Abstract

Raman spectral imaging has been widely used as a very important analytical tool in various fields. For obtaining the high spectral signal-to-noise ratio Raman images, the long integration time is necessary, which is placing a limit on the application of Raman spectral imaging. We introduce a simple and feasible numerical method of the Three-dimensional Low Rank Estimation (3D-LRE), which can speed up the data acquisition process of the Raman spectral imaging. The spectral signal-to-noise ratio of the Raman images can be increased by over 75 times and the speed of the data acquisition can be improved by over 30 times. By combining with line-scan or multifocus-scan techniques, the Raman images can be obtained in a few seconds.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  7. Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
    [Crossref] [PubMed]
  8. S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
    [Crossref] [PubMed]
  9. J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
    [Crossref] [PubMed]
  10. W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
    [Crossref] [PubMed]
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  12. N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
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  16. C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
    [Crossref] [PubMed]
  17. H. N. Noothalapati Venkata and S. Shigeto, “Stable isotope-labeled Raman imaging reveals dynamic proteome localization to lipid droplets in single fission yeast cells,” Chem. Biol. 19(11), 1373–1380 (2012).
    [Crossref] [PubMed]
  18. H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (4)

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
[Crossref] [PubMed]

S. Yabumoto and H. O. Hamaguchi, “Tilted Two-Dimensional Array Multifocus Confocal Raman Microspectroscopy,” Anal. Chem. 89(14), 7291–7296 (2017).
[Crossref] [PubMed]

X. Ma, H. Wang, Y. Wang, D. Chen, W. Chen, and Q. Li, “Improving the resolution and the throughput of spectrometers by a digital projection slit,” Opt. Express 25(19), 23045–23050 (2017).
[Crossref] [PubMed]

2014 (1)

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

2013 (2)

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

T. Lee, H. Mundoor, D. G. Gann, T. J. Callahan, and I. I. Smalyukh, “Imaging of director fields in liquid crystals using stimulated Raman scattering microscopy,” Opt. Express 21(10), 12129–12134 (2013).
[Crossref] [PubMed]

2012 (2)

C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
[Crossref] [PubMed]

H. N. Noothalapati Venkata and S. Shigeto, “Stable isotope-labeled Raman imaging reveals dynamic proteome localization to lipid droplets in single fission yeast cells,” Chem. Biol. 19(11), 1373–1380 (2012).
[Crossref] [PubMed]

2011 (3)

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE T. Geosci. Rem. 49(6), 2014–2039 (2011).
[Crossref]

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Rev. 53(2), 217–288 (2011).
[Crossref]

D. Chen, Z. Chen, and E. Grant, “Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry,” Anal. Bioanal. Chem. 400(2), 625–634 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (2)

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

P. Lasch, A. Hermelink, and D. Naumann, “Correction of axial chromatic aberrations in confocal Raman microspectroscopic measurements of a single microbial spore,” Analyst (Lond.) 134(6), 1162–1170 (2009).
[Crossref] [PubMed]

2008 (2)

2003 (1)

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

2001 (1)

1998 (1)

R. Appel, W. Xu, T. W. Zerda, and Z. Hu, “Direct Observation of Polymer Network Structure in Macroporous N-Isopropylacrylamide Gel by Raman Microscopy,” Macromolecules 31(15), 5071–5074 (1998).
[Crossref] [PubMed]

1997 (1)

G. M. Shim and B. C. Wilson, “Development of an in vivo Raman spectroscopic system for diagnostic applications,” J. Raman Spectrosc. 28(2–3), 131–142 (1997).
[Crossref]

1996 (1)

D. Wolf Ingrid, “Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits,” Semicond. Sci. Technol. 11(2), 139–154 (1996).
[Crossref]

1980 (1)

P. M. Kroonenberg and J. de Leeuw, “Principal component analysis of three-mode data by means of alternating least squares algorithms,” Psychometrika 45(1), 69–97 (1980).
[Crossref]

Ando, M.

C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
[Crossref] [PubMed]

Appel, R.

R. Appel, W. Xu, T. W. Zerda, and Z. Hu, “Direct Observation of Polymer Network Structure in Macroporous N-Isopropylacrylamide Gel by Raman Microscopy,” Macromolecules 31(15), 5071–5074 (1998).
[Crossref] [PubMed]

Ben-Amotz, D.

Benzerara, K.

Bernard, S.

Beyssac, O.

Bioucas-Dias, J. M.

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE T. Geosci. Rem. 49(6), 2014–2039 (2011).
[Crossref]

Cai, T. T.

Callahan, T. J.

Chen, D.

X. Ma, H. Wang, Y. Wang, D. Chen, W. Chen, and Q. Li, “Improving the resolution and the throughput of spectrometers by a digital projection slit,” Opt. Express 25(19), 23045–23050 (2017).
[Crossref] [PubMed]

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

D. Chen, Z. Chen, and E. Grant, “Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry,” Anal. Bioanal. Chem. 400(2), 625–634 (2011).
[Crossref] [PubMed]

Chen, R.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Chen, W.

Chen, Z.

D. Chen, Z. Chen, and E. Grant, “Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry,” Anal. Bioanal. Chem. 400(2), 625–634 (2011).
[Crossref] [PubMed]

Cheng, M.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

de Leeuw, J.

P. M. Kroonenberg and J. de Leeuw, “Principal component analysis of three-mode data by means of alternating least squares algorithms,” Psychometrika 45(1), 69–97 (1980).
[Crossref]

Du, J.

W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
[Crossref] [PubMed]

Duraipandian, S.

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

Feng, S.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Gann, D. G.

Golbabaee, M.

M. Golbabaee and P. Vandergheynst, “Hyperspectral Image Compressed Sensing Via Low-Rank and Joint-Sparse Matrix Recovery,” Int. Conf. Acoust. Spee, 2741–2744 (2012).
[Crossref]

Grant, E.

D. Chen, Z. Chen, and E. Grant, “Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry,” Anal. Bioanal. Chem. 400(2), 625–634 (2011).
[Crossref] [PubMed]

Greve, J.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Halko, N.

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Rev. 53(2), 217–288 (2011).
[Crossref]

Hamaguchi, H. O.

S. Yabumoto and H. O. Hamaguchi, “Tilted Two-Dimensional Array Multifocus Confocal Raman Microspectroscopy,” Anal. Chem. 89(14), 7291–7296 (2017).
[Crossref] [PubMed]

C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
[Crossref] [PubMed]

M. Okuno and H. O. Hamaguchi, “Multifocus confocal Raman microspectroscopy for fast multimode vibrational imaging of living cells,” Opt. Lett. 35(24), 4096–4098 (2010).
[Crossref] [PubMed]

He, W.

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

Hermelink, A.

P. Lasch, A. Hermelink, and D. Naumann, “Correction of axial chromatic aberrations in confocal Raman microspectroscopic measurements of a single microbial spore,” Analyst (Lond.) 134(6), 1162–1170 (2009).
[Crossref] [PubMed]

Hu, Z.

R. Appel, W. Xu, T. W. Zerda, and Z. Hu, “Direct Observation of Polymer Network Structure in Macroporous N-Isopropylacrylamide Gel by Raman Microscopy,” Macromolecules 31(15), 5071–5074 (1998).
[Crossref] [PubMed]

Huang, C. K.

C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
[Crossref] [PubMed]

Huang, Z.

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Huang, Z. X.

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

Ilancheran, A.

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

Iordache, M.

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE T. Geosci. Rem. 49(6), 2014–2039 (2011).
[Crossref]

Jaggi, M.

M. Jaggi, “Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization,” in Proceedings of the 30th International Conference on International Conference on Machine Learning-Volume 28 (2013), pp. 427–435.

Jing, C.

W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
[Crossref] [PubMed]

Kraan, Y.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Kroonenberg, P. M.

P. M. Kroonenberg and J. de Leeuw, “Principal component analysis of three-mode data by means of alternating least squares algorithms,” Psychometrika 45(1), 69–97 (1980).
[Crossref]

Lasch, P.

P. Lasch, A. Hermelink, and D. Naumann, “Correction of axial chromatic aberrations in confocal Raman microspectroscopic measurements of a single microbial spore,” Analyst (Lond.) 134(6), 1162–1170 (2009).
[Crossref] [PubMed]

Lee, T.

Lenferink, A.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Li, Q.

Li, Q. F.

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

Li, Y.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Lin, J.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Liu, W.

W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
[Crossref] [PubMed]

Lou, T. T.

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

Low, J. J.

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

Ma, X.

Macleod, N. A.

Martinsson, P. G.

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Rev. 53(2), 217–288 (2011).
[Crossref]

Matousek, P.

Mundoor, H.

Naumann, D.

P. Lasch, A. Hermelink, and D. Naumann, “Correction of axial chromatic aberrations in confocal Raman microspectroscopic measurements of a single microbial spore,” Analyst (Lond.) 134(6), 1162–1170 (2009).
[Crossref] [PubMed]

Ng, J.

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

Noothalapati Venkata, H. N.

H. N. Noothalapati Venkata and S. Shigeto, “Stable isotope-labeled Raman imaging reveals dynamic proteome localization to lipid droplets in single fission yeast cells,” Chem. Biol. 19(11), 1373–1380 (2012).
[Crossref] [PubMed]

Okuno, M.

Otto, C.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Plaza, A.

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE T. Geosci. Rem. 49(6), 2014–2039 (2011).
[Crossref]

Shen, H. F.

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

Shigeto, S.

C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
[Crossref] [PubMed]

H. N. Noothalapati Venkata and S. Shigeto, “Stable isotope-labeled Raman imaging reveals dynamic proteome localization to lipid droplets in single fission yeast cells,” Chem. Biol. 19(11), 1373–1380 (2012).
[Crossref] [PubMed]

Shim, G. M.

G. M. Shim and B. C. Wilson, “Development of an in vivo Raman spectroscopic system for diagnostic applications,” J. Raman Spectrosc. 28(2–3), 131–142 (1997).
[Crossref]

Smalyukh, I. I.

Tan, Z.

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

Tropp, J. A.

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Rev. 53(2), 217–288 (2011).
[Crossref]

Uzunbajakava, N.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Vandergheynst, P.

M. Golbabaee and P. Vandergheynst, “Hyperspectral Image Compressed Sensing Via Low-Rank and Joint-Sparse Matrix Recovery,” Int. Conf. Acoust. Spee, 2741–2744 (2012).
[Crossref]

Volokhina, E.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Vrensen, G.

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Wang, H.

X. Ma, H. Wang, Y. Wang, D. Chen, W. Chen, and Q. Li, “Improving the resolution and the throughput of spectrometers by a digital projection slit,” Opt. Express 25(19), 23045–23050 (2017).
[Crossref] [PubMed]

W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
[Crossref] [PubMed]

Wang, Y.

Wilson, B. C.

G. M. Shim and B. C. Wilson, “Development of an in vivo Raman spectroscopic system for diagnostic applications,” J. Raman Spectrosc. 28(2–3), 131–142 (1997).
[Crossref]

Wolf Ingrid, D.

D. Wolf Ingrid, “Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits,” Semicond. Sci. Technol. 11(2), 139–154 (1996).
[Crossref]

Xie, S.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Xu, K. X.

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

Xu, W.

R. Appel, W. Xu, T. W. Zerda, and Z. Hu, “Direct Observation of Polymer Network Structure in Macroporous N-Isopropylacrylamide Gel by Raman Microscopy,” Macromolecules 31(15), 5071–5074 (1998).
[Crossref] [PubMed]

Yabumoto, S.

S. Yabumoto and H. O. Hamaguchi, “Tilted Two-Dimensional Array Multifocus Confocal Raman Microspectroscopy,” Anal. Chem. 89(14), 7291–7296 (2017).
[Crossref] [PubMed]

Yu, Y.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Yuan, Q. Q.

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

Zeng, H.

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

Zerda, T. W.

R. Appel, W. Xu, T. W. Zerda, and Z. Hu, “Direct Observation of Polymer Network Structure in Macroporous N-Isopropylacrylamide Gel by Raman Microscopy,” Macromolecules 31(15), 5071–5074 (1998).
[Crossref] [PubMed]

Zhang, D. M.

Zhang, H. Y.

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

Zhang, L. P.

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

Zheng, W.

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

Zong, J.

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

Anal. Bioanal. Chem. (1)

D. Chen, Z. Chen, and E. Grant, “Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry,” Anal. Bioanal. Chem. 400(2), 625–634 (2011).
[Crossref] [PubMed]

Anal. Chem. (2)

S. Yabumoto and H. O. Hamaguchi, “Tilted Two-Dimensional Array Multifocus Confocal Raman Microspectroscopy,” Anal. Chem. 89(14), 7291–7296 (2017).
[Crossref] [PubMed]

C. K. Huang, M. Ando, H. O. Hamaguchi, and S. Shigeto, “Disentangling dynamic changes of multiple cellular components during the yeast cell cycle by in vivo multivariate Raman imaging,” Anal. Chem. 84(13), 5661–5668 (2012).
[Crossref] [PubMed]

Analyst (Lond.) (2)

S. Duraipandian, W. Zheng, J. Ng, J. J. Low, A. Ilancheran, and Z. Huang, “Non-invasive analysis of hormonal variations and effect of postmenopausal Vagifem treatment on women using in vivo high wavenumber confocal Raman spectroscopy,” Analyst (Lond.) 138(14), 4120–4128 (2013).
[Crossref] [PubMed]

P. Lasch, A. Hermelink, and D. Naumann, “Correction of axial chromatic aberrations in confocal Raman microspectroscopic measurements of a single microbial spore,” Analyst (Lond.) 134(6), 1162–1170 (2009).
[Crossref] [PubMed]

Appl. Spectrosc. (3)

Biophys. J. (1)

N. Uzunbajakava, A. Lenferink, Y. Kraan, E. Volokhina, G. Vrensen, J. Greve, and C. Otto, “Nonresonant confocal Raman imaging of DNA and protein distribution in apoptotic cells,” Biophys. J. 84(6), 3968–3981 (2003).
[Crossref] [PubMed]

Biosens. Bioelectron. (2)

J. Lin, R. Chen, S. Feng, Y. Li, Z. Huang, S. Xie, Y. Yu, M. Cheng, and H. Zeng, “Rapid delivery of silver nanoparticles into living cells by electroporation for surface-enhanced Raman spectroscopy,” Biosens. Bioelectron. 25(2), 388–394 (2009).
[Crossref] [PubMed]

W. Liu, H. Wang, J. Du, and C. Jing, “Raman microspectroscopy of nucleus and cytoplasm for human colon cancer diagnosis,” Biosens. Bioelectron. 97, 70–74 (2017).
[Crossref] [PubMed]

Chem. Biol. (1)

H. N. Noothalapati Venkata and S. Shigeto, “Stable isotope-labeled Raman imaging reveals dynamic proteome localization to lipid droplets in single fission yeast cells,” Chem. Biol. 19(11), 1373–1380 (2012).
[Crossref] [PubMed]

IEEE T. Geosci. Rem. (1)

M. Iordache, J. M. Bioucas-Dias, and A. Plaza, “Sparse unmixing of hyperspectral data,” IEEE T. Geosci. Rem. 49(6), 2014–2039 (2011).
[Crossref]

IEEE T. Geosci. Remote (1)

H. Y. Zhang, W. He, L. P. Zhang, H. F. Shen, and Q. Q. Yuan, “Hyperspectral Image Restoration Using Low-Rank Matrix Recovery,” IEEE T. Geosci. Remote 52(8), 4729–4743 (2014).
[Crossref]

J. Agric. Food Chem. (1)

Z. Tan, T. T. Lou, Z. X. Huang, J. Zong, K. X. Xu, Q. F. Li, and D. Chen, “Single-Drop Raman Imaging Exposes the Trace Contaminants in Milk,” J. Agric. Food Chem. 65(30), 6274–6281 (2017).
[Crossref] [PubMed]

J. Raman Spectrosc. (1)

G. M. Shim and B. C. Wilson, “Development of an in vivo Raman spectroscopic system for diagnostic applications,” J. Raman Spectrosc. 28(2–3), 131–142 (1997).
[Crossref]

Macromolecules (1)

R. Appel, W. Xu, T. W. Zerda, and Z. Hu, “Direct Observation of Polymer Network Structure in Macroporous N-Isopropylacrylamide Gel by Raman Microscopy,” Macromolecules 31(15), 5071–5074 (1998).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Psychometrika (1)

P. M. Kroonenberg and J. de Leeuw, “Principal component analysis of three-mode data by means of alternating least squares algorithms,” Psychometrika 45(1), 69–97 (1980).
[Crossref]

Semicond. Sci. Technol. (1)

D. Wolf Ingrid, “Micro-Raman spectroscopy to study local mechanical stress in silicon integrated circuits,” Semicond. Sci. Technol. 11(2), 139–154 (1996).
[Crossref]

SIAM Rev. (1)

N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions,” SIAM Rev. 53(2), 217–288 (2011).
[Crossref]

Other (3)

M. Golbabaee and P. Vandergheynst, “Hyperspectral Image Compressed Sensing Via Low-Rank and Joint-Sparse Matrix Recovery,” Int. Conf. Acoust. Spee, 2741–2744 (2012).
[Crossref]

G. Xiawei, Q. Yao, and J. T. Kwok, “Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm,” AAAI. (2017).

M. Jaggi, “Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization,” in Proceedings of the 30th International Conference on International Conference on Machine Learning-Volume 28 (2013), pp. 427–435.

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Figures (3)

Fig. 1
Fig. 1 (a) A Raman images cube of the mixture, which is composed of norfloxacin and penicillin potassium. For a point in the cube, the sectional views of the three-dimensional structure are shown in (b), (c) and (d). (b1), (c1) and (d1) are the sectional views of the Raman images in an integration time of 3 s. (b2), (c2) and (d2) are from the recovering Raman images in an integration time of 0.1 s. (b3), (c3) and (d3) are from the Raman images by the 3D-LRE method in an integration time of 0.1 s. (b4), (c4) and (d4) show the ranks of the sectional views in (b1-b3), (c1-c3) and (d1-d3), respectively.

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Fig. 2
Fig. 2 The spectra of norfloxacin and penicillin potassium are shown in (a) and (b), respective. The sectional views of the control Raman images from the spectra of (a1) 570 cm−1 and (b1) 750 cm−1. The sectional views of the test Raman images from the spectra of (a2) 570 cm−1 and (b2) 750 cm−1. The sectional views of the 3D-LRE Raman images from the spectra of (a3) 570 cm−1 and (b3) 750 cm−1.

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Fig. 3
Fig. 3 Spectra of (a) the control Raman images, (b1) the test Raman images, (b2) the 3D-LRE Raman images, (b3) the FFT Raman images, (b4) the WT images and (b5) the Smoothing images.

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Equations (6)

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

B 0 =ALS(A)
s t+1 =ALS(A− B t )
r t+1 =arg min r∈[0,1] (A−( B t +r( s t+1 − B t )))
B t+1 =(1− r t+1 ) B t + r t+1 s t+1
ALS( B t+1 ) s t+1 >m
k= ∑ ( f 0 ) 2 ∑ (f− f 0 ) 2

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