Sparsity and Compressed Sensing in Mono-Static and Multi-Static Radar Imaging

Part of the Signals and Communication Technology book series (SCT)


This chapter is concerned with the application of sparsity and compressed sensing ideas in imaging radars, also known as synthetic aperture radars (SARs). We provide a brief overview of how sparsity-driven imaging has recently been used in various radar imaging scenarios. We then focus on the problem of imaging from undersampled data, and point to recent work on the exploitation of compressed sensing theory in the context of radar imaging. We consider and describe in detail the geometry and measurement model for multi-static radar imaging, where spatially distributed multiple transmitters and receivers are involved in data collection from the scene to be imaged. The mono-static case, where transmitters and receivers are collocated is treated as a special case. For both the mono-static and the multi-static scenarios we examine various ways and patterns of undersampling the data. These patterns reflect spectral and spatial diversity trade-offs. Characterization of the expected quality of the reconstructed images in these scenarios prior to actual data collection is a problem of central interest in task planning for multi-mode radars. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance in imaging sparse scenes. With this motivation we propose a closely related, but more effective parameter we call the \(t_\%\)-average mutual coherence as a sensing configuration quality measure and examine its ability to predict reconstruction quality in various mono-static and ultra-narrow band multi-static configurations.


  1. 1.
    Potter LC, Ertin E, Parker JT, Çetin M (2010) Sparsity and compressed sensing in radar imaging. Proc. IEEE 98:1006–1020CrossRefGoogle Scholar
  2. 2.
    Çetin M, Karl WC (2001) Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization. IEEE Trans Image Process 10:623–631CrossRefMATHGoogle Scholar
  3. 3.
    Çetin M, Karl WC, Willsky AS (2006) Feature-preserving regularization method for complex-valued inverse problems with application to coherent imaging. Opt Eng 45(1):017003CrossRefGoogle Scholar
  4. 4.
    Candes EJ, Romberg J, Tao T (2006) Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetCrossRefGoogle Scholar
  6. 6.
    Donoho DL, Elad M, Temlyakov V (2006) Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans Inf Theory 52(1):6–18MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lustig M, Donoho DL, Pauly JM (2007) Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med 58:1182–1195CrossRefGoogle Scholar
  8. 8.
    Jakowatz CV, Wahl DE, Eichel PS, Ghiglian DC, Thompson PA (1996) Spotlight-mode synthetic aperture radar: a signal processing approach. Kluwer Academic Publishers, NorwellCrossRefGoogle Scholar
  9. 9.
    Stojanovic I, Çetin M, Karl WC (2013) Compressed sensing of monostatic and multistatic SAR. IEEE Geosci Remote Sens LettGoogle Scholar
  10. 10.
    Donoho DL, Elad M (2003) Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization. Proc Nat Acad Sci 100(5):2197–2202MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Gribonval R, Nielsen M (2003) Sparse representations in unions of bases. IEEE Trans Inf Theory 49(12):3320–3325MathSciNetCrossRefGoogle Scholar
  12. 12.
    Fuchs J-J (2004) On sparse representations in arbitrary redundant bases. IEEE Trans Inf Theory 50(6):1341–1344CrossRefGoogle Scholar
  13. 13.
    Malioutov DM, Çetin M, Willsky AS (2004) Optimal sparse representations in general overcomplete bases. Proc IEEE Int Conf Acoust Speech Signal Process 2: 793–796Google Scholar
  14. 14.
    Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20:33–61MathSciNetCrossRefGoogle Scholar
  15. 15.
    Daubechies I, Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math 57(11):1413–1457CrossRefMATHGoogle Scholar
  16. 16.
    Figueiredo MAT, Nowak RD, Wright SJ (2007) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J Sel Top Sign Proces 1(4):586–597CrossRefGoogle Scholar
  17. 17.
    Kim S-J, Koh K, Lustig M, Boyd S, Gorinevsky D (2007) An interior-point method for large-scale l1-regularized least squares. IEEE J Sel Top Sig Process 1(4):606–617CrossRefGoogle Scholar
  18. 18.
    Van den Berg E, Friedlander MP (2008) Probing the pareto frontier for basis pursuit solutions. SIAM J Sci Comput 31(2):890–912MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Hale ET, Yin W, Zhang Y (2008) Fixed-point continuation for \(\ell _1\)-minimization: methodology and convergence. SIAM J Optim 19:1107–1130MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Wright SJ, Nowak RD, Figueiredo MAT (2009) Sparse reconstruction by separable approximation. IEEE Trans Sig Process 57(7):2479–2493MathSciNetCrossRefGoogle Scholar
  21. 21.
    Mallat S, Zhang Z (1993) Matching pursuits with time-frequency dictionaries. IEEE Trans Sig Process 41(12):3397–3415CrossRefMATHGoogle Scholar
  22. 22.
    Tropp JA (2004) Greed is good: algorithmic results for sparse approximation. IEEE Trans Inf Theory 50(10):2231–2242MathSciNetCrossRefGoogle Scholar
  23. 23.
    Candes EJ, Romberg J (2007) Sparsity and incoherence in compressive sampling. Inverse Prob 23(3):969–985MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Donoho DL, Huo X (2001) Uncertainty principles and ideal atomic decomposition. IEEE Trans Inf Theory 47(7):2845–2862MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Elad M (2007) Optimized projections for compressed sensing. IEEE Trans Sig Process 55(12):5695–5702MathSciNetCrossRefGoogle Scholar
  26. 26.
    Samadi S, Çetin M, Masnadi-Shirazi MA (2009) Multiple feature-enhanced synthetic aperture radar imaging. In Zelnio EG, Garber FD (eds) Proceedings algorithms for synthetic aperture Radar imagery XVI. Proceedings SPIE, Orlando, FL, USAGoogle Scholar
  27. 27.
    Geman D, Yang C (1995) Nonlinear image recovery with half-quadratic regularization. IEEE Trans Image Process 4(7):932–946CrossRefGoogle Scholar
  28. 28.
    Çetin M, Karl WC, Castañón DA (2003) Feature enhancement and ATR performance using non-quadratic optimization-based SAR imaging. IEEE Trans Aerosp Electron Syst 39(4):1375–1395CrossRefGoogle Scholar
  29. 29.
    Çetin M, Lanterman A (2005) Region-enhanced passive radar imaging. IEE Proc Radar Sonar Navig 152(3):185–194CrossRefGoogle Scholar
  30. 30.
    Moses RL, Potter LC, Çetin M (2004) Wide angle SAR imaging. In Zelnio EG, Garber FD (eds) Proceedings algorithms for synthetic aperture radar imagery XI. Proceedings SPIE, Orlando, FL, USAGoogle Scholar
  31. 31.
    Çetin M, Moses RL (2005) SAR imaging from partial-aperture data with frequency-band omissions. In Zelnio EG, Garber FD (eds) Proceedings algorithms for synthetic aperture radar imagery XII. Proceedings SPIE, Orlando, FL, USA, 2005Google Scholar
  32. 32.
    Ertin E, Austin CD, Sharma S, Moses RL, Potter LC (2007) GOTCHA experience report: three-dimensional SAR imaging with complete circular apertures. In Zelnio EG, Garber FD, (eds) Proceedings algorithms for synthetic aperture radar imagery XIV, volume 6568 of Proceedings SPIE, Orlando, FL, USA, April 2007Google Scholar
  33. 33.
    Stojanovic I, Çetin M, Karl WC (2008) Joint space aspect reconstruction of wide-angle SAR exploiting sparsity. In Zelnio EG, Garber FD (eds) Proceedings algorithms for synthetic aperture radar imagery XV volume 7337 of Proceedings SPIE, Orlando, FL, USA p 697005Google Scholar
  34. 34.
    Varshney KR, Çetin M, Fisher JW III, Willsky AS (2008) Sparse signal representation in structured dictionaries with application to synthetic aperture radar. IEEE Trans Sig Process 56(8):3548–3561CrossRefGoogle Scholar
  35. 35.
    Tan X, Roberts W, Li J, Stoica P (2011) Sparse learning via iterative minimization with application to MIMO radar imaging. IEEE Trans Sig Process 59(3):1088–1101MathSciNetCrossRefGoogle Scholar
  36. 36.
    Batu Ö, Çetin M ( 2008) Hyper-parameter selection in non-quadratic regularization-based radar image formation. In Zelnio EG, Garber FD (eds) Proceedings of algorithms for synthetic aperture radar imagery XV. Proceedings of SPIE, Orlando, FL, USA, March 2008Google Scholar
  37. 37.
    Önhon Ö, Çetin M (2012) A sparsity-driven approach for joint SAR imaging and phase error correction. IEEE Trans Image Process 21(4):2075–2088MathSciNetCrossRefGoogle Scholar
  38. 38.
    Herman MA, Strohmer T (2009) High-resolution radar via compressed sensing. IEEE Trans Sig Process 57(6):2275–2284MathSciNetCrossRefGoogle Scholar
  39. 39.
    Yoon YS, Amin MG (2008) Compressed sensing technique for high-resolution radar imaging. In Ivan Kadar (ed) Proceedings signal processing, sensor fusion, and target recognition XVII, volume 6968 SPIE Orlando, FL, USAGoogle Scholar
  40. 40.
    Baraniuk R, Steeghs P (2007) Compressive radar imaging. In: Proceedings IEEE radar conference, pp 128–133Google Scholar
  41. 41.
    Bhattacharya S, Blumensath T, Mulgrew B, Davies M (2007) Fast encoding of synthetic aperture radar raw data using compressed sensing. In: Proceedings IEEE 14th Workshop on Statistical signal processing, pp 448–452Google Scholar
  42. 42.
    Gürbüz C, McClellan J, Scott R Jr (2009) A compressive sensing data acquisition and imaging method for stepped frequency gprs. IEEE Trans Sig Process 57(7):2640–2650CrossRefGoogle Scholar
  43. 43.
    Subotic NS, Thelen B, Cooper K, Buller W, Parker J, Browning J, Beyer H (2008) Distributed RADAR waveform design based on compressive sensing considerations. In Proceedings IEEE Radar Conference, p 1–6Google Scholar
  44. 44.
    Ender JHG (2010) On compressive sensing applied to radar. Sig Process 90(5):1402–1414CrossRefMATHGoogle Scholar
  45. 45.
    Stojanovic I, Karl WC, Çetin M (2009) Compressed sensing of mono-static and multi-static SAR. In Zelnio EG, Garber FD (eds) Proceedings algorithms for synthetic aperture radar imagery XVI volume 7337 of Proceedings SPIE, Orlando, FL, USA p 733705Google Scholar
  46. 46.
    Patel VM, Easley GR, Healy DM, Chellappa R (2010) Compressed synthetic aperture radar IEEE J Sel Top Sig Process 4(2): 244–254Google Scholar
  47. 47.
    Chen CY, Vaidyanathan PP (2008) Compressed sensing in MIMO radar. In: Proceedings 42nd asilomar conference on signals, systems and computers, pp 41–44 2008Google Scholar
  48. 48.
    Strohmer T, Friedlander B (2009) Compressed sensing for MIMO radar - algorithms and performance. In Proceedings asilomar conference on signals, systems and computers pp 464–468Google Scholar
  49. 49.
    Petropulu AP, Yu Y, Poor HV ( 2008) Distributed MIMO radar using compressive sampling. In: Proceedings asilomar conference on signals, systems and computers pp 203–207Google Scholar
  50. 50.
    Yu Y, Petropulu AP, Poor HV ( 2010) MIMO radar using compressive sampling. IEEE J Sel Top Sig Process 4(1):146–163Google Scholar
  51. 51.
    van den Berg E, Friedlander MP (2007) SPGL1: a solver for large-scale sparse reconstruction.
  52. 52.
    Himed B, Bascom H, Clancy J, Wicks MC (2001) Tomography of moving targets (TMT). In Fujisada H, Lurie JB, Weber K, (eds) Proceedings sensors, systems, and next-generation satellites V. vol 4540 of Proceedings SPIE, Toulouse, France pp 608–619Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ivana Stojanović
    • 1
  • Müjdat Çetin
    • 2
  • W. Clem Karl
    • 3
  1. 1.Scientific Systems Company, 500 West Cummings ParkWoburnUSA
  2. 2.Sabancı University, Faculty of Engineering and Natural SciencesIstanbulTurkey
  3. 3.Department of Electrical and Computer EngineeringBoston UniversityBostonUSA

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