resolution SAR phase correction," IEEE Trans. Aerospace and Electronic Systems, Vol. 30, No. 3, 827-835, 1994.
doi:10.1109/7.303752

27. Morrison, R. L., M. N. Do, and D. C. Munson, "MCA: A multichannel approach to SAR autofocus," IEEE Trans. Image Process., Vol. 18, No. 4, 840-853, 2009.
doi:10.1109/TIP.2009.2012883

28. Liu, K.-H., A. Wiesel, and D. C. Munson, "Synthetic aperture radar autofocus based on a bilinear model," IEEE Trans. Image Process., Vol. 21, No. 5, 2735-2746, 2012.
doi:10.1109/TIP.2012.2183881

29. Onhon, N. O. and M. A. Çetin, "Sparsity-driven approach for joint SAR imaging and phase error correction," IEEE Trans. Image Process., Vol. 21, No. 4, 2075-2088, 2012.
doi:10.1109/TIP.2011.2179056

30. Ugur, S. and O. Arian, "SAR image reconstruction and autofocus by compressed sensing," Digital Signal Processing, Vol. 22, No. 6, 923-932, 2012.
doi:10.1016/j.dsp.2012.07.011

31. Fornasier, M. and H. Rauhut, "Compressive sensing," Handbook of Mathematical Methods in Imaging, Vol. 1, 187-229, Springer, 2010.

32. Zhao, Y. B. and D. Li, "Reweighted l₁--minimization for sparse solutions to underdetermined linear systems," SIAM Journal on Optimization, Vol. 22, No. 3, 1065-1088, 2012.
doi:10.1137/110847445

33. Luo, Z. Q., W. K. Ma, A. M. Cho, et al. "Semidefinite relaxation of quadratic optimization problems," IEEE Signal Processing Magazine, Vol. 27, No. 3, 20-34, 2010.
doi:10.1109/MSP.2010.936019

34. Grant, M., S. Boyd, and Y. Ye, CVX users' guide, Available Online at: http://cvxr.com/cvx/doc, Accessed Dec. 10, 2012.

35. So, M., J. Zhang, and Y. Ye, "On approximating complex quadratic optimization problems via semidefinite programming relaxations," Mathematical Programming, Vol. 110, No. 1, 93-110, 2007.
doi:10.1007/s10107-006-0064-6

Dr. Shun-Jun Wei

Dr. Xiao-Ling Zhang