Skip to main content
SpringerLink
Log in

Numerical simulation of tomographic-SAR imaging and object reconstruction using compressive sensing with L 1/2-norm regularization

  • Article
  • Electromagnetics
  • Published:
Chinese Science Bulletin

Abstract

By making use of multiple acquisitions of synthetic aperture radar (SAR) observations over the same area, tomographic-SAR (tomo-SAR) technology can achieve three-dimensional (3-D) imaging of the objects of interest. The compressive sensing (CS) approach has been applied to deal with the sparseness of the elevation signals. Due to its sparsity and convexity, the L 1-norm regularization, as an approximated L 0-norm with an exact solution, has been employed in CS to reconstruct the reflectivity profile of the objects. In this paper, based on our studies on polarimetric scattering and SAR imaging simulations, we produce numerical multi-pass tomo-SAR observations of the terrain object. Then, we present the CS with novel L 1/2-norm regularization to realize 3-D reconstruction. As a non-convex optimization problem, the L 1/2-norm regularization is solved by an iterative algorithm. This numerical simulation of tomo-SAR imaging and 3-D reconstruction of the object modeling can be of great help for parameterized analysis of tomo-SAR imagery. As an example, a tomo-SAR image and 3-D reconstruction of the Beijing National Stadium model are presented.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Franceschetti G, Lanari R (1999) Synthetic aperture radar processing. CRC Press, Boca Raton

    Google Scholar 

  2. Reigber A, Moreira A (2000) First demonstration of airborne SAR tomography using multibaseline L-band data. IEEE Trans Geosci Remote 38:2142–2152

    Article  Google Scholar 

  3. Sauer S, Ferro-Famil L, Reigber A et al (2008) 3D urban remote sensing using dual-baseline POL-InSAR images at L-band. IEEE Geosci Remote Sens Symp 4:IV-145

    Google Scholar 

  4. Zhu X, Bamler R (2010) Very high resolution spaceborne SAR tomography in urban environment. IEEE Trans Geosci Remote 48:4296–4308

    Article  Google Scholar 

  5. Gini F, Lombardini F (2002) Multilook APES for multibaseline SAR interferometry. IEEE Trans Signal Process 50:1800–1803

    Article  Google Scholar 

  6. Lombardini F, Gini F, Matteucci P et al (2001) Application of array processing techniques to multibaseline InSAR for layover solution. In: Proceeding of the radar conference 2001. IEEE, pp 210–215

  7. Nannini M, Scheiber R, Moreira A (2009) Estimation of the minimum number of tracks for SAR tomography. IEEE Trans Geosci Remote 47:531–543

    Article  Google Scholar 

  8. Candes EJ, Wakin MB, Boyd SP (2008) Enhancing sparsity by reweighted L1 minimization. J Fourier Anal Appl 14:877–905

    Article  Google Scholar 

  9. Donoho DL (2006) Compressed sensing. IEEE Trans Inform Theory 52:1289–1306

    Article  Google Scholar 

  10. Candès EJ, Romberg J, Tao T et al (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory 52:489–509

    Article  Google Scholar 

  11. Xu Z, Zhang H (2010) L1/2 regularization. Sci China Inf Sci 53:1159–1169

    Article  Google Scholar 

  12. Candès EJ (2006) Compressive sampling. In: Proceedings of the international congress of mathematicians, Madrid, Spain, August 22–30, 2006, pp 1433–1452

  13. Chen SS, Donoho DL, Saunders MA (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20:33–61

    Article  Google Scholar 

  14. Candès EJ, Wakin MB (2008) An introduction to compressive sampling. IEEE Signal Process Mag 25:21–30

    Article  Google Scholar 

  15. Boyd SP, Vandenberghe L (2004) Convex optimization. Cambridge university press, Cambridge

    Book  Google Scholar 

  16. Manual, F.U.s., Suite 6.0. EM Software & Systems-SA (Pty) Ltd, 2010. p 32

  17. Xu F, Jin YQ (2009) Bidirectional analytic ray tracing for fast computation of composite scattering from electric-large target over a randomly rough surface. IEEE Trans Antennas Propag 57:1495–1505

    Article  Google Scholar 

  18. Jin YQ, Xu F (2013) Polarimetric scattering and SAR information retrieval. Wiley, Hoboken

    Book  Google Scholar 

  19. Munson DC Jr, O’Brien JD, Jenkins W (1983) A tomographic formulation of spotlight-mode synthetic aperture radar. Proc IEEE 71:917–925

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory for Information Science of Electromagnetic Waves (MoE), Fudan University, Shanghai, 200433, China

    Xiao Wang, Feng Xu & Ya-Qiu Jin

Authors
  1. Xiao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ya-Qiu Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya-Qiu Jin.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Xu, F. & Jin, YQ. Numerical simulation of tomographic-SAR imaging and object reconstruction using compressive sensing with L 1/2-norm regularization. Chin. Sci. Bull. 59, 4600–4607 (2014). https://doi.org/10.1007/s11434-014-0554-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11434-014-0554-5

Keywords

Search

Navigation