Abstract

We study optical imaging of tissues in the mesoscopic scattering regime in which light multiply scatters in tissues but is not fully diffusive. We use the radiative transport equation to model light propagation and an 1-optimization method to solve the inverse source problem. We show that recovering the location and strength of several point-like sources that are close to each other is not possible when using angle-averaged measurements. The image reliability is limited by a spatial scale that is on the order of the transport mean-free path, even under the most ideal conditions. However, by using just a few angle-resolved measurements, the proposed method is able to overcome this limitation.

© 2013 Optical Society of America

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2012

2010

2009

L. Florescu, J. C. Schotland, and V. A. Markel, Phys. Rev. E 79, 036607 (2009).
[CrossRef]

2008

I. Langmore, Inverse Probl. 24, 015024 (2008).
[CrossRef]

2007

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

2006

D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. J. Candés, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

2005

2004

A. D. Kim, J. Opt. Soc. Am. A 21, 820 (2004).
[CrossRef]

J. Sharpe, Annu. Rev. Biomed. Eng. 6, 209 (2004).
[CrossRef]

2002

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

1999

S. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

Ahlgren, U.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Arridge, S.

S. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

Arridge, S. R.

Baldock, R.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Candés, E. J.

E. J. Candés, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Correia, T.

Davidson, D.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Donoho, D.

D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Favicchio, R.

Florescu, L.

L. Florescu, V. A. Markel, and J. C. Schotland, Phys. Rev. E 81, 016602 (2010).
[CrossRef]

L. Florescu, J. C. Schotland, and V. A. Markel, Phys. Rev. E 79, 036607 (2009).
[CrossRef]

Gao, H.

Hecksher-Sørenson, J.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Hill, B.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Kim, A. D.

Langmore, I.

I. Langmore, Inverse Probl. 24, 015024 (2008).
[CrossRef]

Markel, V. A.

L. Florescu, V. A. Markel, and J. C. Schotland, Phys. Rev. E 81, 016602 (2010).
[CrossRef]

L. Florescu, J. C. Schotland, and V. A. Markel, Phys. Rev. E 79, 036607 (2009).
[CrossRef]

Ntziachristos, V.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

G. M. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, Opt. Lett. 30, 409 (2005).
[CrossRef]

Perrimon, N.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

Perry, P.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Pitsouli, C.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

Razansky, D.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

Ripoll, J.

Romberg, J.

E. J. Candés, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Ross, A.

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Schotland, J. C.

L. Florescu, V. A. Markel, and J. C. Schotland, Phys. Rev. E 81, 016602 (2010).
[CrossRef]

L. Florescu, J. C. Schotland, and V. A. Markel, Phys. Rev. E 79, 036607 (2009).
[CrossRef]

Sharpe, J.

J. Sharpe, Annu. Rev. Biomed. Eng. 6, 209 (2004).
[CrossRef]

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Soloviev, V. Y.

Soubret, A.

Spiliopoulos, G.

Tao, T.

E. J. Candés, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Turner, G. M.

Vinegoni, C.

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

Zacharakis, G.

Zhao, H.

Annu. Rev. Biomed. Eng.

J. Sharpe, Annu. Rev. Biomed. Eng. 6, 209 (2004).
[CrossRef]

IEEE Trans. Inf. Theory

D. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. J. Candés, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Inverse Probl.

S. Arridge, Inverse Probl. 15, R41 (1999).
[CrossRef]

I. Langmore, Inverse Probl. 24, 015024 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Methods

C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, Nat. Methods 5, 45 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

L. Florescu, J. C. Schotland, and V. A. Markel, Phys. Rev. E 79, 036607 (2009).
[CrossRef]

L. Florescu, V. A. Markel, and J. C. Schotland, Phys. Rev. E 81, 016602 (2010).
[CrossRef]

Science

J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørenson, R. Baldock, and D. Davidson, Science 296, 541 (2002).
[CrossRef]

Other

CVX Research, Inc., “CVX: Matlab Software for Disciplined Convex Programming,” http://cvxr.com/cvx .

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Figures (2)

Fig. 1.
Fig. 1.

Method’s ability to detect two point sources using half (left image) or all (right image) of the available angle-averaged measurements at the boundary grid. Regions of success are in white and regions where the method fails are shaded.

Fig. 2.
Fig. 2.

(a) Source distribution to be reconstructed. Here, x/* is the distance along the boundary grid and z/* the distance away from the detectors. (b) Reconstructed source distribution using scalar flux measurements over the boundary grid. (c) Reconstructed source distribution using angle-resolved measurements of the radiance over half of the boundary grid points.

Equations (2)

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

F(ρ)=s^·n^>0I(s^,ρ)s^·n^ds^,
minx{Axb2+αx1}.

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