Abstract

Fluorescence molecular tomography (FMT) is a promising imaging modality and has been actively studied in the past two decades since it can locate the specific tumor position three-dimensionally in small animals. However, it remains a challenging task to obtain fast, robust and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden, the noisy measurement and the ill-posed nature of the inverse problem. In this paper we propose a nonuniform preconditioning method in combination with L1 regularization and ordered subsets technique (NUMOS) to take care of the different updating needs at different pixels, to enhance sparsity and suppress noise, and to further boost convergence of approximate solutions for fluorescence molecular tomography. Using both simulated data and phantom experiment, we found that the proposed nonuniform updating method outperforms its popular uniform counterpart by obtaining a more localized, less noisy, more accurate image. The computational cost was greatly reduced as well. The ordered subset (OS) technique provided additional 5 times and 3 times speed enhancements for simulation and phantom experiments, respectively, without degrading image qualities. When compared with the popular L1 algorithms such as iterative soft-thresholding algorithm (ISTA) and Fast iterative soft-thresholding algorithm (FISTA) algorithms, NUMOS also outperforms them by obtaining a better image in much shorter period of time.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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  23. X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. 43, 1053–1062 (2004).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  26. I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.,  57, 1413–1457 (2004).
    [Crossref]
  27. A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci.,  2(1), 183–202 (2009).
    [Crossref]
  28. D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
    [Crossref] [PubMed]
  29. D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).
  30. Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
    [Crossref]
  31. C. Chen, F. Tian, H. Liu, and J. Huang, “Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging,” IEEE Trans. Med. Imaging. doi:
    [Crossref]
  32. D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Advances in Neural Information Processing Systems (2000), pp. 556–562.
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    [Crossref]
  34. A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
    [Crossref]

2014 (3)

D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59, 2901–2912 (2014).
[Crossref] [PubMed]

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39, 4156–4159 (2014).
[Crossref] [PubMed]

2013 (1)

D. Kim, D. Pal, J.-B. Thibault, and J. Fessler, “Accelerating ordered subsets image reconstruction for x-ray ct using spatially nonuniform optimization transfer,” IEEE Trans. Med. Imaging 32, 1965–1978 (2013).
[Crossref] [PubMed]

2012 (2)

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, “Preconditioning of the fluorescence diffuse optical tomography sensing matrix based on compressive sensing,” Opt. Lett. 37, 4326–4328 (2012).
[Crossref] [PubMed]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57, 1459 (2012).
[Crossref] [PubMed]

2011 (5)

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

C. Li, Y. Yang, G. S. Mitchell, and S. R. Cherry, “Simultaneous pet and multispectral 3-dimensional fluorescence optical tomography imaging system,” J. Nucl. Med. 52, 1268–1275 (2011).
[Crossref] [PubMed]

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

2010 (3)

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[Crossref] [PubMed]

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29, 1075–1087 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (1)

E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31(2), 890–912 (2008).
[Crossref]

2005 (1)

V. Ntziachristos, J. Ripoll, L. 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]

2004 (3)

S. R. Cherry, “In vivo molecular and genomic imaging: new challenges for imaging physics,” Phys. Med. Bio. 49, R13 (2004).
[Crossref]

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.,  57, 1413–1457 (2004).
[Crossref]

X. Song, B. W. Pogue, S. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. 43, 1053–1062 (2004).
[Crossref] [PubMed]

2003 (1)

F. Fedele, J. Laible, and M. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[Crossref]

1999 (2)

R. Weissleder, C.-H. Tung, U. Mahmood, and A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[Crossref] [PubMed]

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Bio. 44, 2835 (1999).
[Crossref]

1997 (1)

J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997).
[Crossref] [PubMed]

1994 (1)

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref] [PubMed]

1993 (1)

A. R. De Pierro, “On the relation between the ISRA and the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 12, 328–333 (1993).
[Crossref] [PubMed]

1986 (1)

M. E. Daube-Witherspoon and G. Muehllehner, “An iterative image space reconstruction algorthm suitable for volume ect,” IEEE Trans. Med. Imaging 5, 61–66 (1986).
[Crossref] [PubMed]

1945 (1)

L. R. Dice, “Measures of the amount of ecologic association between species,” Ecology 26, 297–302 (1945).
[Crossref]

Ahn, S.

Ale, A.

Alexandrakis, G.

Arridge, S. R.

S. R. Arridge and M. Schweiger, “Inverse methods for optical tomography,” in Information Processing in Medical Imaging (Springer, 1993), pp. 259–277.
[Crossref]

Baikejiang, R.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

Baritaux, J. C.

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29, 1075–1087 (2010).
[Crossref] [PubMed]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci.,  2(1), 183–202 (2009).
[Crossref]

Bello, M.

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

Bettina, Keszthelyi

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Bogdanov, A.

R. Weissleder, C.-H. Tung, U. Mahmood, and A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[Crossref] [PubMed]

Bouman, C. A.

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

Can, A.

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

Chen, C.

C. Chen, F. Tian, H. Liu, and J. Huang, “Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging,” IEEE Trans. Med. Imaging. doi:
[Crossref]

Cherry, S. R.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57, 1459 (2012).
[Crossref] [PubMed]

C. Li, Y. Yang, G. S. Mitchell, and S. R. Cherry, “Simultaneous pet and multispectral 3-dimensional fluorescence optical tomography imaging system,” J. Nucl. Med. 52, 1268–1275 (2011).
[Crossref] [PubMed]

C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17, 7571–7585 (2009).
[Crossref] [PubMed]

S. R. Cherry, “In vivo molecular and genomic imaging: new challenges for imaging physics,” Phys. Med. Bio. 49, R13 (2004).
[Crossref]

Clinthorne, N. H.

J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997).
[Crossref] [PubMed]

Cong, W.

Daubechies, I.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.,  57, 1413–1457 (2004).
[Crossref]

Daube-Witherspoon, M. E.

M. E. Daube-Witherspoon and G. Muehllehner, “An iterative image space reconstruction algorthm suitable for volume ect,” IEEE Trans. Med. Imaging 5, 61–66 (1986).
[Crossref] [PubMed]

David, Agard

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

De Mol, C.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.,  57, 1413–1457 (2004).
[Crossref]

De Pierro, A. R.

A. R. De Pierro, “On the relation between the ISRA and the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 12, 328–333 (1993).
[Crossref] [PubMed]

Defrise, M.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.,  57, 1413–1457 (2004).
[Crossref]

Dehghani, H.

Dice, L. R.

L. R. Dice, “Measures of the amount of ecologic association between species,” Ecology 26, 297–302 (1945).
[Crossref]

Dinten, J. M.

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

Doyley, M. M.

Dutta, J.

Eppstein, M.

F. Fedele, J. Laible, and M. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[Crossref]

Erdogan, H.

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Bio. 44, 2835 (1999).
[Crossref]

Fang, Xu

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Fedele, F.

F. Fedele, J. Laible, and M. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[Crossref]

Feng, J.

Fessler, J.

D. Kim, D. Pal, J.-B. Thibault, and J. Fessler, “Accelerating ordered subsets image reconstruction for x-ray ct using spatially nonuniform optimization transfer,” IEEE Trans. Med. Imaging 32, 1965–1978 (2013).
[Crossref] [PubMed]

Fessler, J. A.

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Bio. 44, 2835 (1999).
[Crossref]

J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997).
[Crossref] [PubMed]

Ficaro, E. P.

J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997).
[Crossref] [PubMed]

Friedlander, M. P.

E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31(2), 890–912 (2008).
[Crossref]

Gerdes, M.

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

Han, D.

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[Crossref] [PubMed]

Hassler, K.

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29, 1075–1087 (2010).
[Crossref] [PubMed]

Hervé, L.

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

Hsieh, J.

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

Huang, J.

C. Chen, F. Tian, H. Liu, and J. Huang, “Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging,” IEEE Trans. Med. Imaging. doi:
[Crossref]

Hudson, H. M.

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref] [PubMed]

Intes, X.

Jiang, S.

Jin, A.

John, Sedat

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Kim, D.

D. Kim, D. Pal, J.-B. Thibault, and J. Fessler, “Accelerating ordered subsets image reconstruction for x-ray ct using spatially nonuniform optimization transfer,” IEEE Trans. Med. Imaging 32, 1965–1978 (2013).
[Crossref] [PubMed]

Klaus, Mueller

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Laible, J.

F. Fedele, J. Laible, and M. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[Crossref]

Lange, K.

J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997).
[Crossref] [PubMed]

K. Lange, “The MM algorithm,” in Optimization (Springer, 2013), pp. 185–219.
[Crossref]

Larkin, R. S.

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref] [PubMed]

Leahy, R.

Leahy, R. M.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57, 1459 (2012).
[Crossref] [PubMed]

Lee, D. D.

D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Advances in Neural Information Processing Systems (2000), pp. 556–562.

Li, C.

D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59, 2901–2912 (2014).
[Crossref] [PubMed]

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57, 1459 (2012).
[Crossref] [PubMed]

C. Li, Y. Yang, G. S. Mitchell, and S. R. Cherry, “Simultaneous pet and multispectral 3-dimensional fluorescence optical tomography imaging system,” J. Nucl. Med. 52, 1268–1275 (2011).
[Crossref] [PubMed]

C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17, 7571–7585 (2009).
[Crossref] [PubMed]

Liu, H.

F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt. 48, 2496–2504 (2009).
[Crossref] [PubMed]

C. Chen, F. Tian, H. Liu, and J. Huang, “Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging,” IEEE Trans. Med. Imaging. doi:
[Crossref]

Liu, K.

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

Ma, X.

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

Mahmood, U.

R. Weissleder, C.-H. Tung, U. Mahmood, and A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[Crossref] [PubMed]

Mars, J. I.

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

Mel, Jones

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Mitchell, G. S.

C. Li, Y. Yang, G. S. Mitchell, and S. R. Cherry, “Simultaneous pet and multispectral 3-dimensional fluorescence optical tomography imaging system,” J. Nucl. Med. 52, 1268–1275 (2011).
[Crossref] [PubMed]

C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17, 7571–7585 (2009).
[Crossref] [PubMed]

Montcuquet, A. S.

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

Muehllehner, G.

M. E. Daube-Witherspoon and G. Muehllehner, “An iterative image space reconstruction algorthm suitable for volume ect,” IEEE Trans. Med. Imaging 5, 61–66 (1986).
[Crossref] [PubMed]

Navarro, F.

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

Ntziachristos, V.

A. Jin, B. Yazici, A. Ale, and V. Ntziachristos, “Preconditioning of the fluorescence diffuse optical tomography sensing matrix based on compressive sensing,” Opt. Lett. 37, 4326–4328 (2012).
[Crossref] [PubMed]

V. Ntziachristos, J. Ripoll, L. 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]

Pal, D.

D. Kim, D. Pal, J.-B. Thibault, and J. Fessler, “Accelerating ordered subsets image reconstruction for x-ray ct using spatially nonuniform optimization transfer,” IEEE Trans. Med. Imaging 32, 1965–1978 (2013).
[Crossref] [PubMed]

Paulsen, K. D.

Pogue, B. W.

Qin, C.

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[Crossref] [PubMed]

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. 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]

Sauer, K. D.

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

Schweiger, M.

S. R. Arridge and M. Schweiger, “Inverse methods for optical tomography,” in Information Processing in Medical Imaging (Springer, 1993), pp. 259–277.
[Crossref]

Seung, H. S.

D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Advances in Neural Information Processing Systems (2000), pp. 556–562.

Song, X.

Tao, X.

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

Teboulle, M.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci.,  2(1), 183–202 (2009).
[Crossref]

Thibault, J.-B.

D. Kim, D. Pal, J.-B. Thibault, and J. Fessler, “Accelerating ordered subsets image reconstruction for x-ray ct using spatially nonuniform optimization transfer,” IEEE Trans. Med. Imaging 32, 1965–1978 (2013).
[Crossref] [PubMed]

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

Tian, F.

F. Tian, G. Alexandrakis, and H. Liu, “Optimization of probe geometry for diffuse optical brain imaging based on measurement density and distribution,” Appl. Opt. 48, 2496–2504 (2009).
[Crossref] [PubMed]

C. Chen, F. Tian, H. Liu, and J. Huang, “Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging,” IEEE Trans. Med. Imaging. doi:
[Crossref]

Tian, J.

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[Crossref] [PubMed]

Tosteson, T. D.

Tung, C.-H.

R. Weissleder, C.-H. Tung, U. Mahmood, and A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[Crossref] [PubMed]

Unser, M.

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29, 1075–1087 (2010).
[Crossref] [PubMed]

van den Berg, E.

E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31(2), 890–912 (2008).
[Crossref]

Wang, G.

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. 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]

Wei, Xu

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. 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]

R. Weissleder, C.-H. Tung, U. Mahmood, and A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[Crossref] [PubMed]

Woolfe, F.

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

Yang, H.

Yang, X.

Yang, Y.

C. Li, Y. Yang, G. S. Mitchell, and S. R. Cherry, “Simultaneous pet and multispectral 3-dimensional fluorescence optical tomography imaging system,” J. Nucl. Med. 52, 1268–1275 (2011).
[Crossref] [PubMed]

Yazici, B.

Yu, Z.

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

Yuan, Z.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

Zhang, B.

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[Crossref] [PubMed]

Zhao, L.

Zhao, Y.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

Zhu, D.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59, 2901–2912 (2014).
[Crossref] [PubMed]

Zhu, S.

Appl. Opt. (2)

Comm. Pure Appl. Math. (1)

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math.,  57, 1413–1457 (2004).
[Crossref]

Comput. Meth. Programs Biomed. (1)

Xu Fang, Xu Wei, Jones Mel, Keszthelyi Bettina, Sedat John, Agard David, and Mueller Klaus, “On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs,” Comput. Meth. Programs Biomed. 98(3), 261–270 (2010).
[Crossref]

Ecology (1)

L. R. Dice, “Measures of the amount of ecologic association between species,” Ecology 26, 297–302 (1945).
[Crossref]

IEEE Trans. Bio-Med. Eng. (1)

A. S. Montcuquet, L. Hervé, F. Navarro, J. M. Dinten, and J. I. Mars, “In vivo fluorescence spectra unmixing and autofluorescence removal by sparse nonnegative matrix factorization,” IEEE Trans. Bio-Med. Eng. 58, 2554–2565 (2011).
[Crossref]

IEEE Trans. Image Process. (2)

F. Woolfe, M. Gerdes, M. Bello, X. Tao, and A. Can, “Autofluorescence removal by non-negative matrix factorization,” IEEE Trans. Image Process. 20, 1085–1093 (2011).
[Crossref]

Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, “Fast model-based x-ray ct reconstruction using spatially nonhomogeneous icd optimization,” IEEE Trans. Image Process. 20, 161–175 (2011).
[Crossref]

IEEE Trans. Med. Imaging (7)

D. Kim, D. Pal, J.-B. Thibault, and J. Fessler, “Accelerating ordered subsets image reconstruction for x-ray ct using spatially nonuniform optimization transfer,” IEEE Trans. Med. Imaging 32, 1965–1978 (2013).
[Crossref] [PubMed]

M. E. Daube-Witherspoon and G. Muehllehner, “An iterative image space reconstruction algorthm suitable for volume ect,” IEEE Trans. Med. Imaging 5, 61–66 (1986).
[Crossref] [PubMed]

A. R. De Pierro, “On the relation between the ISRA and the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging 12, 328–333 (1993).
[Crossref] [PubMed]

J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997).
[Crossref] [PubMed]

H. M. Hudson and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[Crossref] [PubMed]

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29, 1075–1087 (2010).
[Crossref] [PubMed]

C. Chen, F. Tian, H. Liu, and J. Huang, “Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging,” IEEE Trans. Med. Imaging. doi:
[Crossref]

J. Comput. Phys. (1)

F. Fedele, J. Laible, and M. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[Crossref]

J. Nucl. Med. (1)

C. Li, Y. Yang, G. S. Mitchell, and S. R. Cherry, “Simultaneous pet and multispectral 3-dimensional fluorescence optical tomography imaging system,” J. Nucl. Med. 52, 1268–1275 (2011).
[Crossref] [PubMed]

Nat. Biotechnol. (2)

R. Weissleder, C.-H. Tung, U. Mahmood, and A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[Crossref] [PubMed]

V. Ntziachristos, J. Ripoll, L. 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. (2)

Photonics (1)

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of regularization methods in fluorescence molecular tomography,” Photonics 1, 95–109 (2014).
[Crossref]

Phys. Med. Bio. (2)

S. R. Cherry, “In vivo molecular and genomic imaging: new challenges for imaging physics,” Phys. Med. Bio. 49, R13 (2004).
[Crossref]

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Bio. 44, 2835 (1999).
[Crossref]

Phys. Med. Biol. (2)

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57, 1459 (2012).
[Crossref] [PubMed]

D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59, 2901–2912 (2014).
[Crossref] [PubMed]

SIAM J. Imaging Sci. (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci.,  2(1), 183–202 (2009).
[Crossref]

SIAM J. Sci. Comput. (1)

E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31(2), 890–912 (2008).
[Crossref]

SPIE Medical Imaging (1)

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” in “SPIE Medical Imaging,” pp. 79651C (2011).

Other (3)

D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” in Advances in Neural Information Processing Systems (2000), pp. 556–562.

S. R. Arridge and M. Schweiger, “Inverse methods for optical tomography,” in Information Processing in Medical Imaging (Springer, 1993), pp. 259–277.
[Crossref]

K. Lange, “The MM algorithm,” in Optimization (Springer, 2013), pp. 185–219.
[Crossref]

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Figures (4)

Algorithm 1:
Algorithm 1: NUMOS
Fig. 1
Fig. 1 The coronary sections from bottom to top of the simulated mouse: (a) Truth and reconstructions with our proposed NUMOS algorithm using λ1 = 1.0E-03 and (b) nOS = 1, (c) nOS = 16, (d) nOS = 32, (e) nOS = 64, and (f) nOS = 128, respectively.
Fig. 2
Fig. 2 The coronary sections from bottom to top of the cubic phantom: (a) the truth (PET) and reconstructions with our proposed NUMOS algorithm using λ1 = 5.0E+03 and (b) nOS = 1, (c) nOS = 16, (d) nOS = 32, (e) nOS = 64, and (f) nOS = 128, respectively.
Fig. 3
Fig. 3 The coronary sections from bottom to top of the cubic phantom: L1 regularized reconstructions with parameter λ1 = 5.0E+03 using (a) ISTA [26, 28], (b) FISTA [27, 29], (c) FISTA with backtracking line search [27] and (d) NUMOS algorithm with nOS = 1, respectively.

Tables (3)

Tables Icon

Table 1 Metrics for simulated mouse: reconstructed using NUMOS with nOS = 1, 16, 32, 64, and 128, respectively, and λ1 = 1.0E-03 v.s. uniform weighting with non-convex L1/2 regularization, λ1/2 = 4.0E-05, the best result among different regularization methods [6]. The overall best performance is highlighted in bold.

Tables Icon

Table 2 Metrics for cubic phantom, reconstructed using NUMOS with λ1 = 5.0E+03, and nOS = 1, 16, 32, 64, and 128, respectively, v.s. uniform weighting with L1/2, λ1/2 = 5.0E+07, the best result among different regularization methods [6]. The overall best performance is highlighted in bold.

Tables Icon

Table 3 Metrics for cubic phantom, reconstructed by L1 regularization with parameter λ1 = 5.0E+03, using (a) ISTA, (b) FISTA, (c) FISTA with backtracking line search, and (d) NUMOS with nOS = 1, respectively.

Equations (9)

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

{ ( D ex ( r ) Φ ex ( r ) ) + μ a , ex ( r ) Φ ex ( r ) = S ex ( r ) n ( D ex ( r ) Φ ex ( r ) ) + α ex Φ ex ( r ) = 0 ( D em ( r ) Φ em ( r ) ) + μ a , em ( r ) Φ em ( r ) = Φ ex ( r ) S em ( r ) n ( D em ( r ) Φ em ( r ) ) + α em Φ em ( r ) = 0
Ax = b
x ^ = arg min x , x 0 Φ ( x ) : = 1 2 A x b 2 2 + λ R ( x ) ,
Φ sur ( x ) Φ ( x ) , for all x ; Φ sur ( x k ) = Φ ( x k ) , at point x k ; Φ sur ( x k ) = Φ ( x k ) , at x k .
1 2 b Ax 2 2 = 1 2 i = 1 N m ( b i ( A x ) i ) 2 1 2 i = 1 N m j = 1 N n β i j { b i ( A x k ) i a i j β i j ( x j x j k ) } 2 = j = 1 N n { ( x j x j k ) 2 2 i = 1 N m a i j 2 β i j x j i = 1 N m a i j ( b i ( A x k ) i ) + constant }
x j , L k + 1 = ( x j k + i = 1 N m a i j ( b i ( A x k ) i ) λ 1 κ j ) + ,
β i j M = a i j x j k l = 1 N n a i l x l k .
x j , L 1 M , k + 1 = x j k ( ( A t b ) j λ 1 ) + ( A t A x k ) j .
x j , L 1 A , k + 1 = ( x j k + ( A t b ) j ( A t A x k ) j λ 1 ( A t A 1 N n ) j ) + ,

Metrics