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).
[CrossRef]

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).
[CrossRef]

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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Figures (6)

Fig. 1
Fig. 1

Noiseless EEM model affected by attenuation. The top and bottom rows are the visualizations of Eqs. (2) and (5), respectively.

Fig. 2
Fig. 2

Simulated fluorescence emission and excitation spectra of two fluorophores and an absorption spectrum of the standard dataset are shown on the left. Continuous and dotted lines represent emission and excitation spectra, respectively. The contribution of each fluorophore to signals are simulated to be the same. The estimated absorption spectrum is also shown in the bottom-left figure. The performance of AFMU is evaluated on various (a) SNR levels in measurements, (b) sampling intervals, (c) numbers of fluorophores and (d) spectral overlaps of the two fluorophores.

Fig. 3
Fig. 3

The left column shows the simulated arbitrary distribution patterns of two fluorophores used for the standard dataset. The pattern for each fluorophore is generated based on the two dimensional discrete Fourier transform basis functions. The performance of AFTU is evaluated in respect of normalized root mean squared error of the estimated contributions. The robustness of AFTU is evaluated with (a) SNR levels in measurements, (b) sampling interval of emission channel, (c) number of fluorophores and (d) spectral overlap of the two fluorophores.

Fig. 4
Fig. 4

Molecular fraction of Fluorophore 1 of the standard dataset for the simulation of fluorescence spectral imaging. The original fraction, its estimation by AFTU and its pixel-by-pixel estimation error (NRMSE) are shown from left to right, respectively. Similar to Eq. 8, NRMSE is computed at each pixel.

Fig. 5
Fig. 5

Experimental results of fluorescence spectroscopy. The fluorescence spectra are measured with the right angle geometry. Eight samples were prepared with different concentrations of DCM in ethanol, while all of them had the same concentration of Rhodamine 123. The relative concentration of DCM in Sample 1–8 is set to be 1, 2, 4, 8, 20, 40, 80 and 120. (a) Measured emission and excitation spectra of 4-(Dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) and Rhodamine 123. (b) Relative concentrations of DCM in the eight solutions are estimated by AFMU and LU from the measured EEM, and the estimated values are compared with experimentally-measured relative concentrations. (c) Reconstruction errors of the eight samples are calculated from the Euclidean distance between the measured EEM and the reconstructed EEM from the estimated concentration and the absorption spectrum. The reconstruction errors are compared between AFMU and LU. (d, e) The measured EEM and the residuals of AFMU and LU for Sample 1 and 8, respectively. Residuals are computed from the difference between a measured EEM and a corresponding reconstructed EEM.

Fig. 6
Fig. 6

Spectrally unmixed images of the microsphere and the cellular specimen. (a) Schematic illustration of the microsphere. The core and shell are stained with different fluorophores. (b) Emission spectra of the two fluorophores staining the microsphere. (c) Emission spectra of the two fluorophores, TRITC and Alexa Fluor 568, staining the cellular sample. (d) Unmixed images of the stained microsphere. The second and third rows show the unmixed images of the microsphere. The first row shows the merged images of the second and third rows. The left and middle columns show the unmixed results on the same spectral image dataset captured through a hemoglobin layer. The right column shows the unmixed results by LU of the datasets captured without a hemoglobin layer. The fourth row shows the contribution from each fluorophore on the yellow line of the top-row images. The white bar in the top-left image is a scale bar whose length is 5 nm. (e) Unmixed images of the cellular specimen. Actin filaments and β tubulin are stained with Alexa Fluor 568 (Fluorophore 1, represented in red) and TRITC (Fluorophore 2, represented in green). The first, second and third rows are shown in the same way as for (d). The images in the fourth row are the magnified images of the yellow box region of the third-row images. The white scale bar in the top-left image is 20 nm. All images are represented in pseudocolor.

Equations (17)

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

F ( λ ex , λ em ) = M 1 10 ( A ( λ ex ) + A ( λ em ) ) / 2 n = 1 N I 0 ( λ ex ) ϕ n c n ε n ( λ ex ) γ n ( λ em ) + e ,
F = M 1 ( w 1 w 2 ) A D B + E ,
min w ^ 1 , w ^ 2 , D ^ F ( w ^ 1 w ^ 2 ) A D ^ B F subject to 0 w ^ 1 , w ^ 2 1 , D ^ 0 .
f k ( λ ex , λ em ) = M 2 E 0 , k ( λ ex ) p g 1 , k ( λ ex ) g 2 , k ( λ em ) n = 1 N s n ( λ ex ) t n ( λ em ) u n , k ,
= M 2 𝒱 n = 1 N s n ° t n ° u n +
= M 2 𝒱 [ [ S , T , U ] ] + ,
min 𝒱 ^ , S ^ , U ^ 𝒱 ^ [ [ S ^ , T , U ^ ] ] F subject to 0 𝒱 ^ 1 , S ^ 0 , U ^ 0 .
NRMSE = c ^ c ^ 2 c c 2 2 2 / c c 2 2 2 .
NRMSE = U ˜ U ¨ 2 2 U ¨ 2 2 .
c ^ c ^ ( ( W ^ 2 B ) ( W ^ 1 A ) ) vec ( F ) ( ( W ^ 2 B ) ( W ^ 1 A ) ) ( W ^ 2 B ) ( W ^ 1 A ) ) c ^ ,
w ^ 1 ( ( A D ^ B ) F ) w ^ 2 ( ( A D ^ B ) ( A D ^ B ) ) ( w ^ 2 w ^ 2 ) ,
w ^ 2 ( ( A D ^ B ) F ) w ^ 1 ( ( A D ^ B ) ( A D ^ B ) ) ( w ^ 1 w ^ 1 ) ,
P Q = [ p 1 q 1 p 2 q 2 p L 3 q L 3 ]
S ^ S ^ ( 1 ) ( U ^ ( V ^ 2 T ) ) ( ( V ^ 1 S ^ ) ( U ^ ( V ^ 2 T ) ) ) ( U ^ ( V ^ 2 T ) ) ,
U ^ U ^ ( 3 ) ( ( V ^ 2 T ^ ) ( V ^ 1 S ) ) ( U ^ ( V ^ 2 T ^ ) ( V ^ 1 S ) ) ) ( ( V ^ 2 T ^ ) ( V ^ 1 S ) ) ,
v ^ 1 ( ( 1 ) ( 𝒱 ^ [ [ S ^ , T , U ^ ] ] ) ( 1 ) ) v ^ 2 ( ( 𝒱 ^ [ [ S ^ , T , U ^ ] ] ) ( 1 ) ( 𝒱 ^ [ [ S ^ , T , U ^ ] ] ) ( 1 ) ) ( V ^ 2 V ^ 2 ) ,
v ^ 2 ( ( 2 ) ( 𝒱 ^ [ [ S ^ , T , U ^ ] ] ) ( 2 ) ) v ^ 1 ( ( 𝒱 ^ [ [ S ^ , T , U ^ ] ] ) ( 2 ) ( 𝒱 ^ [ [ S ^ , T , U ^ ] ] ) ( 2 ) ) ( V ^ 1 V ^ 1 ) ,

Metrics