Abstract

We report a new image processing technique for the structured illumination microscopy designed to work with low signals, with the goal of reducing photobleaching and phototoxicity of the sample. Using a pre-filtering process to estimate experimental parameters and total variation as a constraint to reconstruct, we obtain two orders of magnitude of exposure reduction while maintaining the resolution improvement and image quality compared to a standard structured illumination microscopy. The algorithm is validated on both fixed and live cell data with results confirming that we can image more than 15x more time points compared to the standard technique.

© 2014 Optical Society of America

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  1. T. A. Klar, S. W. Hell, “Subdiffraction resolution in far-field fluorescence microscopy,” Opt. Lett. 24, 954–956 (1999).
    [CrossRef]
  2. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at naometer resolution,” Science 313, 1642–1645 (2006).
    [CrossRef] [PubMed]
  3. M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
    [CrossRef] [PubMed]
  4. B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
    [CrossRef] [PubMed]
  5. T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, S. Weiss, “Achieving increased resolution and more pixels with superresoltion optical fluctuation imaging (sofi),” Opt. Express 18, 18875–18885 (2010).
    [CrossRef] [PubMed]
  6. F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
    [CrossRef]
  7. L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
    [CrossRef] [PubMed]
  8. L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena 60, 259–268 (1992).
    [CrossRef]
  9. Y. Wang, J. Yang, W. Yin, Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
    [CrossRef]
  10. S. Setzer, G. Steidl, T. Teuber, “Deblurring poissonian images by split Bregman techniques,” J. Vis. Commun. Image Representation 21, 193–199 (2010).
    [CrossRef]
  11. N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
    [CrossRef] [PubMed]
  12. S. A. Shroff, J. R. Fienup, D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A 26, 413–424 (2009).
    [CrossRef]
  13. K. Wicker, O. Mandula, G. Best, R. Fiolka, R. Heintzmann, “Phase optimization for strucutured illumination microscopy,” Opt. Express 21, 2032–2049 (2013).
    [CrossRef] [PubMed]
  14. T. Goldstein, S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Img. Sci. 2, 323–343 (2009).
    [CrossRef]
  15. W. Yin, S. Osher, “Error forgetting of Bregman iteration,” J. Sci. Comput. 54, 684–695 (2013).
    [CrossRef]
  16. F. Cichos, C. Von Borczyskowski, M. Orrit, “Power-law intermittency of single emitters,” Curr. Opin. Colloid Interface Sci. 12, 272–284 (2007).
    [CrossRef]
  17. L. Shao, P. Kner, E. H. Rego, M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8, 1044–1046 (2011).
    [CrossRef] [PubMed]

2013 (2)

2011 (2)

L. Shao, P. Kner, E. H. Rego, M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8, 1044–1046 (2011).
[CrossRef] [PubMed]

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

2010 (2)

S. Setzer, G. Steidl, T. Teuber, “Deblurring poissonian images by split Bregman techniques,” J. Vis. Commun. Image Representation 21, 193–199 (2010).
[CrossRef]

T. Dertinger, R. Colyer, R. Vogel, J. Enderlein, S. Weiss, “Achieving increased resolution and more pixels with superresoltion optical fluctuation imaging (sofi),” Opt. Express 18, 18875–18885 (2010).
[CrossRef] [PubMed]

2009 (3)

S. A. Shroff, J. R. Fienup, D. R. Williams, “Phase-shift estimation in sinusoidally illuminated images for lateral superresolution,” J. Opt. Soc. Am. A 26, 413–424 (2009).
[CrossRef]

L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
[CrossRef] [PubMed]

T. Goldstein, S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Img. Sci. 2, 323–343 (2009).
[CrossRef]

2008 (3)

Y. Wang, J. Yang, W. Yin, Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[CrossRef]

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

2007 (1)

F. Cichos, C. Von Borczyskowski, M. Orrit, “Power-law intermittency of single emitters,” Curr. Opin. Colloid Interface Sci. 12, 272–284 (2007).
[CrossRef]

2006 (2)

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

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

1999 (1)

1992 (1)

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena 60, 259–268 (1992).
[CrossRef]

Agard, D. A.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Bates, M.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Best, G.

Betzig, E.

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

Blanc-Feraud, L.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Bonifacino, J. S.

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

Cande, W. Z.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Carlton, P. M.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Cichos, F.

F. Cichos, C. Von Borczyskowski, M. Orrit, “Power-law intermittency of single emitters,” Curr. Opin. Colloid Interface Sci. 12, 272–284 (2007).
[CrossRef]

Colyer, R.

Davidson, M. W.

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

Del Bue, A.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

Dertinger, T.

Dey, N.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Diaspro, A.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

Donnorso, M. P.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

Enderlein, J.

Faretta, M.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

Fatemi, E.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena 60, 259–268 (1992).
[CrossRef]

Fienup, J. R.

Fiolka, R.

Furia, L.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

Goldstein, T.

T. Goldstein, S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Img. Sci. 2, 323–343 (2009).
[CrossRef]

Golubovskaya, I. N.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Gustafsson, M. G.

L. Shao, P. Kner, E. H. Rego, M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8, 1044–1046 (2011).
[CrossRef] [PubMed]

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Heintzmann, R.

K. Wicker, O. Mandula, G. Best, R. Fiolka, R. Heintzmann, “Phase optimization for strucutured illumination microscopy,” Opt. Express 21, 2032–2049 (2013).
[CrossRef] [PubMed]

L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
[CrossRef] [PubMed]

Hell, S. W.

Hess, H. F.

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

Hirvonen, L. M.

L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
[CrossRef] [PubMed]

Huang, B.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Kam, Z.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Klar, T. A.

Kner, P.

L. Shao, P. Kner, E. H. Rego, M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8, 1044–1046 (2011).
[CrossRef] [PubMed]

Lavagnino, Z.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[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, H. F. Hess, “Imaging intracellular fluorescent proteins at naometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

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

Mandula, O.

K. Wicker, O. Mandula, G. Best, R. Fiolka, R. Heintzmann, “Phase optimization for strucutured illumination microscopy,” Opt. Express 21, 2032–2049 (2013).
[CrossRef] [PubMed]

L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
[CrossRef] [PubMed]

Olenych, S.

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

Olivo-Marin, J.-C.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Orrit, M.

F. Cichos, C. Von Borczyskowski, M. Orrit, “Power-law intermittency of single emitters,” Curr. Opin. Colloid Interface Sci. 12, 272–284 (2007).
[CrossRef]

Osher, S.

W. Yin, S. Osher, “Error forgetting of Bregman iteration,” J. Sci. Comput. 54, 684–695 (2013).
[CrossRef]

T. Goldstein, S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Img. Sci. 2, 323–343 (2009).
[CrossRef]

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena 60, 259–268 (1992).
[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, H. F. Hess, “Imaging intracellular fluorescent proteins at naometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Rego, E. H.

L. Shao, P. Kner, E. H. Rego, M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8, 1044–1046 (2011).
[CrossRef] [PubMed]

Roux, P.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Rudin, L. I.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena 60, 259–268 (1992).
[CrossRef]

Sedat, J. W.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Setzer, S.

S. Setzer, G. Steidl, T. Teuber, “Deblurring poissonian images by split Bregman techniques,” J. Vis. Commun. Image Representation 21, 193–199 (2010).
[CrossRef]

Shao, L.

L. Shao, P. Kner, E. H. Rego, M. G. Gustafsson, “Super-resolution 3D microscopy of live whole cells using structured illumination,” Nat. Methods 8, 1044–1046 (2011).
[CrossRef] [PubMed]

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Shroff, S. A.

Sougrat, R.

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

Steidl, G.

S. Setzer, G. Steidl, T. Teuber, “Deblurring poissonian images by split Bregman techniques,” J. Vis. Commun. Image Representation 21, 193–199 (2010).
[CrossRef]

Teuber, T.

S. Setzer, G. Steidl, T. Teuber, “Deblurring poissonian images by split Bregman techniques,” J. Vis. Commun. Image Representation 21, 193–199 (2010).
[CrossRef]

Vogel, R.

Von Borczyskowski, C.

F. Cichos, C. Von Borczyskowski, M. Orrit, “Power-law intermittency of single emitters,” Curr. Opin. Colloid Interface Sci. 12, 272–284 (2007).
[CrossRef]

Wang, C. R.

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Wang, W.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, J. Yang, W. Yin, Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[CrossRef]

Weiss, S.

Wicker, K.

K. Wicker, O. Mandula, G. Best, R. Fiolka, R. Heintzmann, “Phase optimization for strucutured illumination microscopy,” Opt. Express 21, 2032–2049 (2013).
[CrossRef] [PubMed]

L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
[CrossRef] [PubMed]

Williams, D. R.

Yang, J.

Y. Wang, J. Yang, W. Yin, Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[CrossRef]

Yin, W.

W. Yin, S. Osher, “Error forgetting of Bregman iteration,” J. Sci. Comput. 54, 684–695 (2013).
[CrossRef]

Y. Wang, J. Yang, W. Yin, Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[CrossRef]

Zanacchi, F. C.

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

Zerubia, J.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Zhang, Y.

Y. Wang, J. Yang, W. Yin, Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci. 1, 248–272 (2008).
[CrossRef]

Zhuang, X.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Zimmer, C.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Biophys J. (1)

M. G. Gustafsson, L. Shao, P. M. Carlton, C. R. Wang, I. N. Golubovskaya, W. Z. Cande, D. A. Agard, J. W. Sedat, “Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination,” Biophys J. 94, 4957–4970 (2008).
[CrossRef] [PubMed]

Curr. Opin. Colloid Interface Sci. (1)

F. Cichos, C. Von Borczyskowski, M. Orrit, “Power-law intermittency of single emitters,” Curr. Opin. Colloid Interface Sci. 12, 272–284 (2007).
[CrossRef]

Eur. Biophys. J. (1)

L. M. Hirvonen, K. Wicker, O. Mandula, R. Heintzmann, “Structured illumination microscopy of a living cell,” Eur. Biophys. J. 38, 807–812 (2009).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Sci. Comput. (1)

W. Yin, S. Osher, “Error forgetting of Bregman iteration,” J. Sci. Comput. 54, 684–695 (2013).
[CrossRef]

J. Vis. Commun. Image Representation (1)

S. Setzer, G. Steidl, T. Teuber, “Deblurring poissonian images by split Bregman techniques,” J. Vis. Commun. Image Representation 21, 193–199 (2010).
[CrossRef]

Microsc. Res. Tech. (1)

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3d confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260–266 (2006).
[CrossRef] [PubMed]

Nat. Methods (2)

F. C. Zanacchi, Z. Lavagnino, M. P. Donnorso, A. Del Bue, L. Furia, M. Faretta, A. Diaspro, “Live-cell 3D super-resolution imaging in thick biological samples,” Nat. Methods 8, 1047–1049 (2011).
[CrossRef]

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Supplementary Material (4)

» Media 1: AVI (296 KB)     
» Media 2: AVI (469 KB)     
» Media 3: AVI (3735 KB)     
» Media 4: AVI (2022 KB)     

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Figures (8)

Fig. 1
Fig. 1

Central bands of beads data with high and low signal levels indicated by “H” or “L” inside the parenthesis. (Left column: high exposure with transmission filter set at 10%; Right: low exposure with transmission filter set at 0.1%. The exposure time for both cases is 5 ms). DL: diffraction limited image (a–b); 0th band (the central band) is the Fourier transform of the average of 5 phase-shifted images, the amplitudes of which at the fz = 0 plane are shown in (c–d). Cross-sections of 0th bands (e–f): the vertical lines mark the lateral cutoff frequency of the objective; solid line (blue online) is averaged over the fx and fy axes while the dashed line (red online) is averaged over other areas at the fz = 0 plane.

Fig. 2
Fig. 2

Actin results with high and low signal levels indicated by “H” or “L” inside the parenthesis (Transmission filter is 30% for high signal and 1% for low signal; exposure times are 10 ms for both cases.) Wiener: reconstructed by the standard Wiener filtering where experimental parameters are estimated without pre-filtering; WP: Wiener method with pre-filtering. Scale bar: 5 μm.

Fig. 3
Fig. 3

Reconstructed beads images with two exposure levels as shown in Fig. 1. Wiener: reconstructed by standard Wiener method; WP: by Wiener method with pre-filtering; TV: by TV method with pre-filtering. The letters “H” and “L” in the parenthesis mean high and low signal respectively. Scale bar: 0.7 μm.

Fig. 4
Fig. 4

Single beads profile along x,y,z. In each plot, the left side shows the result from the standard Wiener method and the right side shows the result from TV method.

Fig. 5
Fig. 5

Actin results where the exposure setting are: transmission filter 0.1% and exposure time 30 ms. The peak photon number detected is ∼ 100. (a) DL: diffraction limited image (shown with increased contrast to see structures); (b) Wiener: reconstructed by the standard Wiener method; TV: reconstructed by TV method. Zoom-in versions corresponding to the white box in (a) are shown in (c)–(e). Scale bar in (a): 10μm; in (f): 2μm.

Fig. 6
Fig. 6

SIM images reconstructed by Wiener filter and TV method where the data is taken with high exposures. Maximum intensity projection of the 3D images are shown here. Top row (a–c): results from the standard Wiener method (time lapse video shown in Media 1); Bottom Row (d–f): results from the TV method (time lapse video shown in Media 2). White scale bar in (a): 5 μm.

Fig. 7
Fig. 7

SIM images with low exposures. Maximum intensity projection of the 3D images are shown here. Top row (a–d): reconstructed with the standard Wiener method (time lapse video shown in Media 3); Bottom Row (e–h): reconstructed with our TV method (time lapse video shown in Media 4). White scale bar in (e): 5 μm.

Fig. 8
Fig. 8

Intensity decay with high and low exposure experiments whose results are shown in Fig. 6 and 7. Dashed line (blue online) is the power law curve for the high signal case and the solid line (blue online) is the power law curve for the low signal case.

Equations (13)

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S ( k ) = d , m a d , m * O m * ( k + m p d ) I d , m ( k + m p d ) d , m | a d , m O m ( k + m p d ) | 2 + w 2 A ( k ) .
I d , m ( k + m p d ) a d , m O m ( k + m p d ) = I d , 0 ( k ) O 0 ( k ) ,
a d , m = I d , m ( k + m p d ) O 0 ( k ) I d , 0 ( k ) O m ( k + m p d )
a d , m = S d , 0 ol , * ( k ) S d , m ol ( k ) d k | S d , 0 ol ( k ) | 2 d k ,
S d , m ol ( k ) = I d , m ( k + m p d ) O 0 ( k ) | O m ( k + m p d ) | 2 + | O 0 ( k ) | 2 S d , 0 ol ( k ) = I d , 0 ( k ) O m ( k + m p d ) | O m ( k + m p d ) | 2 + | O 0 ( k ) | 2
I d , 0 ( k ) = { 0 where | k , k x , k y | Δ k , I d , 0 ( k ) elsewhere ;
min s ( | s | 1 + μ 2 d , m | s e j 2 π m p d r ( a d , m p d , m ) i d , m | 2 ) d x d y d z ,
( s n + 1 , W n + 1 ) = min s , W ( | W | 1 + μ 2 d , m | s e j 2 π m p d r ( a d , m p d , m ) i d , m | 2 + β 2 | W s b n | 2 ) d x d y d z
b n + 1 = b n + ( s n + 1 W n + 1 ) .
s n + 1 = min s ( μ 2 d , m | s e j 2 π m p d r ( a d , m p d , m ) i d , m | 2 + β 2 | W n s b n | 2 ) d x d y d z
W n + 1 = min W ( | W | 1 + β 2 | W s n + 1 b n | 2 ) d x d y d z .
s n + 1 = 1 ( ( T ( W n b n ) ) + μ β d , m a d , m * O m * ( k + m p d ) I d , m ( k + m p d ) | ( ) | 2 + μ β d , m | a d , m O m ( k + m p d ) | 2 ) ;
W n + 1 = { ( | s + b | 1 β ) s | s | , where | s + b | > 1 β , | s | > 0 0 , elsewhere ;

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