## Three-dimensional localization and optical imaging of objects in turbid media with independent component analysis

Applied Optics, Vol. 44, Issue 10, pp. 1889-1897 (2005)

http://dx.doi.org/10.1364/AO.44.001889

Acrobat PDF (400 KB)

### Abstract

A new approach for optical imaging and localization of objects in turbid media that makes use of the independent component analysis (ICA) from information theory is demonstrated. Experimental arrangement realizes a multisource illumination of a turbid medium with embedded objects and a multidetector acquisition of transmitted light on the medium boundary. The resulting spatial diversity and multiple angular observations provide robust data for three-dimensional localization and characterization of absorbing and scattering inhomogeneities embedded in a turbid medium. ICA of the perturbations in the spatial intensity distribution on the medium boundary sorts out the embedded objects, and their locations are obtained from Green's function analysis based on any appropriate light propagation model. Imaging experiments were carried out on two highly scattering samples of thickness approximately 50 times the transport mean-free path of the respective medium. One turbid medium had two embedded absorptive objects, and the other had four scattering objects. An independent component separation of the signal, in conjunction with diffusive photon migration theory, was used to locate the embedded inhomogeneities. In both cases, improved lateral and axial localizations of the objects over the result obtained by use of common photon migration reconstruction algorithms were achieved. The approach is applicable to different medium geometries, can be used with any suitable photon propagation model, and is amenable to near-real-time imaging applications.

© 2005 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.5280) Medical optics and biotechnology : Photon migration

(170.7050) Medical optics and biotechnology : Turbid media

**Citation**

M. Xu, M. Alrubaiee, S. K. Gayen, and R. R. Alfano, "Three-dimensional localization and optical imaging of objects in turbid media with independent component analysis," Appl. Opt. **44**, 1889-1897 (2005)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-10-1889

Sort: Year | Journal | Reset

### References

- G. Muller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, and P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (SPIE, Bellingham, Wash., 1993).
- A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48, 38-40 (1995).
- M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography," Opt. Lett. 20, 426-428 (1995).
- S. K. Gayen and R. R. Alfano, "Emerging optical biomedical imaging techniques," Opt. Photon. News 7, 17-22 (1996).
- J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine: I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).
- S. R. Arridge and J. C. Hebden, "Optical imaging in medicine: II. Modelling and reconstruction," Phys. Med. Biol. 42, 841-853 (1997).
- 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).
- S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
- D. Grosenick, H. Wabnitz, H. H. Rinneberg, K. T. Moesta, and P. M. Schlag, "Development of a time-domain optical mammograph and first in vivo applications," Appl. Opt. 38, 2927-2943 (1999).
- V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, and R. Cubeddu, "Quantification by random walk of the optical parameters of nonlocalized abnormalities embedded within tissuelike phantoms," Opt. Lett. 25, 951-953 (2000).
- V. A. Markel and J. C. Schotland, "Inverse scattering for the diffusion equation with general boundary conditions," Phys. Rev. E 64, 035601 (2001).
- A. H. Hielscher and S. Bartel, "Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography," J. Biomed. Opt. 6, 183-192 (2001).
- M. Xu, M. Lax, and R. R. Alfano, "Time-resolved Fourier optical diffuse tomography," J. Opt. Soc. Am. A 18, 1535-1542 (2001).
- B. A. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, "Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities," IEEE J. Sel. Top. Quantum Electron. 9, 199-209 (2003).
- H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, "Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results," Appl. Opt. 42, 135-145 (2003).
- J. C. Hebden, D. A. Boas, J. S. George, and A. J. Durkin, "Topics in biomedical optics: introduction," Appl. Opt. 42, 2869-3329 (2003).
- W. Cai, M. Xu, and R. R. Alfano, "Three dimensional radiative transfer tomography for turbid media," IEEE J. Sel. Top. Quantum Electron. 9, 189-198 (2003).
- L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, "Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate," Science 253, 769-771 (1991).
- R. R. Alfano, X. Liang, L. Wang, and P. Ho, "Time-resolved imaging of translucent droplets in highly scattering media," Science 264, 1913-1914 (1994).
- W. Cai, M. Lax, and R. R. Alfano, "Analytical solution of the elastic Boltzmann transport equation in an infinite uniform medium using cumulant expansion," J. Phys. Chem. B 104, 3996-4000 (2000).
- W. Cai, M. Lax, and R. R. Alfano, "Analytical solution of the polarized photon transport equation in an infinite uniform medium using cumulant expansion," Phys. Rev. E 63, 016606 (2000).
- M. Xu, W. Cai, M. Lax, and R. R. Alfano, "Photon migration in turbid media using a cumulant approximation to radiative transfer," Phys. Rev. E 65, 066609 (2002).
- F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).
- A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, and R. Nossal, "Photon path-length distributions for transmission through optically turbid slabs," Phys. Rev. E 48, 810-818 (1993).
- A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, and R. Nossal, "Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments," Appl. Opt. 37, 1973-1981 (1998).
- P. Comon, "Independent component analysis - a new concept?" Signal Process. 36, 287-314 (1994).
- A. J. Bell, "Information theory, independent component analysis, and applications," in Unsupervised Adaptive Filtering, Vol. I, S. Haykin, ed. (Wiley, New York, 2000), pp. 237-264.
- D. Nuzillard and J.-M. Nuzillard, "Application of blind source separation to 1-D and 2-D nuclear magnetic resonance spectroscopy," IEEE Signal Process. Lett. 5, 209-211 (1998).
- R. Vigário, J. Särelä, V. Jousmäki, M. Hämäläinen, and E. Oja, "Independent component approach to the analysis of EEG and MEG recordings," IEEE Trans. Biomed. Eng. 47, 589-593 (2000).
- A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, New York, 2001).
- P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vols. I and II.
- M. Xu, W. Cai, M. Lax, and R. R. Alfano, "A photon transport forward model for imaging in turbid media," Opt. Lett. 26, 1066-1068 (2001).
- S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
- M. Lax, V. Nayaramamurti, and R. C. Fulton, "Classical diffusion photon transport in a slab," in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, and A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229-237.
- J. X. Zhu, D. J. Pine, and D. A. Weitz, "Internal reflection of diffusive light in random media," Phys. Rev. A 44, 3948-3959 (1991).
- R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromber, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
- S. Roberts and R. Everson, eds., Independent Component Analysis: Principles and Practice (Cambridge U. Press, Cambridge, UK, 2001).
- J.-F. Cardoso, "Blind signal separation: statistical principles," Proc. IEEE 86, 2009-2025 (1998).
- M. V. Klein, Optics (Wiley, New York, 1970).
- H. Heusmann, J. Kölzer, and G. Mitic, "Characterization of female breasts in vivo by time resolved and spectroscopic measurements in near infrared spectroscopy," J. Biomed. Opt. 1, 425-434 (1996).
- H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, and M. J. C. van Gemert, "Light scattering in intralipid-10% in the wavelength range of 400-1100 nm," Appl. Opt. 30, 4507-4514 (1991).
- D. J. Hall, J. C. Hebden, and D. T. Delpy, "Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method," Appl. Opt. 36, 7270-7276 (1997).
- Q. Fu, F. Seier, S. K. Gayen, and R. R. Alfano, "High-average-power kilohertz-repetition-rate sub-100‐fs Ti:sapphire amplifier system," Opt. Lett. 22, 712-714 (1997).

## 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.