Abstract

Localization-based super-resolution microscopy (or called localization microscopy) rely on repeated imaging and localization of active molecules, and the spatial resolution enhancement of localization microscopy is built upon the sacrifice of its temporal resolution. Developing algorithms for high-density localization of active molecules is a promising approach to increase the speed of localization microscopy. Here we present a new algorithm called SSM_BIC for such purpose. The SSM_BIC combines the advantages of the Structured Sparse Model (SSM) and the Bayesian Information Criterion (BIC). Through simulation and experimental studies, we evaluate systematically the performance between the SSM_BIC and the conventional Sparse algorithm in high-density localization of active molecules. We show that the SSM_BIC is superior in processing single molecule images with weak signal embedded in strong background.

© 2011 OSA

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2011 (4)

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8(6), 499–505 (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]

X. Q. Li, G. H. Shi, and Y. D. Zhang, “Time-domain interpolation on graphics processing unit,” J. Innovative Opt. Health Sci. 4(1), 89–95 (2011).
[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(5), 1377–1393 (2011).
[Crossref] [PubMed]

2010 (6)

T. W. Quan, P. C. Li, F. Long, S. Q. Zeng, Q. M. Luo, P. N. Hedde, G. U. Nienhaus, and Z. L. Huang, “Ultra-fast, high-precision image analysis for localization-based super resolution microscopy,” Opt. Express 18(11), 11867–11876 (2010).
[Crossref] [PubMed]

S. H. DeCenzo, M. C. DeSantis, and Y. M. Wang, “Single-image separation measurements of two unresolved fluorophores,” Opt. Express 18(16), 16628–16639 (2010).
[Crossref] [PubMed]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[Crossref] [PubMed]

2009 (2)

T. J. Gould, V. V. Verkhusha, and S. T. Hess, “Imaging biological structures with fluorescence photoactivation localization microscopy,” Nat. Protoc. 4(3), 291–308 (2009).
[Crossref] [PubMed]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

2008 (1)

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5(8), 687–694 (2008).
[Crossref] [PubMed]

2007 (2)

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]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

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

2004 (3)

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101(17), 6462–6465 (2004).
[Crossref] [PubMed]

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101(31), 11298–11303 (2004).
[Crossref] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

1996 (1)

Z. Gao, Y. Lai, and Z. Hu, “A generalized gradient projection method for optimization problems with equality and inequality constraints about arbitrary initial point,” Acta Appl. Math. Sin. 12(1), 40–49 (1996).
[Crossref]

1995 (1)

Y. Cheng, “Mean shift, mode seeking, and clustering,” IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995).
[Crossref]

1976 (2)

D. Mayne and E. Polak, “Feasible directions algorithms for optimization problems with equality and inequality constraints,” Math. Program. 11(1), 67–80 (1976).
[Crossref]

M. Elbaum and P. Diament, “SNR in photocounting images of rough objects in partially coherent light,” Appl. Opt. 15(9), 2268–2275 (1976).
[Crossref] [PubMed]

Babcock, H.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[Crossref] [PubMed]

Bates, M.

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

Bertaux, N.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5(8), 687–694 (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]

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]

Byars, J. M.

Cheng, Y.

Y. Cheng, “Mean shift, mode seeking, and clustering,” IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995).
[Crossref]

Davidson, M.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[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]

DeCenzo, S. H.

DeSantis, M. C.

Diament, P.

Elbaum, M.

Fuchs, J.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

Gao, Z.

Z. Gao, Y. Lai, and Z. Hu, “A generalized gradient projection method for optimization problems with equality and inequality constraints about arbitrary initial point,” Acta Appl. Math. Sin. 12(1), 40–49 (1996).
[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(11), 4258–4272 (2006).
[Crossref] [PubMed]

Gordon, M. P.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101(17), 6462–6465 (2004).
[Crossref] [PubMed]

Gould, T. J.

T. J. Gould, V. V. Verkhusha, and S. T. Hess, “Imaging biological structures with fluorescence photoactivation localization microscopy,” Nat. Protoc. 4(3), 291–308 (2009).
[Crossref] [PubMed]

Ha, T.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101(17), 6462–6465 (2004).
[Crossref] [PubMed]

He, J.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8(6), 499–505 (2011).
[Crossref] [PubMed]

Hedde, P. N.

T. W. Quan, P. C. Li, F. Long, S. Q. Zeng, Q. M. Luo, P. N. Hedde, G. U. Nienhaus, and Z. L. Huang, “Ultra-fast, high-precision image analysis for localization-based super resolution microscopy,” Opt. Express 18(11), 11867–11876 (2010).
[Crossref] [PubMed]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

Heilemann, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Hell, S. W.

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[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.

T. J. Gould, V. V. Verkhusha, and S. T. Hess, “Imaging biological structures with fluorescence photoactivation localization microscopy,” Nat. Protoc. 4(3), 291–308 (2009).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[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]

Hu, Z.

Z. Gao, Y. Lai, and Z. Hu, “A generalized gradient projection method for optimization problems with equality and inequality constraints about arbitrary initial point,” Acta Appl. Math. Sin. 12(1), 40–49 (1996).
[Crossref]

Huang, B.

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[Crossref] [PubMed]

Huang, F.

Huang, Z. L.

Jones, S. A.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8(6), 499–505 (2011).
[Crossref] [PubMed]

Joseph, N.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[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]

Lai, Y.

Z. Gao, Y. Lai, and Z. Hu, “A generalized gradient projection method for optimization problems with equality and inequality constraints about arbitrary initial point,” Acta Appl. Math. Sin. 12(1), 40–49 (1996).
[Crossref]

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Li, P. C.

Li, X. Q.

X. Q. Li, G. H. Shi, and Y. D. Zhang, “Time-domain interpolation on graphics processing unit,” J. Innovative Opt. Health Sci. 4(1), 89–95 (2011).
[Crossref]

Lidke, K. A.

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]

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

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.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (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]

Long, F.

Luo, Q. M.

Manley, S.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

Marguet, D.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5(8), 687–694 (2008).
[Crossref] [PubMed]

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(11), 4258–4272 (2006).
[Crossref] [PubMed]

Mayne, D.

D. Mayne and E. Polak, “Feasible directions algorithms for optimization problems with equality and inequality constraints,” Math. Program. 11(1), 67–80 (1976).
[Crossref]

Mets, L.

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101(31), 11298–11303 (2004).
[Crossref] [PubMed]

Nienhaus, G. U.

T. W. Quan, P. C. Li, F. Long, S. Q. Zeng, Q. M. Luo, P. N. Hedde, G. U. Nienhaus, and Z. L. Huang, “Ultra-fast, high-precision image analysis for localization-based super resolution microscopy,” Opt. Express 18(11), 11867–11876 (2010).
[Crossref] [PubMed]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

Ober, R. J.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[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]

Olivo-Marin, J. C.

Oswald, F.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

Patterson, G.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

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

Polak, E.

D. Mayne and E. Polak, “Feasible directions algorithms for optimization problems with equality and inequality constraints,” Math. Program. 11(1), 67–80 (1976).
[Crossref]

Qu, X. H.

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101(31), 11298–11303 (2004).
[Crossref] [PubMed]

Quan, T. W.

Ram, S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Rieger, B.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

Rigneault, H.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5(8), 687–694 (2008).
[Crossref] [PubMed]

Rust, M. J.

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

Sauer, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Scherer, N. F.

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101(31), 11298–11303 (2004).
[Crossref] [PubMed]

Schüttpelz, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Schwartz, S. L.

Selvin, P. R.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101(17), 6462–6465 (2004).
[Crossref] [PubMed]

Sergé, A.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5(8), 687–694 (2008).
[Crossref] [PubMed]

Shi, G. H.

X. Q. Li, G. H. Shi, and Y. D. Zhang, “Time-domain interpolation on graphics processing unit,” J. Innovative Opt. Health Sci. 4(1), 89–95 (2011).
[Crossref]

Shim, S. H.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8(6), 499–505 (2011).
[Crossref] [PubMed]

Smith, C. S.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Tscherepanow, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[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).
[Crossref] [PubMed]

Van De Linde, S.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Verkhusha, V. V.

T. J. Gould, V. V. Verkhusha, and S. T. Hess, “Imaging biological structures with fluorescence photoactivation localization microscopy,” Nat. Protoc. 4(3), 291–308 (2009).
[Crossref] [PubMed]

Wang, Y. M.

Ward, E. S.

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

Wiedenmann, J.

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

Wolter, S.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

Wu, D.

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101(31), 11298–11303 (2004).
[Crossref] [PubMed]

Zeng, S. Q.

Zerubia, J.

Zhang, B.

Zhang, Y. D.

X. Q. Li, G. H. Shi, and Y. D. Zhang, “Time-domain interpolation on graphics processing unit,” J. Innovative Opt. Health Sci. 4(1), 89–95 (2011).
[Crossref]

Zhuang, X.

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8(6), 499–505 (2011).
[Crossref] [PubMed]

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[Crossref] [PubMed]

Zhuang, X. W.

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

Acta Appl. Math. Sin. (1)

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[Crossref]

Annu. Rev. Phys. Chem. (1)

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61(1), 345–367 (2010).
[Crossref] [PubMed]

Appl. Opt. (2)

Biomed. Opt. Express (1)

Biophys. J. (3)

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref] [PubMed]

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82(5), 2775–2783 (2002).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref] [PubMed]

Cell (1)

B. Huang, H. Babcock, and X. Zhuang, “Breaking the diffraction barrier: super-resolution imaging of cells,” Cell 143(7), 1047–1058 (2010).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Y. Cheng, “Mean shift, mode seeking, and clustering,” IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 790–799 (1995).
[Crossref]

J. Innovative Opt. Health Sci. (1)

X. Q. Li, G. H. Shi, and Y. D. Zhang, “Time-domain interpolation on graphics processing unit,” J. Innovative Opt. Health Sci. 4(1), 89–95 (2011).
[Crossref]

J. Microsc. (1)

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. Van De Linde, M. Heilemann, and M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237(1), 12–22 (2010).
[Crossref] [PubMed]

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D. Mayne and E. Polak, “Feasible directions algorithms for optimization problems with equality and inequality constraints,” Math. Program. 11(1), 67–80 (1976).
[Crossref]

Nat. Methods (6)

S. A. Jones, S. H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods 8(6), 499–505 (2011).
[Crossref] [PubMed]

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5(8), 687–694 (2008).
[Crossref] [PubMed]

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

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref] [PubMed]

P. N. Hedde, J. Fuchs, F. Oswald, J. Wiedenmann, and G. U. Nienhaus, “Online image analysis software for photoactivation localization microscopy,” Nat. Methods 6(10), 689–690 (2009).
[Crossref] [PubMed]

Nat. Protoc. (1)

T. J. Gould, V. V. Verkhusha, and S. T. Hess, “Imaging biological structures with fluorescence photoactivation localization microscopy,” Nat. Protoc. 4(3), 291–308 (2009).
[Crossref] [PubMed]

Opt. Express (2)

Proc. Natl. Acad. Sci. U.S.A. (2)

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101(17), 6462–6465 (2004).
[Crossref] [PubMed]

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101(31), 11298–11303 (2004).
[Crossref] [PubMed]

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

S. W. Hell, “Far-field optical nanoscopy,” Science 316(5828), 1153–1158 (2007).
[Crossref] [PubMed]

Other (3)

C. Hegde, M. F. Duarte, and V. Cevher, “Compressive sensing recovery of spike trains using a structured sparsity model,” in Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS), (Saint-Malo, France) (2009), pp. 13–16.

K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. (Springer, 2002).

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

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Figures (6)

Fig. 1
Fig. 1

Localizing simulated images with SSM_BIC and SA. (a) A brief description of the SSM_BIC. Circles and crosses represent the real and pre-estimated positions of active molecules, respectively. (b) Simulated images (100 × 100 pixels) containing active molecules with different densities shown in the left corner of the corresponding images. (c) The performance of SSM_BIC and SA in analyzing images with different number of active molecules.

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Fig. 2
Fig. 2

Capability of SSM_BIC in resolving molecule pairs. (a) Sample images for molecule pairs with different distances, where each molecule emits 350 photons. (b) The performance of SSM_BIC and SA in resolving molecule pairs with different signal intensities and separate distances. Note that the background is 100 photons per pixel for all simulations.

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Fig. 3
Fig. 3

TIRF image from a stack of 600 image frames (a) and super-resolution images reconstructed by SA (b) and SSM_BIC (c). The green arrows show some densely labeled structures. The data in (b) was further analyzed to give the histograms of background (d) and the total number of detected photons from single molecules (e). The mean values of individual histograms are shown in the right corner of the corresponding figures. Scale bar: 2 μm.

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Fig. 4
Fig. 4

Dependence of detection rate on threshold and optimal model selection in SSM_BIC. (a, upper) Simulated images containing active molecule pairs with a distance of 250 nm and different signal levels. (a, lower) Detection efficiency of SSM_BIC and Gaussian deflation (GD) using a given threshold of 0.4. (b) Influence of threshold on detection rate in SSM_BIC. (c) Comparison on optimal model selection between BIC and minimal training error.

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Fig. 5
Fig. 5

Performance of SSM_BIC in the identification of molecule pairs with strong signal. Note that the background is 100 photons per pixel for all simulations.

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Fig. 6
Fig. 6

The performance of SSM_BIC in the identification of the molecule pair with non-equal emission. Note that the background is 100 photons per pixel for all simulations.

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Equations (6)

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L ( o 1 , o 2 , ⋯ , o n ) ⊗ P S F = F
F i , j = ∑ l = 1 n A l exp ( − ( i − o l x ) 2 + ( j − o l y ) 2 2 ω 2 )
S i , j = P o i s ( F i , j + N b )
e * = − arg min e ∑ i , j = 1 m ( L i , j ) 2 e i , j s u b j e c t   t o :   ∑ i , j = 1 m e i , j ≤ n         e i − 1 , j + e i − 1 , j + 1 + e i , j − 1 + e i , j + e i , j + 1 ≤ 1   ( i , j = 2 , 3 , ⋯ , m − 1 )
( A ⌢ 1 , o ⌢ 1 x , o ⌢ 1 y ; A ⌢ 2 , o ⌢ 2 x , o ⌢ 2 y ; , ⋯ , N ⌢ b ) = arg min ( ∑ 1 ≤ i , j ≤ m F i , j + N b ) − ( ∑ 1 ≤ i , j ≤ m S i , j log ( F i , j + N b ) ) s u b j e c t     t o :     A i > 0 , o i x > 0 , o i y > 0 ,   ( i = 1 , 2 , ⋯ , s ) ; N b > 0
B I C ( s ) = ∑ i , j = 1 ( S i , j − F ⌢ i , j − N ⌢ b ) 2 / S i , j + ( log m 2 ) ( 3 s + 1 )

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