volume | PIER Journals

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.

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. Google Scholar

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. Google Scholar

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. Google Scholar

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

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, Jan. 1997.
doi:10.1109/36.551946 Google Scholar

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, Dec. 2002.
doi:10.1109/TGRS.2002.1176146 Google Scholar

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. Google Scholar

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, Nov. 2005. Google Scholar

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, Sep. 1991.
doi:10.1109/42.97598 Google Scholar

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, Apr. 2009.
doi:10.1109/LGRS.2008.2012123 Google Scholar

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, Feb. 2006. Google Scholar

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

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

14. Eldar, Y. C., G. Kutyniok, and , Compressed Sensing: Theory and Applications, Cambridge University Press, 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. Google Scholar

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, Jan. 2011.
doi:10.1163/156939311795762024 Google Scholar

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, Dec. 2007.
doi:10.1002/mrm.21391 Google Scholar

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

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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. Google Scholar

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. Google Scholar

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, Jun. 2010.
doi:10.1109/TSP.2010.2044253 Google Scholar

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, Apr. 2010.
doi:10.1109/JSTSP.2010.2042414 Google Scholar

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, Nov. 2010..
doi:10.1109/TIT.2010.2070191 Google Scholar

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, Jul. 2011..
doi:10.1109/TASL.2010.2090656 Google Scholar

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

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

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, Sept. 2011. Google Scholar

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

35. Yang, , J. G., J. Thompson, X. T. Huang, 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 Google Scholar

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 Google Scholar

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. Google Scholar

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

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, Apr. 2010.
doi:10.1109/JSTSP.2010.2042412 Google Scholar

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

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, Apr. 2003.
doi:10.1029/2002RS002695 Google Scholar

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

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, Dec. 2007.
doi:10.1109/TIT.2007.909108 Google Scholar

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, Apr. 2007.
doi:10.1109/JSTSP.2007.910281 Google Scholar

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, Jul. 2009.
doi:10.1109/TSP.2009.2016892 Google Scholar

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 Google Scholar

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 Google Scholar

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

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 Google Scholar

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

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, Jan. 2007.
doi:10.1109/LGRS.2006.886427 Google Scholar

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, Feb. 2003.
doi:10.1109/TMI.2002.808360 Google Scholar

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, Nov. 2002.
doi:10.1109/TMI.2002.806423 Google Scholar

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

Dr. Shiyong Li

Dr. Xi Zhou

Dr. Bailing Ren

Professor Hou-Jun Sun

Professor Xin Lv