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

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2003 (4)

B. A. Brooksby, H. Dehghani, B. W. Pogue, 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).
[CrossRef]

H. Dehghani, B. W. Pogue, S. P. Poplack, K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42, 135–145 (2003).
[CrossRef] [PubMed]

J. C. Hebden, D. A. Boas, J. S. George, A. J. Durkin, “Topics in biomedical optics: introduction,” Appl. Opt. 42, 2869–3329 (2003).
[CrossRef]

W. Cai, M. Xu, R. R. Alfano, “Three dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. 9, 189–198 (2003).
[CrossRef]

2002 (1)

M. Xu, W. Cai, M. Lax, R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E 65,066609 (2002).
[CrossRef]

2001 (4)

M. Xu, W. Cai, M. Lax, R. R. Alfano, “A photon transport forward model for imaging in turbid media,” Opt. Lett. 26, 1066–1068 (2001).
[CrossRef]

V. A. Markel, J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E 64,035601 (2001).
[CrossRef]

A. H. Hielscher, S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef] [PubMed]

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier optical diffuse tomography,” J. Opt. Soc. Am. A 18, 1535–1542 (2001).
[CrossRef]

2000 (4)

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

V. Chernomordik, D. Hattery, A. H. Gandjbakhche, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, R. Cubeddu, “Quantification by random walk of the optical parameters of nonlocalized abnormalities embedded within tissuelike phantoms,” Opt. Lett. 25, 951–953 (2000).
[CrossRef]

R. Vigário, J. Särelä, V. Jousmäki, M. Hämäläinen, E. Oja, “Independent component approach to the analysis of EEG and MEG recordings,” IEEE Trans. Biomed. Eng. 47, 589–593 (2000).
[CrossRef] [PubMed]

1999 (3)

1998 (3)

J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE 86, 2009–2025 (1998).
[CrossRef]

D. Nuzillard, 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).
[CrossRef]

A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. 37, 1973–1981 (1998).
[CrossRef]

1997 (4)

D. J. Hall, J. C. Hebden, D. T. Delpy, “Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method,” Appl. Opt. 36, 7270–7276 (1997).
[CrossRef]

Q. Fu, F. Seier, S. K. Gayen, R. R. Alfano, “High-average-power kilohertz-repetition-rate sub-100-fs Ti:sapphire amplifier system,” Opt. Lett. 22, 712–714 (1997).
[CrossRef] [PubMed]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

1996 (2)

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7, 17–22 (1996).
[CrossRef]

H. Heusmann, J. Kölzer, 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).
[CrossRef] [PubMed]

1995 (2)

1994 (3)

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, B. J. Tromber, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
[CrossRef]

P. Comon, “Independent component analysis—a new concept?” Signal Process. 36, 287–314 (1994).
[CrossRef]

R. R. Alfano, X. Liang, L. Wang, P. Ho, “Time-resolved imaging of translucent droplets in highly scattering media,” Science 264, 1913–1914 (1994).
[CrossRef] [PubMed]

1993 (1)

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

1991 (3)

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Alfano, R. R.

W. Cai, M. Xu, R. R. Alfano, “Three dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. 9, 189–198 (2003).
[CrossRef]

M. Xu, W. Cai, M. Lax, R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E 65,066609 (2002).
[CrossRef]

M. Xu, W. Cai, M. Lax, R. R. Alfano, “A photon transport forward model for imaging in turbid media,” Opt. Lett. 26, 1066–1068 (2001).
[CrossRef]

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier optical diffuse tomography,” J. Opt. Soc. Am. A 18, 1535–1542 (2001).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38, 4237–4246 (1999).
[CrossRef]

Q. Fu, F. Seier, S. K. Gayen, R. R. Alfano, “High-average-power kilohertz-repetition-rate sub-100-fs Ti:sapphire amplifier system,” Opt. Lett. 22, 712–714 (1997).
[CrossRef] [PubMed]

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News 7, 17–22 (1996).
[CrossRef]

R. R. Alfano, X. Liang, L. Wang, P. Ho, “Time-resolved imaging of translucent droplets in highly scattering media,” Science 264, 1913–1914 (1994).
[CrossRef] [PubMed]

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Alrubaiee, M.

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Bartel, S.

A. H. Hielscher, S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef] [PubMed]

Bell, A. J.

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.

Boas, D. A.

Bonner, R. F.

A. H. Gandjbakhche, G. H. Weiss, R. F. Bonner, R. Nossal, “Photon path-length distributions for transmission through optically turbid slabs,” Phys. Rev. E 48, 810–818 (1993).
[CrossRef]

Brooksby, B. A.

B. A. Brooksby, H. Dehghani, B. W. Pogue, 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).
[CrossRef]

Cai, W.

W. Cai, M. Xu, R. R. Alfano, “Three dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. 9, 189–198 (2003).
[CrossRef]

M. Xu, W. Cai, M. Lax, R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E 65,066609 (2002).
[CrossRef]

M. Xu, W. Cai, M. Lax, R. R. Alfano, “A photon transport forward model for imaging in turbid media,” Opt. Lett. 26, 1066–1068 (2001).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38, 4237–4246 (1999).
[CrossRef]

Cardoso, J.-F.

J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE 86, 2009–2025 (1998).
[CrossRef]

Chance, B.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Chernomordik, V.

Comon, P.

P. Comon, “Independent component analysis—a new concept?” Signal Process. 36, 287–314 (1994).
[CrossRef]

Cubeddu, R.

Dehghani, H.

B. A. Brooksby, H. Dehghani, B. W. Pogue, 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).
[CrossRef]

H. Dehghani, B. W. Pogue, S. P. Poplack, K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42, 135–145 (2003).
[CrossRef] [PubMed]

Delpy, D. T.

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

D. J. Hall, J. C. Hebden, D. T. Delpy, “Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method,” Appl. Opt. 36, 7270–7276 (1997).
[CrossRef]

Durkin, A. J.

Feng, T.-C.

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vols. I and II.

Fu, Q.

Fulton, R. C.

M. Lax, V. Nayaramamurti, R. C. Fulton, “Classical diffusion photon transport in a slab,” in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), pp. 229–237.

Gandjbakhche, A. H.

Gayen, S. K.

George, J. S.

Grosenick, D.

Hall, D. J.

Hämäläinen, M.

R. Vigário, J. Särelä, V. Jousmäki, M. Hämäläinen, E. Oja, “Independent component approach to the analysis of EEG and MEG recordings,” IEEE Trans. Biomed. Eng. 47, 589–593 (2000).
[CrossRef] [PubMed]

Haskell, R. C.

Hattery, D.

Hebden, J. C.

Heusmann, H.

H. Heusmann, J. Kölzer, 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).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef] [PubMed]

Ho, P.

R. R. Alfano, X. Liang, L. Wang, P. Ho, “Time-resolved imaging of translucent droplets in highly scattering media,” Science 264, 1913–1914 (1994).
[CrossRef] [PubMed]

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[CrossRef] [PubMed]

Hyvärinen, A.

A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis (Wiley, New York, 2001).
[CrossRef]

Jousmäki, V.

R. Vigário, J. Särelä, V. Jousmäki, M. Hämäläinen, E. Oja, “Independent component approach to the analysis of EEG and MEG recordings,” IEEE Trans. Biomed. Eng. 47, 589–593 (2000).
[CrossRef] [PubMed]

Karhunen, J.

A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis (Wiley, New York, 2001).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970).

Kölzer, J.

H. Heusmann, J. Kölzer, 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).
[CrossRef] [PubMed]

Lax, M.

M. Xu, W. Cai, M. Lax, R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E 65,066609 (2002).
[CrossRef]

M. Xu, W. Cai, M. Lax, R. R. Alfano, “A photon transport forward model for imaging in turbid media,” Opt. Lett. 26, 1066–1068 (2001).
[CrossRef]

M. Xu, M. Lax, R. R. Alfano, “Time-resolved Fourier optical diffuse tomography,” J. Opt. Soc. Am. A 18, 1535–1542 (2001).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, M. Lax, 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).
[CrossRef]

W. Cai, S. K. Gayen, M. Xu, M. Zevallos, M. Alrubaiee, M. Lax, R. R. Alfano, “Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements,” Appl. Opt. 38, 4237–4246 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of specimen 1 comprising an Intralipid-10% suspension in water with two long cylindrical absorbing objects of absorption coefficient 0.23 mm−1.

Fig. 2
Fig. 2

Schematic diagram of specimen 2 obtained from University College London. It is a solid rectangular block embedded with four 5-mm-diameter and 5-mm-long scattering cylindrical objects with their centers on the central plane. The absorption and scattering characteristics of the specimens and the lateral positions of the four cylinders are described in the text.

Fig. 3
Fig. 3

Schematic diagram of the experimental arrangement for imaging objects embedded in a turbid medium. Inset shows the 2-D array in the input plane that is scanned across the incident laser beam.

Fig. 4
Fig. 4

Normalized independent spatial intensity distributions as a function of the lateral position x at the input (or source) plane (first row) and the exit (or detector) plane (second row) generated by ICA for the two absorbing cylinders in specimen 1. The horizontal profile of the intensity distributions on the source plane (diamond) and on the detector plane (circle) are displayed in the third row. Solid curves show the respective Green’s-function fit used for obtaining the locations of the objects.

Fig. 5
Fig. 5

Independent spatial intensity distributions at the exit (or detector) plane generated by ICA corresponding to objects with scattering coefficients: (a) 4 times, (b) 2 times, (c) 1.5 times, and (d) 1.1 times that of the material of the slab in specimen 2. Horizontal profiles of the intensity distributions in (a)–(d) are shown by circles in (e)–(h), respectively, with solid curves representing the Green’s function fit used for extracting object locations.

Tables (1)

Tables Icon

Table 1 Comparison of Known and OPTICA-Determined Positions of the Four Targetsa

Equations (13)

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ϕ sca ( r d ,     r s ) = - G ( r d ,     r ) δ μ a ( r ) c G ( r ,     r s ) d 3 r - d 3 r δ D ( r ) c r G ( r d ,     r ) · r G ( r ,     r s )
G ( r ,     r ) G ( ρ , z , z ) = 1 4 π D k = - [ exp ( - κ r k + ) r k + - exp ( - κ r k - ) r k - ] , r k ± = [ ρ 2 + ( z z ± 2 k d ) 2 ] 1 / 2
- ϕ sca ( r d ,     r s ) = j = 1 J G ( r d ,     r j ) q j G ( r j ,     r s ) ,
x ( r s ) = A s ( r s ) .
A = [ G ( r d 1 ,     r 1 ) G ( r d 1 ,     r 2 ) G ( r d 1 ,     r J ) G ( r d 2 ,     r 1 ) G ( r d 2 ,     r 2 ) G ( r d 2 ,     r J ) G ( r d m ,     r 1 ) G ( r d m ,     r 2 ) G ( r d m ,     r J ) ] ,
s j ( r s ) = α j G ( r j ,     r s ) , a j ( r d ) = β j G ( r d ,     r j ) ,
min r j , α j , β j { r s [ α j - 1 s j ( r s ) - G ( r j ,     r s ) ] 2 + r d [ β j - 1 a j ( r d ) - G ( r d ,     r j ) ] 2 } .
g ( r ,     r ) = 1 4 π D k = - + [ ( κ r k + + 1 ) exp ( - κ r k + ) ( r k + ) 3 - ( κ r k - + 1 ) exp ( - κ r k - ) ( r k - ) 3 ] ,
g z ( r ,     r ) = 1 4 π D k = - + { ( z - z + 2 k d ) ( κ r k + + 1 ) × exp ( - κ r k + ) ( r k + ) 3 - ( z + z - 2 k d ) × ( κ r k - + 1 ) exp ( - κ r k - ) ( r k - ) 3 } ,
ϕ sca ( r d ,     r s ) = - d 3 r δ D ( r ) c { [ ( x - x d ) ( x - x s ) + ( y - y d ) ( y - y s ) ] g ( r ,     r d ) g ( r ,     r s ) + g z ( r ,     r d ) g z ( r ,     r s ) } .
- ϕ sca ( r d ,     r s ) = j = 1 J g z ( r j ,     r d ) q j g z ( r j ,     r s ) + j = 1 J ρ d j × cos θ d g ( r j ,     r d ) q j ρ s j cos θ s g ( r j ,     r s ) + j = 1 J ρ d j sin θ d g ( r j ,     r d ) q j ρ s j × sin θ s g ( r j ,     r s ) ,
q j g z ( r j ,     r s ) ,             q j ρ s j cos θ s g ( r j ,     r s ) ,             q j ρ s j sin θ s g ( r j ,     r s ) ,
g z ( r j ,     r d ) ,             ρ d j cos θ d g ( r j ,     r d ) ,             ρ d j sin θ d g ( r j ,     r d ) ,

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