Abstract

Image reconstruction in fluorescence diffuse optical tomography (FDOT) is a highly ill-posed inverse problem due to a large number of unknowns and limited measurements. In FDOT, the fluorophore distribution is often sparse in the imaging domain, since most fluorophores are designed to accumulate in relatively small regions. Compressive sensing theory has shown that sparse signals can be recovered exactly from only a small number of measurements when the forward sensing matrix is sufficiently incoherent. In this Letter, we present a method of preconditioning the FDOT forward matrix to reduce its coherence. The reconstruction results using real data obtained from a phantom experiment show visual and quantitative improvements due to preconditioning in conjunction with convex relaxation and greedy-type sparse signal recovery algorithms.

© 2012 Optical Society of America

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References

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2011 (2)

L. Zhou and B. Yazici, IEEE Trans. Image Process. 20, 1094 (2011).
[CrossRef]

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, IEEE Trans. Med. Imag. 15, 13695 (2011).

2010 (2)

2009 (1)

J. Duarte-Carvajalino and G. Sapiro, IEEE Trans. Image Process. 18, 1395 (2009).
[CrossRef]

2007 (3)

Adibi, A.

Bresler, Y.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, IEEE Trans. Med. Imag. 15, 13695 (2011).

Davis, S.

Dehghani, H.

Deliolanis, N.

Duarte-Carvajalino, J.

J. Duarte-Carvajalino and G. Sapiro, IEEE Trans. Image Process. 18, 1395 (2009).
[CrossRef]

Durduran, T.

Eftekhar, A.

Elad, M.

M. Elad, IEEE Trans. Signal Process. 55, 5695 (2007).
[CrossRef]

Giannoula, A.

Huang, J.

Hyde, D.

Jiang, S.

Jin, A.

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. (to be published).

Kim, J. M.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, IEEE Trans. Med. Imag. 15, 13695 (2011).

Lasser, T.

Lee, O.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, IEEE Trans. Med. Imag. 15, 13695 (2011).

Mohajerani, P.

Ntziachristos, V.

N. Deliolanis, T. Lasser, D. Hyde, A. Soubret, J. Ripoll, and V. Ntziachristos, Opt. Lett. 32, 382 (2010).
[CrossRef]

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. (to be published).

Paulsen, K.

Pogue, B.

Ripoll, J.

Sapiro, G.

J. Duarte-Carvajalino and G. Sapiro, IEEE Trans. Image Process. 18, 1395 (2009).
[CrossRef]

Soubret, A.

Suzen, M.

Wang, J.

Yazici, B.

L. Zhou and B. Yazici, IEEE Trans. Image Process. 20, 1094 (2011).
[CrossRef]

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. (to be published).

Ye, J. C.

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, IEEE Trans. Med. Imag. 15, 13695 (2011).

Zhou, L.

L. Zhou and B. Yazici, IEEE Trans. Image Process. 20, 1094 (2011).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Image Process. (2)

L. Zhou and B. Yazici, IEEE Trans. Image Process. 20, 1094 (2011).
[CrossRef]

J. Duarte-Carvajalino and G. Sapiro, IEEE Trans. Image Process. 18, 1395 (2009).
[CrossRef]

IEEE Trans. Med. Imag. (1)

O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, IEEE Trans. Med. Imag. 15, 13695 (2011).

IEEE Trans. Signal Process. (1)

M. Elad, IEEE Trans. Signal Process. 55, 5695 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (1)

A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Image Process. (to be published).

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Figures (4)

Fig. 1.
Fig. 1.

Configuration of (a) the silicon phantom and (b) the cross section of the fluorophore yield at z=1cm (middle) of the silicon phantom.

Fig. 2.
Fig. 2.

(a) Top 40% values of all the normalized inner products between different pairs of columns in A and (b) the cumulative coherence of A as a function of k.

Fig. 3.
Fig. 3.

Cross sections at z=1cm (middle) of the reconstructed phantom using greedy algorithms.

Fig. 4.
Fig. 4.

Cross sections at z=1cm (middle) of the phantom using convex relaxation techniques.

Tables (1)

Tables Icon

Table 1. SBNR of the Reconstructed Images Using Preconditioning and Different Sparsity Promoting Reconstruction Algorithms

Equations (8)

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

Γi,j=Ωgm(j)(r)ϕx(i)(r)μ(r),
y=Γ+ϵ=Ax+ϵ,
MAy=MAAx+MAϵ=Apre+MAϵ,
MA=(ΣAΣAT)1/2UAT.
MA=(ΣAΣAT+λI)1/2UAT,
minxx such that ypreAprex2ε,
rAp,q=|ap,aq|ap2aq2,
M1(k,A)=maxpmax|Q|=k,pQqQ|ap,aq|ap2aq2,

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