Abstract

We consider the joint use of spectral and temporal data for multiplexed fluorescence molecular tomography to enable high-throughput imaging of multiple fluorescent targets in bulk tissue. This is a challenging problem due to the narrow near-infrared diagnostic window and relatively broad emission spectra of common fluorophores, and the distortion (“redshift”) that the fluorophore signals undergo as they propagate through tissue. We show through a Cramér-Rao lower bound analysis that demixing with spectral-temporal data could result in an order of magnitude improvement in performance over either modality alone. To cope with the resulting large data set, we propose a novel two-stage algorithm that decouples the demixing and tomographic reconstruction operations. In this work we concentrate on the demixing stage. We introduce an approach which incorporates ideas from sparse subspace clustering and compressed sensing and does not require a regularization parameter. We report on simulations in which we simultaneously demixed four fluorophores with closely overlapping spectral and temporal profiles in a 25 mm diameter cross-sectional area with a root-mean-square error of less than 3% per fluorophore, as well as on studies of sensitivity of the method to model mismatch.

© 2015 Optical Society of America

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References

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2015 (1)

2014 (4)

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

S. S. Hou, W. L. Rice, B. J. Bacskai, and A. T. N. Kumar, “Tomographic lifetime imaging using combined early and late-arriving photons,” Opt. Lett. 39(5), 1165–1168 (2014).
[Crossref] [PubMed]

V. Pera, D. H. Brooks, and M. Niedre, “On the use of the Cramér-Rao lower bound for diffuse optical imaging system design,” J. Biomed. Opt. 19(2), 025002 (2014).
[Crossref] [PubMed]

S. Foucart and D. Koslicki, “Sparse recovery by means of nonnegative least squares,” IEEE Signal Process. Lett. 21(4), 498–502 (2014).
[Crossref]

2013 (5)

M. Slawski and M. Hein, “Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization,” Electron. J. Statist. 7, 3004–3056 (2013).
[Crossref]

N. Meinshausen, “Sign-constrained least squares estimation for high-dimensional regression,” Electron. J. Statist. 7, 1607–1631 (2013).
[Crossref]

E. L. Dyer, A. C. Sankaranarayanan, and R. G. Baraniuk, “Greedy feature selection for subspace clustering,” J. Machine Learning Research 14(1), 2487–2517 (2013).

M. Soltanolkotabi, E. Elhamifar, and E. J. Candès, “Robust subspace clustering,” Annals of Statistics 42(2), 669–699 (2013).
[Crossref]

E. Elhamifar and R. Vidal, “Sparse subspace clustering: algorithm, theory, and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2765–2781 (2013).
[Crossref] [PubMed]

2012 (5)

R. W. Holt, K. M. Tichauer, H. Dehghani, B. W. Pogue, and F. Leblond, “Multiple-gate time domain diffuse fluorescence tomography allows more sparse tissue sampling without compromising image quality,” Opt. Lett. 37(13), 2559–2561 (2012).
[Crossref] [PubMed]

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Y. Zhan, A. T. Eggebrecht, J. P. Culver, and H. Dehghani, “Singular value decomposition based regularization prior to spectral mixing improves crosstalk in dynamic imaging using spectral diffuse optical tomography,” Biomed. Opt. Express 3(9), 2036–2049 (2012).
[Crossref] [PubMed]

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

P. C. Hansen and M. Saxild-Hansen, “AIR Tools – A MATLAB package of algebraic iterative reconstruction methods,” J. Comput. Appl. Math. 236, 2167–2178 (2012).
[Crossref]

2011 (2)

2010 (1)

S. B. Raymond, D. A. Boas, B. J. Bacskai, and A. T. N. Kumar, “Lifetime-based tomographic multiplexing,” J. Biomed. Opt. 15(4), 046011 (2010).
[Crossref] [PubMed]

2008 (4)

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008).
[Crossref] [PubMed]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

A. M. Bruckstein, M. Elad, and M. Zibulevsky, “On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations,” IEEE Trans. Inform. Theory 54(11), 4813–4820 (2008).
[Crossref]

2007 (1)

2005 (3)

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, 4225–4241 (2005).
[Crossref] [PubMed]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imag. 24(10), 1377–1386 (2005).
[Crossref]

J. Swartling, J. Svensson, D. Bengtsson, K. Terike, and S. Andersson-Engels, “Fluorescence spectra provide information on the depth of fluorescent lesions in tissue,” Appl. Opt. 44(10), 1934–1941 (2005).
[Crossref] [PubMed]

2004 (1)

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

2002 (2)

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, (7)757–760 (2002).
[Crossref] [PubMed]

N. Keshava and J. F. Mustard, “Spectral Unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[Crossref]

1999 (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18(3), 262–271 (1999).
[Crossref]

1997 (1)

R. Bro and S. D. Jong, “A fast non-negativity-constrained least squares algorithm,” J. Chemometr. 11, 393–401 (1997).
[Crossref]

1992 (1)

D. L. Donoho, I. M. Johnstone, J. C. Hoch, and A. S. Stern, “Maximum entropy and the nearly black object,” J. R. Statist. Soc. B 54, (1), 41–81 (1992).

1988 (1)

M. Unser and M. Eden, “Maximum likelihood estimation of linear signal parameters for Poisson processes,” IEEE Trans. Acoust. Speech Signal Process. 36, 942–945 (1988).
[Crossref]

Aikawa, E.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

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, 4225–4241 (2005).
[Crossref] [PubMed]

Andersson-Engels, S.

Arridge, S. R.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Bacskai, B. J.

S. S. Hou, W. L. Rice, B. J. Bacskai, and A. T. N. Kumar, “Tomographic lifetime imaging using combined early and late-arriving photons,” Opt. Lett. 39(5), 1165–1168 (2014).
[Crossref] [PubMed]

S. B. Raymond, D. A. Boas, B. J. Bacskai, and A. T. N. Kumar, “Lifetime-based tomographic multiplexing,” J. Biomed. Opt. 15(4), 046011 (2010).
[Crossref] [PubMed]

Bai, J.

J. Bai and Z. Xu, “Fluorescence molecular tomography,” in Molecular Imaging: Fundamentals and Applications, J. Tian, ed. (Springer, 2013).
[Crossref]

Baraniuk, R. G.

E. L. Dyer, A. C. Sankaranarayanan, and R. G. Baraniuk, “Greedy feature selection for subspace clustering,” J. Machine Learning Research 14(1), 2487–2517 (2013).

Beard, P. C.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Bengtsson, D.

Bioucas-dias, J. M.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Boas, D. A.

Bogdanov, A.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Bremer, C.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, (7)757–760 (2002).
[Crossref] [PubMed]

Bro, R.

R. Bro and S. D. Jong, “A fast non-negativity-constrained least squares algorithm,” J. Chemometr. 11, 393–401 (1997).
[Crossref]

Brooks, D. H.

V. Pera, D. H. Brooks, and M. Niedre, “On the use of the Cramér-Rao lower bound for diffuse optical imaging system design,” J. Biomed. Opt. 19(2), 025002 (2014).
[Crossref] [PubMed]

V. Pera, D. H. Brooks, and M. Niedre, “A sparse nonnegative demixing algorithm with intrinsic regularization for multiplexed fluorescence tomography,” in IEEE 12th International Symposium on Biomedical Imaging (IEEE, 2015) pp. 1044–1047.

Bruckstein, A. M.

A. M. Bruckstein, M. Elad, and M. Zibulevsky, “On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations,” IEEE Trans. Inform. Theory 54(11), 4813–4820 (2008).
[Crossref]

Candès, E. J.

M. Soltanolkotabi, E. Elhamifar, and E. J. Candès, “Robust subspace clustering,” Annals of Statistics 42(2), 669–699 (2013).
[Crossref]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Chanussot, J.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Chatziioannou, A. F.

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, 4225–4241 (2005).
[Crossref] [PubMed]

Chen, J.

Cox, B.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Culver, J. P.

Dale, A. M.

Darne, C.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

de Kleine, R. H.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

Dehghani, H.

Dobigeon, N.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Donoho, D. L.

D. L. Donoho, I. M. Johnstone, J. C. Hoch, and A. S. Stern, “Maximum entropy and the nearly black object,” J. R. Statist. Soc. B 54, (1), 41–81 (1992).

Du, Q.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Dyer, E. L.

E. L. Dyer, A. C. Sankaranarayanan, and R. G. Baraniuk, “Greedy feature selection for subspace clustering,” J. Machine Learning Research 14(1), 2487–2517 (2013).

Eden, M.

M. Unser and M. Eden, “Maximum likelihood estimation of linear signal parameters for Poisson processes,” IEEE Trans. Acoust. Speech Signal Process. 36, 942–945 (1988).
[Crossref]

Eggebrecht, A. T.

Elad, M.

A. M. Bruckstein, M. Elad, and M. Zibulevsky, “On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations,” IEEE Trans. Inform. Theory 54(11), 4813–4820 (2008).
[Crossref]

Elhamifar, E.

M. Soltanolkotabi, E. Elhamifar, and E. J. Candès, “Robust subspace clustering,” Annals of Statistics 42(2), 669–699 (2013).
[Crossref]

E. Elhamifar and R. Vidal, “Sparse subspace clustering: algorithm, theory, and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2765–2781 (2013).
[Crossref] [PubMed]

Foucart, S.

S. Foucart and D. Koslicki, “Sparse recovery by means of nonnegative least squares,” IEEE Signal Process. Lett. 21(4), 498–502 (2014).
[Crossref]

Gader, P.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Gao, F.

Graves, E.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Hansen, P. C.

P. C. Hansen and M. Saxild-Hansen, “AIR Tools – A MATLAB package of algebraic iterative reconstruction methods,” J. Comput. Appl. Math. 236, 2167–2178 (2012).
[Crossref]

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18(3), 262–271 (1999).
[Crossref]

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).

Hein, M.

M. Slawski and M. Hein, “Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization,” Electron. J. Statist. 7, 3004–3056 (2013).
[Crossref]

Hielscher, A. H.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18(3), 262–271 (1999).
[Crossref]

Hoch, J. C.

D. L. Donoho, I. M. Johnstone, J. C. Hoch, and A. S. Stern, “Maximum entropy and the nearly black object,” J. R. Statist. Soc. B 54, (1), 41–81 (1992).

Holt, R. W.

Hou, S. S.

Intes, X.

Johnstone, I. M.

D. L. Donoho, I. M. Johnstone, J. C. Hoch, and A. S. Stern, “Maximum entropy and the nearly black object,” J. R. Statist. Soc. B 54, (1), 41–81 (1992).

Jong, S. D.

R. Bro and S. D. Jong, “A fast non-negativity-constrained least squares algorithm,” J. Chemometr. 11, 393–401 (1997).
[Crossref]

Josephson, L.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

Keshava, N.

N. Keshava and J. F. Mustard, “Spectral Unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[Crossref]

Kirsch, D. G.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

Klose, A. D.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18(3), 262–271 (1999).
[Crossref]

Koslicki, D.

S. Foucart and D. Koslicki, “Sparse recovery by means of nonnegative least squares,” IEEE Signal Process. Lett. 21(4), 498–502 (2014).
[Crossref]

Krishnaprasad, P. S.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition,” in IEEE Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers (IEEE, 1993), pp. 40–44.

Kumar, A. T. N.

S. S. Hou, W. L. Rice, B. J. Bacskai, and A. T. N. Kumar, “Tomographic lifetime imaging using combined early and late-arriving photons,” Opt. Lett. 39(5), 1165–1168 (2014).
[Crossref] [PubMed]

S. B. Raymond, D. A. Boas, B. J. Bacskai, and A. T. N. Kumar, “Lifetime-based tomographic multiplexing,” J. Biomed. Opt. 15(4), 046011 (2010).
[Crossref] [PubMed]

Laufer, J. G.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).

Leblond, F.

Li, Z.

Lu, Y.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

Marjono, A.

Meinshausen, N.

N. Meinshausen, “Sign-constrained least squares estimation for high-dimensional regression,” Electron. J. Statist. 7, 1607–1631 (2013).
[Crossref]

Mustard, J. F.

N. Keshava and J. F. Mustard, “Spectral Unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[Crossref]

Niedre, M.

V. Pera, D. H. Brooks, and M. Niedre, “On the use of the Cramér-Rao lower bound for diffuse optical imaging system design,” J. Biomed. Opt. 19(2), 025002 (2014).
[Crossref] [PubMed]

Z. Li and M. Niedre, “Hybrid use of early and quasi-continuous wave photons in time-domain tomographic imaging for improved resolution and quantitative accuracy,” Biomed. Opt. Express 2(3), 665–679 (2011).
[Crossref] [PubMed]

V. Pera, D. H. Brooks, and M. Niedre, “A sparse nonnegative demixing algorithm with intrinsic regularization for multiplexed fluorescence tomography,” in IEEE 12th International Symposium on Biomedical Imaging (IEEE, 2015) pp. 1044–1047.

Niedre, M. J.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

Ntziachristos, V.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imag. 24(10), 1377–1386 (2005).
[Crossref]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, (7)757–760 (2002).
[Crossref] [PubMed]

Parente, M.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Pati, Y. C.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition,” in IEEE Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers (IEEE, 1993), pp. 40–44.

Pera, V.

V. Pera, D. H. Brooks, and M. Niedre, “On the use of the Cramér-Rao lower bound for diffuse optical imaging system design,” J. Biomed. Opt. 19(2), 025002 (2014).
[Crossref] [PubMed]

V. Pera, D. H. Brooks, and M. Niedre, “A sparse nonnegative demixing algorithm with intrinsic regularization for multiplexed fluorescence tomography,” in IEEE 12th International Symposium on Biomedical Imaging (IEEE, 2015) pp. 1044–1047.

Pian, Q.

Plaza, A.

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

Pogue, B. W.

Rannou, F. R.

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, 4225–4241 (2005).
[Crossref] [PubMed]

Raymond, S. B.

S. B. Raymond, D. A. Boas, B. J. Bacskai, and A. T. N. Kumar, “Lifetime-based tomographic multiplexing,” J. Biomed. Opt. 15(4), 046011 (2010).
[Crossref] [PubMed]

Rezaiifar, R.

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition,” in IEEE Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers (IEEE, 1993), pp. 40–44.

Rice, W. L.

Ripoll, J.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imag. 24(10), 1377–1386 (2005).
[Crossref]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Sankaranarayanan, A. C.

E. L. Dyer, A. C. Sankaranarayanan, and R. G. Baraniuk, “Greedy feature selection for subspace clustering,” J. Machine Learning Research 14(1), 2487–2517 (2013).

Saxild-Hansen, M.

P. C. Hansen and M. Saxild-Hansen, “AIR Tools – A MATLAB package of algebraic iterative reconstruction methods,” J. Comput. Appl. Math. 236, 2167–2178 (2012).
[Crossref]

Schellenberger, E. A.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Selb, J.

Sevick-Muraca, E. M.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

Slawski, M.

M. Slawski and M. Hein, “Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization,” Electron. J. Statist. 7, 3004–3056 (2013).
[Crossref]

Soltanolkotabi, M.

M. Soltanolkotabi, E. Elhamifar, and E. J. Candès, “Robust subspace clustering,” Annals of Statistics 42(2), 669–699 (2013).
[Crossref]

Soubret, A.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imag. 24(10), 1377–1386 (2005).
[Crossref]

Stern, A. S.

D. L. Donoho, I. M. Johnstone, J. C. Hoch, and A. S. Stern, “Maximum entropy and the nearly black object,” J. R. Statist. Soc. B 54, (1), 41–81 (1992).

Svensson, J.

Swartling, J.

Tanikawa, Y.

Terike, K.

Tichauer, K. M.

Tung, C.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, (7)757–760 (2002).
[Crossref] [PubMed]

Unser, M.

M. Unser and M. Eden, “Maximum likelihood estimation of linear signal parameters for Poisson processes,” IEEE Trans. Acoust. Speech Signal Process. 36, 942–945 (1988).
[Crossref]

Valim, N.

N. Valim, “Instrumentation and methods for time-resolved diffuse fluorescence imaging,” Ph.D. Dissertation (Northeastern University, 2014), Chap. 5.

Venugopal, V.

Vidal, R.

E. Elhamifar and R. Vidal, “Sparse subspace clustering: algorithm, theory, and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2765–2781 (2013).
[Crossref] [PubMed]

Wakin, M. B.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Wang, L. V.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Wang, Y.

Y. Wang and H. Xu, “Noisy sparse subspace clustering,” in Proceedings of the 30th International Conference on Machine Learning (2013).

Weissleder, R.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, (7)757–760 (2002).
[Crossref] [PubMed]

Wu, H.

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

Xu, H.

Y. Wang and H. Xu, “Noisy sparse subspace clustering,” in Proceedings of the 30th International Conference on Machine Learning (2013).

Xu, Z.

J. Bai and Z. Xu, “Fluorescence molecular tomography,” in Molecular Imaging: Fundamentals and Applications, J. Tian, ed. (Springer, 2013).
[Crossref]

Yamada, Y.

Yao, R.

Yessayan, D.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Zhan, Y.

Zhang, L.

Zhao, H.

Zhao, L.

Zibulevsky, M.

A. M. Bruckstein, M. Elad, and M. Zibulevsky, “On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations,” IEEE Trans. Inform. Theory 54(11), 4813–4820 (2008).
[Crossref]

Annals of Statistics (1)

M. Soltanolkotabi, E. Elhamifar, and E. J. Candès, “Robust subspace clustering,” Annals of Statistics 42(2), 669–699 (2013).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (3)

Electron. J. Statist. (2)

M. Slawski and M. Hein, “Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization,” Electron. J. Statist. 7, 3004–3056 (2013).
[Crossref]

N. Meinshausen, “Sign-constrained least squares estimation for high-dimensional regression,” Electron. J. Statist. 7, 1607–1631 (2013).
[Crossref]

IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. (1)

J. M. Bioucas-dias, A. Plaza, N. Dobigeon, M. Parente, Q. Du, P. Gader, and J. Chanussot, “Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 5(2), 354–379 (2012).
[Crossref]

IEEE Signal Process. Lett. (1)

S. Foucart and D. Koslicki, “Sparse recovery by means of nonnegative least squares,” IEEE Signal Process. Lett. 21(4), 498–502 (2014).
[Crossref]

IEEE Signal Process. Mag. (2)

N. Keshava and J. F. Mustard, “Spectral Unmixing,” IEEE Signal Process. Mag. 19(1), 44–57 (2002).
[Crossref]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

IEEE Trans. Acoust. Speech Signal Process. (1)

M. Unser and M. Eden, “Maximum likelihood estimation of linear signal parameters for Poisson processes,” IEEE Trans. Acoust. Speech Signal Process. 36, 942–945 (1988).
[Crossref]

IEEE Trans. Inform. Theory (1)

A. M. Bruckstein, M. Elad, and M. Zibulevsky, “On the uniqueness of nonnegative sparse solutions to underdetermined systems of equations,” IEEE Trans. Inform. Theory 54(11), 4813–4820 (2008).
[Crossref]

IEEE Trans. Med. Imag. (2)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imag. 18(3), 262–271 (1999).
[Crossref]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imag. 24(10), 1377–1386 (2005).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

E. Elhamifar and R. Vidal, “Sparse subspace clustering: algorithm, theory, and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 35(11), 2765–2781 (2013).
[Crossref] [PubMed]

J. Biomed. Opt. (3)

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

S. B. Raymond, D. A. Boas, B. J. Bacskai, and A. T. N. Kumar, “Lifetime-based tomographic multiplexing,” J. Biomed. Opt. 15(4), 046011 (2010).
[Crossref] [PubMed]

V. Pera, D. H. Brooks, and M. Niedre, “On the use of the Cramér-Rao lower bound for diffuse optical imaging system design,” J. Biomed. Opt. 19(2), 025002 (2014).
[Crossref] [PubMed]

J. Chemometr. (1)

R. Bro and S. D. Jong, “A fast non-negativity-constrained least squares algorithm,” J. Chemometr. 11, 393–401 (1997).
[Crossref]

J. Comput. Appl. Math. (1)

P. C. Hansen and M. Saxild-Hansen, “AIR Tools – A MATLAB package of algebraic iterative reconstruction methods,” J. Comput. Appl. Math. 236, 2167–2178 (2012).
[Crossref]

J. Machine Learning Research (1)

E. L. Dyer, A. C. Sankaranarayanan, and R. G. Baraniuk, “Greedy feature selection for subspace clustering,” J. Machine Learning Research 14(1), 2487–2517 (2013).

J. R. Statist. Soc. B (1)

D. L. Donoho, I. M. Johnstone, J. C. Hoch, and A. S. Stern, “Maximum entropy and the nearly black object,” J. R. Statist. Soc. B 54, (1), 41–81 (1992).

Nat. Med. (1)

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, (7)757–760 (2002).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Med. Biol. (2)

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).
[Crossref]

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, 4225–4241 (2005).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105(49), 19126–19131 (2008).
[Crossref] [PubMed]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Other (9)

J. Bai and Z. Xu, “Fluorescence molecular tomography,” in Molecular Imaging: Fundamentals and Applications, J. Tian, ed. (Springer, 2013).
[Crossref]

N. Valim, “Instrumentation and methods for time-resolved diffuse fluorescence imaging,” Ph.D. Dissertation (Northeastern University, 2014), Chap. 5.

http://www.lifetechnologies.com/us/en/home/life-science.html

L. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging (Wiley, 2007).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

V. Pera, D. H. Brooks, and M. Niedre, “A sparse nonnegative demixing algorithm with intrinsic regularization for multiplexed fluorescence tomography,” in IEEE 12th International Symposium on Biomedical Imaging (IEEE, 2015) pp. 1044–1047.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, 1974).

Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition,” in IEEE Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers (IEEE, 1993), pp. 40–44.

Y. Wang and H. Xu, “Noisy sparse subspace clustering,” in Proceedings of the 30th International Conference on Machine Learning (2013).

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Figures (13)

Fig. 1
Fig. 1 Solid lines: fluorophore spectral signatures for AF 750 (red) and AF 790 (cyan) using data from [7]. Red dotted line: “redshifted” spectrum for AF 750 using optical properties for “skin” in [8] with a distance of 20 mm from fluorophore to detector.
Fig. 2
Fig. 2 Schematic of time-resolved hyperspectral tomographic imaging system.
Fig. 3
Fig. 3 (a) Emission spectra and lifetimes (in ns in parentheses) for four common fluorophores: Alexa Fluor 680, 700, 750 and 790; data from [7]. (b) Spectral-temporal signatures associated with each fluorophore; each two-dimensional signature was concatenated into a vector. (c) Cramér-Rao lower bounds for root-mean-square (RMS) demixing error for three data types with all four fluorophores present. Lower values indicate better performance.
Fig. 4
Fig. 4 Data processing algorithm flowchart. Demixing of each source-detector pair measurement is accomplished in Stage 1; tomographic reconstructions for each fluorophore are performed in Stage 2.
Fig. 5
Fig. 5 Distribution of pathlengths (mm) for nearest source-detector pair. Color indicates sum of distance to source (s) and detector (d) from that location; lines show where that sum equals 23, 25, and 27 mm.
Fig. 6
Fig. 6 Spectral-temporal signature of AF 680 as a function of position in sample (7 of 10 spectral channels shown). Redshifting increases with increasing distance to detector, even if pathlength remains constant at 25 mm.
Fig. 7
Fig. 7 Extended Library II: (a) Sampling locations as a function of distance to source and detector; inset shows minimum distance between samples. (b) Coherence of library, measured as ST S. Note that signatures are normalized to unit norm, as explained in text.
Fig. 8
Fig. 8 Source-detector configuration and distribution of four fluorophores in sample in “standard positions.” Source (s) and detectors (d) rotate around sample, taking measurements every 5 degrees.
Fig. 9
Fig. 9 Values of absorption (µa) and reduced scattering ( μ s ) coefficients per spectral channel for “skin” with scaling constants applied (see text for details). Values labeled “1” (dotted line) reflect the information provided in [8].
Fig. 10
Fig. 10 Demixing results for none (a) and significant redshifting (b). Values reported are averages of 10 trials; standard error bars are smaller than symbols so not shown. “Randomized positions” represents performance variation over 50 trials with Extended Library I and refers to cases where positions of the four fluorophores in the sample were randomized.
Fig. 11
Fig. 11 Number of significant coefficients in solution vector ak as a function of target size. Crosses indicate average value (computed over 648 measurement estimates); triangles indicate maximum value. “Fraction” is [number of significant coefficients] divided by 344, which is the total number of signatures in the signal subspace. Target size is quantified in terms of radius (r) and illustrated graphically.
Fig. 12
Fig. 12 Tomographic reconstructions of 3-mm diameter fluorescent targets with redshifting.
Fig. 13
Fig. 13 Demixing results in the presence of mismatch between Extended Library II and input fluorophore signals. Legend refers to scale factor (γ) applied to optical properties used to generate signal (see text for details). Values reported are averages of 10 trials; standard error bars are smaller than symbols so not shown.

Equations (17)

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

m ( r s , r d , λ , t ) = λ Δ λ λ t Δ t t 0 t 0 t β G x ( r , r s , t ) η ( r , λ ) τ exp ( t t τ ) × G m ( r d , r , λ , t t ) d t d t d t d λ d 3 r ,
η ( r , λ ) = ε c ( r ) Q M ( λ ) ,
m ( r s , r d , λ , t ) = λ Δ λ λ t Δ t t 0 t J ( r , r s , r d , λ , t ) η ( r , λ ) τ exp ( t t τ ) d t d t d λ d 3 r
J ( r , r s , r d , λ , t ) = 0 t β G x ( r , r s , t ) G m ( r d , r , λ , t t ) d t .
m ( k , λ , t ) = Jc ,
J = [ J ( λ 1 , t 1 ) [ E ] 1 , 1 J ( λ 1 , t 1 ) [ E ] 1 , F J ( λ L , t T ) [ E ] L T , 1 J ( λ L , t T ) [ E ] L T , F ] Δ v ,
E = [ ε 1 Q 1 M 1 ( λ 1 ) τ 1 exp ( t t 1 τ 1 ) ε 2 Q 2 M 2 ( λ 1 ) τ 2 exp ( t t 1 τ 2 ) ε F Q F M F ( λ 1 ) τ F exp ( t t 1 τ F ) ε 1 Q 1 M 1 ( λ L ) τ 1 exp ( t t T τ 1 ) ε 2 Q 2 M 2 ( λ L ) τ 2 exp ( t t T τ 2 ) ε F Q F M F ( λ L ) τ F exp ( t t T τ F ) ] ,
c = [ c 1 c 2 c F ] ,
m ( λ , t ) = J ˜ c + n ,
C C R L B = ( J ˜ T R 1 J ˜ ) 1 ,
m k = S a k + n ,
S = [ S 1 S 2 S F ] ,
a k = [ a k , 1 a k , 2 a k , F ] ,
min a k ¯ 0 m k S a k 2 2 ,
m k ( f ) = S f a k , f .
e ( f ) = M ^ f M f F M f F ,
μ ¯ a ( λ , γ ) = γ [ μ a ( λ ) < μ a ( λ ) > ] + < μ a ( λ ) > , μ ¯ s ( λ , γ ) = γ [ μ s ( λ ) < μ s ( λ ) > ] + < μ s ( λ ) > ,

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