Abstract

Existing methods of interpreting fluorescence lifetime imaging microscopy (FLIM) images are based on comparing the intensity and lifetime values at each pixel with those of known fluorophores. This method becomes unwieldy and subjective in many practical applications where there are several fluorescing species contributing to the bulk fluorescence signal, and even more so in the case of multispectral FLIM. Non-negative matrix factorization (NMF) is a multivariate data analysis technique aimed at extracting non-negative signatures of pure components and their non-negative abundances from an additive mixture of those components. In this paper, we present the application of NMF to multispectral time-domain FLIM data to obtain a new set of FLIM features (relative abundance of constituent fluorophores). These features are more intuitive and easier to interpret than the standard fluorescence intensity and lifetime values. The proposed approach, unlike several FLIM data analysis methods, is not limited by the number of constituent fluorescing species or their possibly complex decay dynamics. Moreover, the new set of FLIM features can be obtained by processing raw multispectral FLIM intensity data, thereby rendering time deconvolution unnecessary and resulting in lesser computational time and relaxed SNR requirements. The performance of the NMF method was validated on simulated and experimental multispectral time-domain FLIM data. The NMF features were also compared against the standard intensity and lifetime features, in terms of their ability to discriminate between different types of atherosclerotic plaques.

© 2012 OSA

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  1. J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
    [CrossRef] [PubMed]
  2. M. Mycek, K. Schomacker, and N. Nishioka, “Colonic polyp differentiation using time-resolved autofluorescence spectroscopy,” Gastrointest. Endosc.48, 390–394 (1998).
    [CrossRef] [PubMed]
  3. L. Marcu, “Fluorescence lifetime in cardiovascular diagnostics,” J. Biomed. Opt.15, 011106 (2010).
    [CrossRef] [PubMed]
  4. J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
    [CrossRef] [PubMed]
  5. P. Verveer, A. Squire, and P. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
    [CrossRef] [PubMed]
  6. G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
    [CrossRef] [PubMed]
  7. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).
    [CrossRef]
  8. K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
    [CrossRef] [PubMed]
  9. A. Clayton, Q. Hanley, and P. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc.213, 1–5 (2004).
    [CrossRef]
  10. S. Schlachter, S. Schwedler, A. Esposito, G. Kaminski Schierle, G. Moggridge, and C. Kaminski, “A method to unmix multiple fluorophores in microscopy images with minimal a priori information,” Opt. Express17, 22747–22760 (2009).
    [CrossRef]
  11. A. Cichocki, R. Zdunek, A. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation (Wiley, 2009).
    [PubMed]
  12. S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
    [CrossRef] [PubMed]
  13. R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
    [CrossRef] [PubMed]
  14. N. Keshava and J. Mustard, “Spectral unmixing,” IEEE Signal Process Mag. 19, 44–57 (2002).
    [CrossRef]
  15. H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
    [CrossRef]
  16. J. Nascimento and J. Dias, “Does independent component analysis play a role in unmixing hyperspectral data?” IEEE Trans. Geosci. Remote Sens.43, 175–187 (2005).
    [CrossRef]
  17. J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches,” Proc. SPIE7830, 78300A (2010).
    [CrossRef]
  18. T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
    [CrossRef]
  19. J. Nascimento and J. Dias, “Vertex component analysis: a fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens.43, 898–910 (2005).
    [CrossRef]
  20. J. Boardman, “Automating spectral unmixing of aviris data using convex geometry concepts,” in Summaries of the 4th Annual JPL Airborne Geoscience Workshop (1993), Vol. 1, pp. 11–14.
  21. M. Winter, “N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data,” Proc. SPIE3753, 266–275 (1999).
    [CrossRef]
  22. M. Craig, “Minimum-volume transforms for remotely sensed data,” IEEE Trans. Geosci. Remote Sens.32, 542–552 (1994).
    [CrossRef]
  23. R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, “Minimum determinant constraint for non-negative matrix factorization,” in Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation (2009), pp. 106–113.
    [CrossRef]
  24. J. Li and J. Bioucas-Dias, “Minimum volume simplex analysis: a fast algorithm to unmix hyperspectral data,” in IEEE International Geoscience and Remote Sensing Symposium, 2008 (IEEE, 2008), Vol. III, pp. 250–253.
  25. J. Bioucas-Dias, “A variable splitting augmented lagrangian approach to linear spectral unmixing,” in First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2009, (IEEE, 2009), pp. 1–4.
    [CrossRef]
  26. P. Pande and J. Jo, “Automated analysis of fluorescence lifetime imaging microscopy (flim) data based on the laguerre deconvolution method,” IEEE Trans. Biomed. Eng.58, 172–181 (2011).
    [CrossRef]
  27. D. Hosmer and S. Lemeshow, Applied Logistic Regression, (Wiley-Interscience, 2000).
    [CrossRef]
  28. J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning (Springer, 2001).
  29. E. Chong and S. Żak, An introduction to Optimization (Wiley-Interscience, 2004).
  30. J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
    [CrossRef]
  31. M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
    [CrossRef] [PubMed]
  32. C. I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens.42, 608–619 (2004).
    [CrossRef]
  33. A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
    [CrossRef]
  34. J. B. Lee, A. S. Woodyatt, and M. Berman, “Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform,” IEEE Trans. Geosci. Remote Sens.28, 295–304 (1990).
    [CrossRef]

2012 (1)

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

2011 (1)

P. Pande and J. Jo, “Automated analysis of fluorescence lifetime imaging microscopy (flim) data based on the laguerre deconvolution method,” IEEE Trans. Biomed. Eng.58, 172–181 (2011).
[CrossRef]

2010 (4)

L. Marcu, “Fluorescence lifetime in cardiovascular diagnostics,” J. Biomed. Opt.15, 011106 (2010).
[CrossRef] [PubMed]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches,” Proc. SPIE7830, 78300A (2010).
[CrossRef]

S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (3)

G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
[CrossRef] [PubMed]

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
[CrossRef]

2007 (1)

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

2006 (1)

R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
[CrossRef] [PubMed]

2005 (2)

J. Nascimento and J. Dias, “Vertex component analysis: a fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens.43, 898–910 (2005).
[CrossRef]

J. Nascimento and J. Dias, “Does independent component analysis play a role in unmixing hyperspectral data?” IEEE Trans. Geosci. Remote Sens.43, 175–187 (2005).
[CrossRef]

2004 (2)

C. I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens.42, 608–619 (2004).
[CrossRef]

A. Clayton, Q. Hanley, and P. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc.213, 1–5 (2004).
[CrossRef]

2002 (1)

N. Keshava and J. Mustard, “Spectral unmixing,” IEEE Signal Process Mag. 19, 44–57 (2002).
[CrossRef]

2001 (1)

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

2000 (1)

P. Verveer, A. Squire, and P. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

1999 (1)

M. Winter, “N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data,” Proc. SPIE3753, 266–275 (1999).
[CrossRef]

1998 (1)

M. Mycek, K. Schomacker, and N. Nishioka, “Colonic polyp differentiation using time-resolved autofluorescence spectroscopy,” Gastrointest. Endosc.48, 390–394 (1998).
[CrossRef] [PubMed]

1994 (1)

M. Craig, “Minimum-volume transforms for remotely sensed data,” IEEE Trans. Geosci. Remote Sens.32, 542–552 (1994).
[CrossRef]

1993 (1)

J. Boardman, “Automating spectral unmixing of aviris data using convex geometry concepts,” in Summaries of the 4th Annual JPL Airborne Geoscience Workshop (1993), Vol. 1, pp. 11–14.

1990 (1)

J. B. Lee, A. S. Woodyatt, and M. Berman, “Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform,” IEEE Trans. Geosci. Remote Sens.28, 295–304 (1990).
[CrossRef]

1988 (1)

A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
[CrossRef]

Amari, S.

A. Cichocki, R. Zdunek, A. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation (Wiley, 2009).
[PubMed]

Applegate, B.

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
[CrossRef] [PubMed]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

Bastiaens, P.

P. Verveer, A. Squire, and P. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

Berman, M.

J. B. Lee, A. S. Woodyatt, and M. Berman, “Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform,” IEEE Trans. Geosci. Remote Sens.28, 295–304 (1990).
[CrossRef]

A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
[CrossRef]

Bioucas-Dias, J.

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches,” Proc. SPIE7830, 78300A (2010).
[CrossRef]

J. Li and J. Bioucas-Dias, “Minimum volume simplex analysis: a fast algorithm to unmix hyperspectral data,” in IEEE International Geoscience and Remote Sensing Symposium, 2008 (IEEE, 2008), Vol. III, pp. 250–253.

J. Bioucas-Dias, “A variable splitting augmented lagrangian approach to linear spectral unmixing,” in First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2009, (IEEE, 2009), pp. 1–4.
[CrossRef]

Bird, D.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Boardman, J.

J. Boardman, “Automating spectral unmixing of aviris data using convex geometry concepts,” in Summaries of the 4th Annual JPL Airborne Geoscience Workshop (1993), Vol. 1, pp. 11–14.

Brandon, J.

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

Burke, A.

R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
[CrossRef] [PubMed]

Chan, T.

T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
[CrossRef]

Chang, C. I.

C. I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens.42, 608–619 (2004).
[CrossRef]

Chi, C.

T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
[CrossRef]

Chong, E.

E. Chong and S. Żak, An introduction to Optimization (Wiley-Interscience, 2004).

Chu, A. C.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Cichocki, A.

A. Cichocki, R. Zdunek, A. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation (Wiley, 2009).
[PubMed]

Clayton, A.

A. Clayton, Q. Hanley, and P. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc.213, 1–5 (2004).
[CrossRef]

Clubb, F.

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

Cole, M.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Craig, M.

M. Craig, “Minimum-volume transforms for remotely sensed data,” IEEE Trans. Geosci. Remote Sens.32, 542–552 (1994).
[CrossRef]

Craig, M. D.

A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
[CrossRef]

Dias, J.

J. Nascimento and J. Dias, “Does independent component analysis play a role in unmixing hyperspectral data?” IEEE Trans. Geosci. Remote Sens.43, 175–187 (2005).
[CrossRef]

J. Nascimento and J. Dias, “Vertex component analysis: a fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens.43, 898–910 (2005).
[CrossRef]

Dowling, K.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Du, Q.

C. I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens.42, 608–619 (2004).
[CrossRef]

Dunsby, C.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Eickhoff, J.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Eliceiri, K.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Elson, D. S.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Esposito, A.

Farb, A.

R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
[CrossRef] [PubMed]

French, P.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

French, P. M. W.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Friedman, J.

J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning (Springer, 2001).

Gadella, T.

G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
[CrossRef] [PubMed]

Geladi, P.

H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
[CrossRef]

Gendron-Fitzpatrick, A.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Gimenez-Conti, I.

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

Goedhart, J.

G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
[CrossRef] [PubMed]

Grahn, H.

H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
[CrossRef]

Green, A. A.

A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
[CrossRef]

Hanley, Q.

A. Clayton, Q. Hanley, and P. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc.213, 1–5 (2004).
[CrossRef]

Hastie, T.

J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning (Springer, 2001).

Hosmer, D.

D. Hosmer and S. Lemeshow, Applied Logistic Regression, (Wiley-Interscience, 2000).
[CrossRef]

Jo, J.

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

P. Pande and J. Jo, “Automated analysis of fluorescence lifetime imaging microscopy (flim) data based on the laguerre deconvolution method,” IEEE Trans. Biomed. Eng.58, 172–181 (2011).
[CrossRef]

S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
[CrossRef] [PubMed]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

Jones, R.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Kaminski, C.

Kaminski Schierle, G.

Keely, P.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Keshava, N.

N. Keshava and J. Mustard, “Spectral unmixing,” IEEE Signal Process Mag. 19, 44–57 (2002).
[CrossRef]

Kolodgie, F.

R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
[CrossRef] [PubMed]

Kremers, G.

G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
[CrossRef] [PubMed]

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).
[CrossRef]

Lang, E.

R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, “Minimum determinant constraint for non-negative matrix factorization,” in Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation (2009), pp. 106–113.
[CrossRef]

Lee, J. B.

J. B. Lee, A. S. Woodyatt, and M. Berman, “Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform,” IEEE Trans. Geosci. Remote Sens.28, 295–304 (1990).
[CrossRef]

Lee, K.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Lemeshow, S.

D. Hosmer and S. Lemeshow, Applied Logistic Regression, (Wiley-Interscience, 2000).
[CrossRef]

Lévêque-Fort, S.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Lever, M.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Li, J.

J. Li and J. Bioucas-Dias, “Minimum volume simplex analysis: a fast algorithm to unmix hyperspectral data,” in IEEE International Geoscience and Remote Sensing Symposium, 2008 (IEEE, 2008), Vol. III, pp. 250–253.

Ma, W.

T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
[CrossRef]

Marcu, L.

L. Marcu, “Fluorescence lifetime in cardiovascular diagnostics,” J. Biomed. Opt.15, 011106 (2010).
[CrossRef] [PubMed]

McGinty, J.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Moggridge, G.

Munro, I.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Mustard, J.

N. Keshava and J. Mustard, “Spectral unmixing,” IEEE Signal Process Mag. 19, 44–57 (2002).
[CrossRef]

Mycek, M.

M. Mycek, K. Schomacker, and N. Nishioka, “Colonic polyp differentiation using time-resolved autofluorescence spectroscopy,” Gastrointest. Endosc.48, 390–394 (1998).
[CrossRef] [PubMed]

Nascimento, J.

J. Nascimento and J. Dias, “Does independent component analysis play a role in unmixing hyperspectral data?” IEEE Trans. Geosci. Remote Sens.43, 175–187 (2005).
[CrossRef]

J. Nascimento and J. Dias, “Vertex component analysis: a fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens.43, 898–910 (2005).
[CrossRef]

Neil, M. A. A.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Nishioka, N.

M. Mycek, K. Schomacker, and N. Nishioka, “Colonic polyp differentiation using time-resolved autofluorescence spectroscopy,” Gastrointest. Endosc.48, 390–394 (1998).
[CrossRef] [PubMed]

Pande, P.

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

P. Pande and J. Jo, “Automated analysis of fluorescence lifetime imaging microscopy (flim) data based on the laguerre deconvolution method,” IEEE Trans. Biomed. Eng.58, 172–181 (2011).
[CrossRef]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
[CrossRef] [PubMed]

Park, J.

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
[CrossRef] [PubMed]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

Phan, A.

A. Cichocki, R. Zdunek, A. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation (Wiley, 2009).
[PubMed]

Plaza, A.

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches,” Proc. SPIE7830, 78300A (2010).
[CrossRef]

Pöppel, G.

R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, “Minimum determinant constraint for non-negative matrix factorization,” in Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation (2009), pp. 106–113.
[CrossRef]

Ramanujam, N.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Requejo-Isidro, J.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Riching, K.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Schachtner, R.

R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, “Minimum determinant constraint for non-negative matrix factorization,” in Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation (2009), pp. 106–113.
[CrossRef]

Schlachter, S.

Schomacker, K.

M. Mycek, K. Schomacker, and N. Nishioka, “Colonic polyp differentiation using time-resolved autofluorescence spectroscopy,” Gastrointest. Endosc.48, 390–394 (1998).
[CrossRef] [PubMed]

Schwedler, S.

Shrestha, S.

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

S. Shrestha, B. Applegate, J. Park, X. Xiao, P. Pande, and J. Jo, “High-speed multispectral fluorescence lifetime imaging implementation for in vivo applications,” Opt. Lett.35, 2558–2560 (2010).
[CrossRef] [PubMed]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

Siegel, J.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Skala, M.

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

Squire, A.

P. Verveer, A. Squire, and P. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

Stamp, G. W.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Switzer, P.

A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
[CrossRef]

Teixeira, F.

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Tibshirani, R.

J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning (Springer, 2001).

Tomé, A.

R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, “Minimum determinant constraint for non-negative matrix factorization,” in Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation (2009), pp. 106–113.
[CrossRef]

Van Munster, E.

G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
[CrossRef] [PubMed]

Verveer, P.

A. Clayton, Q. Hanley, and P. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc.213, 1–5 (2004).
[CrossRef]

P. Verveer, A. Squire, and P. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

Virmani, R.

R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
[CrossRef] [PubMed]

Wang, Y.

T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
[CrossRef]

Webb, S.

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Winter, M.

M. Winter, “N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data,” Proc. SPIE3753, 266–275 (1999).
[CrossRef]

Woodyatt, A. S.

J. B. Lee, A. S. Woodyatt, and M. Berman, “Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform,” IEEE Trans. Geosci. Remote Sens.28, 295–304 (1990).
[CrossRef]

Xiao, X.

Zak, S.

E. Chong and S. Żak, An introduction to Optimization (Wiley-Interscience, 2004).

Zdunek, R.

A. Cichocki, R. Zdunek, A. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation (Wiley, 2009).
[PubMed]

Atherosclerosis (1)

J. Park, P. Pande, S. Shrestha, F. Clubb, B. Applegate, and J. Jo, “Biochemical characterization of atherosclerotic plaques by endogenous multispectral fluorescence lifetime imaging microscopy,” Atherosclerosis220, 394–401 (2012).
[CrossRef]

Biophys. J. (2)

P. Verveer, A. Squire, and P. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

G. Kremers, E. Van Munster, J. Goedhart, and T. Gadella, “Quantitative lifetime unmixing of multiexponentially decaying fluorophores using single-frequency fluorescence lifetime imaging microscopy,” Biophys. J.95, 378–389 (2008).
[CrossRef] [PubMed]

Biophys. J. (1)

K. Lee, J. Siegel, S. Webb, S. Lévêque-Fort, M. Cole, R. Jones, K. Dowling, M. Lever, and P. French, “Application of the stretched exponential function to fluorescence lifetime imaging,” Biophys. J.81, 1265–1274 (2001).
[CrossRef] [PubMed]

Br. J. Dermatol. (1)

J. McGinty, C. Dunsby, F. Teixeira, J. Requejo-Isidro, I. Munro, D. S. Elson, M. A. A. Neil, A. C. Chu, P. M. W. French, and G. W. Stamp, “Fluorescence lifetime imaging distinguishes basal cell carcinoma from surrounding uninvolved skin,” Br. J. Dermatol.159(1), 152–161 (2008).
[CrossRef] [PubMed]

Gastrointest. Endosc. (1)

M. Mycek, K. Schomacker, and N. Nishioka, “Colonic polyp differentiation using time-resolved autofluorescence spectroscopy,” Gastrointest. Endosc.48, 390–394 (1998).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens. (1)

J. Nascimento and J. Dias, “Vertex component analysis: a fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens.43, 898–910 (2005).
[CrossRef]

IEEE Trans. Signal. Process. (1)

T. Chan, W. Ma, C. Chi, and Y. Wang, “A convex analysis framework for blind separation of non-negative sources,” IEEE Trans. Signal. Process.56, 5120–5134 (2008).
[CrossRef]

IEEE Signal Process Mag (1)

N. Keshava and J. Mustard, “Spectral unmixing,” IEEE Signal Process Mag. 19, 44–57 (2002).
[CrossRef]

IEEE Trans. Biomed. Eng. (2)

P. Pande and J. Jo, “Automated analysis of fluorescence lifetime imaging microscopy (flim) data based on the laguerre deconvolution method,” IEEE Trans. Biomed. Eng.58, 172–181 (2011).
[CrossRef]

J. Jo, B. Applegate, J. Park, S. Shrestha, P. Pande, I. Gimenez-Conti, and J. Brandon, “In vivo simultaneous morphological and biochemical optical imaging of oral epithelial cancer,” IEEE Trans. Biomed. Eng.57, 2596–2599 (2010).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens. (3)

A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens.26, 65–74 (1988).
[CrossRef]

J. B. Lee, A. S. Woodyatt, and M. Berman, “Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform,” IEEE Trans. Geosci. Remote Sens.28, 295–304 (1990).
[CrossRef]

M. Craig, “Minimum-volume transforms for remotely sensed data,” IEEE Trans. Geosci. Remote Sens.32, 542–552 (1994).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

J. Nascimento and J. Dias, “Does independent component analysis play a role in unmixing hyperspectral data?” IEEE Trans. Geosci. Remote Sens.43, 175–187 (2005).
[CrossRef]

C. I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens.42, 608–619 (2004).
[CrossRef]

J. Biomed. Opt. (1)

M. Skala, K. Riching, D. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. Eliceiri, P. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt.12, 024014 (2007).
[CrossRef] [PubMed]

J. Am. Coll. Cardiol. (1)

R. Virmani, A. Burke, A. Farb, and F. Kolodgie, “Pathology of the vulnerable plaque,” J. Am. Coll. Cardiol.47, C13–C18 (2006).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

L. Marcu, “Fluorescence lifetime in cardiovascular diagnostics,” J. Biomed. Opt.15, 011106 (2010).
[CrossRef] [PubMed]

J. Microsc. (1)

A. Clayton, Q. Hanley, and P. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc.213, 1–5 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (2)

M. Winter, “N-FINDR: An algorithm for fast autonomous spectral end-member determination in hyperspectral data,” Proc. SPIE3753, 266–275 (1999).
[CrossRef]

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression-based approaches,” Proc. SPIE7830, 78300A (2010).
[CrossRef]

Summaries of the 4th Annual JPL Airborne Geoscience Workshop (1)

J. Boardman, “Automating spectral unmixing of aviris data using convex geometry concepts,” in Summaries of the 4th Annual JPL Airborne Geoscience Workshop (1993), Vol. 1, pp. 11–14.

Other (9)

H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
[CrossRef]

R. Schachtner, G. Pöppel, A. Tomé, and E. Lang, “Minimum determinant constraint for non-negative matrix factorization,” in Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation (2009), pp. 106–113.
[CrossRef]

J. Li and J. Bioucas-Dias, “Minimum volume simplex analysis: a fast algorithm to unmix hyperspectral data,” in IEEE International Geoscience and Remote Sensing Symposium, 2008 (IEEE, 2008), Vol. III, pp. 250–253.

J. Bioucas-Dias, “A variable splitting augmented lagrangian approach to linear spectral unmixing,” in First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2009, (IEEE, 2009), pp. 1–4.
[CrossRef]

D. Hosmer and S. Lemeshow, Applied Logistic Regression, (Wiley-Interscience, 2000).
[CrossRef]

J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning (Springer, 2001).

E. Chong and S. Żak, An introduction to Optimization (Wiley-Interscience, 2004).

A. Cichocki, R. Zdunek, A. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation (Wiley, 2009).
[PubMed]

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).
[CrossRef]

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Figures (13)

Fig. 1:
Fig. 1:

All possible non-negative linear combinations of s1 and s2 lie in the blue shaded unbounded area contained within s1 and s2. xn represents one such data vector. Normalizing data vectors to unit L1-norm length amounts to rescaling them such that the tip of the rescaled data vectors lie on the portion of the unit L1 norm circle (shown in dotted lines) contained between the normalized end-member signatures 1 and 2, i.e. on the line S1S2, which represents a 1-D simplex.

Fig. 2:
Fig. 2:

In the general case, all possible non-negative linear combinations of s1 s2 and s3 lie in the blue shaded unbounded volume enclosed by s1 s2 and s3. On imposing the full-additivity constraint all possible non-negative linear combinations of s1 s2 and s3 are constrained to lie on the triangle S1S2S3, which represents a 2-D simplex.

Fig. 3:
Fig. 3:

Schematic illustrating the process of obtaining the normalized intensity maps and lifetime maps from a 3 channel multispectral FLIM data cube. The first step in this process is splitting the spectro-temporal cube into three temporal cubes: one cube per wavelength channel, shown in blue arrows. The normalized intensity and lifetime maps are then obtained from the temporal cubes by a normalization procedure (dashed lines, also see legend) and time deconvolution (solid lines) respectively. These maps constitute the standard FLIM features.

Fig. 4:
Fig. 4:

Schematic showing the process of performing NMF on a multispectral FLIM data cube. The 3-D spectro-temporal cube is unfolded and normalized to obtain a 2-D data matrix X. The data matrix is then factorized to yield the mixing matrix S and the relative abundance matrix A, columns of which are reshaped to obtain end-member relative abundance maps. These abundance maps constitute the NMF FLIM features.

Fig. 5:
Fig. 5:

True end-member profiles (dark shade) plotted over estimated profiles (light shade) for the simulation study discussed in the text. The profiles are plotted on a semilog (y) axis to highlight the differences between the two profiles that were indistinguishable on a linear scale

Fig. 6:
Fig. 6:

Scatter plot showing good agreement between the estimated and true relative abundances. Black dashed line represents the line of perfect fit (y = x).

Fig. 7:
Fig. 7:

(a) Normalized intensity and (b) lifetimes in the three channels for the true and estimated end-member profiles. Results indicate good agreement between the spectro-temporal characteristics of the two profiles

Fig. 8:
Fig. 8:

End-member signatures obtained from the artery multispectral FLIM data. Based on the spectro-temporal characteristics, the end-members were identified as collagen (red, solid line), lipids (green, dotted line) and elastin (black, dashed line)

Fig. 10:
Fig. 10:

(a) Steady state spectra for collagen, lipids (LDL) and elastin obtained from time-resolved measurements (b) log-transformed fluorescence decays for collagen, lipids and elastin fitted to straight lines, where the negative inverse slope is equal to a fluorophore’s average lifetime. Deviation from a straight line indicates the non-mono-exponential nature of the decay.

Fig. 9:
Fig. 9:

Standard FLIM features: normalized intensity and lifetime maps (A–C & D–F resp.) and NMF FLIM features: relative abundance maps (G–I) for three homogeneous samples, one from each (a) High Collagen, (b) High Lipids and (c) Low Collagen/Lipids class. Also shown are the representative histology sections for each class (J).

Fig. 11:
Fig. 11:

The multinomial logistic regression classifier for the NMF features partitions the feature space into three regions corresponding to the three classes: High Collagen (HC), High Lipids (HL) and Low Collagen/Lipids (LCL) seperated by linear decision boundaries (white region)

Fig. 12:
Fig. 12:

Confusion matrix for the standard FLIM features (left) and the NMF FLIM features (right). The diagonal entries indicate the number of pixels that were correctly classified, while the off-diagonal entries indicate the misclassified pixels.

Fig. 13:
Fig. 13:

Standard FLIM features: normalized intensity and lifetime maps (A–C & D–F resp.) and NMF FLIM features: relative abundance maps (G–I) for three heterogeneous samples with regions of: (a) HC and LCL (b) HC, HL and LCL, and (c) HL and LCL. Also shown are the histology sections from the center of the sample (K) with matching regions in the classification maps obtained from the NMF features (J) and the standard FLIM features (L) shown in orange arrows. Pixels in the classification maps are color coded as red for HC, green for HL and black for LCL

Equations (7)

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

x n = a 1 , n s 1 + a 2 , n s 2 + + a K , n s K x n = S a n ,
x ˜ n = x n x n 1 = k = 1 K a k , n s k x n 1 = k = 1 K ( a k , n s k 1 x n 1 ) ( s k s k 1 ) = k = 1 K a ˜ k , n s ˜ k ,
arg max 𝒬 log | det ( 𝒬 ) | subject to 𝒬 𝒳 0 , 1 K T 𝒬 𝒳 = 1 N T .
arg max 𝒬 log | det ( 𝒬 ) | + λ 𝒬 𝒳 h subject to 1 K T 𝒬 𝒳 = 1 N T ,
log Pr ( Class = c | Z = z ) Pr ( Class = C | Z = z ) = β c , 0 + β c T z , c = 1 , 2 , C 1 ,
( β ) = n = 1 N c = 1 C 1 y n , c log exp ( β c , 0 + β c T z n ) 1 + c exp ( β c , 0 + β c T z n ) ,
WMAPE = n = 1 N | x n x ˜ n x n | x n n = 1 N x n × 100 %

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