PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 135 > pp. 583-599

A COMPRESSIVE SENSING APPROACH FOR SYNTHETIC APERTURE IMAGING RADIOMETERS

By S. Li, X. Zhou, B. Ren, H.-J. Sun, and X. Lv

Full Article PDF (349 KB)

Abstract:
The aperture synthesis technology represents a promising new approach to microwave radiometers for high-resolution observations of the Earth from geostationary orbit. However, the future application of the new technology may be limited by its large number of antennas, receivers, and correlators. In order to reduce significantly the complexity of the on-board hardware requirements, a novel method based on the recently developed theory of compressive sensing (CS) is proposed in this paper. Due to the fact that the brightness temperature distributions of the Earth have a sparse representation in some proper transform domain-for example, in terms of spatial finite-differences or their wavelet coefficients, we use the CS approach to significantly undersample the visibility function. Thus the number of antennas, receivers, and correlators can be further reduced than those based on the traditional methods that obey the Shannon/Nyquist sampling theorem. The reconstruction is performed by minimizing the l1 norm of a transformed image. The effectiveness of the proposed approach is validated by numerical simulations using the image corresponding to AMSU-A over the Pacific.

Citation:
S. Li, X. Zhou, B. Ren, H.-J. Sun, and X. Lv, "A Compressive Sensing Approach for Synthetic Aperture Imaging Radiometers," Progress In Electromagnetics Research, Vol. 135, 583-599, 2013.
doi:10.2528/PIER12110603
http://www.jpier.org/PIER/pier.php?paper=12110603

References:
1. Bonafoni, , S., , F. Alimenti, G. Angelucci, and G. Tasselli, , "Mi-crowave radiometry imaging for forest fire detection: A simulation study," Progress In Electromagnetics Research,, Vol. 112, 77-92, 2011.

2. Giamalaki, , M. I. , I. S. Karanasiou, and , "Enhancement of a microwave radiometry imaging system's performance using left handed materials," left handed materials , Vol. 117, 253-265, 2011.

3. Kraft, , U. R., "Two-dimensional aperture synthesis radiometers in a low earth orbit mission and instrument analysis," IEEE International Geoscience and Remote Sensing Symposium, Vol. 2, 866-868, 1996.

4. Le Vine, , D. M. , J. C. Good, and , "Aperture synthesis for microwave radiometers in space," NASA Tech. Memo. 85033, Goddard Space Flight Center, , 1983.

5. Camps, A., J. Bara, I. C. Sanahuja, and F. Torres, , "The processing of hexagonally sampled signals with standard rectangular techniques: Application to 2-D large aperture synthesis interferometric radiometers," IEEE Trans. Geoscience and Remote Sensing, Vol. 35, No. 1, 183-190, 1997.
doi:10.1109/36.551946

6. Anterrieu, , E., , Anterrieu, E., P. Waldteufel, and A. Lannes, , "functions for 2-D hexagonally sampled synthetic aperture imaging radiometers," IEEE Trans. Geoscience and Remote Sensing , Vol. 40, No. 12, 2531-2542, 2002.
doi:10.1109/TGRS.2002.1176146

7. He, , B. Y. , J. Wu, and , "Two dimensional least redundant array for interferometric synthetic aperture radiometer," IEEE International Geoscience and Remote Sensing Symposium,, Vol. 7, 4371-4373, 2003.

8. Wu, , J., , H. Liu, B. Y. He, and W. Y. Sun, "The rotate mother & son satellite system for passive microwave imaging," China Patent, App. No. 200510123633.2, Pub. CN1782734, 2005.

9. Jackson, J. I., C. H. Meyer, D. G. Nishimura, and A. Macovski, "Selection of a convolution function for Fourier inversion using gridding," IEEE Trans. Medical Imaging, Vol. 10, No. 3, 473-478, 1991.
doi:10.1109/42.97598

10. Zhou, , X., , H. J. Sun, J. W. He, and X. Lv, "NUFFT-based iterative reconstruction algorithm for synthetic aperture imagingradiometers," IEEE Geoscience and Remote Sensing Letters , Vol. 6, No. 2, 273-276, 2009.
doi:10.1109/LGRS.2008.2012123

11. Candµes, , E. J., J. Romberg, and T. Tao, , "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,", Vol. 52, No. 2, 489-509, 2006.

12. Donoho, , D., , "Compressed sensing," IEEE Trans. Information Theory, Vol. 52, No. 4, 1289-1306, 2006..
doi:10.1109/TIT.2006.871582

13. Candµes, , E. J., M. Wakin, and , "An introduction to compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 21-30, 2008.
doi:10.1109/MSP.2007.914731

14. Eldar, Y. C. , G. Kutyniok, and , Compressed Sensing: Theory and Applications, Cambridge University Press, Cambridge, 2012.
doi:10.1017/CBO9780511794308

15. Lao, , D., M. W. Lenox, and G. Akabani, "The sparsity-promoted solution to the undersampling tof-pet imaging: Numerical simulations," Progress In Electromagnetics Research,, Vol. 133, 235-258, 2013.

16. Zhang, , Y., and A two-level iterative, "A two-level iterative reconstruction method for compressed sensing MRI," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 8--9, 1081-109, 2011.
doi:10.1163/156939311795762024

17. Lustig, , M., D. Donoho, and J. M. Pauly, , "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Resonance in Medicine, Vol. 58, No. 6, 1182-1195, 2007.
doi:10.1002/mrm.21391

18. Lustig, , M., , D. Donoho, J. Santos, and J. Pauly, , "Compressed sensing MRI," IEEE Signal Processing Magazine, Vol. 25, No. 2, 72-82, 2008.
doi:10.1109/MSP.2007.914728

19. 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

20. 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.

21. 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

22. Li, , J., , S. Zhang, and J. Chang, , "Applications of compressed sensing for multiple transmitters multiple azimuth beams SAR imaging," Progress In Electromagnetics Research, Vol. 127, 259-275, 2012.
doi:10.2528/PIER12021307

23. 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.

24. Peng, , X., , W. Tan, Y. Wang, W. Hong, and Y. Wu, "Convolution back-projection imaging algorithm for downward-looking sparse back-projection imaging algorithm for downward-looking sparse," Progress In Electromagnetics Research, Vol. 129, 287-313, 2012.

25. Xing, , S., , D. Dai, Y. Li, and X. Wang, "Polarimetric SAR tomography using L2;1 mixed norm sparse reconstruction method," Progress In Electromagnetics Research, Vol. 130, 105-130, 2012.

26. You, , Y., H. Xu, C.-S. Li, and L. Zhang, , "Data acquisition and processing of parallel frequency SAR based on compressive sensing," Progress In Electromagnetics Research, Vol. 133, 199-215, 2013.

27. Gedalyahu, K., Y. C. Eldar, and , "Time-delay estimation from low-rate samples: A union of subspaces approach," IEEE Trans. Signal Processing, Vol. 58, No. 6, 3017-3031, 2010.
doi:10.1109/TSP.2010.2044253

28. Mishali, M. , Y. C. Eldar, and , "From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals," IEEE Journal of Selected Topics in Signal Processing,, Vol. 4, No. 2, 375-391, 2010.
doi:10.1109/JSTSP.2010.2042414

29. Haupt, , J., , W. U. Bajwa, G. Raz, and R. Nowak, , "Toeplitz compressed sensing matrices with applications to sparse channel estimation," IEEE Trans. Information Theory, Vol. 56, No. 11, 5862-5875, 2010..
doi:10.1109/TIT.2010.2070191

30. Hirvonen, , T., , C. Tzagkarakis, A. Mouchtaris, and P. Tsakalides, "Single-channel and multi-channel sinusoidal audio coding using compressed sensing," IEEE Trans. Audio, Speech, and Language IEEE Trans. Audio, Speech, and Language, Vol. 19, No. 5, 1382-1395, 2011..
doi:10.1109/TASL.2010.2090656

31. Davenport, , M. A., , et al., "Single- pixel imaging via compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 83-91, 2008.
doi:10.1109/MSP.2007.914730

32. Wiaux, Y., et al., "Compressed sensing imaging techniques for radio interferometry," Monthly Notices of the Royal Astronomical Society, Vol. 395, No. 3, 1733-1742, 2009.
doi:10.1111/j.1365-2966.2009.14665.x

33. McEwen, J. D., Y. Wiaux, and , "Compressed sensing for radio interferometric imaging: Review and future direction," IEEE International Conference on Image Processing, 1313-1316, 2011.

34. Muthukrishnan, S., , S., , Data Streams: Algorithms and Applications, Now Publishers, Hanover, MA, 2005..

35. Yang, , J. G., , et al., "Random-frequency SAR imaging based on compressed sensing," IEEE Trans. Geoscience and Remote Sensing,, No. 99, 1-12, 2012.
doi:10.1109/TGRS.2012.2220147

36. Becker, , S., , J. Bobin, and E. Candes, , "NESTA: A fast and accurate first-order method for sparse recovery," SIAM Journal on Imaging Sciences,, Vol. 4, No. 1, 1-39, 2011.
doi:10.1137/090756855

37. Tropp, , J. A., , A. C. Gilbert, and M. J. Strauss, "Algorithm for simultaneous sparse approximation. Part I: Greedy pursuit Signal Processing,", Vol. 86, 572-588, 2006.

38. Needell, , D., , "Topics in compressed sensing," Ph.D. Dissertation, Mathematics, , 2009.

39. Needell, , D., R. Vershynin, and , "recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," IEEE Journal of Selected Topics in Signal Processing , Vol. 4, No. 2, 310-316, 2010.
doi:10.1109/JSTSP.2010.2042412

40. Corbella, , I., , et al., "The visibility function in interferometric aperture synthesis radiometry," IEEE Trans. Geoscience and Remote Sensing, Vol. 42, No. 8, 1677-1682, 2004.
doi:10.1109/TGRS.2004.830641

41. Butora, R., , R., , M. Martin-Neira, and A. L. Rivada-Antich, "Fringe-washing function calibration in aperture synthesis microwave radiometry," Radio Science, Vol. 38, No. 2, 15-1-15-5, 2003.
doi:10.1029/2002RS002695

42. Romberg, , J., , "Imaging via compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 14-20, 2008.
doi:10.1109/MSP.2007.914729

43. Tropp, , J., A. Gilbert, and , "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Information Theory, Vol. 53, No. 12, 4655-4666, 2007.
doi:10.1109/TIT.2007.909108

44. Figueiredo, , M. A. T., , R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE Journal of Selected Topics in Signal Processing, Vol. 1, No. 4, 586-597, 2007.
doi:10.1109/JSTSP.2007.910281

45. Wright, , S. J., R. D. Nowak, and M. A. T. Figueiredo, "Sparse reconstruction by separable approximation ," IEEE Trans. Signal Processing, Vol. 57, No. 7, 2479-2493, 2009.
doi:10.1109/TSP.2009.2016892

46. Beck, , A., M. Teboulle, and , "Fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM Journal on Imaging Sciences, Vol. 2, No. 1, 183-202, 2009.
doi:10.1137/080716542

47. Hale, , E. T. and Fixed-point continuation for, "Fixed-point continuation for l1 minimization: Methodology and convergence," SIAM Journal on Optimization, Vol. 19, No. 3, 1107-1130, 2008.
doi:10.1137/070698920

48. Nesterov, , Y., , "Introductory Lectures on Convex Optimization. A Basic Course," Kluwer Academic Publishers, 2004.

49. Nesterov, Y., , "Smooth minimization of non-smooth functions," Math. Program. Ser. A, Vol. 103, 127-152, 2005.
doi:10.1007/s10107-004-0552-5

50. Nesterov, Y., , "Gradient methods for minimizing composite objective function," Technical Report 2007/76, CORE, Universite catholique de Louvain, , 2007.

51. Torres, , F., , A. B. Tanner, S. T. Brown, and B. H. Lambrigsten, "Robust array configuration for a microwave interferometric radiometer: Application to the GeoSTAR project," IEEE Geoscience and Remote Sensing Letters, Vol. 4, No. 1, 97-101, 2007.
doi:10.1109/LGRS.2006.886427

52. Sutton, , B. P., , D. C. Noll, and J. A. Fessler, , "Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities," IEEE Trans. Medical Imaging,, Vol. 22, No. 2, 178-188, 2003.
doi:10.1109/TMI.2002.808360

53. Bronstein, M. M., A. M. Bronstein, M. Zibulevsky, and H. Azhari, "Reconstruction in diffraction ultrasound tomography using nonuniform FFT," IEEE Trans. Medical Imaging, Vol. 21, No. 11, 1395-1401, 2002.
doi:10.1109/TMI.2002.806423

54. Yunyue, L., , Y. Zhang, and J. Claerbout, "Hyperbolic estimation of sparse models from erratic data," Geophysics, , Vol. 77, No. 1, V1-V9, 2012.


© Copyright 2014 EMW Publishing. All Rights Reserved