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Science China Information Sciences

, Volume 55, Issue 8, pp 1722–1754 | Cite as

Sparse microwave imaging: Principles and applications

  • BingChen ZhangEmail author
  • Wen Hong
  • YiRong Wu
Review Special Issue

Abstract

This paper provides principles and applications of the sparse microwave imaging theory and technology. Synthetic aperture radar (SAR) is an important method of modern remote sensing. During decades microwave imaging technology has achieved remarkable progress in the system performance of microwave imaging technology, and at the same time encountered increasing complexity in system implementation. The sparse microwave imaging introduces the sparse signal processing theory to radar imaging to obtain new theory, new system and new methodology of microwave imaging. Based on classical SAR imaging model and fundamental theories of sparse signal processing, we can derive the model of sparse microwave imaging, which is a sparse measurement and recovery problem and can be solved with various algorithms. There exist several fundamental points that must be considered in the efforts of applying sparse signal processing to radar imaging, including sparse representation, measurement matrix construction, unambiguity reconstruction and performance evaluation. Based on these considerations, the sparse signal processing could be successfully applied to radar imaging, and achieve benefits in several aspects, including improvement of image quality, reduction of data amount for sparse scene and enhancement of system performance. The sparse signal processing has also been applied in several specific radar imaging applications.

Keywords

sparse microwave imaging sparse signal processing compressive sensing synthetic aperture radar radar imaging 

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References

  1. 1.
    Curlander J C, McDonough R N. Synthetic Aperture Radar: Systems and Signal Processing. New York: Wiley, 1991zbMATHGoogle Scholar
  2. 2.
    Henderson F M, Lewis A J. Principles and applications of imaging radar. In: Manual of Remote Sensing. New York: John Wiley and Sons, 1998Google Scholar
  3. 3.
    Wiley C, Ariz P. Pulsed Doppler Radar Methods and Apparatus. US Patent 3,196,436. 1965Google Scholar
  4. 4.
    Wiley C A. Synthetic aperture radars: a paradigm for technology evolution. IEEE Trans Aerosp Electron Syst, 1985: 21: 440–443Google Scholar
  5. 5.
    Wikipedia. Synthetic Aperture Radar. https://en.wikipedia.org/wiki/Synthetic_aperture_radar
  6. 6.
  7. 7.
    Jordan R L. The Seasat-A synthetic aperture radar system. IEEE J Ocean Eng, 1980, 5: 154–164Google Scholar
  8. 8.
  9. 9.
    DLR. TerraSAR-X-Germany’s radar eye in space. http://www.dlr.de/eo/en/desktopdefault.aspx/tabid-5725/9296_read-15979/
  10. 10.
    Jakowatz C V, Wahl D E, Eichel P H, et al. Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach. Norwell: Kluwer Academic Publishers, 1996Google Scholar
  11. 11.
    Massonnet D, Souyris J C. Imaging with Synthetic Aperture Radar. Lausanne: EFPL Press, 2008Google Scholar
  12. 12.
    Brown W M, Porcello L J. An introduction to synthetic-aperture radar. IEEE Spectrum, 1969, 6: 52–62Google Scholar
  13. 13.
    Sherwin C W, Ruina J P, Rawcliffe R D. Some early developments in synthetic aperture radar systems. IRE Trans Military Electron, 1962, 1051: 111–115Google Scholar
  14. 14.
    Moore G E. Cramming more components onto integrated circuits. Electron Mag, 1998, 86: 82–85Google Scholar
  15. 15.
    Woodward P M. Probability and Information Theory, with Application to Radar. New York: Pergamon, 1953Google Scholar
  16. 16.
    Cook C E, Bernfeld M. Radar Signals-An Introduction to Theory and Application. Norwood: Artech House, 1993Google Scholar
  17. 17.
    Nyquist H. Certain topics in telegraph transmission theory. Trans Amer Inst Electr Engin, 1928, 47: 617–644Google Scholar
  18. 18.
    Shannon C E. Communication in the presence of noise. Proc IRE, 1949, 37: 10–21MathSciNetGoogle Scholar
  19. 19.
    Baraniuk R G, Candès E, Elad M, et al. Applications of sparse representation and compressive sensing. Proc IEEE, 2010, 98: 906–09Google Scholar
  20. 20.
    Russell B. History of Western Philosophy. London: George Allen & Unwin Ltd, 1946Google Scholar
  21. 21.
    Donoho D L. Compressed Sensing. IEEE Trans Inf Theory, 2006. 52: 1289–1306MathSciNetGoogle Scholar
  22. 22.
    Candès E J, Tao T. Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans Inf Theory, 2006, 52: 5406–5425Google Scholar
  23. 23.
    Candès E J, Romberg J K, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math, 2006, 59: 1207–1223zbMATHGoogle Scholar
  24. 24.
    Mallat S, Yu G. Super-resolution with sparse mixing estimators. IEEE Trans Image Process, 2010, 19: 2889–2900MathSciNetGoogle Scholar
  25. 25.
    Zhang Y, Mei S, Chen Q, et al. A novel image/video coding method based on compressed sensing theory. In: Proc of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Las Vegas, 2008. 1361–1364Google Scholar
  26. 26.
    Berger C R, Zhou S, Preisig J, et al. Sparse channel estimation for multicarrier underwater acoustic communication: from subspace methods to compressed sensing. IEEE Trans Signal Process, 2010, 58: 1708–1721MathSciNetGoogle Scholar
  27. 27.
    Baraniuk R, Steeghs P. Compressive radar imaging. In: Proc of IEEE Radar Conference, Boston, 2007. 128–133Google Scholar
  28. 28.
    Patel V M, Easley G R, Healy D, et al. Compressed synthetic aperture radar. IEEE J Sel Top Signal Process, 2010, 4: 244–254Google Scholar
  29. 29.
    Ender J H G. On compressive sensing applied to radar. Signal Process, 2010, 90: 1402–1414zbMATHGoogle Scholar
  30. 30.
    Wu Y R. Studies on theory, system, and methodology of Sparse Microwave Imaging. Statement Tasks and Project Plan of 973 Program: 2009Google Scholar
  31. 31.
    Cumming I G, Wong F H. Digital Signal Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood: Artech House, 2004Google Scholar
  32. 32.
    Raney R K, Runge H, Bamler R, et al. Precision SAR processing using chirp scaling. IEEE Trans Geosci Remote Sens, 1994, 32: 786–799Google Scholar
  33. 33.
    Bamler R. A comparison of range-Doppler and wavenumber domain SAR focusing algorithms. IEEE Trans Geosci Remote Sens, 1992, 30: 706–713Google Scholar
  34. 34.
    Basu S, Bresler Y. O(N 2 log2 N) filtered backprojection reconstruction algorithm for tomography. IEEE Trans Image Process, 2000, 9: 1760–1773MathSciNetzbMATHGoogle Scholar
  35. 35.
    Xiao S, Munson Jr D C, Basu S, et al. An N 2 logN back-projection algorithm for SAR image formation. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2000Google Scholar
  36. 36.
    Suess M, Grafmüller B, Zahn R. A novel high resolution, wide swath SAR system.In: Proc of IEEE International Geoscience and Remoye Sensing Symposium (IGARSS), Sydney, 2001. 1013–1015Google Scholar
  37. 37.
    Suess M. Side-Looking Synthetic Aperture Radar System. European Patent 1,241,487. 2006Google Scholar
  38. 38.
    Currie A, Brown M A. Wide-swath SAR. IEE Proc F Radar Signal Process, 1992, 139: 122–135Google Scholar
  39. 39.
    Elad M. Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. New York: Springer, 2010zbMATHGoogle Scholar
  40. 40.
    Mallat S G, Zhang Z. Matching pursuits with time-frequency dictionaries. IEEE Trans Signal Process, 1993, 41: 3397–3415zbMATHGoogle Scholar
  41. 41.
    Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM J Sci Comput, 1999, 20: 33–61MathSciNetzbMATHGoogle Scholar
  42. 42.
    Candès E J, Tao T. Decoding by linear programming. IEEE Trans Inf Theory, 2005, 51: 4203–4215Google Scholar
  43. 43.
    Candès E, Tao T. The Dantzig selector: Statistical estimation when p is much larger than n. The Annal Stat, 2007, 35: 2313–2351zbMATHGoogle Scholar
  44. 44.
    Candès E J, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory, 2006, 52: 489–509zbMATHGoogle Scholar
  45. 45.
    Candès E, Romberg J. Sparsity and incoherence in compressive sampling. Inverse Problem, 2007, 23: 969–985zbMATHGoogle Scholar
  46. 46.
    Tsaig Y, Donoho D L. Extensions of compressed sensing. Signal Process, 2006, 86: 549–571zbMATHGoogle Scholar
  47. 47.
    Baraniuk R G. More is less: Signal processing and the data deluge. Science, 2011, 331: 717–719Google Scholar
  48. 48.
    Baron D, Wakin M B, Duarte M F, et al. Distributed Compressed Sensing. Technical Report. Rice: Rice University, 2005, http://dsp.rice.edu/cs/ Google Scholar
  49. 49.
    Duarte M F, Sarvotham S, Baron D, et al. Distributed compressed sensing of jointly sparse signals. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2005. 1537–1541Google Scholar
  50. 50.
    Zhang Z, Zhang B C, Hong W, et al. Waveform design for Lq regularization based radar imaging and an approach to radar imaging with non-moving platform. In: Proc of European Conference on Synthetic Aperture Radar (EuSAR), Nuremberg, 2012Google Scholar
  51. 51.
    Ahmed N, Natarajan T, Rao K R. Discrete cosine transform. IEEE Trans Comput, 1974, 100: 90–93MathSciNetGoogle Scholar
  52. 52.
    Daubechies I. Ten Lectures on Wavelets. Philadelphia: SIAM Publications, 2006Google Scholar
  53. 53.
    Ron A, Shen Z. Affine systems in L 2(d): the analysis of the Analysis operator. J Function Analys, 1997, 148: 408–447MathSciNetzbMATHGoogle Scholar
  54. 54.
    Velisavljevic V, Dragotti P L, Vetterli M. Directional wavelet transforms and frames. In: Proc of Int Conf Image Processing, Rochester, 2002. 589–592Google Scholar
  55. 55.
    Candès E J. Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges. Technical Report. DTIC Document, 2000. www.curvelet.org/papers/Curve99.pdf
  56. 56.
    Olshausen B A, Field D J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996, 381: 607–609Google Scholar
  57. 57.
    Oliver C, Quegan S. Understanding Synthetic Aperture Radar Images. Raleigh: SciTech Publishing, 2004Google Scholar
  58. 58.
    Tian Y, Jiang C L, Lin Y G, et al. An evaluation method for sparse microwave imaging radar system using phase diagrams. In: Proc of CIE Radar Conference, Chengdu, 2011Google Scholar
  59. 59.
    Zhang B C, Jiang H, Hong W, et al. Synthetic aperture radar imaging of sparse targets via compressed sensing. In: Proc of 8th European Conference on Synthetic Aperture Radar (EUSAR), Aachen, 2010Google Scholar
  60. 60.
    Jiang H, Zhang B C, Lin Y G, et al. Random noise SAR based on compressed sensing. In: Proc of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Honolulu, 2010. 4624–4627Google Scholar
  61. 61.
    Shastry M C, Narayanan R M, Rangaswamy M. Compressive radar imaging using white stochastic waveforms. In: Proc of International Waveform Diversity and Design Conference (WDD), Niagara Falls, 2010. 90–94Google Scholar
  62. 62.
    Bahai A R S, Saltzberg B R, Ergen M. Multi-Carrier Digital Communications: Theory and Applications of OFDM. New York, NY: Springer Science and Business Media Inc, 2004Google Scholar
  63. 63.
    Berger C R, Zhou S, Willett P, et al. Compressed sensing for OFDM/MIMO radar. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2008. 213–217Google Scholar
  64. 64.
    Berger C R, Demissie B, Heckenbach J, et al. Signal processing for passive radar using OFDM waveforms. IEEE J Sel Top Signal Process, 2010, 4: 226–238Google Scholar
  65. 65.
    Vetterli M, Marziliano P, Blu T. Sampling signals with finite rate of innovation. IEEE Trans Signal Process, 2002, 50: 1417–1428MathSciNetGoogle Scholar
  66. 66.
    Healy D. Analog-to-Information (A-to-I). 2005. http://www.darpa.mil/mto/solicitations/baa05-35/s/index.html. dARPA/MTO Broad Agency Announcement (BAA) #05-35
  67. 67.
    Healy D, Brady D J. Compression at the physical interface. IEEE Signal Process Mag, 2008, 25: 67–71Google Scholar
  68. 68.
    Laska J N, Kirolos S, Duarte M F, et al. Theory and implementation of an analog-to-information converter using random demodulation. In: Proc of IEEE International Symposium on Circuits and Systems (ISCAS), New Orleans, 2007. 1959–1962Google Scholar
  69. 69.
    Eldar Y C. Compressed Sensing of Analog Signals. Comput Res Reposit, 2008Google Scholar
  70. 70.
    Mishali M, Eldar Y C, Elron A. Xampling, Part I: Practice. ArXiv:09110519. 2009. http://arxiv.org/pdf/0911.0519v3
  71. 71.
    Mishali M, Eldar Y C. From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals. IEEE J Sel Top Signal Process, 2010, 4: 375–391Google Scholar
  72. 72.
    Mishali M, Eldar Y, Dounaevsky O, et al. Xampling: Analog to digital at sub-Nyquist rates. IET Circ Dev Syst, 2011, 5: 8–20Google Scholar
  73. 73.
    Mishali M, Eldar Y C. Xampling: Compressed sensing of analog signals. ArXiv:11032960. 2011. http://arxiv.org/pdf/1103.2960
  74. 74.
    Tropp J A, Laska J N, Duarte M F, et al. Beyond Nyquist: Efficient sampling of sparse bandlimited signals. IEEE Trans Inf Theory, 2010, 56: 520–544MathSciNetGoogle Scholar
  75. 75.
    Balakrishnan A. On the problem of time jitter in sampling. IRE Trans Inform Theory, 1962, 8: 226–236zbMATHGoogle Scholar
  76. 76.
    Sun J P, Zhang Y X, Chen Z B, et al. A novel spaceborne SAR wide-swath imaging approach based on Poisson disk-like nonuniform sampling and compressive sensing. Sci China Inf Sci, 2012, 55: 1876–1887Google Scholar
  77. 77.
    Candès E J, Wakin M B. An introduction to compressive sampling. IEEE Signal Process Mag, 2008, 25, 2: 21–30Google Scholar
  78. 78.
    Carrara W G, Goodman R S, Majewski R M. Spotlight Synthetic Aperture Radar-Signal Processing Algorithms. Norwood, 1995Google Scholar
  79. 79.
    Belcher D P, Baker C J. High resolution processing of hybrid strip-map/spotlight mode SAR. IEE Proc Radar Sonar Nav, 1996, 143: 366–374Google Scholar
  80. 80.
    Mittermayer J, Lord R, Borner E. Sliding spotlight SAR processing for TerraSAR-X using a new formulation of the extended chirp scaling algorithm. In: Proc of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Toulouse, 2003. 1462–1464Google Scholar
  81. 81.
    De Zan F, Guarnieri A M. TOPSAR: Terrain observation by progressive scans. IEEE Trans Geosci Remote Sens, 2006, 44: 2352–2360Google Scholar
  82. 82.
    Tropp J A, Wright S J. Computational methods for sparse solution of linear inverse problems. Proc IEEE, 2010, 98: 948–958Google Scholar
  83. 83.
    Kim S J, Koh K, Lustig M, et al. An interior-point method for large-scale l1-regularized least squares. IEEE J Sel Top Signal Process, 2007, 1: 606–617Google Scholar
  84. 84.
    Candès E, Romberg J. l1-magic: Recovery of sparse signals via convex Programming. 2005. www.acm.caltech.edu/l1magic/downloads/l1magic.pdf
  85. 85.
    Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J Sel Top Signal Process, 2007, 1: 586–597Google Scholar
  86. 86.
    Van Den Berg E, Friedlander M. Probing the Pareto frontier for basis pursuit solutions. SIAM J Sci Comput, 2008, 31: 890–912MathSciNetzbMATHGoogle Scholar
  87. 87.
    Daubechies I, Defrise M, De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math, 2004, 57: 1413–1457zbMATHGoogle Scholar
  88. 88.
    Bioucas-Dias J M, Figueiredo M A T. Two-step algorithms for linear inverse problems with non-quadratic regularization. In: Proc of IEEE Int Conf Image Processing, San Antonio, 2007Google Scholar
  89. 89.
    Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imag Sci, 2009, 2: 183–202MathSciNetzbMATHGoogle Scholar
  90. 90.
    Yin W, Osher S, Goldfarb D, et al. Bregman iterative algorithms for L1-minimization with applications to compressed sensing. SIAM J Imag Sci, 2008, 1: 143–168MathSciNetzbMATHGoogle Scholar
  91. 91.
    Hale E T, Yin W, Zhang Y. Fixed-point continuation for L1 minimization: methodology and convergence. SIAM J Optim, 2008: 1107–1130Google Scholar
  92. 92.
    Hale E T, Yin W, Zhang Y. Fixed-point continuation applied to compressed sensing: implementation and numerical experiments. J Comput Math, 2010, 28: 170–194MathSciNetzbMATHGoogle Scholar
  93. 93.
    Becker S, Bobin J, Candès E. NESTA: A fast and accurate first-order method for sparse recovery. ArXiv: 09043367, 2009. http://arxiv.org/pdf/0904.3367
  94. 94.
    Becker S R, Candès E J, Grant M C. Templates for convex cone problems with applications to sparse signal recovery. Math Program Comput, 2011, 3: 165–218MathSciNetGoogle Scholar
  95. 95.
    Yang J, Zhang Y. Alternating direction algorithms for 1-problems in compressive sensing. ArXiv:09121185, 2009. http://arxiv.org/pdf/0912.1185
  96. 96.
    Lu Z, Pong T K, Zhang Y. An Method for Finding Dantzig Selectors. ArXiv: 10114604, 2010. http://arxiv.org/pdf/1011.4604
  97. 97.
    Davenport M A, Duarte M F, Eldar Y C, et al. Chapter I: Introduction to compressed sensing. In: Compressed Sensing: Theory and Applications. Cambridge: Cambridge University Press, 2012Google Scholar
  98. 98.
    Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory, 2007, 53: 4655–4666MathSciNetGoogle Scholar
  99. 99.
    Donoho D L, Drori I, Tsaig Y, et al. Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit. Technical Report. Department of Statistics, Stanford University, 2006. http://nmetis.dk/pic/Speciale/HenrikPedersen/Henrik%20Pederse%ns%20Artikler/Compressed%20Sensing/Donoho.pdf
  100. 100.
    Blumensath T, Davies M E. Gradient pursuits. IEEE Trans Signal Process, 2008, 56: 2370–2382MathSciNetGoogle Scholar
  101. 101.
    Dai W, Milenkovic O. Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans Inf Theory, 2009, 55: 2230–2249MathSciNetGoogle Scholar
  102. 102.
    Needell D, Vershynin R. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE J Sel Top Signal Process, 2010, 4: 310–316Google Scholar
  103. 103.
    Needell D, Tropp J A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Appl Comput Harmon Analys, 2009, 26: 301–321MathSciNetzbMATHGoogle Scholar
  104. 104.
    Blumensath T, Davies M E. Iterative hard thresholding for compressed sensing. Appl Comput Harmon Analys, 2009, 27: 265–274MathSciNetzbMATHGoogle Scholar
  105. 105.
    Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process Lett, 2007, 14: 707–710Google Scholar
  106. 106.
    Rao B D, Kreutz-Delgado K. An affine scaling methodology for best basis selection. IEEE Trans Signal Process, 1999, 47: 187–200MathSciNetzbMATHGoogle Scholar
  107. 107.
    Chartrand R, Yin W. Iteratively reweighted algorithms for compressive sensing. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2008. 3869–3872Google Scholar
  108. 108.
    Daubechies I, DeVore R, Fornasier M, et al. Iteratively reweighted least squares minimization for sparse recovery. Commun Pure Appl Math, 2010, 63: 1–38MathSciNetzbMATHGoogle Scholar
  109. 109.
    Krishnan D, Fergus R. Fast image deconvolution using hyper-Laplacian priors. In: Advances in Neural Information Processing Systems (NIPS), 2009. 1033–1041Google Scholar
  110. 110.
    Xu Z B, Zhang H, Wang Y, et al. L 1/2 regularizer. Sci China Inf Sci, 2010, 53: 1159–1169MathSciNetGoogle Scholar
  111. 111.
    Wipf D P, Rao B D. Sparse Bayesian learning for basis selection. IEEE Trans Signal Process, 2004, 52: 2153–2164MathSciNetGoogle Scholar
  112. 112.
    Ji S, Xue Y, Carin L. Bayesian compressive sensing. IEEE Trans Signal Process, 2008, 56: 2346–2356MathSciNetGoogle Scholar
  113. 113.
    Ji S, Dunson D, Carin L. Multitask compressive sensing. IEEE Trans Signal Process, 2009, 57: 92–106MathSciNetGoogle Scholar
  114. 114.
    Babacan S D, Mancera L, Molina R, et al. Non-convex priors in Bayesian compressed sensing. In: Proc of 17th European Signal Processing Conference (EUSIPCO), Glasgow, 2009Google Scholar
  115. 115.
    Yoon Y S, Amin M G. Compressed sensing technique for high-resolution radar imaging. In: Proc SPIE, 2008. 6968Google Scholar
  116. 116.
    Stojanovic I, Karl W C, Çetin M. Compressed sensing of monostatic and multistatic SAR. In: Proc SPIE, 2009. 7337Google Scholar
  117. 117.
    Huang Q, Qu L, Wu B, et al. UWB through-wall imaging based on compressive sensing. IEEE Trans Geosci Remote Sens, 2010, 48: 1408–1415Google Scholar
  118. 118.
    Jiang C L, Jiang H, Zhang B C, et al. SNR analysis for SAR imaging from raw data via compressed sensing. In: Proc of European Conference on Synthetic Aperture Radar (EUSAR), Nuremberg, 2012Google Scholar
  119. 119.
    Austin C D, Ertin E, Moses R L. Sparse Multipass 3D SAR imaging: applications to the GOTCHA data set. In: Proc SPIE, 2009. 7337Google Scholar
  120. 120.
    Zhang L, Xing M, Qiu C W, et al. Resolution enhancement for inversed synthetic aperture radar imaging under low SNR via improved compressive sensing. IEEE Trans Geosci Remote Sens, 2010. 48,10: 3824–3838Google Scholar
  121. 121.
    Xie X C, Zhang Y H. High-resolution imaging of moving train by ground-based radar with compressive sensing. Electron Lett, 2010, 46: 529–531Google Scholar
  122. 122.
    Alonso M T, López-Dekker P, Mallorqui J J. A novel strategy for radar imaging based on compressive sensing. IEEE Trans Geosci Remote Sens, 2010, 48: 4285–4295Google Scholar
  123. 123.
    Wu Y R, Xu Z B, Hong W, et al. Sparse SAR Imaging Algorithm based on SAR Raw Data Simulator (in Chinese). China Patent, 201110182202.9. 2012Google Scholar
  124. 124.
    Andrecut M. Fast GPU implementation of sparse signal recovery from random projections. ArXiv: 08091833, 2008. http://arxiv.org/pdf/0809.1833
  125. 125.
    Borghi A, Darbon J, Peyronnet S, et al. A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures. Technical Report. 2008. http://www-micrel.deis.unibo.it/benini/files/MD/cam08-64.pdf
  126. 126.
    Liu B, Zou Y M, Ying L. SparseSENSE: application of compressed sensing in parallel MRI. In: Proc of International Conference on Information Technology and Applications in Biomedicine (ITAB), Shenzhen, 2008. 127–130Google Scholar
  127. 127.
    Chang C H, Ji J. Compressed sensing MRI with multichannel data using multicore processors. Magn Reson Med, 2010, 64: 1135–1139Google Scholar
  128. 128.
    Tropp J A. Greed is good: Algorithmic results for sparse approximation. IEEE Trans Inf Theory, 2004, 50: 2231–2242MathSciNetGoogle Scholar
  129. 129.
    Ben-Haim Z, Eldar Y C, Elad M. Coherence-based performance guarantees for estimating a sparse vector under random noise. IEEE Trans Signal Process, 2010, 58: 5030–5043MathSciNetGoogle Scholar
  130. 130.
    Stanley H E. Introduction to Phase Transitions and Critical Phenomena. Oxford: Oxford Press, 1987Google Scholar
  131. 131.
    Donoho D, Stodden V. Breakdown point of model selection when the number of variables exceeds the number of observations. In: Proc of IEEE International Joint Conference on Neural Network (IJCNN), Vancouver, 2006. 1916–1921Google Scholar
  132. 132.
    Donoho D L, Tsaig Y. Fast Solution of L1-Norm Minimization Problems When the Solution May Be Sparse. Technical Report. Dept. of Statistics, Stanford University, 2006. http://www-dsp.rice.edu/files/cs/FastL1.pdf
  133. 133.
    Donoho D, Tanner J. Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing. Philosoph Trans Royal Soc A Math Phys Engin Sci, 2009, 367: 4273–4293MathSciNetzbMATHGoogle Scholar
  134. 134.
    Donoho D, Jin J. Feature selection by higher criticism thresholding achieves the optimal phase diagram. Philosoph Trans Royal Soc A Math Phys Engin Sci, 2009, 367: 4449–4470MathSciNetzbMATHGoogle Scholar
  135. 135.
    Zhu X X, Bamler R. Super-resolution power and robustness of compressive sensing for spectral estimation with application to spaceborne tomographic SAR. IEEE Trans Geosci Remote Sens, 2012, 50: 247–258Google Scholar
  136. 136.
    Herman M A, Strohmer T. High-resolution radar via compressed sensing. IEEE Trans Signal Process, 2009, 57: 2275–2284MathSciNetGoogle Scholar
  137. 137.
    Jiang H. Study on Processing Algorithm and Analysis of Imaging Performance of Compressed Sensing Radar via Information Theory. Master’s thesis. Beijing: Institute of Electronics, Chinese Academy of Sciences, 2011Google Scholar
  138. 138.
    Jiang C L, Zhang B C, Zhang Z, et al. Experimental results and analysis of Sparse Microwave Imaging from spaceborne radar raw data. Sci China Inf Sci, 2012, 55: 1801–1815MathSciNetGoogle Scholar
  139. 139.
    Zhang B C, Hong W, Wu Y R, et al. A Radar Imaging Azimuth Ambiguity Reducing Method Based on q Regularization (in Chinese). China Patent, 201110310655.5. 2012.Google Scholar
  140. 140.
    Lin Y G, Zhang B C, Jiang H, et al. Multi-channel SAR imaging based on distributed compressive sensing. Sci China Inf Sci, 2012, 55: 245–259MathSciNetGoogle Scholar
  141. 141.
    Lin Y G, Zhang B C, Hong W, et al. Along-track interferometric SAR imaging based on distributed compressed sensing. Electron Lett, 2010, 46: 85–860Google Scholar
  142. 142.
    Lin Y G. Study on Multi-channel SAR Imaging Based on Compressive Sensing. Ph.D. thesis. Beijing: Institute of Electronics, Chinese Academy of Sciences, 2011Google Scholar
  143. 143.
    Farhat N H, Werner C L, Chu T H. Prospects for three-dimensional projective and tomographic imaging radar networks. Radio Sci, 1984, 19: 1347–1355Google Scholar
  144. 144.
    Mahafza B R, Sajjadi M. Three-dimensional SAR imaging using linear array in transverse motion. IEEE Trans Aerosp Electron Syst, 1996, 32: 499–510Google Scholar
  145. 145.
    Reigber A, Moreira A. First demonstration of airborne SAR tomography using multibaseline L-band data. IEEE Trans Geosci Remote Sens, 2000, 38: 2142–2152Google Scholar
  146. 146.
    Zhu X X, Bamler R. Tomographic SAR inversion by L1-norm regularization — the compressive sensing approach. IEEE Trans Geosci Remote Sens, 2010, 48: 3839–3846Google Scholar
  147. 147.
    Baselice F, Ferraioli G, Pascazio V. Three dimensional reconstruction using COSMO-SkyMed high-resolution data. In: Proceedings of Microwaves, Radar and Remote Sensing Symposium (MRRS), 2011. 161–164Google Scholar
  148. 148.
    Budillon A, Evangelista A, Schirinzi G. Three-dimensional SAR focusing from multipass signals using compressive sampling. IEEE Trans Geosci Remote Sens, 2011, 49: 488–499Google Scholar
  149. 149.
    Zhu X X, Bamler R. Very High Resolution SAR tomography via compressive sensing. In: Proc of Fringe Workshop Advances in the Science and Applications of SAR Interferometry, Frascati, 2009Google Scholar
  150. 150.
    Zhu X X, Bamler R. Compressive sensing for high resolution differential SAR tomography-the SL1MMER algorithm. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Honolulu, 2010. 17–20Google Scholar
  151. 151.
    Zhu X X, Bamler R. Within the resolution cell: Super-resolution in tomographic SAR imaging. In: Proc of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Vancouver, 2011. 2401–2404Google Scholar
  152. 152.
    Zhu X X, Bamler R. Demonstration of Super-Resolution for Tomographic SAR Imaging in Urban Environment. IEEE Trans Geosci Remote Sens, 2012, in pressGoogle Scholar
  153. 153.
    Khomchuk P, Bilik I, Kasilingam D. Compressive sensing-based SAR tomography. In: Proc of IEEE Radar Conference, Washington, 2010. 354–358Google Scholar
  154. 154.
    Tan W X. Study on Theory and Algorithms for Three-Dimensional Synthetic Aperture Radar Imaging. Ph.D. thesis. Beijing: Institute of Electronics, Chinese Academy of Science, 2009Google Scholar
  155. 155.
    Wehner D R. High Resolution Radar. Norwood: Artech House Inc, 1987Google Scholar
  156. 156.
    Zhang L, Xing M, Qiu C W, et al. Achieving higher resolution ISAR imaging with limited pulses via compressed sampling. IEEE Geosci Remote Sens Lett, 2009, 6: 567–71Google Scholar
  157. 157.
    Wang H, Quan Y, Xing M, et al. ISAR imaging via sparse probing frequencies. IEEE Geosci Remote Sens Lett, 2011, 8: 451–455Google Scholar
  158. 158.
    Zhang L, Qiao Z, Xing M, et al. High-resolution ISAR imaging with sparse stepped-frequency waveforms. IEEE Trans Geosci Remote Sens, 2011, 49: 4630–4651Google Scholar
  159. 159.
    Lei Z, Qiao Z, Xing M, et al. High resolution ISAR imaging by exploiting sparse apertures. IEEE Trans Anten Propag, 2011, 60: 997–1008Google Scholar
  160. 160.
    Zhu F, Zhang Q, Xiang Y, et al. Compressive Sensing in ISAR spectrogram data transmission. In: Proc of Asian-Pacific Conference on Synthetic Aperture Radar (APSAR), Xi’an, 2009. 89–92Google Scholar
  161. 161.
    Zhu F, Zhang Q, Lei Q, et al. Reconstruction of moving target’s HRRP using sparse frequency-stepped chirp signal. IEEE Sensors J, 2011, 11: 2327–2334Google Scholar
  162. 162.
    Ye F, Liang D, Zhu J. ISAR enhancement technology based on compressed sensing. Electron Lett, 2011, 47: 620–621Google Scholar
  163. 163.
    Rao W, Li G, Wang X, et al. ISAR imaging of uniformly rotating targets via parametric weighted L1 minimization. In: Proc of Asian-Pacific Conference on Synthetic Aperture Radar (APSAR), Seoul, 2011Google Scholar
  164. 164.
    Daniels D J. Surface-penetrating radar. Electron Commun Engin J, 1996, 8: 165–182Google Scholar
  165. 165.
    Daniels D J. Ground Penetrating Radar. Herts: The Institution of Engineering and Technology, 2004Google Scholar
  166. 166.
    Gurbuz A C, McClellan J H, Scott W R. Compressive sensing for subsurface imaging using ground penetrating radar. Signal Process, 2009, 89: 1959–1972zbMATHGoogle Scholar
  167. 167.
    Feng X, Sato M. Pre-stack migration applied to GPR for landmine detection. Inverse Problem, 2004, 20: S99zbMATHGoogle Scholar
  168. 168.
    Stolt R H. Migration by Fourier transform. Geophysics, 1978, 43: 23–48Google Scholar
  169. 169.
    Gurbuz A C, McClellan J H, Scott W R. Compressive sensing for GPR imaging. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2007. 2223–2227Google Scholar
  170. 170.
    Gurbuz A C, McClellan J H, Scott W R. GPR imaging using compressed measurements. In: Proc of IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Boston, 2008. 11–13Google Scholar
  171. 171.
    Suksmono A B, Bharata E, Lestari A A, et al. A compressive SFCW-GPR system. In: Proc of 12th Int Conf on Ground Penet Radar, Birmingham, 2008. 16–19Google Scholar
  172. 172.
    Suksmono A B, Bharata E, Lestari A A, et al. Compressive stepped-frequency continuous-wave ground-penetrating radar. IEEE Geosci Remote Sens Lett, 2010, 7: 665–669Google Scholar
  173. 173.
    Gurbuz A C, McClellan J H, Scott W R. A compressive sensing data acquisition and imaging method for stepped frequency GPRs. IEEE Trans Signal Process, 2009, 57: 2640–2650MathSciNetGoogle Scholar
  174. 174.
    Soldovieri F, Solimene R, Ahmad F. A fast data acquisition and processing scheme for through-the-wall radar imaging. In: Proc SPIE, 2011. 8021Google Scholar
  175. 175.
    Varshney K R, CII J W, et al. Joint image formation and anisotropy characterization in wide-angle SAR. In: Proc SPIE, 2006. 6237Google Scholar
  176. 176.
    Stojanovic I, C Proceedings of SPIE, 2008. 6970Google Scholar
  177. 177.
    Soumekh M. Reconnaissance with slant plane circular SAR imaging. IEEE Trans Image Process, 1996, 5: 1252–1265Google Scholar
  178. 178.
    Potter L C, Ertin E, Parker J T, et al. Sparsity and compressed sensing in radar imaging. Proc IEEE, 2010, 98: 1006–1020Google Scholar
  179. 179.
    Lin Y, Hong W, Tan W X, et al. Compressed sensing technique for circular SAR imaging. In: Proc of IET International Radar Conference, Guilin, 2009Google Scholar
  180. 180.
    Lin Y. Study on Algorithms for Circular Synthetic Aperture Radar Imaging. Ph.D. thesis. Beijing: Institute of Electronics, Chinese Academy of Sciences, 2011Google Scholar
  181. 181.
    Fishler E, Haimovich A, Blum R, et al. MIMO radar: An idea whose time has come. In: Proc of IEEE Radar Conference, Philadelphia, 2004. 71–78Google Scholar
  182. 182.
    Li J, Stoica P. MIMO Radar Signal Processing. Hoboken: Wiley, 2009Google Scholar
  183. 183.
    Bliss D W, Forsythe K W. Multiple-input multiple-output (MIMO) radar and imaging: degrees of freedom and resolution. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2003. 54–59Google Scholar
  184. 184.
    Chen C Y, Vaidyanathan P P. Compressed sensing in MIMO radar. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2008. 41–44Google Scholar
  185. 185.
    Strohmer T, Friedlander B. Compressed sensing for MIMO radar-algorithms and performance. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2009. 464–468Google Scholar
  186. 186.
    Petropulu A P, Yu Y, Poor H V. Distributed MIMO radar using compressive sampling. In: Conference Record of Asilomar Conference on Signals, Systems and Computers (ACSSC), Pacific Grove, 2008. 203–207Google Scholar
  187. 187.
    Yu Y, Petropulu A, Poor H V. MIMO radar using compressive sampling. IEEE J Sel Top Signal Process, 2010, 4: 146–163Google Scholar
  188. 188.
    Yu Y, Petropulu A, Poor H. Measurement matrix design for compressive sensing based MIMO radar. IEEE Trans Signal Process, 2011, 59: 5338–5352MathSciNetGoogle Scholar
  189. 189.
    Gogineni S, Nehorai A. Target estimation using sparse modeling for distributed MIMO radar. IEEE Trans Signal Process, 2011, 59: 5315–5325MathSciNetGoogle Scholar
  190. 190.
    Tan X, Roberts W, Li J, et al. Sparse learning via iterative minimization with application to MIMO radar imaging. IEEE Trans Signal Process, 2011, 59: 1088–1101MathSciNetGoogle Scholar
  191. 191.
    Berger C R, Zhou S, Willett P. Signal extraction using compressed sensing for passive radar with OFDM signals. In: Proc of 11th International Conference on Information Fusion, Cologne, 2008Google Scholar
  192. 192.
    Xu H, He X, Yin Z, et al. Compressive sensing MIMO radar imaging based on inverse scattering model. In: Proc of IEEE International Conference on Signal Processing (ICSP), Beijing, 2010. 1999–2002Google Scholar
  193. 193.
    Wang J, Li G, Zhang H, et al. SAR Imaging of Moving Targets via Compressive Sensing. ArXiv: 11041074, 2011. http://arxiv.org/pdf/1104.1074
  194. 194.
    Khwaja A S, Ma J. Applications of compressed sensing for SAR moving-target velocity estimation and image compression. IEEE Trans Instrum Meas, 2011, 60: 2848–2860Google Scholar
  195. 195.
    Stojanovic I, Karl W C. Imaging of moving targets with multi-static SAR using an overcomplete dictionary. IEEE J Sel Top Signal Process, 2010, 4: 164–176Google Scholar
  196. 196.
    Ferrara M, Jackson J, Stuff M. Three-dimensional sparse-aperture moving-target imaging. In: Proceedings of SPIE, 2008. 6970Google Scholar
  197. 197.
    Benz U, Strodl K, Moreira A. A comparison of several algorithms for SAR raw data compression. IEEE Trans Geosci Remote Sens, 1995, 33: 1266–1276Google Scholar
  198. 198.
    Kwok R, Johnson W. Block adaptive quantization of Magellan SAR data. IEEE Trans Geosci Remote Sens, 1989, 27: 375–383Google Scholar
  199. 199.
    Bhattacharya S, Blumensath T, Mulgrew B, et al. Fast encoding of synthetic aperture radar raw data using compressed sensing. In: Proc of 14th IEEE Workshop on Statistical Signal Processing, Madison, 2007. 448–452Google Scholar
  200. 200.
    Bhattacharya S, Blumensath T, Mulgrew B, et al. Synthetic aperture radar raw data encoding using compressed sensing. In: Proc of IEEE Radar Conference, Rome, 2008Google Scholar
  201. 201.
    Sarvotham S, Baron D, Baraniuk R G. Measurements vs. bits: Compressed sensing meets information theory. In: Proc of 44th Allerton Conf Comm Ctrl Computing, Monticello, 2006Google Scholar
  202. 202.
    Wainwright M J. Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting. IEEE Trans Inf Theory, 2009, 55: 5728–5741MathSciNetGoogle Scholar
  203. 203.
    Aeron S, Saligrama V, Zhao M. Information theoretic bounds for compressed sensing. IEEE Trans Inf Theory, 2010, 56: 5111–5130MathSciNetGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Science and Technology on Microwave Imaging LaboratoryBeijingChina
  2. 2.Institute of ElectronicsChinese Academy of SciencesBeijingChina

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