Abstract

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

2017 (1)

Y. Zhu, A. K. Jha, J. K. Dreyer, H. N. D. Le, J. U. Kang, P. E. Roland, D. F. Wong, and A. Rahmim, “A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing,” Proc. SPIE 10059, 1005911 (2017).
[Crossref]

2015 (2)

2014 (3)

2013 (3)

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref]

A. K. Jha, E. Clarkson, M. A. Kupinski, and H. H. Barrett, “Joint reconstruction of activity and attenuation map using LM SPECT emission data,” Medical Imaging 2013: Physics of Medical Imaging 8668, 86681W (2013).
[Crossref]

D. Ma, P. Wolf, A. V. Clough, and T. G. Schmidt, “The performance of MLEM for dynamic imaging from simulated few-view, multi-pinhole SPECT,” IEEE Trans. Nucl. Sci. 60(1), 115–123 (2013).
[Crossref]

2012 (5)

2011 (6)

PS. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
[Crossref]

X. Liu, F. Liu, Y. Zhang, and J. Bai, “Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis,” IEEE Trans. Med. Imag. 30(9), 1591–1604 (2011).
[Crossref]

O. Lee, J. Kim, Y. Bresler, and J. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30(5), 1129–1142 (2011).
[Crossref]

N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
[Crossref] [PubMed]

F. Stuker, J. Ripoll, and M. Rudin, “Fluorescence molecular tomography: principles and potential for pharmaceutical research,” Pharmaceutics 3(2), 229–274 (2011).
[Crossref] [PubMed]

L. Zhou and B. Yazici, “Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography in the presence of measurement noise,” IEEE Trans. Image Process. 20(4), 1049–1111 (2011).

2010 (2)

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(8), 8630–8646 (2010).
[Crossref]

L. Cao and J. Peter, “Bayesian reconstruction strategy of fluorescence-mediated tomography using an integrated SPECT-CT-OT system,” Phys. Med. Biol. 55(9), 2693 (2010).
[Crossref] [PubMed]

2009 (6)

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]

Q. Fang and D. A. Boas, “Monte carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[Crossref] [PubMed]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25(12), 123010 (2009).
[Crossref]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51(1), 34–81 (2009).
[Crossref]

F. Leblond, H. Dehghani, D. Kepshire, and B. W Pogue, “Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations,” J. Opt. Soc. Am. A 26(6), 1444–1457 (2009).
[Crossref]

SB Raymond, ATN Kumar, DA Boas, and BJ Bacskai, “Optimal parameters for near infrared fluorescence imaging of amyloid plaques in alzheimer’s disease mouse models,” Phys. Med. Biol. 54(20), 6201 (2009).
[Crossref] [PubMed]

2008 (1)

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (3)

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[Crossref] [PubMed]

J. Qi and R. M. Leahy, “Iterative reconstruction techniques in emission computed tomography,” Phys. Med. Biol. 51(15), R541 (2006).
[Crossref] [PubMed]

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8,1–33 (2006).
[Crossref] [PubMed]

2005 (2)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225 (2005).
[Crossref] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R Arridge, and J. P Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913 (2005).
[Crossref] [PubMed]

2004 (2)

W. P. Segars, B. M. W. Tsui, E. C. Frey, G. A. Johnson, and S. S. Berr, “Development of a 4-D digital mouse phantom for molecular imaging research,” Mol. Imag. Biol. 6(3), 149–159 (2004).
[Crossref]

J. H. Chang, J. MM Anderson, and J. R Votaw, “Regularized image reconstruction algorithms for Positron Emission Tomography,” IEEE Trans. Med. Imag. 23(9), 1165–1175 (2004).
[Crossref]

2003 (2)

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[Crossref] [PubMed]

R. M. Lewitt and S. Matej, “Overview of methods for image reconstruction from projections in emission computed tomography,” Proc. IEEE 91(10), 1588–1611 (2003).
[Crossref]

2002 (1)

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29(5), 803–809 (2002).
[Crossref] [PubMed]

2001 (1)

1998 (1)

G. Kontaxakis and L. G Strauss, “Maximum likelihood algorithms for image reconstruction in Positron Emission Tomography,” Radionuclides Oncol. 8, 73–106 (1998)

1993 (1)

J. Llacer, E. Veklerov, K. J. Coakley, E. J. Hoffman, and J. Nunez, “Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies,” IEEE Trans. Med. Imag. 12(2), 215–231 (1993).
[Crossref]

1987 (1)

K. Lange, M. Bahn, and R. Little, “A theoretical study of some maximum likelihood algorithms for emission and transmission tomography,” IEEE Trans. Med. Imag. 6(2), 106–114 (1987).
[Crossref]

1985 (1)

Y. Vardi, L. Shepp, and L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80(389), 8–20 (1985).
[Crossref]

Adhikari, L.

L. Adhikari, D. Zhu, C. Li, and R. F. Marcia, “Nonconvex reconstruction for low-dimensional fluorescence molecular tomographic poisson observations,” 2015 IEEE International Conference on Image Processing (ICIP), 2404–2408 (2015).

Aguirre, A.

N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
[Crossref] [PubMed]

Ahn, S.

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(6), 1459 (2012).
[Crossref] [PubMed]

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

Ale, A.

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225 (2005).
[Crossref] [PubMed]

An, Y.

Anderson, J. MM

J. H. Chang, J. MM Anderson, and J. R Votaw, “Regularized image reconstruction algorithms for Positron Emission Tomography,” IEEE Trans. Med. Imag. 23(9), 1165–1175 (2004).
[Crossref]

Antich, P. P.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[Crossref] [PubMed]

Arridge, S.

Arridge, S. R

PS. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
[Crossref]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R Arridge, and J. P Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913 (2005).
[Crossref] [PubMed]

Arridge, S. R.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25(12), 123010 (2009).
[Crossref]

Bacskai, BJ

SB Raymond, ATN Kumar, DA Boas, and BJ Bacskai, “Optimal parameters for near infrared fluorescence imaging of amyloid plaques in alzheimer’s disease mouse models,” Phys. Med. Biol. 54(20), 6201 (2009).
[Crossref] [PubMed]

Bahn, M.

K. Lange, M. Bahn, and R. Little, “A theoretical study of some maximum likelihood algorithms for emission and transmission tomography,” IEEE Trans. Med. Imag. 6(2), 106–114 (1987).
[Crossref]

Bai, J.

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref]

X. Liu, F. Liu, Y. Zhang, and J. Bai, “Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis,” IEEE Trans. Med. Imag. 30(9), 1591–1604 (2011).
[Crossref]

Barrett, H. H

Barrett, H. H.

A. K. Jha, E. Clarkson, M. A. Kupinski, and H. H. Barrett, “Joint reconstruction of activity and attenuation map using LM SPECT emission data,” Medical Imaging 2013: Physics of Medical Imaging 8668, 86681W (2013).
[Crossref]

A. K. Jha, M. A. Kupinski, T. Masumura, E. Clarkson, A. V. Maslov, and H. H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29(8), 1741–1757 (2012).
[Crossref]

H. H. Barrett and K. J. Myers, Foundations of Image Science, 1 ed. (Wiley, 2004).

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]

Berr, S. S.

W. P. Segars, B. M. W. Tsui, E. C. Frey, G. A. Johnson, and S. S. Berr, “Development of a 4-D digital mouse phantom for molecular imaging research,” Mol. Imag. Biol. 6(3), 149–159 (2004).
[Crossref]

Biswal, N. C

N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
[Crossref] [PubMed]

Boas, D. A.

Q. Fang and D. A. Boas, “Monte carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[Crossref] [PubMed]

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[Crossref] [PubMed]

Boas, DA

SB Raymond, ATN Kumar, DA Boas, and BJ Bacskai, “Optimal parameters for near infrared fluorescence imaging of amyloid plaques in alzheimer’s disease mouse models,” Phys. Med. Biol. 54(20), 6201 (2009).
[Crossref] [PubMed]

Bouman, C. A.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

Bresler, Y.

O. Lee, J. Kim, Y. Bresler, and J. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30(5), 1129–1142 (2011).
[Crossref]

Bruckstein, A. M.

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D. Ma, P. Wolf, A. V. Clough, and T. G. Schmidt, “The performance of MLEM for dynamic imaging from simulated few-view, multi-pinhole SPECT,” IEEE Trans. Nucl. Sci. 60(1), 115–123 (2013).
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J. Llacer, E. Veklerov, K. J. Coakley, E. J. Hoffman, and J. Nunez, “Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies,” IEEE Trans. Med. Imag. 12(2), 215–231 (1993).
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S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
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G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
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W. P. Segars, B. M. W. Tsui, E. C. Frey, G. A. Johnson, and S. S. Berr, “Development of a 4-D digital mouse phantom for molecular imaging research,” Mol. Imag. Biol. 6(3), 149–159 (2004).
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Jin, A.

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N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
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Kupinski, M. A.

A. K. Jha, E. Clarkson, M. A. Kupinski, and H. H. Barrett, “Joint reconstruction of activity and attenuation map using LM SPECT emission data,” Medical Imaging 2013: Physics of Medical Imaging 8668, 86681W (2013).
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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(6), 1459 (2012).
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O. Lee, J. Kim, Y. Bresler, and J. Ye, “Compressive diffuse optical tomography: noniterative exact reconstruction using joint sparsity,” IEEE Trans. Med. Imag. 30(5), 1129–1142 (2011).
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Lewis, M. A.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
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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(6), 1459 (2012).
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K. Lange, M. Bahn, and R. Little, “A theoretical study of some maximum likelihood algorithms for emission and transmission tomography,” IEEE Trans. Med. Imag. 6(2), 106–114 (1987).
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J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
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J. Llacer, E. Veklerov, K. J. Coakley, E. J. Hoffman, and J. Nunez, “Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies,” IEEE Trans. Med. Imag. 12(2), 215–231 (1993).
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Ma, D.

D. Ma, P. Wolf, A. V. Clough, and T. G. Schmidt, “The performance of MLEM for dynamic imaging from simulated few-view, multi-pinhole SPECT,” IEEE Trans. Nucl. Sci. 60(1), 115–123 (2013).
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PS. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
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A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Med. Imag. 23(6), 2609–2624 (2014).
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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(20), 4326–4328 (2012).
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V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26(12), 893–895 (2001).
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J. Llacer, E. Veklerov, K. J. Coakley, E. J. Hoffman, and J. Nunez, “Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies,” IEEE Trans. Med. Imag. 12(2), 215–231 (1993).
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N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
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L. Cao and J. Peter, “Bayesian reconstruction strategy of fluorescence-mediated tomography using an integrated SPECT-CT-OT system,” Phys. Med. Biol. 55(9), 2693 (2010).
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PS. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230(19), 7364–7383 (2011).
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J. Qi and R. M. Leahy, “Iterative reconstruction techniques in emission computed tomography,” Phys. Med. Biol. 51(15), R541 (2006).
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Rahmim, A.

A. K. Jha, Y. Zhu, S. Arridge, D. F. Wong, and A. Rahmim, “Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging,” Biomed. Opt. Express 9(4), 1389–1407 (2018).
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[Crossref]

Y. Zhu, A. K. Jha, D. Wong, and A. Rahmim, “Improved sparse reconstruction for fluorescence molecular tomography with poisson noise modeling,” Biophotonics Congress: Biomedical Optics Congress 2018, JTu3A.51 (2018).

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G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50(17), 4225 (2005).
[Crossref] [PubMed]

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SB Raymond, ATN Kumar, DA Boas, and BJ Bacskai, “Optimal parameters for near infrared fluorescence imaging of amyloid plaques in alzheimer’s disease mouse models,” Phys. Med. Biol. 54(20), 6201 (2009).
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N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
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Y. Zhu, A. K. Jha, J. K. Dreyer, H. N. D. Le, J. U. Kang, P. E. Roland, D. F. Wong, and A. Rahmim, “A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing,” Proc. SPIE 10059, 1005911 (2017).
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D. Ma, P. Wolf, A. V. Clough, and T. G. Schmidt, “The performance of MLEM for dynamic imaging from simulated few-view, multi-pinhole SPECT,” IEEE Trans. Nucl. Sci. 60(1), 115–123 (2013).
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W. P. Segars, B. M. W. Tsui, E. C. Frey, G. A. Johnson, and S. S. Berr, “Development of a 4-D digital mouse phantom for molecular imaging research,” Mol. Imag. Biol. 6(3), 149–159 (2004).
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Y. Vardi, L. Shepp, and L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80(389), 8–20 (1985).
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Slavine, N. V.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[Crossref] [PubMed]

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N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
[Crossref] [PubMed]

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G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[Crossref] [PubMed]

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G. Kontaxakis and L. G Strauss, “Maximum likelihood algorithms for image reconstruction in Positron Emission Tomography,” Radionuclides Oncol. 8, 73–106 (1998)

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F. Stuker, J. Ripoll, and M. Rudin, “Fluorescence molecular tomography: principles and potential for pharmaceutical research,” Pharmaceutics 3(2), 229–274 (2011).
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[Crossref]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R Arridge, and J. P Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913 (2005).
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Y. Vardi, L. Shepp, and L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80(389), 8–20 (1985).
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T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R Arridge, and J. P Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913 (2005).
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J. Llacer, E. Veklerov, K. J. Coakley, E. J. Hoffman, and J. Nunez, “Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies,” IEEE Trans. Med. Imag. 12(2), 215–231 (1993).
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J. H. Chang, J. MM Anderson, and J. R Votaw, “Regularized image reconstruction algorithms for Positron Emission Tomography,” IEEE Trans. Med. Imag. 23(9), 1165–1175 (2004).
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Weissleder, R.

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29(5), 803–809 (2002).
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D. Ma, P. Wolf, A. V. Clough, and T. G. Schmidt, “The performance of MLEM for dynamic imaging from simulated few-view, multi-pinhole SPECT,” IEEE Trans. Nucl. Sci. 60(1), 115–123 (2013).
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Y. Zhu, A. K. Jha, D. Wong, and A. Rahmim, “Improved sparse reconstruction for fluorescence molecular tomography with poisson noise modeling,” Biophotonics Congress: Biomedical Optics Congress 2018, JTu3A.51 (2018).

Wong, D. F.

A. K. Jha, Y. Zhu, S. Arridge, D. F. Wong, and A. Rahmim, “Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging,” Biomed. Opt. Express 9(4), 1389–1407 (2018).
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Xu, Y.

N. C Biswal, A. Aguirre, Y. Xu, S. Zanganeh, Q. Zhu, C. Pavlik, M. B Smith, L. T Kuhn, and K. P Claffey, “Imaging tumor hypoxia by near-infrared fluorescence tomography,” J. Biomed. Opt. 16(6), 066009 (2011).
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Yao, R.

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A. Jin, B. Yazici, and V. Ntziachristos, “Light illumination and detection patterns for fluorescence diffuse optical tomography based on compressive sensing,” IEEE Trans. Med. Imag. 23(6), 2609–2624 (2014).
[Crossref]

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(20), 4326–4328 (2012).
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Figures (10)

Fig. 1
Fig. 1 (a) The experimental setup of cube phantom. (b) Cross section at y = 2.5 cm of the simulated phantom.
Fig. 2
Fig. 2 (a) The experimental setup of mouse phantom. (b) Cross section of digital mouse phantom at z = 16mm.
Fig. 3
Fig. 3 Cross sections at y = 2.5 cm reconstructed by MLEM with different iteration number n for the cube phantom. SNR=18dB. The reconstructed images are from MLEM with uniform initial estimate for the top row and MLEM with sparse initial estimate for the bottom row.
Fig. 4
Fig. 4 Quantitative results of different reconstruction methods as functions of iteration number for cube phantom. (a) Plot of ROI bias vs. number of iterations. (b) Plot of ROI spatial variance vs. number of iterations. (c) Plot of ROI spatial variance vs. ROI bias. (d) Plot of background bias vs. number of iterations. (e) Plot of background variance vs. number of iterations. (f) Plot of RMSE vs. number of iterations.
Fig. 5
Fig. 5 Quantitative results of different reconstruction methods as functions of SNR for cube phantom. (a) Plot of ROI bias vs. SNR. (b) Plot of ROI variance vs. SNR. (c) Plot of background bias vs. SNR. (d) Plot of background variance vs. SNR. (e) Plot of RMSE vs. SNR.
Fig. 6
Fig. 6 Quantitative results of different reconstruction methods as functions of iteration number for digital mouse phantom. (a) Plot of ROI bias vs. number of iterations. (b) Plot of ROI spatial variance vs. number of iterations. (c) Plot of ROI spatial variance vs. ROI bias. (d) Plot of background bias vs. number of iterations. (e) Plot of background variance vs. number of iterations. (f) Plot of RMSE vs. number of iterations.
Fig. 7
Fig. 7 Quantitative results of different reconstruction methods as functions of SNR for digital mouse phantom. (a) Plot of ROI bias vs. SNR. (b) Plot of ROI variance vs. SNR. (c) Plot of background bias vs. SNR. (d) Plot of background variance vs. SNR. (e) Plot of RMSE vs. SNR.
Fig. 8
Fig. 8 Cross sections of fluorescence target reconstructed with pure sparse reconstruction method for the top row and the proposed method for the bottom row with different truncation number K for digital mouse phantom for SNR=40dB.
Fig. 9
Fig. 9 Plot of RMSE vs. truncation number for pure sparse reconstruction method and the proposed reconstruction method for different noise levels. (a) Plot of RMSE vs. truncation number for SNR=40 dB. (b) Plot of RMSE vs. truncation number for SNR=20 dB.
Fig. 10
Fig. 10 (a) Image with background noise. The noise spot in the background is marked with red circle. (b) Image without background noise. (c) Plot of fm. (d)Plot of (Gϵ)m and 2(ϕGx2)m

Tables (2)

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Table 1 Optical properties of digital mouse phantom [40]

Tables Icon

Table 2 Computation time required by MLEM for 1000 iterations

Equations (29)

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ϕ e x ( r ) = Ω g e x ( r s , r ) s ( r s ) d r s ,
ϕ e m ( r d ) = Ω g e m ( r , r d ) x ( r ) ϕ e x ( r ) d r ,
Φ = G x ,
G = [ g e m , 1 1 ϕ e x , 1 1 g e m , N 1 ϕ e x , N 1   g e m , 1 N d ϕ e x , 1 1 g e m , N N d ϕ e x , N 1 g e m , 1 1 ϕ e x , 1 2 g e m , N 1 ϕ e x , N 2   g e m , 1 N d ϕ e x , 1 N s g e m , N N d ϕ e x , N N s ]
Φ = G x + n .
l ( x | Φ ) = m = 1 M exp [ ( Gx ) m ] ( Gx ) m ϕ m ϕ m ! ,
L ( x | Φ ) = m = 1 M { ( Gx ) m + ϕ m ln [ ( Gx ) m ] ln ϕ m ! } .
x n L ( x | Φ ) = m = 1 M { G m n + ϕ m ( Gx ) m G m n } .
1 = 1 m = 1 M G m n m = 1 M ϕ m ( Gx ) m G m n .
x ^ n k + 1 = x ^ n k 1 s n m = 1 M ϕ m ( G x ^ k ) m G m n ,
min x x 0 such that Φ Gx 2 ϵ .
Φ = U Σ V T x + n ,
Φ = U t Σ t V t T x + n ,
M Φ = V t T x + Mn .
y = Ax + n .
min x x 1 such that y Ax 2 ϵ .
θ ROI = 1 N R r = 1 N R x r ,
θ B = 1 N B b = 1 N B x b ,
b ROI = 1 R k = 1 R | θ ROI , k θ ROI , k t r u e | ,
b B = 1 R k = 1 R | θ B , k θ B , k t r u e | ,
σ R O I 2 = 1 R ( N R 1 ) k = 1 R r = 1 N R ( x r , k θ ROI , k ) 2 .
σ B 2 = 1 R ( N B 1 ) k = 1 R b = 1 N B ( x b , k θ B , k ) 2 .
RMSE = 1 R k = 1 R i = 1 N ( x i , k x i , k t r u e ) 2 i = 1 N ( x i , k t r u e ) 2 × 100 % ,
D K L , 1 ( Φ , G x 1 ) = m { ( G x 1 ) m ϕ m + ϕ m ln ϕ m ( G x 1 ) m } .
D K L , 2 ( Φ , G x 2 ) = m { ( G x 2 ) m ϕ m + ϕ m ln ϕ m ( G x 2 ) m } .
Δ D K L = D K L , 2 ( Φ , G x 2 ) D K L , 1 ( Φ , G x 1 ) = m { ( G ϵ ) m + ϕ m ln [ 1 + ( G ϵ ) m ( G x 2 ) m ] } .
f m ( G ϵ ) m + ϕ m [ ( G ϵ ) m ( G x 2 ) m 1 2 ( ( G ϵ ) m ( G x 2 ) m ) 2 ] .
( G ϵ ) m , 1 = 0 ,
( G ϵ ) m , 2 = 2 ( G x 2 ) m [ ϕ m ( G x 2 ) m ] ϕ m 2 [ ϕ m ( G x 2 ) m ] ,

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