Abstract

In the recent years, there has been an increase in applications of non-contact diffusion optical tomography. Especially when the objective is the recovery of fluorescence targets. The non-contact acquisition systems with the use of a CCD-camera produce much denser sampled boundary data sets than fibre-based systems. When model-based reconstruction methods are used, that rely on the inversion of a derivative operator, the large number of measurements poses a challenge since the explicit formulation and storage of the Jacobian matrix could be in general not feasible. This problem is aggravated further in applications, where measurements at multiple wavelengths are used. We present a matrix-free model-based reconstruction method, that addresses the problems of large data sets and reduces the computational cost and memory requirements for the reconstruction. The idea behind the matrix-free method is that information about the Jacobian matrix could be available through matrix times vector products so that the creation and storage of big matrices can be avoided. We tested the method for multiple wavelength fluorescence tomography with simulated and experimental data from phantom experiments, and we found substantial benefits in computational times and memory requirements.

© 2009 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2008 (2)

2007 (2)

2006 (1)

2005 (5)

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 41207 (2005).
[Crossref] [PubMed]

Z. M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, “Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets,” Opt. Lett. 30, 3338–3340 (2005).
[Crossref]

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

M. Schweiger, S. Arridge, and I. Nissila, “GaussNewton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[Crossref] [PubMed]

2003 (3)

2001 (2)

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).
[Crossref]

1998 (1)

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Alerstam, E.

Andersson-Engels, S.

Arridge, S.

M. Schweiger, S. Arridge, and I. Nissila, “GaussNewton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[Crossref] [PubMed]

Arridge, S. R.

Bading, J. R.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Chaudhari, A.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Cherry, S. R.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Choe, R.

Conti, P. S.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Corkan, A.

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Corlu, A.

Culver, J. P.

Darvas, F.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Davis, S.C.

Dehghani, H.

Du, H.

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Durduran, T.

Economou, E. N.

Fuh, R. A.

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Garofalakis, A.

Gossage, K. W.

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 41207 (2005).
[Crossref] [PubMed]

Graves, E.

E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[Crossref] [PubMed]

Hillman, E. M. C.

Holboke, M. J.

Hoyt, C. C.

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 41207 (2005).
[Crossref] [PubMed]

Jiang, S.

Kioussis, D.

Leahy, R. M.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Levenson, R. M.

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 41207 (2005).
[Crossref] [PubMed]

Li, J.

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Lindsey, J. S.

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Mamalaki, C.

Mansfield, J. R.

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 41207 (2005).
[Crossref] [PubMed]

Markel, V. A.

Meyer, H.

Moats, R. A.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Nissila, I.

M. Schweiger, S. Arridge, and I. Nissila, “GaussNewton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[Crossref] [PubMed]

Ntziachristos, V.

Panasyuk, G. Y.

Patterson, M.S.

Paulsen, K.D.

Pogue, B.W.

Psycharakis, S.

Ripoll, J.

H. Meyer, A. Garofalakis, G. Zacharakis, S. Psycharakis, C. Mamalaki, D. Kioussis, E. N. Economou, V. Ntziachristos, and J. Ripoll, “Noncontact optical imaging in mice with full angular coverage and automatic surface extraction,” Appl. Opt. 46, 3617–3627 (2007).
[Crossref] [PubMed]

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[Crossref] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Noncontact optical tomography of turbid media,” Opt. Lett. 28, 1701–1703 (2003).
[Crossref] [PubMed]

Rosen, M. A.

Schnall, M. D.

Schotland, J. C.

Schulz, R. B.

Schweiger, M.

Smith, D. J.

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

Svensson, T.

Wang, L. H. V.

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

Wang, Z. M.

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[Crossref] [PubMed]

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26, 893–895 (2001).
[Crossref]

Yodh, A. G.

Zacharakis, G.

Appl. Opt. (1)

Inverse Problems (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).
[Crossref]

J. Biomed. Opt. (1)

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 41207 (2005).
[Crossref] [PubMed]

Med. Phys. (1)

E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[Crossref] [PubMed]

Nat Biotechnol. (1)

V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat Biotechnol. 23, 313–320 (2005).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (7)

Photocem. Photobiol. (1)

H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, “PhotochemCAD: A computer-aided design and research tool in photochemistry,” Photocem. Photobiol. 68, 141–142 (1998).

Phys. Med. Biol. (2)

M. Schweiger, S. Arridge, and I. Nissila, “GaussNewton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[Crossref] [PubMed]

A. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[Crossref] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

(a) A representation of the experimental setup. The dots in the back of the figure denote source positions and the rectangle in the front the image acquired by the CCD camera. The rod on the left contains the Rhodamine 101 while the one on the right the Rhodamine 6G with spectral responses given in the graph on the right. (b) Estimated quantum yield spectra for Rhodamine 101 and Rhodamine 6G.

Fig. 2.
Fig. 2.

Simulated data reconstruction (using 473 detectors per source) Horizontal and Vertical slice along the middle of the slab for the recovered concentrations using simulated data with added 3% noise at the 580nm and 620nm wavelengths for Rhodamine 101 (a) and Rhodamine 6G (b). The computational time for the traditional method of explicit Jacobian was 15minutes 58sec while for the reconstruction using the matrix-free method was 2minutes 44sec.

Fig. 3.
Fig. 3.

Experimental data reconstruction using 473 detectors per source Horizontal and vertical slice along the middle of the slab for the recovered concentrations using for phantom experimental measurements at the 580nm and 620nm wavelengths for Rhodamine 101 (a) and Rhodamine 6G (b). This reconstruction using the matrix-free method took 4min. 46sec while the computational time for the traditional method with the explicit Jacobian was 17minutes 4sec.

Fig. 4.
Fig. 4.

Experimental data reconstruction using 1665 detectors per source Horizontal and Vertical slice along the middle of the slab for the recovered concentrations using experimental measurements at the 580nm and 620nm wavelengths for Rhodamine 101 (a) and Rhodamine 6G (b). This reconstruction using the matrix-free method took 4min 57sec while the computational time for the traditional method with the explicit Jacobian was 52min 22sec

Tables (2)

Tables Icon

Table 1. Bulk optical properties at the excitation wavelength and emission wavelengths.

Tables Icon

Table 2. Reconstruction times for explicit Jacobian method and the matrix-free using two (580nm and 620nm) wavelengths and two different measurement setups, 475 measurements per source and 1665 positions per source. For the memory allocation calculations, a mesh of 6480 nodes were assumed.

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

h r λ = i η i ( λ ) c i ( r ) , r Ω
( D r λ e + μ a r λ e ) U ( e ) ( r ) = q ( r )
( D r λ f + μ a r λ f ) U ( f ) ( r ) = U ( e ) ( r ) h r λ f ,
U ( ξ ) + 2 ζ D ξ λ U ( e f ) ( ξ ) n = 0 , ξ Ω
y ( ξ ) = D ξ λ U ( ξ ) n = 1 2 ζ U ( ξ ) ξ Ω
g d ( e f ) = 𝓜 [ y ( e f ) ] Ω y ( e f ) ( ξ ) w d ( ξ ) d ξ
g ( f ) = F ( h )
D ( r ) k = 1 P D k b k ( r ) , μ a ( r ) k = 1 P μ k b k ( r ) , h ( r ) k = 1 P h k b k ( r )
U ( r ) = 1 N U v k ( r )
K D μ U = Q
K λ e U ( e ) = Q ,
K λ f U ( f ) = h U ( e ) ,
g Q ( f ) = F Q ( h ) = A Q ( h ) h 𝓜 [ K λ f 1 h K λ e 1 Q ]
J ( sd ) , k ( h ) = U s , k ( e ) U d , k ( f ) +
K λ e U s ( e ) = Q s ,
K λ f U d ( f ) + = Q d + ,
x ̂ = arg min x [ Φ ( x ) 1 2 g meas ( f ) F ( x ) 2 + α Ψ ( x ) ]
( A T A + α Ψ ( x ( k ) ) ) x δ = A T ( g meas ( f ) A x ( k ) ) α Ψ ( x ( k ) )
τ k = arg min τ Φ ( x ( k ) + τ x δ )
x ( k + 1 ) = x ( k ) + τ k x δ
( A T A + α L T L ) x ̂ = A T g meas ( f )
h ̂ ( λ ) = arg min h ( λ ) 1 2 g meas ( f ) ( λ ) A ( λ ) h 2 + α Ψ ( h ( λ ) )
[ η ] c k = h ( λ ) [ η 1 ( λ 1 ) η 2 ( λ 1 ) η n ( λ 1 ) η 1 ( λ 2 ) η 2 ( λ 2 ) η n ( λ 2 ) η 1 ( λ n ) η 2 ( λ n ) η n ( λ n ) ] [ c 1 , k c 2 , k c n , k ] = [ h k ( λ 1 ) h k ( λ 2 ) h k ( λ n ) ]
g ( f ) = g ( f 1 ) g ( f 2 ) g ( f m )
A c l λ = { F ij c λ c l , k c l , k h k ( λ ) } = A ( h ) η l ( λ )
A ( c ) = diag [ A ( h ( λ 1 ) ) , A ( h ( λ 2 ) ) , A ( h ( λ m ) ) ] [ η ]
= [ A ( h ( λ 1 ) ) η 1 ( λ 1 ) A ( h ( λ 1 ) ) η 2 ( λ 1 ) A ( h ( λ 1 ) ) η n ( λ 1 ) A ( h ( λ 2 ) ) η 1 ( λ 2 ) A ( h ( λ 2 ) ) η 2 ( λ 2 ) A ( h ( λ 2 ) ) η n ( λ 2 ) A ( h ( λ m ) ) η 1 ( λ m ) A ( h ( λ m ) ) η 2 ( λ m ) A ( h ( λ m ) ) η n ( λ m ) ]
x ̂ = arg min x 1 2 g ˜ ( f ) F ˜ ( x ) 2 + α Ψ ( x )
g meas ( f ) g ˜ ( f ) = g meas ( f ) , F ( x ) F ˜ ( x ) = g meas ( e ) g proj ( e ) F ( x )
g meas ( f ) g ˜ ( f ) = g meas ( f ) g ¯ ( f ) , F ( x ) F ˜ ( x ) = g meas ( e ) g proj ( e ) g ¯ ( f ) F ( x )
{ z , H z , H j z }

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