OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 23 — Aug. 10, 2007
  • pp: 5805–5822

Statistical detection and imaging of objects hidden in turbid media using ballistic photons

Sina Farsiu, James Christofferson, Brian Eriksson, Peyman Milanfar, Benjamin Friedlander, Ali Shakouri, and Robert Nowak  »View Author Affiliations

Applied Optics, Vol. 46, Issue 23, pp. 5805-5822 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (6030 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We exploit recent advances in active high-resolution imaging through scattering media with ballistic photons. We derive the fundamental limits on the accuracy of the estimated parameters of a mathematical model that describes such an imaging scenario and compare the performance of ballistic and conventional imaging systems. This model is later used to derive optimal single-pixel statistical tests for detecting objects hidden in turbid media. To improve the detection rate of the aforementioned single-pixel detectors, we develop a multiscale algorithm based on the generalized likelihood ratio test framework. Moreover, considering the effect of diffraction, we derive a lower bound on the achievable spatial resolution of the proposed imaging systems. Furthermore, we present the first experimental ballistic scanner that directly takes advantage of novel adaptive sampling and reconstruction techniques.

© 2007 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(100.0100) Image processing : Image processing
(140.0140) Lasers and laser optics : Lasers and laser optics
(320.0320) Ultrafast optics : Ultrafast optics

ToC Category:
Image Processing

Original Manuscript: February 12, 2007
Revised Manuscript: June 27, 2007
Manuscript Accepted: June 24, 2007
Published: August 9, 2007

Virtual Issues
Vol. 2, Iss. 9 Virtual Journal for Biomedical Optics

Sina Farsiu, James Christofferson, Brian Eriksson, Peyman Milanfar, Benjamin Friedlander, Ali Shakouri, and Robert Nowak, "Statistical detection and imaging of objects hidden in turbid media using ballistic photons," Appl. Opt. 46, 5805-5822 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. C. Dunsby and P. M. W. French, "Techniques for depth-resolved imaging through turbid media including coherence-gated imaging," J. Phys. D 36, 207-227 (2003). [CrossRef]
  2. K. Yoo and R. R. Alfano, "Time-resolved coherent and incoherent components of forward light scattering in random media," Opt. Lett. 15, 320-322 (1990). [CrossRef] [PubMed]
  3. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography --principles and applications," Rep. Prog. Phys. 66, 239-303 (2003). [CrossRef]
  4. M. E. Zevallos, S. K. Gayen, M. Alrubaiee, and R. R. Alfano, "Time-gated backscattered ballistic light imaging of objects in turbid water," Appl. Phys. Lett. 86, 0111151-0111153 (2005). [CrossRef]
  5. M. Paciaroni and M. Linne, "Single-shot, two-dimensional ballistic imaging through scattering media," Appl. Opt. 43, 5100-5109 (2004). [CrossRef] [PubMed]
  6. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory," Appl. Opt. 36, 4587-4599 (1997). [CrossRef] [PubMed]
  7. I. Delfino, M. Lepore, and P. L. Indovina, "Experimental tests of different solutions to the diffusion equation for optical characterization of scattering media by time-resolved transmittance," Appl. Opt. 38, 4228-4236 (1999). [CrossRef]
  8. W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, and R. R. Alfano, "Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements," Appl. Opt. 38, 4237-4246 (1999). [CrossRef]
  9. B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227-292 (1997). [CrossRef]
  10. A. Gibson, J. Hebden, and S. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50, R1-R43 (2005). [CrossRef] [PubMed]
  11. H. Lischke, T. J. Loeffler, and A. Fischlin, "Aggregation of individual trees and patches in forest succession models: capturing variability with height structured, random, spatial distributions," Theor. Popul. Biol. 54, 213-236 (1998). [CrossRef]
  12. S. V. Aert, D. V. Dyck, and A. J. den Dekker, "Resolution of coherent and incoherent imaging systems reconsidered--classical criteria and a statistical alternative," Opt. Express 14, 3830-3839 (2006). [CrossRef] [PubMed]
  13. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993), Vol. 1.
  14. L. L. Scharf, Statistical Signal Processing: Detection, Estimation, and Time Series Analysis (Addison-Wesley, 1991).
  15. G. W. Sutton, "Fog hole boring with pulsed high-energy lasers--an exact solution including scattering and absorption," Appl. Opt. 17, 3424-3430 (1978). [CrossRef] [PubMed]
  16. S. M. Kay, Fundamentals of Statistical Signal Processing Detection Theory (Prentice-Hall, 1998), Vol. 2.
  17. M. Shahram and P. Milanfar, "Imaging below the diffraction limit: a statistical analysis," IEEE Trans. Image Processing 13, 677-689 (2004). [CrossRef]
  18. A. Sommerfeld, Optics Lectures on Theortical Physics (Academic, 1954), Vol. 4.
  19. J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005).
  20. G. B. Parrent, Jr. and B. J. Thompson, "On the Fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent background," J. Mod. Opt. 11, 183-193 (1964). [CrossRef]
  21. D. N. Nikogosyan, "Beta barium borate (BBO)," Appl. Phys. A 52, 359-368 (1991). [CrossRef]
  22. M. Ghotbi and M. Ebrahim-Zadeh, "Optical second harmonic generation properties of BiB3O6," Opt. Express 12, 6002-6019 (2004). [CrossRef] [PubMed]
  23. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math. 59, 1207-1223 (2006). [CrossRef]
  24. J. Haupt and R. Nowak, "Signal reconstruction from noisy random projections," IEEE Trans. Inf. Theory 52, 4036-4048 (2006). [CrossRef]
  25. R. Castro, J. Haupt, and R. Nowak, "Compressed sensing vs. active learning," in 2006 International Conference on Acoustics, Speech and Signal Processing (IEEE, 2006), pp. 820-823.
  26. D. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory 52, 6-18 (2006). [CrossRef]
  27. M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, "An architecture for compressive imaging," in 2006 International Conference on Image Processing (IEEE, 2006), pp. 1273-1276. [CrossRef]
  28. R. Castro, R. Willett, and R. Nowak, "Faster rates in regression via active learning," in 2005 Advances in Neural Information Processing Systems 18 (MIT Press, 2005), pp. 179-186.
  29. S. Farsiu, D. Robinson, M. Elad, and P. Milanfar, "Fast and robust multi-frame super-resolution," IEEE Trans. Image Processing 13, 1327-1344 (2004). [CrossRef]
  30. B. Eriksson and R. Nowak, "Maximum likelihood methods for time-resolved imaging through turbid media," in 2006 International Conference on Image Processing (IEEE, 2006), pp. 641-644. [CrossRef]
  31. S. Fantini, S. Walker, M. Franceschini, M. Kaschke, P. Schlag, and K. Moesta, "Assessment of the size, position, and optical properties of breast tumors in vivoo by noninvasive optical methods," Appl. Opt. 37, 1982-1989 (1998). [CrossRef]
  32. F. Anscombe, "The transformation of Poisson, binomial and negative-binomial data," Biometrika 35, 246-254 (1948).
  33. R. Miller, Simultaneous Statistical Inference (Springer, 1991).
  34. A. Gandjbakhche, G. Weiss, R. Bonner, and R. Nossal, "Photon path-length distributions for transmission through optically turbid slabs," Phys. Rev. E 48, 810-818 (1993). [CrossRef]
  35. A. Gandjbakhche, R. Nossal, and R. Bonner, "Resolution limits for optical transillumination of abnormalities deeply embedded in tissues," Med. Phys. 21, 185-191 (1994). [CrossRef] [PubMed]
  36. V. Chernomordik, R. Nossal, and A. Gandjbakhche, "Point spread functions of photons in time-resolved transillumination experiments using simple scaling arguments," Med. Phys. 23, 1857-1861 (1996). [CrossRef] [PubMed]

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