OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 7 — Jul. 1, 2010
  • pp: 1638–1646

Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging

Zhimin Xu and Edmund Y. Lam  »View Author Affiliations

JOSA A, Vol. 27, Issue 7, pp. 1638-1646 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (616 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Terahertz (THz) time-domain imaging is an emerging modality and has attracted a lot of interest. However, existing THz imaging systems often require a long scan time and sophisticated system design. Recently, a new design incorporating compressed sensing (CS) leads to a lower detector cost and shorter scan time, in exchange for computation in an image reconstruction step. In this paper, we develop two reconstruction algorithms that can estimate the underlying scene as accurately as possible. First is a single-band CS reconstruction method, where we show that by making use of prior information about the phase and the correlation between the spatial distributions of the amplitude and phase, the reconstruction quality can be significantly improved over previously published methods. Second, we develop a method that uses the multi-frequency nature of the THz pulse. Through effective use of the spatial sparsity, spectroscopic phase information, and correlations across the hyperspectral bands, our method can further enhance the recovered image quality. This is demonstrated by computation on a set of experimental THz data captured in a single-pixel THz system.

© 2010 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(110.1758) Imaging systems : Computational imaging
(110.6795) Imaging systems : Terahertz imaging

ToC Category:
Imaging Systems

Original Manuscript: December 10, 2009
Revised Manuscript: May 19, 2010
Manuscript Accepted: May 25, 2010
Published: June 16, 2010

Zhimin Xu and Edmund Y. Lam, "Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging," J. Opt. Soc. Am. A 27, 1638-1646 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39, R301–R310 (2006). [CrossRef]
  2. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003). [CrossRef] [PubMed]
  3. S. Wietzke, C. Jöerdens, N. Krumbholz, B. Baudrit, M. Bastian, and M. Koch, “Terahertz imaging: a new non-destructive technique for the quality control of plastic weld joints,” J. Eur. Opt. Soc. Rapid Publ. 2, 07013 (2007). [CrossRef]
  4. R. M. Woodward, “Terahertz technology in global homeland security,” Proc. SPIE 5781, 22–31 (2005). [CrossRef]
  5. N. Karpowicz, H. Zhong, C. Zhang, K.-I. Lin, J.-S. Hwang, J. Xu, and X.-C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005). [CrossRef]
  6. D. Zimdars, “High speed terahertz reflection imaging,” Proc. SPIE 5692, 255–259 (2005). [CrossRef]
  7. W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33, 974–976 (2008). [CrossRef] [PubMed]
  8. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008). [CrossRef]
  9. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006). [CrossRef]
  10. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006). [CrossRef]
  11. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 325–1379 (2007). [CrossRef]
  12. J. J. Fuchs, “Convergence of a sparse representations algorithm applicable to real or complex data,” IEEE J. Sel. Top. Signal Process. 1, 598–605 (2007). [CrossRef]
  13. L. Chaâri, J.-C. Pesquet, A. Benazza-Benyahia, and P. Ciuciu, “Minimization of a sparsity promoting criterion for the recovery of complex-valued signals,” presented at SPARS’09: Signal Processing with Adaptive Sparse Structured Representation, Saint Malo, France, 2009.
  14. A. Luukanen, A. J. Miller, and E. N. Grossman, “Passive hyperspectral terahertz imagery for security screening using a cryogenic microbolometer,” Proc. SPIE 5789, 127–134 (2005). [CrossRef]
  15. M. C. Kemp, A. Glauser, and C. Baker, “Recent developments in people screening using terahertz technology: seeing the world through terahertz eyes,” Proc. SPIE 6212, 62120T (2006). [CrossRef]
  16. Z. Xu and E. Y. Lam, “Hyperspectral reconstruction in biomedical imaging using terahertz systems,” in IEEE International Symposium on Circuits and Systems (IEEE, 2010), pp. 2079–2082.
  17. Z. Xu, W. L. Chan, D. M. Mittleman, and E. Y. Lam, “Sparse reconstruction of complex signals in compressed sensing terahertz imaging,” in Signal Recovery and Synthesis, OSA Technical Digest (CD) (Optical Society of America, 2009), paper STuA4.
  18. E. J. Candès, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted l1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008). [CrossRef]
  19. E. van den Berg and M. P. Friedlander, “Probing the pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. (USA) 31, 890–912 (2008). [CrossRef]
  20. E. van den Berg and M. P. Friedlander, “SPGL1: A solver for large-scale sparse reconstruction,” http://www.cs.ubc.ca/labs/scl/spgl1.
  21. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007). [CrossRef]
  22. E. J. Candès and J. Romberg, “l1-magic: Recovery of sparse signals via convex programming,” http://www.acm.caltech.edu/l1magic.
  23. J. L. Marroquin, J. A. Quiroga, and R. Rodriguez-Vera, “Piecewise smooth phase reconstruction,” Opt. Lett. 24, 1802–1804 (1999). [CrossRef]
  24. G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express 17, 624–639 (2009). [CrossRef] [PubMed]
  25. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009). [CrossRef] [PubMed]
  26. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009). [CrossRef] [PubMed]
  27. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008). [CrossRef] [PubMed]
  28. J. Ma and M. Fenn, “Combined complex ridgelet shrinkage and total variation minimization,” SIAM J. Sci. Comput. (USA) 28, 984–1000 (2006). [CrossRef]
  29. I. Atkinson, F. Kamalabadi, and D. L. Jones, “Wavelet-based hyperspectral image estimation,” in IEEE International Geoscience and Remote Sensing SymposiumIEEE, (2003), pp. 743–745.
  30. I. Atkinson, F. Kamalabadi, S. Mohan, and D. L. Jones, “Asymptotically optimal blind estimation of multichannel images,” IEEE Trans. Image Process. 15, 992–1007 (2006). [CrossRef] [PubMed]
  31. R. M. Willett and R. D. Nowak, “Multiscale poisson intensity and density estimation,” IEEE Trans. Inf. Theory 53, 3171–3187 (2007). [CrossRef]
  32. K. Krishnamurthy and R. M. Willett, “Multiscale reconstruction of photon-limited hyperspectral data,” in IEEE/SP 14th Workshop on Statistical Signal Processing, (IEEE, 2007), pp. 596–600. [CrossRef]
  33. D. L. Donoho and X. Huo, “Beamlets and multiscale image analysis,” in Multiscale and Multiresolution Methods: Theory and Applications, T.J.Barth, T.Chan, and R.Haimes, eds., Lecture Notes in Computational Science and Engineering (Springer, 2001), pp. 149–196.
  34. L. Duvillaret, F. Garet, and J.-L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited