Abstract

In fluorescence measurements, light is often absorbed and scattered by a sample both for excitation and emission, resulting in the measured spectra to be distorted. Conventional linear unmixing methods computationally separate overlapping spectra but do not account for these effects. We propose a new algorithm for fluorescence unmixing that accounts for the attenuation-related distortion effect on fluorescence spectra. Using a matrix representation, we derive forward measurement formation and a corresponding inverse method; the unmixing algorithm is based on nonnegative matrix factorization. We also demonstrate how this method can be extended to a higher-dimensional tensor form, which is useful for unmixing overlapping spectra observed under the attenuation effect in spectral imaging microscopy. We evaluate the proposed methods in simulation and experiments and show that it outperforms a conventional, linear unmixing method when absorption and scattering contributes to the measured signals, as in deep tissue imaging.

© 2014 Optical Society of America

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2014 (2)

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[CrossRef]

S. Henrot, C. Soussen, M. Dossot, and D. Brie, “Does deblurring improve geometrical hyperspectral unmixing?” IEEE Trans. Image Process. 23, 1169–1180 (2014).
[CrossRef] [PubMed]

2013 (3)

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

K. R. Murphy, C. A. Stedmon, D. Graeber, and R. Bro, “Fluorescence spectroscopy and multi-way techniques. PARAFAC,” Anal. Methods 5, 6557–6566 (2013).
[CrossRef]

I. Urbančič, Z. Arsov, A. Ljubetič, D. Biglino, and J. Štrancar, “Bleaching-corrected fluorescence microspectroscopy with nanometer peak position resolution,” Opt. Express 21, 25291–25306 (2013).
[CrossRef]

2012 (1)

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: Compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graphics 31, 80 (2012).
[CrossRef]

2011 (1)

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

2009 (5)

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Rev. 51, 455–500 (2009).
[CrossRef]

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

X. Luciani, S. Mounier, R. Redon, and A. Bois, “A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition,” Chemometr. Intell. Lab. 96, 227–238 (2009).
[CrossRef]

S. Schlachter, S. Schwedler, A. Esposito, G. S. Kaminski Schierle, G. D. Moggridge, and C. F. Kaminski, “A method to unmix multiple fluorophores in microscopy images with minimal a priori information,” Opt. Express 17, 22747–22760 (2009).
[CrossRef]

2008 (1)

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

2007 (2)

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

2006 (3)

B. W. Bader and T. G. Kolda, “Algorithm 862: MATLAB tensor classes for fast algorithm prototyping,” ACM Trans. Math. Software 32, 635–653 (2006).
[CrossRef]

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry A 69A, 735–747 (2006).
[CrossRef]

R. S. Bradley and M. S. Thorniley, “A review of attenuation correction techniques for tissue fluorescence,” J. R. Soc. Interface 3, 1–13 (2006).
[CrossRef] [PubMed]

2004 (1)

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86, 1739–1752 (2004).
[CrossRef] [PubMed]

2002 (1)

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

2001 (1)

1999 (1)

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef] [PubMed]

1996 (1)

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Arsov, Z.

Bader, B. W.

T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Rev. 51, 455–500 (2009).
[CrossRef]

B. W. Bader and T. G. Kolda, “Algorithm 862: MATLAB tensor classes for fast algorithm prototyping,” ACM Trans. Math. Software 32, 635–653 (2006).
[CrossRef]

Bar-Am, I.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Bennis, R. A.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Biglino, D.

Bois, A.

X. Luciani, S. Mounier, R. Redon, and A. Bois, “A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition,” Chemometr. Intell. Lab. 96, 227–238 (2009).
[CrossRef]

Borisy, G. G.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Bradley, J.

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Bradley, R. S.

R. S. Bradley and M. S. Thorniley, “A review of attenuation correction techniques for tissue fluorescence,” J. R. Soc. Interface 3, 1–13 (2006).
[CrossRef] [PubMed]

Brie, D.

S. Henrot, C. Soussen, M. Dossot, and D. Brie, “Does deblurring improve geometrical hyperspectral unmixing?” IEEE Trans. Image Process. 23, 1169–1180 (2014).
[CrossRef] [PubMed]

Bro, R.

K. R. Murphy, C. A. Stedmon, D. Graeber, and R. Bro, “Fluorescence spectroscopy and multi-way techniques. PARAFAC,” Anal. Methods 5, 6557–6566 (2013).
[CrossRef]

Cavaliere-Jaricot, S.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

Charpak, S.

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Chen, Z.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Chua, M.

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

Clements, I.

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

Dewhirst, F. E.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Dossot, M.

S. Henrot, C. Soussen, M. Dossot, and D. Brie, “Does deblurring improve geometrical hyperspectral unmixing?” IEEE Trans. Image Process. 23, 1169–1180 (2014).
[CrossRef] [PubMed]

Draft, R. W.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Du, H.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

du Manoir, S.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Ducros, M.

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Esposito, A.

Feld, M. S.

Ferguson-Smith, M. A.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Garini, Y.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry A 69A, 735–747 (2006).
[CrossRef]

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Georgakoudi, I.

Georget, V.

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

Girod, A.

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

Grabolle, M.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

Graeber, D.

K. R. Murphy, C. A. Stedmon, D. Graeber, and R. Bro, “Fluorescence spectroscopy and multi-way techniques. PARAFAC,” Anal. Methods 5, 6557–6566 (2013).
[CrossRef]

Griesbeck, O.

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Hasegawa, Y.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Henrot, S.

S. Henrot, C. Soussen, M. Dossot, and D. Brie, “Does deblurring improve geometrical hyperspectral unmixing?” IEEE Trans. Image Process. 23, 1169–1180 (2014).
[CrossRef] [PubMed]

Hirsch, M.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: Compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graphics 31, 80 (2012).
[CrossRef]

Hogg, K.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[CrossRef]

Kaminski, C. F.

Kaminski Schierle, G. S.

Kang, H.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Kirchhoff, F.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Kolda, T. G.

T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Rev. 51, 455–500 (2009).
[CrossRef]

B. W. Bader and T. G. Kolda, “Algorithm 862: MATLAB tensor classes for fast algorithm prototyping,” ACM Trans. Math. Software 32, 635–653 (2006).
[CrossRef]

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2007).

Lanman, D.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: Compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graphics 31, 80 (2012).
[CrossRef]

Ledbetter, D. H.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Lee, D. D.

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef] [PubMed]

Lichtman, J. W.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Liu, S.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Livet, J.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Ljubetic, A.

Lu, J.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Luciani, X.

X. Luciani, S. Mounier, R. Redon, and A. Bois, “A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition,” Chemometr. Intell. Lab. 96, 227–238 (2009).
[CrossRef]

Marrison, J.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[CrossRef]

McNamara, G.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry A 69A, 735–747 (2006).
[CrossRef]

Mitkovski, M.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Miyazaki, S.

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86, 1739–1752 (2004).
[CrossRef] [PubMed]

Moggridge, G. D.

Moreaux, L.

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Mounier, S.

X. Luciani, S. Mounier, R. Redon, and A. Bois, “A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition,” Chemometr. Intell. Lab. 96, 227–238 (2009).
[CrossRef]

Müller, M. G.

Murphy, K. R.

K. R. Murphy, C. A. Stedmon, D. Graeber, and R. Bro, “Fluorescence spectroscopy and multi-way techniques. PARAFAC,” Anal. Methods 5, 6557–6566 (2013).
[CrossRef]

Nann, T.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

Neher, E.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Neher, R. A.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Ning, Y.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Nitschke, R.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

O’Toole, P.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[CrossRef]

Oldenbourg, R.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Pawley, J. B.

J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).

Pepperkok, R.

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

Raskar, R.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: Compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graphics 31, 80 (2012).
[CrossRef]

Redon, R.

X. Luciani, S. Mounier, R. Redon, and A. Bois, “A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition,” Chemometr. Intell. Lab. 96, 227–238 (2009).
[CrossRef]

Resch-Genger, U.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

Ried, T.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Rieken, C. W.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Rietdorf, J.

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

Rigby, P.

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

Salmon, W.

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

Sanes, J. R.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Schlachter, S.

Schoell, B.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Schröck, E.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Schwedler, S.

Seung, H. S.

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef] [PubMed]

Shirakawa, H.

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86, 1739–1752 (2004).
[CrossRef] [PubMed]

Soenksen, D.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Sogin, M. L.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Song, J.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Song, M.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Soussen, C.

S. Henrot, C. Soussen, M. Dossot, and D. Brie, “Does deblurring improve geometrical hyperspectral unmixing?” IEEE Trans. Image Process. 23, 1169–1180 (2014).
[CrossRef] [PubMed]

Stedmon, C. A.

K. R. Murphy, C. A. Stedmon, D. Graeber, and R. Bro, “Fluorescence spectroscopy and multi-way techniques. PARAFAC,” Anal. Methods 5, 6557–6566 (2013).
[CrossRef]

Štrancar, J.

Theis, F. J.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Thorniley, M. S.

R. S. Bradley and M. S. Thorniley, “A review of attenuation correction techniques for tissue fluorescence,” J. R. Soc. Interface 3, 1–13 (2006).
[CrossRef] [PubMed]

Tiret, P.

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Urbancic, I.

Valm, A. M.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Veldman, T.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Weissman, T. A.

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

Welch, J. L. M.

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Wetzstein, G.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: Compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graphics 31, 80 (2012).
[CrossRef]

Wienberg, J.

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

Wu, J.

Yang, J.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Young, I. T.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry A 69A, 735–747 (2006).
[CrossRef]

Zeug, A.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Zhang, Q.

Zimmermann, T.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[CrossRef]

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

Zucker, R. M.

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

ACM Trans. Graphics (1)

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: Compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graphics 31, 80 (2012).
[CrossRef]

ACM Trans. Math. Software (1)

B. W. Bader and T. G. Kolda, “Algorithm 862: MATLAB tensor classes for fast algorithm prototyping,” ACM Trans. Math. Software 32, 635–653 (2006).
[CrossRef]

Anal. Methods (1)

K. R. Murphy, C. A. Stedmon, D. Graeber, and R. Bro, “Fluorescence spectroscopy and multi-way techniques. PARAFAC,” Anal. Methods 5, 6557–6566 (2013).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (2)

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86, 1739–1752 (2004).
[CrossRef] [PubMed]

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96, 3791–3800 (2009).
[CrossRef] [PubMed]

Chemometr. Intell. Lab. (1)

X. Luciani, S. Mounier, R. Redon, and A. Bois, “A simple correction method of inner filter effects affecting FEEM and its application to the PARAFAC decomposition,” Chemometr. Intell. Lab. 96, 227–238 (2009).
[CrossRef]

Cytometry A (1)

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry A 69A, 735–747 (2006).
[CrossRef]

Cytometry Part A (1)

R. M. Zucker, P. Rigby, I. Clements, W. Salmon, and M. Chua, “Reliability of confocal microscopy spectral imaging systems: Use of multispectral beads,” Cytometry Part A 71A, 174–189 (2007).
[CrossRef]

FEBS lett. (1)

T. Zimmermann, J. Rietdorf, A. Girod, V. Georget, and R. Pepperkok, “Spectral imaging and linear un-mixing enables improved FRET efficiency with a novel GFP2-YFP FRET pair,” FEBS lett. 531, 245–249 (2002).
[CrossRef] [PubMed]

IEEE Trans. Image Process. (1)

S. Henrot, C. Soussen, M. Dossot, and D. Brie, “Does deblurring improve geometrical hyperspectral unmixing?” IEEE Trans. Image Process. 23, 1169–1180 (2014).
[CrossRef] [PubMed]

J. R. Soc. Interface (1)

R. S. Bradley and M. S. Thorniley, “A review of attenuation correction techniques for tissue fluorescence,” J. R. Soc. Interface 3, 1–13 (2006).
[CrossRef] [PubMed]

Methods Mol. Biol. (1)

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[CrossRef]

Nat. Methods (1)

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5, 763–775 (2008).
[CrossRef] [PubMed]

Nature (2)

J. Livet, T. A. Weissman, H. Kang, R. W. Draft, J. Lu, R. A. Bennis, J. R. Sanes, and J. W. Lichtman, “Transgenic strategies for combinatorial expression of fluorescent proteins in the nervous system,” Nature 450, 56–62 (2007).
[CrossRef] [PubMed]

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef] [PubMed]

Opt. Express (2)

PloS ONE (1)

M. Ducros, L. Moreaux, J. Bradley, P. Tiret, O. Griesbeck, and S. Charpak, “Spectral unmixing: analysis of performance in the olfactory bulb in vivo,” PloS ONE 4, e4418 (2009).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. M. Valm, J. L. M. Welch, C. W. Rieken, Y. Hasegawa, M. L. Sogin, R. Oldenbourg, F. E. Dewhirst, and G. G. Borisy, “Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging,” Proc. Natl. Acad. Sci. U.S.A. 108, 4152–4157 (2011).
[CrossRef] [PubMed]

Rev. Anal. Chem (1)

J. Zhang, S. Liu, J. Yang, M. Song, J. Song, H. Du, and Z. Chen, “Quantitative spectroscopic analysis of heterogeneous systems: chemometric methods for the correction of multiplicative light scattering effects,” Rev. Anal. Chem 32, 113–125 (2013).
[CrossRef]

Science (1)

E. Schröck, S. du Manoir, T. Veldman, B. Schoell, J. Wienberg, M. A. Ferguson-Smith, Y. Ning, D. H. Ledbetter, I. Bar-Am, D. Soenksen, Y. Garini, and T. Ried, “Multicolor spectral karyotyping of human chromosomes,” Science 273, 494–497 (1996).
[CrossRef] [PubMed]

SIAM Rev. (1)

T. G. Kolda and B. W. Bader, “Tensor decompositions and applications,” SIAM Rev. 51, 455–500 (2009).
[CrossRef]

Other (3)

J. B. Pawley, Handbook of Biological Confocal Microscopy (Springer, 2006).

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2007).

B. W. Bader and T. G. Kolda, “Matlab tensor toolbox version 2.5,” available at http://www.sandia.gov/tgkolda/TensorToolbox/ (2012).

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