Abstract

For the ill-posed fluorescent molecular tomography (FMT) inverse problem, the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise. However, the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory, especially for large-scale problems. An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption. The reconstruction results from phantom experiments demonstrate that the proposed algorithm can obtain high spatial resolution and high signal-to-noise ratio, as well as high localization accuracy for fluorescence targets.

© 2013 Optical Society of America

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J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
[CrossRef]

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

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J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

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X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
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J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
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B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

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B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
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Chen, D.

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

Cherry, S. R.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Donoho, D. L.

M. Lustig, D. L. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Dutta, J.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Feng, J.

Gao, H.

Han, D.

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X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
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Jiang, Y.

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

Leahy, R. M.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Leng, S.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

Li, C.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Liu, F.

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
[CrossRef]

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, Ann. Biomed. Eng. 38, 3440 (2010).
[CrossRef]

Liu, J.

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

Liu, S.

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

Liu, X.

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, Ann. Biomed. Eng. 38, 3440 (2010).
[CrossRef]

Luo, J.

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
[CrossRef]

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

Lustig, M.

M. Lustig, D. L. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Manduca, A.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

McCollough, C. H.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

Ntziachristos, V.

Soubret, Antoine, J. Ripoll, and V. Ntziachristos, IEEE Trans. Med. Imaging. 24, 1377 (2005).

J. Ripoll, M. N. Vesperinas, R. Weissleder, and V. Ntziachristos, Opt. Lett. 27, 527 (2002).
[CrossRef]

Pauly, J. M.

M. Lustig, D. L. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Qin, C.

Ramirez-Giraldo, J. C.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

Ripoll, J.

Soubret, Antoine, J. Ripoll, and V. Ntziachristos, IEEE Trans. Med. Imaging. 24, 1377 (2005).

J. Ripoll, M. N. Vesperinas, R. Weissleder, and V. Ntziachristos, Opt. Lett. 27, 527 (2002).
[CrossRef]

Shan, B.

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

Shen, M.

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

Shi, J.

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
[CrossRef]

Soubret,

Soubret, Antoine, J. Ripoll, and V. Ntziachristos, IEEE Trans. Med. Imaging. 24, 1377 (2005).

Tian, J.

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, Opt. Express 18, 8630 (2010).
[CrossRef]

Trzasko, J.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

Vesperinas, M. N.

Wang, D.

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, Ann. Biomed. Eng. 38, 3440 (2010).
[CrossRef]

Wang, X.

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

Weissleder, R.

Yang, X.

Yu, L.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

Zhang, B.

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
[CrossRef]

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, Opt. Express 18, 8630 (2010).
[CrossRef]

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, Ann. Biomed. Eng. 38, 3440 (2010).
[CrossRef]

Zhang, Q.

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

Zhao, H.

Zhu, S.

Ann. Biomed. Eng. (1)

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, Ann. Biomed. Eng. 38, 3440 (2010).
[CrossRef]

IEEE Trans. Med. Imaging. (1)

Soubret, Antoine, J. Ripoll, and V. Ntziachristos, IEEE Trans. Med. Imaging. 24, 1377 (2005).

IEEE Trans. Multimedia (1)

B. Zhang, S. Liu, X. Cao, F. Liu, X. Wang, J. Luo, B. Shan, and J. Bai, IEEE Trans. Multimedia 99, 1 (2013).

Inverse Probl. (1)

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

J. Biomed. Imaging (1)

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, J. Biomed. Imaging 2011, 1 (2011).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, J. Opt. Soc. Am. 30, 437 (2013).
[CrossRef]

Magn. Reson. Med. (1)

M. Lustig, D. L. Donoho, and J. M. Pauly, Magn. Reson. Med. 58, 1182 (2007).
[CrossRef]

Med. Phys. (1)

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, Med. Phys. 38, 2157 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Med. Biol. (1)

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Reconstruction results. (a1) True cross section in the z=26mm plane, (a2) 3D rendering of true fluorescent targets. Slice (b1) and stereo (b2) are the reconstructed results obtained from L1-NCG-100. Slice (c1) and stereo (c2) correspond to re-L1-NCG algorithm. Slice (d1) and stereo (d2) correspond to L1-NCG-1000. Slice (e1) and stereo (e2) correspond to Tikhonov algorithm. (f1) The transverse section of CT image in z=26mm plane. (f2) The transverse overlay of (c1) and (f1).

Fig. 2.
Fig. 2.

Intensity profiles along the dash–dotted lines in Figs. 1(b1), 1(c1), 1(d1), and 1(e1).

Tables (1)

Tables Icon

Table 1. Runtime and Memory Consumption for re-L1-NCG, L1-NCG-1000 and Tikhonov

Equations (9)

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

ϕem(rd,rs)ϕex(rd,rs)=S0υG(rs,rd,λ1)DfG(rd,r,λ2)x(r)G(rs,r,λ1)d3r,
Φf=WX,
argminX0WXΦf22+λX1,
Wnor(i,j)=Wi21i=jor0ij,
XL1=argminX0(f(X)=WnewXΦfnew22+λX1),
Wnew=WWnor;Φfnew=Φf/max(Φf).
f(X)=2WnewT(WnewXΦfnew)+λX1,
XL1k+1=XL1k+tkdk,
dk=f(XL1k)+γkdk1,

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