Abstract

We present a framework for hyperspectral image (HSI) analysis validation, specifically abundance fraction estimation based on HSI measurements of water soluble dye mixtures printed on microarray chips. In our work we focus on the performance of two algorithms, the Least Absolute Shrinkage and Selection Operator (LASSO) and the Spatial LASSO (SPLASSO). The LASSO is a well known statistical method for simultaneously performing model estimation and variable selection. In the context of estimating abundance fractions in a HSI scene, the “sparse” representations provided by the LASSO are appropriate as not every pixel will be expected to contain every endmember. The SPLASSO is a novel approach we introduce here for HSI analysis which takes the framework of the LASSO algorithm a step further and incorporates the rich spatial information which is available in HSI to further improve the estimates of abundance. In our work here we introduce the dye mixture platform as a new benchmark data set for hyperspectral biomedical image processing and show our algorithm’s improvement over the standard LASSO.

© 2012 OSA

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  1. B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (2005).
    [CrossRef]
  2. M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
    [CrossRef] [PubMed]
  3. K. Zuzak, R. Francis, E. Wehner, M. Litorja, J. Cadeddu, and E. Livingston, “Active dlp hyperspectral illumination: a noninvasive, in vivo, system characterization visualizing tissue oxygenation at near video rates,” Anal. Chem.83, 7424–7430 (2011).
    [CrossRef] [PubMed]
  4. B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.16, 16272–16283 (2006).
  5. M. Clarke, D. Allen, D. Samarov, and J. Hwang, “Characterization of hyperspectral imaging and analysis via microarray printing of dyes,” Proc. SPIE.7891, 78910W (2011).
    [CrossRef]
  6. M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).
  7. L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
    [CrossRef]
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  10. F. Green, The Sigma-Aldrich Handbook of Stains, Dyes and Indicators (Aldrich Chem Co Library, 1990).
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    [CrossRef]
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    [CrossRef]
  13. J. Bioucas-Dias and J. Nascimento, “Hyperspectral subspace identification,” IEEE Trans. Geosci. Remote Sens.46, 2435–2445 (2008).
    [CrossRef]
  14. 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]
  15. 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. WHISPERS ’09 (2009), pp. 1–4.
    [CrossRef]
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    [CrossRef]
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  19. J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression approaches,” Proc. SPIE783078300A (2010).
    [CrossRef]
  20. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat.32, 407–499 (2004).
    [CrossRef]
  21. J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, “Pathwise coordinate optimization,” Ann. Appl. Stat.1, 302–332 (2007).
    [CrossRef]
  22. A. Zymnis, S.-J. Kim, J. Skaf, M. Parente, and S. Boyd, “Hyperspectral image unmixing via alternating projected subgradients,” in Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, 2007. ACSSC 2007 (2007), pp. 1164–1168.
    [CrossRef]
  23. A. Zare, “Spatial-spectral unmixing using fuzzy local information,” in 2011 IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2011), pp. 1139–1142.
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2012 (1)

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

2011 (3)

M. Clarke, D. Allen, D. Samarov, and J. Hwang, “Characterization of hyperspectral imaging and analysis via microarray printing of dyes,” Proc. SPIE.7891, 78910W (2011).
[CrossRef]

K. Zuzak, R. Francis, E. Wehner, M. Litorja, J. Cadeddu, and E. Livingston, “Active dlp hyperspectral illumination: a noninvasive, in vivo, system characterization visualizing tissue oxygenation at near video rates,” Anal. Chem.83, 7424–7430 (2011).
[CrossRef] [PubMed]

M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens.49, 2014–2039 (2011).
[CrossRef]

2010 (1)

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression approaches,” Proc. SPIE783078300A (2010).
[CrossRef]

2009 (1)

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. WHISPERS ’09 (2009), pp. 1–4.
[CrossRef]

2008 (1)

J. Bioucas-Dias and J. Nascimento, “Hyperspectral subspace identification,” IEEE Trans. Geosci. Remote Sens.46, 2435–2445 (2008).
[CrossRef]

2007 (1)

J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, “Pathwise coordinate optimization,” Ann. Appl. Stat.1, 302–332 (2007).
[CrossRef]

2006 (3)

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.16, 16272–16283 (2006).

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
[CrossRef]

2005 (2)

B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (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]

2004 (2)

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat.32, 407–499 (2004).
[CrossRef]

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

2001 (1)

J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” J. Am. Stat. Assoc.96, 1348–1360 (2001).
[CrossRef]

1996 (1)

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. B58, 267–288 (1996).

1995 (1)

L. Breiman, “Better subset rergression using the nonnegative garotte,” em Technometrics37, 373–384 (1995).

Allen, D.

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

M. Clarke, D. Allen, D. Samarov, and J. Hwang, “Characterization of hyperspectral imaging and analysis via microarray printing of dyes,” Proc. SPIE.7891, 78910W (2011).
[CrossRef]

M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).

Bioucas-Dias, J.

M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens.49, 2014–2039 (2011).
[CrossRef]

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression approaches,” Proc. SPIE783078300A (2010).
[CrossRef]

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. WHISPERS ’09 (2009), pp. 1–4.
[CrossRef]

J. Bioucas-Dias and J. Nascimento, “Hyperspectral subspace identification,” IEEE Trans. Geosci. Remote Sens.46, 2435–2445 (2008).
[CrossRef]

Boyd, S.

A. Zymnis, S.-J. Kim, J. Skaf, M. Parente, and S. Boyd, “Hyperspectral image unmixing via alternating projected subgradients,” in Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, 2007. ACSSC 2007 (2007), pp. 1164–1168.
[CrossRef]

Breiman, L.

L. Breiman, “Better subset rergression using the nonnegative garotte,” em Technometrics37, 373–384 (1995).

Cadeddu, J.

K. Zuzak, R. Francis, E. Wehner, M. Litorja, J. Cadeddu, and E. Livingston, “Active dlp hyperspectral illumination: a noninvasive, in vivo, system characterization visualizing tissue oxygenation at near video rates,” Anal. Chem.83, 7424–7430 (2011).
[CrossRef] [PubMed]

Cao, Y.

B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (2005).
[CrossRef]

Chang, C.-I.

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

Chen, P.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Clarke, M.

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

M. Clarke, D. Allen, D. Samarov, and J. Hwang, “Characterization of hyperspectral imaging and analysis via microarray printing of dyes,” Proc. SPIE.7891, 78910W (2011).
[CrossRef]

M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).

D. Samarov, J. Hwang, J. Lee, and M. Clarke, “The spatial lasso with applications to unmixing hyperspectral images,” Tech. Rep., National Institute of Standards and Technology (2012).

Cunningham, G.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

DeNovo, R.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Dewhirst, M.

B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (2005).
[CrossRef]

Dias, J.

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]

Donovan, O.

B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (2005).
[CrossRef]

Du, Q.

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

Efron, B.

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat.32, 407–499 (2004).
[CrossRef]

Fan, J.

J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” J. Am. Stat. Assoc.96, 1348–1360 (2001).
[CrossRef]

Francis, R.

K. Zuzak, R. Francis, E. Wehner, M. Litorja, J. Cadeddu, and E. Livingston, “Active dlp hyperspectral illumination: a noninvasive, in vivo, system characterization visualizing tissue oxygenation at near video rates,” Anal. Chem.83, 7424–7430 (2011).
[CrossRef] [PubMed]

Friedman, J.

J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, “Pathwise coordinate optimization,” Ann. Appl. Stat.1, 302–332 (2007).
[CrossRef]

Green, F.

F. Green, The Sigma-Aldrich Handbook of Stains, Dyes and Indicators (Aldrich Chem Co Library, 1990).

Haaland, D.

L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
[CrossRef]

Hastie, T.

J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, “Pathwise coordinate optimization,” Ann. Appl. Stat.1, 302–332 (2007).
[CrossRef]

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat.32, 407–499 (2004).
[CrossRef]

Hofling, H.

J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, “Pathwise coordinate optimization,” Ann. Appl. Stat.1, 302–332 (2007).
[CrossRef]

Hwang, J.

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

M. Clarke, D. Allen, D. Samarov, and J. Hwang, “Characterization of hyperspectral imaging and analysis via microarray printing of dyes,” Proc. SPIE.7891, 78910W (2011).
[CrossRef]

D. Samarov, J. Hwang, J. Lee, and M. Clarke, “The spatial lasso with applications to unmixing hyperspectral images,” Tech. Rep., National Institute of Standards and Technology (2012).

M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).

Iordache, M.-D.

M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens.49, 2014–2039 (2011).
[CrossRef]

Johnstone, I.

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat.32, 407–499 (2004).
[CrossRef]

Jones, H.

L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
[CrossRef]

Kim, S.-J.

A. Zymnis, S.-J. Kim, J. Skaf, M. Parente, and S. Boyd, “Hyperspectral image unmixing via alternating projected subgradients,” in Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, 2007. ACSSC 2007 (2007), pp. 1164–1168.
[CrossRef]

Lee, J.

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).

D. Samarov, J. Hwang, J. Lee, and M. Clarke, “The spatial lasso with applications to unmixing hyperspectral images,” Tech. Rep., National Institute of Standards and Technology (2012).

Li, R.

J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” J. Am. Stat. Assoc.96, 1348–1360 (2001).
[CrossRef]

Litorja, M.

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

K. Zuzak, R. Francis, E. Wehner, M. Litorja, J. Cadeddu, and E. Livingston, “Active dlp hyperspectral illumination: a noninvasive, in vivo, system characterization visualizing tissue oxygenation at near video rates,” Anal. Chem.83, 7424–7430 (2011).
[CrossRef] [PubMed]

M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).

Livingston, E.

K. Zuzak, R. Francis, E. Wehner, M. Litorja, J. Cadeddu, and E. Livingston, “Active dlp hyperspectral illumination: a noninvasive, in vivo, system characterization visualizing tissue oxygenation at near video rates,” Anal. Chem.83, 7424–7430 (2011).
[CrossRef] [PubMed]

Martin, M.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Moeller, B.

B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (2005).
[CrossRef]

Nascimento, J.

J. Bioucas-Dias and J. Nascimento, “Hyperspectral subspace identification,” IEEE Trans. Geosci. Remote Sens.46, 2435–2445 (2008).
[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]

Nieman, L.

L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
[CrossRef]

Overholt, B.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Panjehpour, M.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Parente, M.

A. Zymnis, S.-J. Kim, J. Skaf, M. Parente, and S. Boyd, “Hyperspectral image unmixing via alternating projected subgradients,” in Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, 2007. ACSSC 2007 (2007), pp. 1164–1168.
[CrossRef]

Patterson, M.

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.16, 16272–16283 (2006).

Phan, M.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Plaza, A.

M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE Trans. Geosci. Remote Sens.49, 2014–2039 (2011).
[CrossRef]

J. Bioucas-Dias and A. Plaza, “Hyperspectral unmixing: geometrical, statistical, and sparse regression approaches,” Proc. SPIE783078300A (2010).
[CrossRef]

Pogue, B.

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt.16, 16272–16283 (2006).

Samarov, D.

D. Samarov, M. Clarke, J. Lee, D. Allen, M. Litorja, and J. Hwang, “Validating the lasso algorithm by unmixing spectral signatures in multicolor phantoms,” Proc. SPIE8229, 82290Z (2012).
[CrossRef]

M. Clarke, D. Allen, D. Samarov, and J. Hwang, “Characterization of hyperspectral imaging and analysis via microarray printing of dyes,” Proc. SPIE.7891, 78910W (2011).
[CrossRef]

M. Clarke, J. Lee, D. Samarov, D. Allen, M. Litorja, and J. Hwang, “Designing microarray phantoms for hyper-spectral imaging validation,” Biomed. Opt. Express (to be published).

D. Samarov, J. Hwang, J. Lee, and M. Clarke, “The spatial lasso with applications to unmixing hyperspectral images,” Tech. Rep., National Institute of Standards and Technology (2012).

Sinclair, M.

L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
[CrossRef]

Skaf, J.

A. Zymnis, S.-J. Kim, J. Skaf, M. Parente, and S. Boyd, “Hyperspectral image unmixing via alternating projected subgradients,” in Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, 2007. ACSSC 2007 (2007), pp. 1164–1168.
[CrossRef]

Sorg, B.

B. Sorg, B. Moeller, O. Donovan, Y. Cao, and M. Dewhirst, “Hyperspectral imaging of hemoglobin saturation in tumor microvasculature and tumor hypoxia development,” J. Biomed. Opt.10, 044004 (2005).
[CrossRef]

Tibshirani, R.

J. Friedman, T. Hastie, H. Hofling, and R. Tibshirani, “Pathwise coordinate optimization,” Ann. Appl. Stat.1, 302–332 (2007).
[CrossRef]

B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Ann. Stat.32, 407–499 (2004).
[CrossRef]

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. B58, 267–288 (1996).

Timlin, J.

L. Nieman, M. Sinclair, J. Timlin, H. Jones, and D. Haaland, “Hyperspectral imaging system for quantitative identification and discrimination of fluorescent labels in the presence of autofluorescence,” in 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, 2006 (2006), pp. 1288–1291.
[CrossRef]

Vo-Dinh, T.

M. Martin, M. Wabuyele, P. Chen, M. Panjehpour, M. Phan, B. Overholt, G. Cunningham, D. Wilson, R. DeNovo, and T. Vo-Dinh, “Development of an advanced hyperspectral imaging (hsi) system with applications for cancer detection,” Ann. Biomed. Eng.34, 1061–1068 (2006).
[CrossRef] [PubMed]

Wabuyele, M.

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Figures (5)

Fig. 1
Fig. 1

The design of the microarray printing platform for two dyes. The image on the left depicts the actual array and the image on the right shows the location, concentrations and proportion of each of the dyes.

Fig. 2
Fig. 2

The spectral signatures of the two dyes used in this experiment, as well as the PEG and background signatures.

Fig. 3
Fig. 3

The abundance estimates of AR and NC for the second replicate data set. The color scale on the right indicates the estimated abundance fractions.

Fig. 4
Fig. 4

Indices of the pure and mixed dye locations.

Fig. 5
Fig. 5

Results from CAF estimation using the SPLASSO and LASSO at each dye location. In every subplot the corresponding barplots show the absolute errors (x-axis) of the CAF estimate from ground truth and their corresponding standard errors (vertical line) for the AR and NC dyes.

Equations (10)

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

AR i AR 100 and NC i NC 100 .
y i = X β i , subject to β i l 0 and l = 1 m β i l 1 .
β ^ i ( LASSO ) = arg min β i y i j = 1 m x j β i j 2 + λ | β i | 1 ,
β ^ i l ( LASSO ) = sgn ( β ^ i l ( OLS ) ) ( | β ^ i l ( OLS ) | λ / 2 ) + , l = 1 , , m
β ^ j ( SPLASSO ) = arg min β j i = 1 n y i X β i 2 + λ 1 | β i | 1 + λ 2 j N ( y i ) β i β j 2 w i j .
b r s ( l m ) = { 1 ( r l ) 2 + ( s m ) 2 , l [ r k , r + k ] , m [ s k , s + k ] if ( l , m ) ( r , s ) , 0 otherwise .
c r s ( l m ) = y r s T y l m y r s y l m , l [ r k , r + k ] , m [ s k , s + k ] ,
w r s ( l m ) = b r s ( l m ) c r s ( l m ) .
b ^ i , l = γ β ^ i , l ( OLS ) + ( 1 γ ) α i , l
β ^ i , l ( SPLASSO ) = sgn ( b ^ i , l ) ( | b ^ i , l | λ 1 2 γ ) + .

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