Abstract

In cell biology and other fields the automatic accurate localization of sub-resolution objects in images is an important tool. The signal is often corrupted by multiple forms of noise, including excess noise resulting from the amplification by an electron multiplying charge-coupled device (EMCCD). Here we present our novel Nested Maximum Likelihood Algorithm (NMLA), which solves the problem of localizing multiple overlapping emitters in a setting affected by excess noise, by repeatedly solving the task of independent localization for single emitters in an excess noise-free system. NMLA dramatically improves scalability and robustness, when compared to a general purpose optimization technique. Our method was successfully applied for in vivo localization of fluorescent proteins.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
  29. J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
    [CrossRef] [PubMed]
  30. S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
    [CrossRef]

2013 (5)

M. Coelho, N. Maghelli, I. M. Tolić-Nørrelykke, “Single-molecule imaging in vivo: the dancing building blocks of the cell,” Integr. Biol. (Camb) 5, 748–758 (2013).
[CrossRef]

J. Chao, S. Ram, E. S. Ward, R. J. Ober, “Ultrahigh accuracy imaging modality for super-localization microscopy,” Nat. Methods 10, 335–338 (2013).
[CrossRef] [PubMed]

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

2012 (6)

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

S. Stallinga, B. Rieger, “The effect of background on localization uncertainty in single emitter imaging,” Proceedings of 9th IEEE International Symposium on Biomedical Imaging 2012, 988–991(2012).

R. Starr, S. Stahlheber, A. Small, “Fast maximum likelihood algorithm for localization of fluorescent molecules,” Opt. Lett. 37, 413–415 (2012).
[CrossRef] [PubMed]

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

J. Chao, E. S. Ward, R. J. Ober, “Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices,” Multidimens. Syst. Signal Process. 23, 349–379 (2012).
[CrossRef] [PubMed]

J. Chao, E. S. Ward, R. J. Ober, “Localization accuracy in single molecule microscopy using electron-multiplying charge-coupled device cameras, in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XIX,” Proc. SPIE 8227,p. 82271P (2012).
[CrossRef]

2011 (1)

2010 (2)

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

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

2009 (1)

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

2008 (2)

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

K. Irie, A. E. McKinnon, K. Unsworth, I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19, 045207 (2008).
[CrossRef]

2005 (1)

B. C. Carter, G. T. Shubeita, S. P. Gross, “Tracking single particles: a user-friendly quantitative evaluation,” Phys. Biol. 2, 60–72 (2005).
[CrossRef] [PubMed]

2004 (1)

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

2003 (2)

D. J. Denvir, E. Conroy, “Electron-multiplying CCD: the new ICCD, in Low-Light-Level and Real-Time Imaging Systems, Components, and Applications”, Proc. SPIE 4796, pp. 164–174 (2003).
[CrossRef]

C. H. A. G. Basden, “Photon counting strategies with low light level CCDs,” Monthly Notices of the Royal Astron. Soc. 345, 985–991 (2003).
[CrossRef]

1997 (1)

G. J. Schutz, H. Schindler, T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion.” Biophys. J. 73, 1073–1080 (1997).
[CrossRef] [PubMed]

1995 (1)

L. Xu, M. I. Jordan, “On convergence properties of the EM algorithm for gaussian mixtures,” Neural Comput. 8, 129–151 (1995).
[CrossRef]

1994 (1)

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules.” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

1992 (1)

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

1991 (1)

G. M. Lee, A. Ishihara, K. A. Jacobson, “Direct observation of brownian motion of lipids in a membrane,” Proc. Natl. Acad. Sci. USA 88, 6274–6278 (1991).
[CrossRef] [PubMed]

1977 (1)

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Stat. Soc., B 39, 1–38 (1977).

1964 (1)

M. J. D. Powell, “An efficient method for finding the minimum of a function of several variables without calculating derivatives,” Comput. J. 7, 155–162 (1964).
[CrossRef]

Ananthanarayanan, V.

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

Anderson, C. M.

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

Arganda-Carreras, I.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Basden, C. H. A. G.

C. H. A. G. Basden, “Photon counting strategies with low light level CCDs,” Monthly Notices of the Royal Astron. Soc. 345, 985–991 (2003).
[CrossRef]

Brendler, V.

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

Byars, J. M.

Cardona, A.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Carter, B. C.

B. C. Carter, G. T. Shubeita, S. P. Gross, “Tracking single particles: a user-friendly quantitative evaluation,” Phys. Biol. 2, 60–72 (2005).
[CrossRef] [PubMed]

Chacón, M. R.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Chao, J.

J. Chao, S. Ram, E. S. Ward, R. J. Ober, “Ultrahigh accuracy imaging modality for super-localization microscopy,” Nat. Methods 10, 335–338 (2013).
[CrossRef] [PubMed]

J. Chao, E. S. Ward, R. J. Ober, “Localization accuracy in single molecule microscopy using electron-multiplying charge-coupled device cameras, in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XIX,” Proc. SPIE 8227,p. 82271P (2012).
[CrossRef]

J. Chao, E. S. Ward, R. J. Ober, “Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices,” Multidimens. Syst. Signal Process. 23, 349–379 (2012).
[CrossRef] [PubMed]

Cherry, R. J.

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Coelho, M.

M. Coelho, N. Maghelli, I. M. Tolić-Nørrelykke, “Single-molecule imaging in vivo: the dancing building blocks of the cell,” Integr. Biol. (Camb) 5, 748–758 (2013).
[CrossRef]

Conroy, E.

D. J. Denvir, E. Conroy, “Electron-multiplying CCD: the new ICCD, in Low-Light-Level and Real-Time Imaging Systems, Components, and Applications”, Proc. SPIE 4796, pp. 164–174 (2003).
[CrossRef]

Delivani, P.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Dempster, A. P.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Stat. Soc., B 39, 1–38 (1977).

Denvir, D. J.

D. J. Denvir, E. Conroy, “Electron-multiplying CCD: the new ICCD, in Low-Light-Level and Real-Time Imaging Systems, Components, and Applications”, Proc. SPIE 4796, pp. 164–174 (2003).
[CrossRef]

Eliceiri, K.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Flach, B.

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Frise, E.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Geipel, G.

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

Georgiou, G. N.

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

Ghosh, R. N.

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules.” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

Gross, S. P.

B. C. Carter, G. T. Shubeita, S. P. Gross, “Tracking single particles: a user-friendly quantitative evaluation,” Phys. Biol. 2, 60–72 (2005).
[CrossRef] [PubMed]

Hartenstein, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Hirsch, M.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

Hlavac, V.

M. I. Schlesinger, V. Hlavac, Ten Lectures on Statistical and Structural Pattern Recognition, (Kluwer Academic Publishers, 2002) vol. 24 of Computational Imaging and Vision.
[CrossRef]

Hobson, M. P.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

Huang, F.

Huang, Z.-L.

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

Irie, K.

K. Irie, A. E. McKinnon, K. Unsworth, I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19, 045207 (2008).
[CrossRef]

Ishihara, A.

G. M. Lee, A. Ishihara, K. A. Jacobson, “Direct observation of brownian motion of lipids in a membrane,” Proc. Natl. Acad. Sci. USA 88, 6274–6278 (1991).
[CrossRef] [PubMed]

Jacobson, K. A.

G. M. Lee, A. Ishihara, K. A. Jacobson, “Direct observation of brownian motion of lipids in a membrane,” Proc. Natl. Acad. Sci. USA 88, 6274–6278 (1991).
[CrossRef] [PubMed]

Jordan, M. I.

L. Xu, M. I. Jordan, “On convergence properties of the EM algorithm for gaussian mixtures,” Neural Comput. 8, 129–151 (1995).
[CrossRef]

Joseph, N.

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

Jülicher, F.

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

Kalinina, I.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Kaynig, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Klemm, A. H.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Krull, A.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

Laird, N. M.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Stat. Soc., B 39, 1–38 (1977).

Lee, G. M.

G. M. Lee, A. Ishihara, K. A. Jacobson, “Direct observation of brownian motion of lipids in a membrane,” Proc. Natl. Acad. Sci. USA 88, 6274–6278 (1991).
[CrossRef] [PubMed]

Lidke, K. A.

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

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

Lindner, B.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Longair, M.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Maghelli, N.

M. Coelho, N. Maghelli, I. M. Tolić-Nørrelykke, “Single-molecule imaging in vivo: the dancing building blocks of the cell,” Integr. Biol. (Camb) 5, 748–758 (2013).
[CrossRef]

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

Martin-Fernandez, M. L.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

McKinnon, A. E.

K. Irie, A. E. McKinnon, K. Unsworth, I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19, 045207 (2008).
[CrossRef]

Morrison, I. E.

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Nandi, A.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Ober, R. J.

J. Chao, S. Ram, E. S. Ward, R. J. Ober, “Ultrahigh accuracy imaging modality for super-localization microscopy,” Nat. Methods 10, 335–338 (2013).
[CrossRef] [PubMed]

J. Chao, E. S. Ward, R. J. Ober, “Localization accuracy in single molecule microscopy using electron-multiplying charge-coupled device cameras, in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XIX,” Proc. SPIE 8227,p. 82271P (2012).
[CrossRef]

J. Chao, E. S. Ward, R. J. Ober, “Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices,” Multidimens. Syst. Signal Process. 23, 349–379 (2012).
[CrossRef] [PubMed]

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

Pavin, N.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

Pietzsch, T.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Powell, M. J. D.

M. J. D. Powell, “An efficient method for finding the minimum of a function of several variables without calculating derivatives,” Comput. J. 7, 155–162 (1964).
[CrossRef]

Preibisch, S.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Quan, T.

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

Ram, S.

J. Chao, S. Ram, E. S. Ward, R. J. Ober, “Ultrahigh accuracy imaging modality for super-localization microscopy,” Nat. Methods 10, 335–338 (2013).
[CrossRef] [PubMed]

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

Ramunno-Johnson, D.

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Rao, C.

C. Rao, Linear Statistical Inference and its Applications (Wiley, 1975).

Rieger, B.

S. Stallinga, B. Rieger, “The effect of background on localization uncertainty in single emitter imaging,” Proceedings of 9th IEEE International Symposium on Biomedical Imaging 2012, 988–991(2012).

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

Rolfe, D. J.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

Rubin, D. B.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Stat. Soc., B 39, 1–38 (1977).

Rueden, C.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Saalfeld, S.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Schattat, M.

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

Schindelin, J.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Schindler, H.

G. J. Schutz, H. Schindler, T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion.” Biophys. J. 73, 1073–1080 (1997).
[CrossRef] [PubMed]

Schlesinger, M. I.

M. I. Schlesinger, V. Hlavac, Ten Lectures on Statistical and Structural Pattern Recognition, (Kluwer Academic Publishers, 2002) vol. 24 of Computational Imaging and Vision.
[CrossRef]

Schmid, B.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Schmidt, T.

G. J. Schutz, H. Schindler, T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion.” Biophys. J. 73, 1073–1080 (1997).
[CrossRef] [PubMed]

Schutz, G. J.

G. J. Schutz, H. Schindler, T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion.” Biophys. J. 73, 1073–1080 (1997).
[CrossRef] [PubMed]

Schwartz, S. L.

Shubeita, G. T.

B. C. Carter, G. T. Shubeita, S. P. Gross, “Tracking single particles: a user-friendly quantitative evaluation,” Phys. Biol. 2, 60–72 (2005).
[CrossRef] [PubMed]

Small, A.

Smith, C. S.

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

Spudich, J. A.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Stahlheber, S.

Stallinga, S.

S. Stallinga, B. Rieger, “The effect of background on localization uncertainty in single emitter imaging,” Proceedings of 9th IEEE International Symposium on Biomedical Imaging 2012, 988–991(2012).

Starr, R.

Steinborn, A.

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

Stevenson, G. V.

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

Taut, S.

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

Tinevez, J.-Y.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Tolic-Nørrelykke, I. M.

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

M. Coelho, N. Maghelli, I. M. Tolić-Nørrelykke, “Single-molecule imaging in vivo: the dancing building blocks of the cell,” Integr. Biol. (Camb) 5, 748–758 (2013).
[CrossRef]

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

Tomancak, P.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Unsworth, K.

K. Irie, A. E. McKinnon, K. Unsworth, I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19, 045207 (2008).
[CrossRef]

Vogel, S. K.

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

Wang, Y.

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

Ward, E. S.

J. Chao, S. Ram, E. S. Ward, R. J. Ober, “Ultrahigh accuracy imaging modality for super-localization microscopy,” Nat. Methods 10, 335–338 (2013).
[CrossRef] [PubMed]

J. Chao, E. S. Ward, R. J. Ober, “Localization accuracy in single molecule microscopy using electron-multiplying charge-coupled device cameras, in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XIX,” Proc. SPIE 8227,p. 82271P (2012).
[CrossRef]

J. Chao, E. S. Ward, R. J. Ober, “Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices,” Multidimens. Syst. Signal Process. 23, 349–379 (2012).
[CrossRef] [PubMed]

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

Wareham, R. J.

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

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R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules.” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

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J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

Woodhead, I. M.

K. Irie, A. E. McKinnon, K. Unsworth, I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19, 045207 (2008).
[CrossRef]

Xu, L.

L. Xu, M. I. Jordan, “On convergence properties of the EM algorithm for gaussian mixtures,” Neural Comput. 8, 129–151 (1995).
[CrossRef]

Zeng, S.

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

Biomed. Opt. Express (1)

Biophys. J. (3)

R. N. Ghosh, W. W. Webb, “Automated detection and tracking of individual and clustered cell surface low density lipoprotein receptor molecules.” Biophys. J. 66, 1301–1318 (1994).
[CrossRef] [PubMed]

G. J. Schutz, H. Schindler, T. Schmidt, “Single-molecule microscopy on model membranes reveals anomalous diffusion.” Biophys. J. 73, 1073–1080 (1997).
[CrossRef] [PubMed]

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

Cell (1)

V. Ananthanarayanan, M. Schattat, S. K. Vogel, A. Krull, N. Pavin, I. M. Tolić-Nørrelykke, “Dynein motion switches from diffusive to directed upon cortical anchoring,” Cell 153, 1526–1536 (2013).
[CrossRef] [PubMed]

Comput. J. (1)

M. J. D. Powell, “An efficient method for finding the minimum of a function of several variables without calculating derivatives,” Comput. J. 7, 155–162 (1964).
[CrossRef]

Integr. Biol. (Camb) (1)

M. Coelho, N. Maghelli, I. M. Tolić-Nørrelykke, “Single-molecule imaging in vivo: the dancing building blocks of the cell,” Integr. Biol. (Camb) 5, 748–758 (2013).
[CrossRef]

J. Cell Sci. (1)

C. M. Anderson, G. N. Georgiou, I. E. Morrison, G. V. Stevenson, R. J. Cherry, “Tracking of cell surface receptors by fluorescence digital imaging microscopy using a charge-coupled device camera. low-density lipoprotein and influenza virus receptor mobility at 4 degrees c,” J. Cell Sci. 101 (Pt 2), 415–425 (1992).
[PubMed]

J. Royal Stat. Soc., B (1)

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. Royal Stat. Soc., B 39, 1–38 (1977).

Meas. Sci. Technol. (1)

K. Irie, A. E. McKinnon, K. Unsworth, I. M. Woodhead, “A model for measurement of noise in CCD digital-video cameras,” Meas. Sci. Technol. 19, 045207 (2008).
[CrossRef]

Monthly Notices of the Royal Astron. Soc. (1)

C. H. A. G. Basden, “Photon counting strategies with low light level CCDs,” Monthly Notices of the Royal Astron. Soc. 345, 985–991 (2003).
[CrossRef]

Multidimens. Syst. Signal Process. (1)

J. Chao, E. S. Ward, R. J. Ober, “Fisher information matrix for branching processes with application to electron-multiplying charge-coupled devices,” Multidimens. Syst. Signal Process. 23, 349–379 (2012).
[CrossRef] [PubMed]

Nat. Cell Biol. (1)

I. Kalinina, A. Nandi, P. Delivani, M. R. Chacón, A. H. Klemm, D. Ramunno-Johnson, A. Krull, B. Lindner, N. Pavin, I. M. Tolić-Nørrelykke, “Pivoting of microtubules around the spindle pole accelerates kinetochore capture,” Nat. Cell Biol. 15, 82–87 (2013).
[CrossRef]

Nat. Methods (4)

J. Chao, S. Ram, E. S. Ward, R. J. Ober, “Ultrahigh accuracy imaging modality for super-localization microscopy,” Nat. Methods 10, 335–338 (2013).
[CrossRef] [PubMed]

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676–682 (2012).
[CrossRef] [PubMed]

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

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

Neural Comput. (1)

L. Xu, M. I. Jordan, “On convergence properties of the EM algorithm for gaussian mixtures,” Neural Comput. 8, 129–151 (1995).
[CrossRef]

Opt. Express (1)

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

Opt. Lett. (1)

Phys. Biol. (1)

B. C. Carter, G. T. Shubeita, S. P. Gross, “Tracking single particles: a user-friendly quantitative evaluation,” Phys. Biol. 2, 60–72 (2005).
[CrossRef] [PubMed]

PLoS ONE (1)

M. Hirsch, R. J. Wareham, M. L. Martin-Fernandez, M. P. Hobson, D. J. Rolfe, “A stochastic model for electron multiplication charge-coupled devices – from theory to practice,” PLoS ONE 8, e53671 (2013).
[CrossRef]

PLoS Biol. (1)

S. K. Vogel, N. Pavin, N. Maghelli, F. Jülicher, I. M. Tolić-Nørrelykke, “Self-organization of dynein motors generates meiotic nuclear oscillations,” PLoS Biol. 7, 0918–0928 (2009).
[CrossRef]

Proc. SPIE (2)

D. J. Denvir, E. Conroy, “Electron-multiplying CCD: the new ICCD, in Low-Light-Level and Real-Time Imaging Systems, Components, and Applications”, Proc. SPIE 4796, pp. 164–174 (2003).
[CrossRef]

J. Chao, E. S. Ward, R. J. Ober, “Localization accuracy in single molecule microscopy using electron-multiplying charge-coupled device cameras, in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XIX,” Proc. SPIE 8227,p. 82271P (2012).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

G. M. Lee, A. Ishihara, K. A. Jacobson, “Direct observation of brownian motion of lipids in a membrane,” Proc. Natl. Acad. Sci. USA 88, 6274–6278 (1991).
[CrossRef] [PubMed]

Proceedings of 9th IEEE International Symposium on Biomedical Imaging (1)

S. Stallinga, B. Rieger, “The effect of background on localization uncertainty in single emitter imaging,” Proceedings of 9th IEEE International Symposium on Biomedical Imaging 2012, 988–991(2012).

Spectrochim Acta A Mol Biomol Spectrosc. (1)

A. Steinborn, S. Taut, V. Brendler, G. Geipel, B. Flach, “TRLFS: analysing spectra with an expectation-maximization (EM) algorithm.” Spectrochim Acta A Mol Biomol Spectrosc. 71, 1425–1432 (2008).
[CrossRef] [PubMed]

Other (2)

M. I. Schlesinger, V. Hlavac, Ten Lectures on Statistical and Structural Pattern Recognition, (Kluwer Academic Publishers, 2002) vol. 24 of Computational Imaging and Vision.
[CrossRef]

C. Rao, Linear Statistical Inference and its Applications (Wiley, 1975).

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Figures (4)

Fig. 1
Fig. 1

The NMLA tracks proteins in vivo (a) Image of a fission yeast cell expressing dynein heavy chain tagged with 3 GFPs (Dhc1-3GFP). The white line marks the cell outline, the green arrowhead marks a dynein molecule. The brightest spot is the spindle pole body. (b) The movement of dyneins is visualized in consecutive maximum intensity projections onto the y-axis (see color bar). (c) Schematic representation of the NMLA. The outer loop, which addresses the excess noise, is depicted in blue while the inner loop, which performs the localization, is depicted in gray. (d) Scheme of cell with the 2D trace of a dynein (green, corresponding to the green arrowhead in a) tracked using the NMLA. (e) Projection onto the y-axis of the traces obtained using the NMLA. The green trace is the path of the molecule marked in a.

Fig. 2
Fig. 2

The NMLA and its inner loop closely approach the theoretical bounds in simulation. (a) The standard deviation of the localization results in one dimension as a function of the flux of the blob. The complete NMLA (red squares) and the inner loop (red triangles) were applied to the simulated images. The inner loop was also applied to the same image series without excess noise (blue triangles). The results are compared with theoretical bounds: the Cramer-Rao lower bound (CRLB) for a scenario without excess noise (blue line), the CRLB considering excess noise (red line) and the approximated bound suggested in [13] (black line). The NMLA yields the highest possible precision, given by the CRLB, in settings with excess noise. (b) The standard deviation of the localization results as a function of background flux. The flux of the blob was set to 25 photons. The remaining parameters and the algorithms employed were as in a. Note that the deviation between the theoretical bounds and the results of the estimators (also seen in [23]) is a general feature of the ML localization. In a and b, simulated images (without excess noise outlined in blue, and the same image with excess noise outlined in red) correspond to different values of flux/background flux indicated by the dashed lines under the images. In the images without excess noise the colors indicate the number of photons in each pixel. In the images with excess noise colors indicate the estimated number of photons as described in the Appendix.

Fig. 3
Fig. 3

The standard deviation of the localization results as a function of the measured flux of fluorescent bead images. Three 3000-frame-long movies were obtained using Total Internal Reflection Fluorescence (TIRF) microscopy with different laser powers and EMCCD gain of 300. The pixel size was 106 nm (see Appendix for details). The beads were localized with the NMLA (squares) and its inner loop (triangles). Each pair of a triangle and a square at a certain value of flux corresponds to a single bead; displayed are images of three tracked beads connected to their resulting data point. The results are compared with the CRLB considering excess noise. The background flux used in the calculation of the bound was derived from the average intensities in manually selected empty areas of the movies (see Appendix for details). The inset is an enlarged view of the section corresponding to the low flux region (dashed lines) including the theoretical bound from [13].

Fig. 4
Fig. 4

Th NMLA outperforms Powell’s method with regard to scalability and robustness. (a) Required computation time as a function of the number of emitters. Different numbers of overlapping emitters were tracked with three different implementations of the excess noise aware ML estimator: The computation time required by Powell’s method (circles) grows significantly faster than the time required by the NMLA (squares). A naively parallelized version of the NMLA (diamonds) yields a further improvement. (b) Number of inliers in localization results as a function of the standard deviation of the random initialization. In each frame the algorithms were initialized at a Gaussian distributed random location around the true position of the emitter. Every location estimate closer than 1.3 pixels to the correct location was considered an inlier. The NMLA achieves 100% inliers for higher standard deviations and does not loose as many as Powell’s method.

Equations (35)

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i = 1 M p n i ( n i ; E i ) ,
p S i | n i ( S i | n i ; g ) = S n i 1 exp ( S i g ) g n i ( n i 1 ) ! ,
p I ( I ; θ , E ) = p N ( N ; E ) p I | N ( I | N ; θ ) .
p i ( i ; θ ) = k = 0 m p i | k ( i | k ; θ k ) p k .
θ * = arg max θ p I | N ( I | N ; θ )
E * = arg max E p N ( N ; E ) .
p k | i ( k | i ; θ t ) = p i | k ( i | k ; θ t ) p k k = 0 m p i | k ( i | k ; θ t ) p k
I i , k t = I i p k | i ( k | i ; θ t )
p k t + 1 = i = 1 M I i , k t i = 1 M I i
θ k t + 1 = arg max θ k i = 1 M ( I i , k t ln p i | k ( i | k ; θ k ) )
E ^ k = E p k
E * = i = 1 M I i c
( θ * , E * ) = arg max ( θ , E ) p S ( S ; θ , E ; g )
= arg max ( θ , E ) n n set p S , n ( S , n ; θ , E ; g ) ,
n ^ i t = n = 0 n p S i | n i ( S i | n ; g ) p n i ( n ; θ t , E t ) n = 0 p S i | n i ( S i | n ; g ) p n i ( n ; θ t , E t )
E i t = p i ( i ; θ t ) E t
n ^ i t = E i t S i / g I 0 ( 2 S i E i t / g ) I 1 ( 2 S i E i t / g ) ,
θ t + 1 = arg max θ i = 1 M n ^ i t ln p i ( i ; θ )
E * = i = 1 M n ^ i t
p I ( I ; θ , E ) = N ^ = 0 ( p N ( N ^ ; E ) p I | N ( I | N ; θ ) ) .
p I ( I ; θ , E ) = p N ( N ; E ) p I | N ( I | N ; θ ) .
FIM a b = i = 1 M E S i ; θ , E [ ln q ( S i ; E i ) a ln q ( S i ; E i ) b ]
= i = 1 M S i q ( S i ; E i ) ln q ( S i ; E i ) a ln q ( S i ; E i ) b ,
q ( S i ; E i ) = n = 0 p S i | n i ( S i | n ; g ) p n i ( n ; E i )
= exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 E i E i S i / g I 1 ( 2 E i S i / g ) ,
p n ( n ; E i ) = E i n n ! exp ( E i ) .
n = 0 p S i | n i ( S i | n ; g ) p n ( n ; E i ) = exp ( E i ) δ ( S i ) + n = 1 p S i | n i ( S i | n ; g ) p n ( n ; E i ) = exp ( E i ) δ ( S i ) + n = 1 S i ( n 1 ) exp ( S i / g ) g n ( n 1 ) ! E i n n ! exp ( E i ) = exp ( E i ) δ ( S i ) + exp ( S i / g E i ) n = 1 S i ( n 1 ) E i n g n n ! ( n 1 ) !
exp ( E i ) δ ( S i ) + exp ( S i / g E i ) l = 0 S i l E i E i l g g l l ! ( l + 1 ) ! = exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 E i l = 0 1 l ! ( l + 1 ) ! ( S i E i / g ) l = exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 E i l = 0 1 l ! ( l + 1 ) ! ( S i E i / g ) l E i S i / g E i S i / g = exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 E i E i S i / g l = 0 1 l ! ( l + 1 ) ! ( S i E i / g ) l E i S i / g = exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 E i E i S i / g l = 0 1 l ! ( l + 1 ) ! ( 2 E i S i / g 2 ) 2 l + 1 I 1 ( 2 E i S i / g ) = exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 . E i E i S i / g I 1 ( 2 E i S i / g )
I 1 ( 2 E i S i / g ) = l = 0 1 l ! ( l + 1 ) ! ( 2 E i S i / g 2 ) 2 l + 1
I 1 ( z ) = l = 0 1 l ! ( l + 1 ) ! ( z 2 ) 2 l + 1
n = 1 p S i | n i ( S i | n ; g ) p n ( n ; E i ) n = n = 1 S i ( n 1 ) g n ( n 1 ) ! exp ( S i / g ) exp ( E i ) E i n n ! n = exp ( S i / g E i ) n = 1 S i ( n 1 ) E i n g n ( ( n 1 ) ! ) 2
exp ( S i / g E i ) l = 0 S i l E i E i l g g l ( l ! ) 2 = exp ( S i / g E i ) g 1 E i l = 0 ( S i E i / g ) l ( l ! ) 2 = exp ( α S i E i ) g 1 E i l = 0 1 ( l ! ) 2 ( 2 S i E i / g 2 ) 2 l I 0 ( 2 S i E i / g ) = exp ( S i / g E i ) g 1 E i I 0 ( 2 S i E i / g )
I 0 ( 2 S i E i / g ) = l = 0 1 ( l ! ) 2 ( 2 S i E i / g 2 ) 2 l
I 0 ( z ) = l = 0 1 ( l ! ) 2 ( z 2 ) 2 l
n ^ i = n = 0 p S i | n i ( S i | n ; g ) p n ( n ; E i ) n n = 0 p S i | n i ( S i | n ; g ) p n ( n ; E i ) = exp ( S i / g E i ) g 1 E i I 0 ( 2 S i E i / g ) exp ( E i ) δ ( S i ) + exp ( S i / g E i ) g 1 E i E i S i / g I 1 ( 2 E i S i / g ) = { 0 if S i = 0 S i E i / g I 0 ( 2 S i E i / g ) I 1 ( 2 S i E i / g ) if S i > 0

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