Skip to main content
Log in

Current progress in sparse signal processing applied to radar imaging

  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Sparse signal processing is a signal processing technique that takes advantage of signal’s sparsity, allowing signal to be recovered with a reduced number of samples. Compressive sensing, a new branch of the sparse signal processing, has become a rapidly growing research field. Sparse microwave imaging introduces the sparse signal processing theory to radar imaging to obtain new theories, new systems and new methodologies of microwave imaging. This paper first summarizes the latest application of sparse microwave imaging, including Synthetic Aperture Radar (SAR), tomographic SAR and inverse SAR. As sparse signal processing keeps evolving, an avalanche of results have been obtained. We also highlight its recent theoretical advances, including structured sparsity, off-grid, Bayesian approaches, and point out new research directions in sparse microwave imaging.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Elad M. Sparse and redundant representations: from theory to applications in signal and image processing. New York, NY: Springer, 2010

    Book  Google Scholar 

  2. Yonina C. Compressed Sensing: Theory and Applications. In: Eldar Y, Kutyniok G, ed. Cambridge University Press, 2012

  3. Zhang B C, Hong W, Wu Y. R. Sparse microwave imaging: principles and applications. Sci China Inf Sci, 2012, 55(8): 1722–1754

    Article  MathSciNet  MATH  Google Scholar 

  4. Baraniuk R, Steeghs P. Compressive radar imaging. In: Proc of IEEE Radar Conference, Boston, 2007. 128–133

    Google Scholar 

  5. Patel V M, Easley G R, Healy D, et al. Compressed synthetic aperture radar. IEEE J Sel Top Signal Process, 2010, 4(2): 244–254

    Article  Google Scholar 

  6. Ender J H G. On compressive sensing applied to radar. Signal Process, 2010, 90(5): 1402–1414

    Article  MATH  Google Scholar 

  7. 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(8): 1801–1815

    Article  MathSciNet  Google Scholar 

  8. Stojanovic I, Cetin M, Karl W C. Compressed sensing of monostatic and multistatic SAR. IEEE Geosci Remote Sens Lett, 2013, 10(6): 1444–1448

    Article  Google Scholar 

  9. Sun J P, Zhang Y X, Tian J H, 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(8): 1876–1887

    Article  MathSciNet  MATH  Google Scholar 

  10. Xu H P, You Y N, Li C S, et al. Spotlight SAR sparse sampling and imaging method based on compressive sensing. Sci China Inf Sci, 2012, 55(8): 1816–1829

    Article  MathSciNet  Google Scholar 

  11. Zeng C, Wang M H, Liao G S, et al. Sparse synthetic aperture radar imaging with optimized azimuthal aperture. Sci China Inf Sci, 2012, 55(8): 1852–1859

    Article  MathSciNet  MATH  Google Scholar 

  12. Shastry M C, Narayanan R M, Rangaswamy M. Compressive radar imaging using white stochastic waveforms. In: Proceeding of International Waveform Diversity and Design Conference (WDD), Niagara Falls, 2010. 90–94

    Google Scholar 

  13. Yang J, Thompson J, Huang X, et al. Random-frequency SAR imaging based on compressed sensing. IEEE Trans Geosci Remote Sens, 2013. 51(2): 983–994

    Article  Google Scholar 

  14. Fang J, Xu Z B, Zhang B C, et al. Fast compressed sensing SAR imaging based on approximated observation. IEEE J Sel Topics Appl Earth Observ Remote Sens, accepted

  15. Yang J, Thompson J, Huang X, et al. Segmented reconstruction for compressed sensing SAR imaging. IEEE Trans Geosci Remote Sens, 2013. 51(7): 4214–4225

    Article  Google Scholar 

  16. Fang J, Zeng J S, Xu Z B, et al. Efficient DPCA SAR imaging with fast iterative spectrum reconstruction method. Sci China Inf Sci, 2012, 55(8): 1838–1851

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhu X X, Bamler R. Tomographic SAR inversion by L1-Norm regularization — The compressive sensing approach. IEEE Trans Geosci Remote Sens, 2010, 48(10): 3839–3846

    Article  Google Scholar 

  18. Aguilera E, Nannini M, Reigber A. A data-adaptive compressed sensing approach to polarimetric SAR tomography of forested areas. IEEE Geosci Remote Sens Lett, 2013, 10(3): 543–547

    Article  Google Scholar 

  19. Zhu X X, Bamler R. Let’s do the time warp: multicomponent nonlinear motion estimation in differential SAR tomography. IEEE Geosci Remote Sens Lett, 2011, 8(4): 735–739

    Article  Google Scholar 

  20. 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(1): 247–258

    Article  Google Scholar 

  21. Aguilera E, Nannini M, Reigber A. Multisignal compressed sensing for polarimetric SAR tomography. IEEE Geosci Remote Sens Lett, 2013, 9(5): 871–875

    Article  Google Scholar 

  22. Zhu F, Zhang Q, Luo Y, et al. A novel cognitive ISAR imaging method with random stepped frequency chirp signal. Sci China Inf Sci, 2012, 55(8): 1910–1924

    Article  MathSciNet  MATH  Google Scholar 

  23. Giusti E, Tomei S, Bacci A, et al. Autofocus for CS based ISAR imaging in the presence of Gapped Data. In: 2nd International Workshop on Compressed Sensing Applied to Radar (CoSeRa), 2013

    Google Scholar 

  24. Ugur S, Arikan O, Gubuz A. Autofocused sparse SAR image reconstruction by EMMP algorithm. In: 1st International Workshop on Compressed sensing Applied to Radar (CoSeRa), 2012

    Google Scholar 

  25. Yu X, Rao W, Li G, et al. ISAR motion compensation via parametric compressed sensing. In: IEEE Radar Conference, 2013. 1–4

    Google Scholar 

  26. Ender J H G. A brief review of compressive sensing applied to radar. In: 14th International Radar Symposium (IRS), 2013. 3–16

    Google Scholar 

  27. Zhang L, Xing M D, 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): 3824–3838

    Article  Google Scholar 

  28. Strohmer T. Measure what should be measured: progress and challenges in compressive sensing. IEEE Signal Process Lett, 2012, 19(12): 887–893

    Article  Google Scholar 

  29. Elad M. Sparse and redundant representation modeling — what next? IEEE Signal Process Lett, 2012, 19(12): 922–928

    Article  Google Scholar 

  30. Huang J, Zhang T. The benefit of group sparsity. The Annals Statis, 2010, 38(4): 1978–2004

    Article  MATH  Google Scholar 

  31. Yu G, Sapiro G, Mallat S. Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity. IEEE Trans Image Process, 2012, 21(5): 2481–2499

    Article  MathSciNet  Google Scholar 

  32. Daudet L. Sparse and structured decomposition of audio signals in overcomplete spaces. In: International Conference on Digital Audio Effects, 2004. 1–5

    Google Scholar 

  33. Baraniuk R G, Cevher V, Duarte M F, et al. Model-based compressive sensing. IEEE Trans Inform Theory, 2010, 56(4): 1982–2001

    Article  MathSciNet  Google Scholar 

  34. Zhang B C, Jiang C L, Zhang Z, et al. Azimuth ambiguity suppression for SAR imaging based on group sparse reconstruction. In: 2nd International Workshop on Compressed sensing applied to radar (CoSeRa), 2013

    Google Scholar 

  35. Petropulu A P, Yu Y, Huang J. On exploring sparsity in widely separated MIMO radar. In: 5th IEEE Signals, Systems and Computers Conference(ASILOMAR), 2011. 1496–1500

    Google Scholar 

  36. Gretsistas A, Plumbley M D. A source localization approach based on structured sparsity for broadband far-field sources. In: Proc 4th Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS), Edinburgh, 2011. 35

    Google Scholar 

  37. Leigsnering M, Ahmad F, Amin M. General MIMO Framework for multipath exploitation in through the wall radar imaging. In: 2nd International Workshop on Compressed sensing applied to radar (Co-SeRa), 2013

    Google Scholar 

  38. Herman M A, Strohmer T. High-resolution radar via compressed sensing. IEEE Trans Signal Process, 2009, 57(6): 2275–2284

    Article  MathSciNet  Google Scholar 

  39. Fannjiang A, Liao W. Mismatch and resolution in compressive imaging. In: Proc SPIE, 2011. 81380Y–81380Y

    Google Scholar 

  40. Tang G, Bhaskar B N, Shah P, et al. Compressed sensing off the grid. arXiv:1207.6053. 2012

    Google Scholar 

  41. Fannjiang A, Tseng H C. Compressive radar with off-grid and extended targets. arXiv:1209.6399. 2012

    Google Scholar 

  42. Romer F, Alieiev R, Ibrahim M, et al. An analytical study of sparse recovery algorithms in presence of an off-grid source. In: 2nd International Workshop on Compressed Sensing Applied to Radar (Co-SeRa), 2013

    Google Scholar 

  43. Minner M. Off-Grid compressive sensing MIMO radar. In: 2nd International Workshop on Compressed Sensing Applied to Radar (CoSeRa), 2013

    Google Scholar 

  44. Prünte L. Off-Grid compressed sensing for GMTI using SAR images. In: 2nd International Workshop on Compressed Sensing Applied to Radar (CoSeRa), 2013

    Google Scholar 

  45. Teke O, Gurbuz A, Arikan O. Sparse delay-doppler image reconstruction under off-grid problem. In: 2nd International Workshop on Compressed Sensing Applied to Radar (CoSeRa), 2013

    Google Scholar 

  46. Ji S H, Ya X, Lawrence C. Bayesian compressive sensing. IEEE Trans Signal Process, 2008, 56(6): 2346–2356

    Article  MathSciNet  Google Scholar 

  47. Derin B S, Molina R, Katsaggelos A K. Bayesian compressive sensing using Laplace priors. IEEE Trans Image Process, 2010, 19(1): 53–63

    Article  MathSciNet  Google Scholar 

  48. Donoho D L, Maleki A, Montanari A. Message passing algorithms for compressed sensing: I. motivation and construction. In: IEEE Information Theory Workshop (ITW), 2010

    Google Scholar 

  49. Donoho D L, Maleki A, Montanari A. Message passing algorithms for compressed sensing: II. analysis and validation. In: IEEE Proceedings of Information Theory Workshop (ITW), 2010

    Google Scholar 

  50. Xu G, Xing M D, Zhang L. Bayesian inverse synthetic aperture radar imaging. IEEE Geosci Remote Sens Lett, 2011, 8(6): 1150–1154

    Article  Google Scholar 

  51. Raj R G, Zachary C, Love D L. A sparse Bayesian approach to multistatic radar imaging. In: IEEE 45th Asilomar Conference on Signals Systems and Computers (ASILOMAR), 2011

    Google Scholar 

  52. Xu J, Pi Y, Cao Z. Bayesian compressive sensing in synthetic aperture radar imaging. IET Radar Sonar & Nav, 2012, 6(1): 2–8

    Article  Google Scholar 

  53. Daubechies I. Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math, 1988, 41(7): 909–996

    Article  MathSciNet  MATH  Google Scholar 

  54. Bu H X, Bai X, Tao R. Compressed sensing SAR imaging based on sparse representation in fractional Fourier domain. Sci China Inf Sci, 2012, 55: 1789–1800

    Article  MathSciNet  MATH  Google Scholar 

  55. Olshausen B A, Field D J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996, 381: 607–609

    Article  Google Scholar 

  56. Candes E J, Recht B. Exact matrix completion via convex optimization. Found Comput Math, 2009, 9(6): 717–772

    Article  MathSciNet  MATH  Google Scholar 

  57. Wright J, Ganesh A, Rao S, et al. Robust principal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization. Adv Neural Inform Process Syst, 2009(22): 2080–2088

    Google Scholar 

  58. Candes E J, Plan Y. Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements. IEEE Trans Inform Theory, 2011, 57(4): 2342–2359

    Article  MathSciNet  Google Scholar 

  59. Ji S, Dunson D, Carin L. Multitask compressive sensing. IEEE Trans Signal Process, 2009, 57(1): 92–106

    Article  MathSciNet  Google Scholar 

  60. Mishali M, Eldar Y C, Dounaevsky O, et al. Xampling: Analog to digital at sub-Nyquist rates. IET Circ Dev Syst, 2011, 5(1): 8–20

    Article  Google Scholar 

  61. Hunt J, Driscoll T, Mrozack A, et al. Metamaterial apertures for computational imaging. Science, 2013, 339(6117): 310–313

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yao Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, Y., Feng, J., Zhang, B. et al. Current progress in sparse signal processing applied to radar imaging. Sci. China Technol. Sci. 56, 3049–3054 (2013). https://doi.org/10.1007/s11431-013-5415-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-013-5415-y

Keywords

Navigation