Skip to main content
SpringerLink
Log in

Synthetic Aperture Radar Imaging

  • Reference work entry
Handbook of Mathematical Methods in Imaging

Abstract

The purpose of this chapter is to explain the basics of radar imaging and to list a variety of associated open problems. After a short section on the historical background, the chapter includes a derivation of an approximate scalar model for radar data. The basics in inverse synthetic aperture radar (ISAR) are discussed, and a connection is made with the Radon transform. Two types of synthetic aperture radar (SAR), namely, spotlight SAR and stripmap SAR, are outlined. Resolution analysis is included for ISAR and spotlight SAR. Some numerical algorithms are discussed. Finally, the chapter ends with a listing of open problems and a bibliography for further reading.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,200.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baraniuk, R., Steeghs, P.: Compressive radar imaging. In: IEEE Radar Conference, Waltham (2007)

    Book  Google Scholar 

  2. Bethke, B., Valenti, M., How, J.P., Vian, J.: Cooperative vision based estimation and tracking using multiple UAVs. In: Conference on Cooperative Control and Optimization, Gainesville (2007)

    Google Scholar 

  3. Bleistein, N., Cohen, J.K., Stockwell, J.W.: The Mathematics of Multidimensional Seismic Inversion. Springer, New York (2000)

    Google Scholar 

  4. Boerner, W.-M., Yamaguchi, Y.: A state-of-the-art review in radar polarimetry and its applications in remote sensing. IEEE Aerosp. Electron. Syst. Mag. 5, 3–6 (1990)

    Article  Google Scholar 

  5. Borden, B.: Radar Imaging of Airborne Targets. Institute of Physics, Bristol (1999)

    Book  Google Scholar 

  6. Borden, B.: Mathematical problems in radar inverse scattering. Inverse Probl. 18, R1–R28 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bowen, E.G.: Radar Days. Hilgar, Bristol (1987)

    Google Scholar 

  8. Buderi, R.: The Invention That Changed the World. Simon & Schuster, New York (1996)

    Google Scholar 

  9. Carrara, W.C., Goodman, R.G., Majewski, R.M.: Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Artech House, Boston (1995)

    MATH  Google Scholar 

  10. Cetin, M., Karl, W.C., Castañon, D.A.: Analysis of the impact of feature-enhanced SAR imaging on ATR performance. In: Algorithms for SAR Imagery IX, Proceedings of SPIE, vol. 4727 (2002)

    Google Scholar 

  11. Chen, V.C., Ling, H.: Time-Frequency Transforms for Radar Imaging and Signal Analysis. Artech House, Boston (2002)

    MATH  Google Scholar 

  12. Cheney, M.: A mathematical tutorial on synthetic aperture radar. SIAM Rev. 43, 301–312 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Cheney, M., Bonneau, R.J.: Imaging that exploits multipath scattering from point scatterers. Inverse Probl. 20, 1691–1711 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Cheney, M., Borden, B.: Imaging moving targets from scattered waves. Inverse Probl. 24, 035005 (2008)

    Article  MathSciNet  Google Scholar 

  15. Cheney, M., Borden, B.: Fundamentals of Radar Imaging. SIAM, Philadelphia (2009)

    Book  MATH  Google Scholar 

  16. Chew, W.C., Song, J.M.: Fast Fourier transform of sparse spatial data to sparse Fourier data. In: IEEE Antenna and Propagation International Symposium, vol. 4, pp. 2324–2327 (2000)

    Google Scholar 

  17. Cloude, S.R.: Polarization coherence tomography. Radio Sci. 41, RS4017 (2006). doi:10.1029/2005RS003436

    Article  Google Scholar 

  18. Cloude, S.R., Papathanassiou, K.P.: Polarimetric SAR interferometry. IEEE Trans. Geosci. Remote Sens. 36(5, part 1), 1551–1565 (1998)

    Google Scholar 

  19. Cook, C.E., Bernfeld, M.: Radar Signals. Academic, New York (1967)

    Google Scholar 

  20. Cumming, I.G., Wong, F.H.: Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Artech House, Boston (2005)

    Google Scholar 

  21. Curlander, J.C., McDonough, R.N.: Synthetic Aperture Radar. Wiley, New York (1991)

    MATH  Google Scholar 

  22. Cutrona, L.J.: Synthetic aperture radar. In: Skolnik, M. (ed.) Radar Handbook, 2nd edn. McGraw-Hill, New York (1990)

    Google Scholar 

  23. Dickey, F.M., Doerry, A.W.: Recovering shape from shadows in synthetic aperture radar imagery. In: Ranney, K.I., Doerry, A.W. (eds.) Radar Sensor Technology XII. Proceedings of SPIE, vol. 6947, pp. 694707 (2008)

    Google Scholar 

  24. Ding, Y., Munson, D.C. Jr.: A fast back-projection algorithm for bistatic SAR imaging. In: Proceedings of the IEEE International Conference on Image Processing, Rochester, 22–25 Sept 2002 (2002)

    Google Scholar 

  25. Edde, B.: Radar: Principles, Technology, Applications. Prentice-Hall, Englewood Cliffs (1993)

    Google Scholar 

  26. Elachi, C.: Spaceborne Radar Remote Sensing: Applications and Techniques. IEEE, New York (1987)

    Google Scholar 

  27. Ertin, E., Austin, C.D., Sharma, S., Moses, R.L., Potter, L.C.: GOTCHA experience report: three-dimensional SAR imaging with complete circular apertures. Proc. SPIE 6568, 656802 (2007)

    Google Scholar 

  28. Fienup, J.R.: Detecting moving targets in SAR imagery by focusing. IEEE Trans. Aerosp. Electron. Syst. 37, 794–809 (2001)

    Article  Google Scholar 

  29. Franceschetti, G., Lanari, R.: Synthetic Aperture Radar Processing. CRC, New York (1999)

    Google Scholar 

  30. Friedlander, F.G.: Introduction to the Theory of Distributions. Cambridge University Press, New York (1982)

    MATH  Google Scholar 

  31. Garnier, J., Sølna, K.: Coherent interferometric imaging for synthetic aperture radar in the presence of noise. Inverse Probl. 24, 055001 (2008)

    Article  Google Scholar 

  32. Giuli, D.: Polarization diversity in radars. Proc. IEEE 74(2), 245–269 (1986)

    Article  MathSciNet  Google Scholar 

  33. Greengard, L., Lee, J.-Y.: Accelerating the nonuniform fast Fourier transform. SIAM Rev. 46, 443–454 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  34. Jackson, J.D.: Classical Electrodynamics, 2nd edn. Wiley, New York (1962)

    Google Scholar 

  35. Jakowatz, C.V., Wahl, D.E., Eichel, P.H., Ghiglia, D.C., Thompson, P.A.: Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach. Kluwer, Boston (1996)

    Book  Google Scholar 

  36. Ishimaru, A.: Wave Propagation and Scattering in Random Media. IEEE, New York (1997)

    MATH  Google Scholar 

  37. Klug, A., Crowther, R.A.: Three-dimensional image reconstruction from the viewpoint of information theory. Nature 238, 435–440 (1972). doi:10.1038/238435a0

    Article  Google Scholar 

  38. Langenberg, K.J., Brandfass, M., Mayer, K., Kreutter, T., Brüll, A., Felinger, P., Huo, D.: Principles of microwave imaging and inverse scattering. EARSeL Adv. Remote Sens. 2, 163–186 (1993)

    Google Scholar 

  39. Lerosey, G., de Rosny, J., Tourin, A., Fink, M.: Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007)

    Article  Google Scholar 

  40. Lee-Elkin, F.: Autofocus for 3D imaging. Proc. SPIE 6970, 69700O (2008)

    Google Scholar 

  41. Mensa, D.L.: High Resolution Radar Imaging. Artech House, Dedham (1981)

    Google Scholar 

  42. Moses, R., Çetin, M., Potter, L.: Wide Angle SAR Imaging (SPIE Algorithms for Synthetic Aperture Radar Imagery XI). SPIE, Orlando (2004)

    Google Scholar 

  43. Natterer, F.: The Mathematics of Computerized Tomography. SIAM, Philadelphia (2001)

    Book  MATH  Google Scholar 

  44. Natterer, F., Wübbeling, F.: Mathematical Methods in Imaging Reconstruction. SIAM, Philadelphia (2001)

    Book  Google Scholar 

  45. Natterer, F., Cheney, M., Borden, B.: Resolution for radar and X-ray tomography. Inverse Probl. 19, S55–S64 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  46. Nguyen, N., Liu, Q.H.: The regular Fourier matrices and nonuniform fast Fourier transforms. SIAM J. Sci. Comput. 21, 283–293 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  47. Newton, R.G.: Scattering Theory of Waves and Particles. Dover, Mineola (2002)

    MATH  Google Scholar 

  48. Nolan, C.J., Cheney, M.: Synthetic aperture inversion for arbitrary flight paths and non-flat topography. IEEE Trans. Image Process. 12, 1035–1043 (2003)

    Article  MathSciNet  Google Scholar 

  49. Nolan, C.J., Cheney, M., Dowling, T., Gaburro, R.: Enhanced angular resolution from multiply scattered waves. Inverse Probl. 22, 1817–1834 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  50. North, D.O.: Analysis of the factors which determine signal/noise discrimination in radar. Report PPR 6C, RCA Laboratories, Princeton (classified) (1943). Reproduction: North, D.O.: An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems. Proc. IEEE 51(7), 1016–1027 (1963)

    Google Scholar 

  51. Oppenheim, A.V., Shafer, R.W.: Digital Signal Processing. Prentice-Hall, Englewood Cliffs (1975)

    MATH  Google Scholar 

  52. O’Sullivan, J.A., Blahut, R.E., Snyder, D.L.: Information-theoretic image formation. IEEE Trans. Inf. Theory 44, 2094–2123 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  53. Oughstun, K.E., Sherman, G.C.: Electromagnetic Pulse Propagation in Causal Dielectrics. Springer, New York (1997)

    Google Scholar 

  54. Perry, R.P., DiPietro, R.C., Fante, R.L.: SAR imaging of moving targets. IEEE Trans Aerosp. Electron. Syst. 35(1), 188–200 (1999)

    Article  Google Scholar 

  55. Pike, R., Sabatier, P.: Scattering: Scattering and Inverse Scattering in Pure and Applied Science. Academic, New York (2002)

    Google Scholar 

  56. Potter, L.C., Moses, R.L.: Attributed scattering centers for SAR ATR. IEEE Trans. Image Process. 6, 79–91 (1997)

    Article  Google Scholar 

  57. Potts, D., Steidl, G., Tasche, M.: Fast Fourier transforms for nonequispaced data: a tutorial. In: Benedetto, J.J., Ferreira, P. (eds.) Modern Sampling Theory: Mathematics and Applications, chap. 12, pp. 249–274. Birkhäuser, Boston (2001)

    Google Scholar 

  58. Ramachandra, K.V.: Kalman Filtering Techniques for Radar Tracking. CRC, Boca Raton (2000)

    Google Scholar 

  59. Rihaczek, A.W.: Principles of High-Resolution Radar. McGraw-Hill, New York (1969)

    Google Scholar 

  60. Skolnik, M.: Introduction to Radar Systems. McGraw-Hill, New York (1980)

    Google Scholar 

  61. Soumekh, M.: Synthetic Aperture Radar Signal Processing with MATLAB Algorithms. Wiley, New York (1999)

    Google Scholar 

  62. Stakgold, I.: Green’s Functions and Boundary Value Problems, 2nd edn. Wiley-Interscience, New York (1997)

    Google Scholar 

  63. Stefanov, P., Uhlmann, G.: Inverse backscattering for the acoustic equation. SIAM J. Math. Anal. 28, 1191–1204 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  64. Stimson, G.W.: Introduction to Airborne Radar. SciTech, Mendham (1998)

    Book  Google Scholar 

  65. Stuff, M.A., Sanchez, P., Biancala, M.: Extraction of three-dimensional motion and geometric invariants. Multidimens. Syst. Signal Process. 14, 161–181 (2003)

    Article  MATH  Google Scholar 

  66. Sullivan, R.J.: Radar Foundations for Imaging and Advanced Concepts. SciTech, Raleigh (2004)

    Book  Google Scholar 

  67. Swords, S.S.: Technical History of the Beginnings of Radar. Peregrinus, London (1986)

    Book  Google Scholar 

  68. Treuhaft, R.N., Siqueira, P.R.: Vertical structure of vegetated land surfaces from interferometric and polarimetric radar. Radio Sci. 35(1), 141–177 (2000)

    Article  Google Scholar 

  69. Treves, F.: Basic Linear Partial Differential Equations. Academic, New York (1975)

    MATH  Google Scholar 

  70. Trischman, J.A., Jones, S., Bloomfield, R., Nelson, E., Dinger, R.: An X-band linear frequency modulated radar for dynamic aircraft measurement. In: AMTA Proceedings, p. 431. AMTA, New York (1994)

    Google Scholar 

  71. Ulaby, F.T., Elachi, C. (eds.): Radar Polarimetry for Geoscience Applications. Artech House, Norwood

    Google Scholar 

  72. Walsh, T.E.: Military radar systems: history, current position, and future forecast. Microw. J 21, 87, 88, 91–95 (1978)

    Google Scholar 

  73. Weglein, A.B., Araùjo, F.V., Carvalho, P.M., Stolt, R.H., Matson, K.H., Coates, R.T., Corrigan, D., Foster, D.J., Shaw, S.A., Zhang, H.: Inverse scattering series and seismic exploration. Inverse Probl. 19, R27–R83 (2003). doi:10.1088/0266-5611/19/6/R01

    Article  MATH  Google Scholar 

  74. Wehner, D.: High-Resolution Radar, 2nd edn. Scitech, Raleigh (1995)

    Google Scholar 

  75. Woodward, P.M.: Probability and Information Theory, with Applications to Radar. McGraw-Hill, New York (1953)

    MATH  Google Scholar 

  76. Xiao, S., Munson, D.C., Basu, S., Bresler, Y.: An N2logN back-projection algorithm for SAR image formation. In: Proceedings of 34th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, 31 Oct–1 Nov 2000

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Naval Postgraduate School and the Air Force Office of Scientific Research which supported the writing of this article under agreement number FA9550-09-1-0013 (because of this support, the US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the US Government).

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, 12180, Troy, NY, USA

    Margaret Cheney

  2. Department of Physics, Naval Postgraduate School of Engineering, 93943, Monterey, CA, USA

    Brett Borden

Authors
  1. Margaret Cheney
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brett Borden
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Margaret Cheney .

Editor information

Editors and Affiliations

  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this entry

Cite this entry

Cheney, M., Borden, B. (2015). Synthetic Aperture Radar Imaging. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_49

Download citation

Publish with us

Policies and ethics

Search

Navigation