Abstract

Single-molecule localization microscopy methods offer high spatial resolution, but they are not always suitable for live cell imaging due to limited temporal resolution. One strategy is to increase the density of photoactivated molecules present in each image, however suitable analysis algorithms for such data are still lacking. We present 3denseSTORM, a new algorithm for localization microscopy which is able to recover 2D or 3D super-resolution images from a sequence of diffraction limited images with high densities of photoactivated molecules. The algorithm is based on sparse support recovery and uses a Poisson noise model, which becomes critical in low-light conditions. For 3D data reconstruction we use the astigmatism and biplane imaging methods. We derive the theoretical resolution limits of the method and show examples of image reconstructions in simulations and in real 2D and 3D biological samples. The method is suitable for fast image acquisition in densely labeled samples and helps facilitate live cell studies with single molecule localization microscopy.

© 2014 Optical Society of America

Full Article  |  PDF Article
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2014 (4)

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
[Crossref] [PubMed]

O. Mandula, I. Š. Šestak, R. Heintzmann, and C. K. I. Williams, “Localisation microscopy with quantum dots using non-negative matrix factorisation,” Opt. Express 22(20), 24594–24605 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (5)

Y. Wang, T. Quan, S. Zeng, and Z.-L. Huang, “PALMER: a method capable of parallel localization of multiple emitters for high-density localization microscopy,” Opt. Express 20(14), 16039–16049 (2012).
[Crossref] [PubMed]

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102(10), 2391–2400 (2012).
[Crossref] [PubMed]

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

K. Xu, H. P. Babcock, and X. Zhuang, “Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton,” Nat. Methods 9(2), 185–188 (2012).
[Crossref] [PubMed]

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

2011 (7)

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(2), 195–200 (2011).
[Crossref] [PubMed]

D. T. Burnette, P. Sengupta, Y. Dai, J. Lippincott-Schwartz, and B. Kachar, “Bleaching/blinking assisted localization microscopy for superresolution imaging using standard fluorescent molecules,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 21081–21086 (2011).
[Crossref] [PubMed]

P. D. Simonson, E. Rothenberg, and P. R. Selvin, “Single-molecule-based super-resolution images in the presence of multiple fluorophores,” Nano Lett. 11(11), 5090–5096 (2011).
[Crossref] [PubMed]

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8(4), 279–280 (2011).
[Crossref] [PubMed]

P. Křížek, I. Raška, and G. M. Hagen, “Minimizing detection errors in single molecule localization microscopy,” Opt. Express 19(4), 3226–3235 (2011).
[Crossref] [PubMed]

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(5), 1377–1393 (2011).
[Crossref] [PubMed]

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(18), 16963–16974 (2011).
[Crossref] [PubMed]

2010 (5)

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010).
[Crossref] [PubMed]

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat. Methods 7(5), 338–339 (2010).
[Crossref] [PubMed]

F. V. Subach, G. H. Patterson, M. Renz, J. Lippincott-Schwartz, and V. V. Verkhusha, “Bright monomeric photoactivatable red fluorescent protein for two-color super-resolution sptPALM of live cells,” J. Am. Chem. Soc. 132(18), 6481–6491 (2010).
[Crossref] [PubMed]

M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19(12), 3133–3145 (2010).
[Crossref] [PubMed]

S. Setzer, G. Steidl, and T. Teuber, “Deblurring Poissonian images by split Bregman techniques,” J. Vis. Commun. Image Represent. 21(3), 193–199 (2010).
[Crossref]

2009 (3)

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

F.-X. Dupé, J. M. Fadili, and J.-L. Starck, “A proximal iteration for deconvolving Poisson noisy images using sparse representations,” IEEE Trans. Image Process. 18(2), 310–321 (2009).
[Crossref] [PubMed]

C. M. Galloway, E. C. Le Ru, and P. G. Etchegoin, “An iterative algorithm for background removal in spectroscopy by wavelet transforms,” Appl. Spectrosc. 63(12), 1370–1376 (2009).
[Crossref] [PubMed]

2008 (3)

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
[Crossref]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

2006 (3)

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

2005 (1)

E. J. Candes and T. Tao, “Decoding by Linear Programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

Babcock, H.

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102(10), 2391–2400 (2012).
[Crossref] [PubMed]

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

Babcock, H. P.

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(23), 28583–28596 (2013).
[Crossref] [PubMed]

K. Xu, H. P. Babcock, and X. Zhuang, “Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton,” Nat. Methods 9(2), 185–188 (2012).
[Crossref] [PubMed]

Badieirostami, M.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010).
[Crossref] [PubMed]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref] [PubMed]

Bennett, B. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Betzig, E.

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Bewersdorf, J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Bioucas-Dias, J. M.

M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19(12), 3133–3145 (2010).
[Crossref] [PubMed]

Biteen, J. S.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[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, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Borkovec, J.

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

D. T. Burnette, P. Sengupta, Y. Dai, J. Lippincott-Schwartz, and B. Kachar, “Bleaching/blinking assisted localization microscopy for superresolution imaging using standard fluorescent molecules,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 21081–21086 (2011).
[Crossref] [PubMed]

Byars, J. M.

Candes, E. J.

E. J. Candes and T. Tao, “Decoding by Linear Programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
[Crossref]

Candès, E. J.

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
[Crossref]

Cao, Y.

Carlini, L.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Chang, H.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

Chen, Y.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

Chromy, B. A.

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat. Methods 7(5), 338–339 (2010).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

Dai, Y.

D. T. Burnette, P. Sengupta, Y. Dai, J. Lippincott-Schwartz, and B. Kachar, “Bleaching/blinking assisted localization microscopy for superresolution imaging using standard fluorescent molecules,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 21081–21086 (2011).
[Crossref] [PubMed]

Davidson, M. 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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Ding, J.

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Dupé, F.-X.

F.-X. Dupé, J. M. Fadili, and J.-L. Starck, “A proximal iteration for deconvolving Poisson noisy images using sparse representations,” IEEE Trans. Image Process. 18(2), 310–321 (2009).
[Crossref] [PubMed]

Elnatan, D.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

Etchegoin, P. G.

Fadili, J. M.

F.-X. Dupé, J. M. Fadili, and J.-L. Starck, “A proximal iteration for deconvolving Poisson noisy images using sparse representations,” IEEE Trans. Image Process. 18(2), 310–321 (2009).
[Crossref] [PubMed]

Figueiredo, M. A. T.

M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of Poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19(12), 3133–3145 (2010).
[Crossref] [PubMed]

Galloway, C. M.

Gould, T. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Gu, L.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

Hagen, G. M.

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
[Crossref] [PubMed]

P. Křížek, I. Raška, and G. M. Hagen, “Minimizing detection errors in single molecule localization microscopy,” Opt. Express 19(4), 3226–3235 (2011).
[Crossref] [PubMed]

Heintzmann, R.

O. Mandula, I. Š. Šestak, R. Heintzmann, and C. K. I. Williams, “Localisation microscopy with quantum dots using non-negative matrix factorisation,” Opt. Express 22(20), 24594–24605 (2014).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Hess, S. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Holden, S.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Holden, S. J.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8(4), 279–280 (2011).
[Crossref] [PubMed]

Huang, B.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9(7), 721–723 (2012).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

Huang, F.

Huang, Z. L.

Huang, Z.-L.

Ji, W.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

Juette, M. F.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Kachar, B.

D. T. Burnette, P. Sengupta, Y. Dai, J. Lippincott-Schwartz, and B. Kachar, “Bleaching/blinking assisted localization microscopy for superresolution imaging using standard fluorescent molecules,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 21081–21086 (2011).
[Crossref] [PubMed]

Kapanidis, A. N.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8(4), 279–280 (2011).
[Crossref] [PubMed]

Kirshner, H.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Krížek, P.

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
[Crossref] [PubMed]

P. Křížek, I. Raška, and G. M. Hagen, “Minimizing detection errors in single molecule localization microscopy,” Opt. Express 19(4), 3226–3235 (2011).
[Crossref] [PubMed]

Laurence, T. A.

T. A. Laurence and B. A. Chromy, “Efficient maximum likelihood estimator fitting of histograms,” Nat. Methods 7(5), 338–339 (2010).
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Le Ru, E. C.

Lessard, M. D.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Lew, M. D.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010).
[Crossref] [PubMed]

Lidke, K. A.

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

D. T. Burnette, P. Sengupta, Y. Dai, J. Lippincott-Schwartz, and B. Kachar, “Bleaching/blinking assisted localization microscopy for superresolution imaging using standard fluorescent molecules,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 21081–21086 (2011).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

F. V. Subach, G. H. Patterson, M. Renz, J. Lippincott-Schwartz, and V. V. Verkhusha, “Bright monomeric photoactivatable red fluorescent protein for two-color super-resolution sptPALM of live cells,” J. Am. Chem. Soc. 132(18), 6481–6491 (2010).
[Crossref] [PubMed]

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Liu, N.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Liu, X.

Liu, Y.

Lord, S. J.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Lv, P.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

Mandula, O.

Manley, S.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Min, J.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Mlodzianoski, M. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[Crossref] [PubMed]

Moerner, W. E.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010).
[Crossref] [PubMed]

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

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(2), 195–200 (2011).
[Crossref] [PubMed]

Mukamel, E. A.

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102(10), 2391–2400 (2012).
[Crossref] [PubMed]

Nagpure, B. S.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5(6), 527–529 (2008).
[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, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Olivier, N.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Ovesný, M.

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
[Crossref] [PubMed]

Patterson, G. H.

F. V. Subach, G. H. Patterson, M. Renz, J. Lippincott-Schwartz, and V. V. Verkhusha, “Bright monomeric photoactivatable red fluorescent protein for two-color super-resolution sptPALM of live cells,” J. Am. Chem. Soc. 132(18), 6481–6491 (2010).
[Crossref] [PubMed]

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(5793), 1642–1645 (2006).
[Crossref] [PubMed]

Pavani, P.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Piestun, R.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
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Quan, T.

Rama, S.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Raška, I.

Renz, M.

F. V. Subach, G. H. Patterson, M. Renz, J. Lippincott-Schwartz, and V. V. Verkhusha, “Bright monomeric photoactivatable red fluorescent protein for two-color super-resolution sptPALM of live cells,” J. Am. Chem. Soc. 132(18), 6481–6491 (2010).
[Crossref] [PubMed]

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(2), 195–200 (2011).
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Rothenberg, E.

P. D. Simonson, E. Rothenberg, and P. R. Selvin, “Single-molecule-based super-resolution images in the presence of multiple fluorophores,” Nano Lett. 11(11), 5090–5096 (2011).
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Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Schwartz, S. L.

Selvin, P. R.

P. D. Simonson, E. Rothenberg, and P. R. Selvin, “Single-molecule-based super-resolution images in the presence of multiple fluorophores,” Nano Lett. 11(11), 5090–5096 (2011).
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Sengupta, P.

D. T. Burnette, P. Sengupta, Y. Dai, J. Lippincott-Schwartz, and B. Kachar, “Bleaching/blinking assisted localization microscopy for superresolution imaging using standard fluorescent molecules,” Proc. Natl. Acad. Sci. U.S.A. 108(52), 21081–21086 (2011).
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Šestak, I. Š.

Setzer, S.

S. Setzer, G. Steidl, and T. Teuber, “Deblurring Poissonian images by split Bregman techniques,” J. Vis. Commun. Image Represent. 21(3), 193–199 (2010).
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Sheng, Y.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
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H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1(1), 6 (2012).
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P. D. Simonson, E. Rothenberg, and P. R. Selvin, “Single-molecule-based super-resolution images in the presence of multiple fluorophores,” Nano Lett. 11(11), 5090–5096 (2011).
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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(5793), 1642–1645 (2006).
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F.-X. Dupé, J. M. Fadili, and J.-L. Starck, “A proximal iteration for deconvolving Poisson noisy images using sparse representations,” IEEE Trans. Image Process. 18(2), 310–321 (2009).
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S. Setzer, G. Steidl, and T. Teuber, “Deblurring Poissonian images by split Bregman techniques,” J. Vis. Commun. Image Represent. 21(3), 193–199 (2010).
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Subach, F. V.

F. V. Subach, G. H. Patterson, M. Renz, J. Lippincott-Schwartz, and V. V. Verkhusha, “Bright monomeric photoactivatable red fluorescent protein for two-color super-resolution sptPALM of live cells,” J. Am. Chem. Soc. 132(18), 6481–6491 (2010).
[Crossref] [PubMed]

Švindrych, Z.

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
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E. J. Candes and T. Tao, “Decoding by Linear Programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005).
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S. Setzer, G. Steidl, and T. Teuber, “Deblurring Poissonian images by split Bregman techniques,” J. Vis. Commun. Image Represent. 21(3), 193–199 (2010).
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Thompson, M. A.

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010).
[Crossref] [PubMed]

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Twieg, R. J.

M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, S. Rama, and P. Pavani, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A. 106(9), 2995–2999 (2009).
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Unser, M.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Uphoff, S.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8(4), 279–280 (2011).
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Verkhusha, V. V.

F. V. Subach, G. H. Patterson, M. Renz, J. Lippincott-Schwartz, and V. V. Verkhusha, “Bright monomeric photoactivatable red fluorescent protein for two-color super-resolution sptPALM of live cells,” J. Am. Chem. Soc. 132(18), 6481–6491 (2010).
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Vonesch, C.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

Wang, Y.

Williams, C. K. I.

Xu, K.

K. Xu, H. P. Babcock, and X. Zhuang, “Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton,” Nat. Methods 9(2), 185–188 (2012).
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Xu, T.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
[Crossref] [PubMed]

Ye, J. C.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
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Zeng, S.

Zhang, W.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9(7), 721–723 (2012).
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Zhang, Y.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
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Zhu, H.

Zhu, L.

L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods 9(7), 721–723 (2012).
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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(23), 28583–28596 (2013).
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H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Opt. Nanoscopy 1(1), 6 (2012).
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E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102(10), 2391–2400 (2012).
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K. Xu, H. P. Babcock, and X. Zhuang, “Dual-objective STORM reveals three-dimensional filament organization in the actin cytoskeleton,” Nat. Methods 9(2), 185–188 (2012).
[Crossref] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319(5864), 810–813 (2008).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
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Appl. Phys. Lett. (1)

M. Badieirostami, M. D. Lew, M. A. Thompson, and W. E. Moerner, “Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane,” Appl. Phys. Lett. 97(16), 161103 (2010).
[Crossref] [PubMed]

Appl. Spectrosc. (1)

Bioinformatics (1)

M. Ovesný, P. Křížek, J. Borkovec, Z. Švindrych, and G. M. Hagen, “ThunderSTORM: a comprehensive ImageJ plug-in for PALM and STORM data analysis and super-resolution imaging,” Bioinformatics 30(16), 2389–2390 (2014).
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Biomed. Opt. Express (1)

Biophys. J. (2)

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102(10), 2391–2400 (2012).
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L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106(11), 2443–2449 (2014).
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C. R. Math. (1)

E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346(9-10), 589–592 (2008).
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Figures (8)

Fig. 1
Fig. 1 Example of construction of the measurement matrix H for 2D and 3D SMLM imaging methods. The left-hand panel shows vectorization and conversion of a 2D PSF into a Toeplitz block matrix with 4-times image oversampling. The right-hand panels show the PSF in the camera image at different axial positions for 3D methods based on astigmatism [15] and biplane [16] imaging.
Fig. 2
Fig. 2 Plot of mutual coherence as a function of multiples of the imaged PSF diameter. Here the PSF is modeled by a rotationally symmetric 2D Gaussian function. Left: radial profile. Right: mutual coherence in 2D space. The threshold value is based on the RIP concept.
Fig. 3
Fig. 3 Mutual coherence for astigmatism-based 3D SMLM. Each graph contains a plot of the mutual coherence between the current PSF section (shown as a horizontal plane) and all other sections. The threshold value is displayed as a “tube.” and is based on the RIP concept. Resolvable molecules lie outside the tube in blue areas.
Fig. 4
Fig. 4 Flowchart of 3denseSTORM algorithm. Both sparse support recovery and debiasing of intensities are iterative processes. Equations (6)-(10) are each solved in single steps since they all have closed form solutions. The debiasing step is performed with a fixed spatial support ensured by zero/infinity weights. For completeness we define 0 ∙ ∞ = 0.
Fig. 5
Fig. 5 Evaluation of high density 3D Monte-Carlo simulations. (a) F1-score, (b) recovered density calculated as the number of true-positive detections per µm2, (c) lateral localization error, (d) axial localization error. The shaded areas correspond to the standard deviation of five repeated measurements.
Fig. 6
Fig. 6 Trefoil knot generated from 100 frames, each containing 30 molecules. The top panel shows the ground-truth data and the results for single-molecule fitting (astigmatism) and 3D-DAOSTORM (astigmatism). The bottom panel shows an example of one raw data frame and results for 3denseSTORM (astigmatic and biplane imaging).
Fig. 7
Fig. 7 Comparison of algorithms on real 2D high-density data [37]. The widefield (WF) image was generated as the standard deviation of the entire sequence of 500 frames. The right panel shows a detail of an area marked by the yellow square in the left image. Intensity profiles were measured and plotted from the reconstructions of 500 frames. All scalebars are 500 nm.
Fig. 8
Fig. 8 Comparison of algorithms on real 3D high-density data (U2-OS cells immuno-labeled for tubulin). The widefield (WF) images for each ROI were generated as the standard deviation of the entire sequence of 400 frames. For visual examination, a 2D image for each method was reconstructed. The yellow arrows in ROI 1 mark high density areas. The rightmost column shows a 3D visualization with color-coded z-coordinates. Intensity profiles were measured in reconstructions in ROI 2 and plotted to compare the methods. All scale bars are 500 nm.

Tables (2)

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Table 1 Results of the 3D Simulation with Trefoil Knot

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Table 2 Execution Times of Examined Algorithms on Data sets from Figs. 7 and 8

Equations (12)

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y ^ =( Hx+b ).
p( y|x,b )= i=1 m ( ( Hx+b ) i y i y i ! exp ( Hxb ) i ) .
p( x )= j=1 n ( w j exp( w j x j ) ) ,
{ x ^ , b ^ }= arg max x,b { p( y|x,b )p( x ) }.
{ x ^ , b ^ }= arg min x,b 0 n { i=1 m [ ( Hx+b ) i y i ln ( Hx+b ) i ] + j=1 n w j x j }.
x ^ (k+1) = arg min x n { Hx+ b ^ (k) ( y ^ (k) + d (k) ) 2 2 +μ x( x ˜ (k) + e (k) ) 2 2 },
y ^ (k+1) = arg min y ¯ 0 m { i=1 m [ y ¯ i y i ln( y ¯ i ) ] + η 2 H x ^ (k+1) + b ^ (k) ( y ¯ + d (k) ) 2 2 },
x ˜ (k+1) = arg min x 0 n { j=1 n | w j (k) x j | + μ 2 x( x ^ (k+1) e (k) ) 2 2 },
d (k+1) = d (k) ( H x ^ (k+1) + b ^ (k) y ^ (k+1) ),
e (k+1) = e (k) ( x ^ (k+1) x ˜ (k+1) ).
( 1 δ K ) x 2 2 Hx 2 2 ( 1+ δ K ) x 2 2
μ( H )= max 1ijn | h i T h j | h i 2 h j 2 ,

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