Abstract

Single-molecule localization microscopy (SMLM), such as stochastic optical reconstruction microscopy and (fluorescence) photoactivated localization microscopy, has enabled superresolution microscopy beyond the diffraction limit. However, the temporal resolution of SMLM is limited by the time needed to acquire sufficient sparse single-molecule activation events to successfully construct a superresolution image. Here, a novel fast SMLM technique is developed to achieve superresolution imaging within a much shortened duration. This technique does not require a faster switching rate or a higher activation density, which may cause signal degradation or photodamage/bleaching, but relies on computational algorithms to reconstruct a high-density superresolution image from a low-density one using the concept of blind image inpainting. Our results demonstrate that the technique reduces the acquisition time by up to two orders of magnitude compared to the conventional method while achieving the same high resolution. We anticipate our technique to enable future real-time live cell imaging with even higher resolution.

© 2017 Optical Society of America

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References

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  2. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
    [Crossref]
  3. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
    [Crossref]
  4. B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: superresolution imaging of cells,” Cell 143, 1047–1058 (2010).
    [Crossref]
  5. C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
    [Crossref]
  6. H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
    [Crossref]
  7. S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
    [Crossref]
  8. F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
    [Crossref]
  9. S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high-density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
    [Crossref]
  10. T. Quan, H. Zhu, X. Liu, Y. Liu, J. Ding, S. Zeng, and Z.-L. Huang, “High-density localization of active molecules using structured sparse model and Bayesian information criterion,” Opt. Express 19, 16963–16974 (2011).
    [Crossref]
  11. L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
    [Crossref]
  12. E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
    [Crossref]
  13. F. Huang, S. L. Schwartz, J. M. Byars, and K. A. Lidke, “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” Biomed. Opt. Express 2, 1377–1393 (2011).
    [Crossref]
  14. H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1, 6 (2012).
    [Crossref]
  15. S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
    [Crossref]
  16. H. P. Babcock, J. R. Moffitt, Y. Cao, and X. Zhuang, “Fast compressed sensing analysis for super-resolution imaging using L1-homotopy,” Opt. Express 21, 28583–28596 (2013).
    [Crossref]
  17. M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
    [Crossref]
  18. M. J. Fadili, J. L. Starck, and F. Murtagh, “Inpainting and zooming using sparse representations,” Comput. J. 52, 64–79 (2009).
    [Crossref]
  19. E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
    [Crossref]
  20. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
    [Crossref]
  21. The implementation of the proposed algorithm and the data to generate Fig. 1, https://doi.org/10.6084/m9.figshare.5229943.
  22. E. J. Candès, J. K. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [Crossref]
  23. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [Crossref]
  24. E. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inform. Theory 52, 5406–5425 (2006).
    [Crossref]
  25. E. J. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
    [Crossref]
  26. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [Crossref]
  27. R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
    [Crossref]

2013 (3)

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

H. P. Babcock, J. R. Moffitt, Y. Cao, and X. Zhuang, “Fast compressed sensing analysis for super-resolution imaging using L1-homotopy,” Opt. Express 21, 28583–28596 (2013).
[Crossref]

2012 (4)

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
[Crossref]

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref]

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1, 6 (2012).
[Crossref]

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

2011 (5)

F. Huang, S. L. Schwartz, J. M. Byars, and K. A. Lidke, “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” Biomed. Opt. Express 2, 1377–1393 (2011).
[Crossref]

T. Quan, H. Zhu, X. Liu, Y. Liu, J. Ding, S. Zeng, and Z.-L. Huang, “High-density localization of active molecules using structured sparse model and Bayesian information criterion,” Opt. Express 19, 16963–16974 (2011).
[Crossref]

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high-density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref]

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
[Crossref]

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

2010 (1)

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: superresolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

2009 (1)

M. J. Fadili, J. L. Starck, and F. Murtagh, “Inpainting and zooming using sparse representations,” Comput. J. 52, 64–79 (2009).
[Crossref]

2008 (2)

E. J. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

2006 (7)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[Crossref]

E. J. Candès, J. K. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inform. Theory 52, 5406–5425 (2006).
[Crossref]

2005 (1)

M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
[Crossref]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[Crossref]

Babcock, H.

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref]

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1, 6 (2012).
[Crossref]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: superresolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

Babcock, H. P.

Baird, M. A.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Bates, M.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref]

Betzig, E.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Bewersdorf, J.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

Boyd, S.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Burnette, D. T.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Byars, J. M.

Candès, E.

E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[Crossref]

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inform. Theory 52, 5406–5425 (2006).
[Crossref]

Candès, E. J.

E. J. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

E. J. Candès, J. K. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Cao, Y.

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Cox, S.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Davidson, M. W.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Demanet, L.

E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[Crossref]

Ding, J.

Donoho, D. L.

E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
[Crossref]

Duim, W. C.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Elad, M.

M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
[Crossref]

Elnatan, D.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
[Crossref]

Fadili, M. J.

M. J. Fadili, J. L. Starck, and F. Murtagh, “Inpainting and zooming using sparse representations,” Comput. J. 52, 64–79 (2009).
[Crossref]

Galbraith, C. G.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

Galbraith, J. A.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

Grünwald, D.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

Hartwich, T. M. P.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

He, J.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Heintzmann, R.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

Holden, S. J.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high-density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref]

Huang, B.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
[Crossref]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: superresolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

Huang, F.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

F. Huang, S. L. Schwartz, J. M. Byars, and K. A. Lidke, “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” Biomed. Opt. Express 2, 1377–1393 (2011).
[Crossref]

Huang, Z.-L.

Jones, G. E.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Jones, S. A.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Jovanovic-Talisman, T.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Kapanidis, A. N.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high-density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref]

Lidke, K. A.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

F. Huang, S. L. Schwartz, J. M. Byars, and K. A. Lidke, “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” Biomed. Opt. Express 2, 1377–1393 (2011).
[Crossref]

Lin, Y.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Lippincott-Schwartz, J.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Liu, X.

Liu, Y.

Long, J. J.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

Moffitt, J. R.

Monypenny, J.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Mothes, W.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Mukamel, E. A.

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref]

Murtagh, F.

M. J. Fadili, J. L. Starck, and F. Murtagh, “Inpainting and zooming using sparse representations,” Comput. J. 52, 64–79 (2009).
[Crossref]

Myers, J. R.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Nieuwenhuizen, R. P. J.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Parikh, N.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Peleato, B.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

Puig, D. L.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

Quan, T.

Querre, P.

M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
[Crossref]

Rieger, B.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

Rivera-Molina, F. E.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Rosten, E.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref]

Schwartz, S. L.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[Crossref]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

Shim, S. H.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
[Crossref]

Shroff, H.

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

Sigal, Y. M.

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1, 6 (2012).
[Crossref]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Stallinga, S.

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

Starck, J. L.

M. J. Fadili, J. L. Starck, and F. Murtagh, “Inpainting and zooming using sparse representations,” Comput. J. 52, 64–79 (2009).
[Crossref]

M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
[Crossref]

Tao, T.

E. J. Candès, J. K. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inform. Theory 52, 5406–5425 (2006).
[Crossref]

Toomre, D.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Uchil, P. D.

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

Uphoff, S.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high-density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref]

Wakin, M.

E. J. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

Ying, L.

E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[Crossref]

Zeng, S.

Zhang, W.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
[Crossref]

Zhu, H.

Zhu, L.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
[Crossref]

Zhuang, X.

H. P. Babcock, J. R. Moffitt, Y. Cao, and X. Zhuang, “Fast compressed sensing analysis for super-resolution imaging using L1-homotopy,” Opt. Express 21, 28583–28596 (2013).
[Crossref]

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1, 6 (2012).
[Crossref]

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref]

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
[Crossref]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: superresolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref]

Appl. Comput. Harmonic Anal. (1)

M. Elad, J. L. Starck, P. Querre, and D. L. Donoho, “Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA),” Appl. Comput. Harmonic Anal. 19, 340–358 (2005).
[Crossref]

Biomed. Opt. Express (1)

Biophys. J. (2)

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

Cell (1)

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: superresolution imaging of cells,” Cell 143, 1047–1058 (2010).
[Crossref]

Comput. J. (1)

M. J. Fadili, J. L. Starck, and F. Murtagh, “Inpainting and zooming using sparse representations,” Comput. J. 52, 64–79 (2009).
[Crossref]

Found. Trends Mach. Learn. (1)

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3, 1–122 (2011).
[Crossref]

IEEE Signal Process. Mag. (1)

E. J. Candès and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[Crossref]

IEEE Trans. Inf. Theory (2)

E. J. Candès, J. K. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
[Crossref]

IEEE Trans. Inform. Theory (1)

E. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inform. Theory 52, 5406–5425 (2006).
[Crossref]

Multiscale Model. Simul. (1)

E. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transforms,” Multiscale Model. Simul. 5, 861–899 (2006).
[Crossref]

Nat. Methods (8)

R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods 10, 557–562 (2013).
[Crossref]

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9, 721–723 (2012).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref]

H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[Crossref]

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cell,” Nat. Methods 8, 499–505 (2011).
[Crossref]

F. Huang, T. M. P. Hartwich, F. E. Rivera-Molina, Y. Lin, W. C. Duim, J. J. Long, P. D. Uchil, J. R. Myers, M. A. Baird, W. Mothes, M. W. Davidson, D. Toomre, and J. Bewersdorf, “Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms,” Nat. Methods 10, 653–658 (2013).
[Crossref]

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high-density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref]

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9, 195–200 (2012).
[Crossref]

Opt. Express (2)

Opt. Nanoscopy (1)

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1, 6 (2012).
[Crossref]

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[Crossref]

Science (1)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Other (1)

The implementation of the proposed algorithm and the data to generate Fig. 1, https://doi.org/10.6084/m9.figshare.5229943.

Supplementary Material (2)

NameDescription
» Code 1       This code includes the implementation of the proposed algorithm and the data to generate Fig. 1
» Supplement 1       Description of algorithm and supplementary figures

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Figures (9)

Fig. 1.
Fig. 1.

Schematic comparison of the proposed blind sparse inpainting method with the conventional SMLM method.

Fig. 2.
Fig. 2.

Simulation results showing (from left to right) a high-density image from 4310 frames, a low-density image from 400 frames, blind inpainting reconstructions from 400 frames and 150 frames, all at 40 nm nominal resolution, and blind inpainting reconstruction from 150 frames but at 80 nm nominal resolution. Top: full field of view. Bottom: top-left region. Scale bars: 2 μm.

Fig. 3.
Fig. 3.

Simulation results for the case of 40 nm nominal resolution. (a) Plots of true positive and false positive rates with respect to the number of frames. (b) Normalized mean square error curve with respect to the number of frames.

Fig. 4.
Fig. 4.

Simulation results. Minimum number of frames to achieve a given Nyquist resolution for the phantom simulation.

Fig. 5.
Fig. 5.

Results from real microtubule STORM data. (a) Images of the full field of view (top) and a selected region of interest (ROI, bottom). From left to right: diffraction-limited image, low-density STORM image using 400 frames, blind inpainting reconstruction from the 400 frame image, and high-density STORM image taken using 34,000 frames, respectively. Scale bars: 2.5 μm. Pixel size: 53 nm. (b) Line profiles of two segments indicated by the white lines in (a), left for segment 1 and right for segment 2. Low: low-density image. High: high-density image. Inpainting: blind inpainting reconstruction. Diffract.: diffraction-limited image.

Fig. 6.
Fig. 6.

Results from a second set of real microtubule STORM data showing images of the full field of view (top) and selected ROI (bottom). From left to right: diffraction-limited image, low-density STORM image using 300 frames, blind inpainting reconstruction from the 300 frame image, and high-density STORM image using 36,000 frames, respectively. Scale bars: 2.5 μm. Pixel size: 53 nm.

Fig. 7.
Fig. 7.

Effect of λ on a real STORM dataset. The results of λ=50 and 100 are seen to lose structural information, while that of λ=500 maintains the resolution and structure when suppressing noise.

Fig. 8.
Fig. 8.

Results from real actin STORM data showing images of the full field of view (top) and selected ROI (bottom). See Fig. S6 in Supplement 1 for other ROIs. From left to right: low-density STORM image using 1000 frames, blind inpainting reconstruction from the 1000 frame image, and high-density STORM image using 115,000 frames, respectively. Scale bars: 1.25 μm. Pixel size: 35 nm.

Fig. 9.
Fig. 9.

Results from real CS-STORM data showing images of the full field of view (top) and selected ROI (bottom). From left to right: low-density STORM image using 50 frames, blind inpainting reconstruction from the 50 frame image, and high-density STORM image using 5000 frames, respectively. Scale bars: 2 μm. Pixel size: 40 nm.

Equations (2)

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xQ=PQx,
minxϕx1+λ2PQxxQ22,

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