Abstract

Single molecule localization microscopy (SMLM) is one of the fastest evolving and most broadly used super-resolving imaging techniques in the biosciences. While image recordings could take up to hours only ten years ago, scientists are now reaching for real-time imaging in order to follow the dynamics of biology. To this end, it is crucial to have data processing strategies available that are capable of handling the vast amounts of data produced by the microscope. In this article, we report on the use of a deep convolutional neural network (CNN) for localizing particles in three dimensions on the basis of single images. In test experiments conducted on fluorescent microbeads, we show that the precision obtained with a CNN can be comparable to that of maximum likelihood estimation (MLE), which is the accepted gold standard. Regarding speed, the CNN performs with about 22k localizations per second more than three orders of magnitude faster than the MLE algorithm of ThunderSTORM. If only five parameters are estimated (3D position, signal and background), our CNN implementation is currently slower than the fastest, recently published GPU-based MLE algorithm. However, in this comparison the CNN catches up with every additional parameter, with only a few percent extra time required per additional dimension. Thus it may become feasible to estimate further variables such as molecule orientation, aberration functions or color. We experimentally demonstrate that jointly estimating Zernike mode magnitudes for aberration modeling can significantly improve the accuracy of the estimates.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2018 (6)

K. J. Martens, A. N. Bader, S. Baas, B. Rieger, and J. Hohlbein, “Phasor based single-molecule localization microscopy in 3d (psmlm-3d): an algorithm for mhz localization rates using standard cpus,” J. Chem. Phys. 148, 123311 (2018).
[Crossref] [PubMed]

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3d single-molecule localization using experimental point spread functions,” Nat. Methods 15, 367 (2018).
[Crossref] [PubMed]

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[Crossref] [PubMed]

E. Nehme, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Deep-storm: super-resolution single-molecule microscopy by deep learning,” Optica 5, 458–464 (2018).
[Crossref]

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[Crossref] [PubMed]

M. Siemons, C. Hulleman, R. Thorsen, C. Smith, and S. Stallinga, “High precision wavefront control in point spread function engineering for single emitter localization,” Opt. Express 26, 8397–8416 (2018).
[Crossref] [PubMed]

2017 (3)

2016 (3)

C. Dong, C. C. Loy, K. He, and X. Tang, “Image super-resolution using deep convolutional networks,” IEEE Transactions on Pattern Analysis Mach. Intell. 38, 295–307 (2016).
[Crossref]

C. Franke, M. Sauer, and S. van de Linde, “Photometry unlocks 3d information from 2d localization microscopy data,” Nat. Methods 14, 41 (2016).
[Crossref] [PubMed]

J. Chao, E. S. Ward, and R. J. Ober, “Fisher information theory for parameter estimation in single molecule microscopy: tutorial,” JOSA A 33, B36–B57 (2016).
[Crossref] [PubMed]

2015 (3)

H. Ma, J. Xu, J. Jin, Y. Gao, L. Lan, and Y. Liu, “Fast and precise 3d fluorophore localization based on gradient fitting,” Sci. Reports 5, 14335 (2015).
[Crossref]

C. Manzo and M. F. Garcia-Parajo, “A review of progress in single particle tracking: from methods to biophysical insights,” Reports on Prog. Phys. 78, 124601 (2015).
[Crossref]

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436 (2015).
[Crossref] [PubMed]

2014 (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, 2389–2390 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (4)

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247, 147–160 (2012).
[Crossref] [PubMed]

H. Ma, F. Long, S. Zeng, and Z.-L. Huang, “Fast and precise algorithm based on maximum radial symmetry for single molecule localization,” Opt. Lett. 37, 2481–2483 (2012).
[Crossref] [PubMed]

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9, 724 (2012).
[Crossref] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3d single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109, 675–679 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (3)

S. Stallinga and B. Rieger, “Accuracy of the gaussian point spread function model in 2d localization microscopy,” Opt. Express 18, 24461–24476 (2010).
[Crossref] [PubMed]

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

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, and M. M. Mhlanga, “Quickpalm: 3d real-time photoactivation nanoscopy image processing in imagej,” Nat. Methods 7, 339 (2010).
[Crossref] [PubMed]

2009 (1)

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

2007 (1)

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

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

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

2005 (1)

2004 (1)

B. M. Hanser, M. G. Gustafsson, D. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216, 32–48 (2004).
[Crossref] [PubMed]

2003 (1)

2000 (1)

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3d imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[Crossref]

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” JOSA 66, 207–211 (1976).
[Crossref]

Agard, D.

B. M. Hanser, M. G. Gustafsson, D. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216, 32–48 (2004).
[Crossref] [PubMed]

Aguet, F.

Aristov, A.

W. Ouyang, A. Aristov, M. Lelek, X. Hao, and C. Zimmer, “Deep learning massively accelerates super-resolution localization microscopy,” Nat. Biotechnol. 36, 460–468 (2018).
[Crossref] [PubMed]

Axelrod, D.

D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247, 147–160 (2012).
[Crossref] [PubMed]

Baas, S.

K. J. Martens, A. N. Bader, S. Baas, B. Rieger, and J. Hohlbein, “Phasor based single-molecule localization microscopy in 3d (psmlm-3d): an algorithm for mhz localization rates using standard cpus,” J. Chem. Phys. 148, 123311 (2018).
[Crossref] [PubMed]

Babcock, H. P.

N. Boyd, E. Jonas, H. P. Babcock, and B. Recht, “Deeploco: Fast 3d localization microscopy using neural networks,” BioRxiv p. 267096 (2018).

Bader, A. N.

K. J. Martens, A. N. Bader, S. Baas, B. Rieger, and J. Hohlbein, “Phasor based single-molecule localization microscopy in 3d (psmlm-3d): an algorithm for mhz localization rates using standard cpus,” J. Chem. Phys. 148, 123311 (2018).
[Crossref] [PubMed]

Barbastathis, G.

Bates, M.

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

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436 (2015).
[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, 1642–1645 (2006).
[Crossref] [PubMed]

Bewersdorf, J.

Bonifacino, J. S.

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

Booth, M. J.

Boothe, T.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

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, 2389–2390 (2014).
[Crossref] [PubMed]

Botcherby, E. J.

Boyd, N.

N. Boyd, E. Jonas, H. P. Babcock, and B. Recht, “Deeploco: Fast 3d localization microscopy using neural networks,” BioRxiv p. 267096 (2018).

Broaddus, C.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Chao, J.

J. Chao, E. S. Ward, and R. J. Ober, “Fisher information theory for parameter estimation in single molecule microscopy: tutorial,” JOSA A 33, B36–B57 (2016).
[Crossref] [PubMed]

Chen, D.

Chollet, F.

F. Chollet, “Keras: Deep learning library for theano and tensorflow,” URL: https://keras.io/k 7 (2015).

Churchman, L. S.

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

Culley, S.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Dally, W. J.

S. Han, H. Mao, and W. J. Dally, “Deep compression: Compressing deep neural network with pruning, trained quantization and huffman coding,” CoRR abs/1510.00149 (2015).

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

Deschamps, J.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3d single-molecule localization using experimental point spread functions,” Nat. Methods 15, 367 (2018).
[Crossref] [PubMed]

Dibrov, A.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Diederik Kingma, J. B.

J. B. Diederik Kingma, “Adam: A Method for Stochastic Optimization,” arXiv e-prints abs/1605.02688 (2014).

Dong, C.

C. Dong, C. C. Loy, K. He, and X. Tang, “Image super-resolution using deep convolutional networks,” IEEE Transactions on Pattern Analysis Mach. Intell. 38, 295–307 (2016).
[Crossref]

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in European Conference on Computer Vision, (Springer, 2014), pp. 184–199.

Ellenberg, J.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3d single-molecule localization using experimental point spread functions,” Nat. Methods 15, 367 (2018).
[Crossref] [PubMed]

Florin, E.-L.

Flyvbjerg, H.

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

Schindler, H.

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3d imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
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Schmidt, D.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Schmidt, U.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Schoen, I.

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3d single-molecule localization using experimental point spread functions,” Nat. Methods 15, 367 (2018).
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G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3d imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
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B. M. Hanser, M. G. Gustafsson, D. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216, 32–48 (2004).
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Segovia-Miranda, F.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Shechtman, Y.

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K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” CoRR abs/1409.1556 (2014).

Sinha, A.

Smith, C.

Solimena, M.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Sougrat, R.

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

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

K. He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in Proceedings of the IEEE International Conference on Computer Vision, (2015), pp. 1026–1034.

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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, 2389–2390 (2014).
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C. Dong, C. C. Loy, K. He, and X. Tang, “Image super-resolution using deep convolutional networks,” IEEE Transactions on Pattern Analysis Mach. Intell. 38, 295–307 (2016).
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C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in European Conference on Computer Vision, (Springer, 2014), pp. 184–199.

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Tomancak, P.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Unser, M.

Valtorta, F.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, and M. M. Mhlanga, “Quickpalm: 3d real-time photoactivation nanoscopy image processing in imagej,” Nat. Methods 7, 339 (2010).
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C. Franke, M. Sauer, and S. van de Linde, “Photometry unlocks 3d information from 2d localization microscopy data,” Nat. Methods 14, 41 (2016).
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M. Jaderberg, A. Vedaldi, and A. Zisserman, “Speeding up convolutional neural networks with low rank expansions,” CoRR abs/1405.3866 (2014).

Wang, H.

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J. Chao, E. S. Ward, and R. J. Ober, “Fisher information theory for parameter estimation in single molecule microscopy: tutorial,” JOSA A 33, B36–B57 (2016).
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M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

M. Weigert, L. Royer, F. Jug, and G. Myers, “Isotropic reconstruction of 3d fluorescence microscopy images using convolutional neural networks,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, (Springer, 2017), pp. 126–134.

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M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Wilson, T.

Xu, J.

H. Ma, J. Xu, J. Jin, Y. Gao, L. Lan, and Y. Liu, “Fast and precise 3d fluorophore localization based on gradient fitting,” Sci. Reports 5, 14335 (2015).
[Crossref]

Xu, K.

T. Kim, S. Moon, and K. Xu, “Information-rich localization microscopy through machine learning,” BioRxiv p. 373878 (2018).

Yu, B.

Zeng, S.

Zerial, M.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

Zhang, X.

K. He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in Proceedings of the IEEE International Conference on Computer Vision, (2015), pp. 1026–1034.

Zhang, Y.

Zhuang, X.

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

Zimmer, C.

W. Ouyang, A. Aristov, M. Lelek, X. Hao, and C. Zimmer, “Deep learning massively accelerates super-resolution localization microscopy,” Nat. Biotechnol. 36, 460–468 (2018).
[Crossref] [PubMed]

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, and M. M. Mhlanga, “Quickpalm: 3d real-time photoactivation nanoscopy image processing in imagej,” Nat. Methods 7, 339 (2010).
[Crossref] [PubMed]

Zisserman, A.

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” CoRR abs/1409.1556 (2014).

M. Jaderberg, A. Vedaldi, and A. Zisserman, “Speeding up convolutional neural networks with low rank expansions,” CoRR abs/1405.3866 (2014).

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, 2389–2390 (2014).
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Biophys. J. (1)

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

IEEE Transactions on Pattern Analysis Mach. Intell. (1)

C. Dong, C. C. Loy, K. He, and X. Tang, “Image super-resolution using deep convolutional networks,” IEEE Transactions on Pattern Analysis Mach. Intell. 38, 295–307 (2016).
[Crossref]

J. Chem. Phys. (1)

K. J. Martens, A. N. Bader, S. Baas, B. Rieger, and J. Hohlbein, “Phasor based single-molecule localization microscopy in 3d (psmlm-3d): an algorithm for mhz localization rates using standard cpus,” J. Chem. Phys. 148, 123311 (2018).
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B. M. Hanser, M. G. Gustafsson, D. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216, 32–48 (2004).
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D. Axelrod, “Fluorescence excitation and imaging of single molecules near dielectric-coated and bare surfaces: a theoretical study,” J. Microsc. 247, 147–160 (2012).
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JOSA (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” JOSA 66, 207–211 (1976).
[Crossref]

JOSA A (1)

J. Chao, E. S. Ward, and R. J. Ober, “Fisher information theory for parameter estimation in single molecule microscopy: tutorial,” JOSA A 33, B36–B57 (2016).
[Crossref] [PubMed]

Nat. Biotechnol. (1)

W. Ouyang, A. Aristov, M. Lelek, X. Hao, and C. Zimmer, “Deep learning massively accelerates super-resolution localization microscopy,” Nat. Biotechnol. 36, 460–468 (2018).
[Crossref] [PubMed]

Nat. Methods (7)

C. Franke, M. Sauer, and S. van de Linde, “Photometry unlocks 3d information from 2d localization microscopy data,” Nat. Methods 14, 41 (2016).
[Crossref] [PubMed]

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

Y. Li, M. Mund, P. Hoess, J. Deschamps, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Real-time 3d single-molecule localization using experimental point spread functions,” Nat. Methods 15, 367 (2018).
[Crossref] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3, 793 (2006).
[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, 689 (2009).
[Crossref] [PubMed]

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, and M. M. Mhlanga, “Quickpalm: 3d real-time photoactivation nanoscopy image processing in imagej,” Nat. Methods 7, 339 (2010).
[Crossref] [PubMed]

R. Parthasarathy, “Rapid, accurate particle tracking by calculation of radial symmetry centers,” Nat. Methods 9, 724 (2012).
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Nature (1)

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436 (2015).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (4)

Optica (3)

Proc. Natl. Acad. Sci. (2)

J. M. Newby, A. M. Schaefer, P. T. Lee, M. G. Forest, and S. K. Lai, “Convolutional neural networks automate detection for tracking of submicron-scale particles in 2d and 3d,” Proc. Natl. Acad. Sci. 115, 9026–9031 (2018).
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S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3d single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109, 675–679 (2012).
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C. Manzo and M. F. Garcia-Parajo, “A review of progress in single particle tracking: from methods to biophysical insights,” Reports on Prog. Phys. 78, 124601 (2015).
[Crossref]

Sci. Reports (1)

H. Ma, J. Xu, J. Jin, Y. Gao, L. Lan, and Y. Liu, “Fast and precise 3d fluorophore localization based on gradient fitting,” Sci. Reports 5, 14335 (2015).
[Crossref]

Science (1)

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

Single Mol. (1)

G. J. Schütz, V. P. Pastushenko, H. J. Gruber, H.-G. Knaus, B. Pragl, and H. Schindler, “3d imaging of individual ion channels in live cells at 40nm resolution,” Single Mol. 1, 25–31 (2000).
[Crossref]

Other (14)

K. He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in Proceedings of the IEEE International Conference on Computer Vision, (2015), pp. 1026–1034.

M. Weigert, U. Schmidt, T. Boothe, A. Müller, A. Dibrov, A. Jain, B. Wilhelm, D. Schmidt, C. Broaddus, S. Culley, M. Rocha-Martins, F. Segovia-Miranda, C. Norden, R. Henriques, M. Zerial, M. Solimena, J. Rink, P. Tomancak, L. Royer, F. Jug, and E. W. Myers, “Content-aware image restoration: Pushing the limits of fluorescence microscopy,” bioRxiv (2017).

M. Weigert, L. Royer, F. Jug, and G. Myers, “Isotropic reconstruction of 3d fluorescence microscopy images using convolutional neural networks,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, (Springer, 2017), pp. 126–134.

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in European Conference on Computer Vision, (Springer, 2014), pp. 184–199.

K. Hayat, “Super-resolution via deep learning,” CoRR abs/1706.09077 (2017).

K. Simonyan and A. Zisserman, “Very deep convolutional networks for large-scale image recognition,” CoRR abs/1409.1556 (2014).

F. Chollet, “Keras: Deep learning library for theano and tensorflow,” URL: https://keras.io/k 7 (2015).

Theano Development Team, “Theano: A Python framework for fast computation of mathematical expressions,” arXiv e-prints abs/1605.02688 (2016).

J. B. Diederik Kingma, “Adam: A Method for Stochastic Optimization,” arXiv e-prints abs/1605.02688 (2014).

N. Boyd, E. Jonas, H. P. Babcock, and B. Recht, “Deeploco: Fast 3d localization microscopy using neural networks,” BioRxiv p. 267096 (2018).

T. Kim, S. Moon, and K. Xu, “Information-rich localization microscopy through machine learning,” BioRxiv p. 373878 (2018).

S. Han, H. Mao, and W. J. Dally, “Deep compression: Compressing deep neural network with pruning, trained quantization and huffman coding,” CoRR abs/1510.00149 (2015).

V. Lebedev, Y. Ganin, M. Rakhuba, I. V. Oseledets, and V. S. Lempitsky, “Speeding-up convolutional neural networks using fine-tuned cp-decomposition,” CoRR abs/1412.6553 (2014).

M. Jaderberg, A. Vedaldi, and A. Zisserman, “Speeding up convolutional neural networks with low rank expansions,” CoRR abs/1405.3866 (2014).

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Figures (9)

Fig. 1
Fig. 1 (a) Experimental setup. (b) Exemplary bead images at different z-stage positions.
Fig. 2
Fig. 2 Schematic representation of the network architecture.
Fig. 3
Fig. 3 Refining the PSF model using phase retrieval: (a) x-z-section of experimental 3D bead image (logarithmic scale). (b) Refined model, calculated by taking into account the retrieved pupil phase aberrations. (c) Calculated, aberration-free bead image section. The bar plot shows the retrieved Zernike magnitudes (Noll scheme [44]).
Fig. 4
Fig. 4 Localization performance of MLE and the CNN on experimental data. (a) Axial position estimates. (b) Axial position accuracies. (c) Lateral localization precisions. (d) Axial localization precisions.
Fig. 5
Fig. 5 Sensitivity of MLE to the choice of initial z-position estimates. (a) Same data as in Fig. 4(a), but with an extended z-range (extension is right to the dashed vertical lines). Close to the in-focus position the MLE results are unreliable. (b) Increasing the initial z-estimates by 200 nm further deteriorates the MLE results.
Fig. 6
Fig. 6 Effect of using a wrong PSF model on z-position estimates. (a) Estimated z-positions when the PSF is falsely assumed to be free of aberrations. (b) z-accuracies for using the aberration-free and refined PSF models.
Fig. 7
Fig. 7 Estimation of aberrations with a CNN. Astigmatism (Z5) with a magnitude of 0.3 rad has been intentionally added to the wavefront using a SLM. A CNN is used to jointly estimate signal, background, 3D position as well as the three Zernike modes for first order astigmatism (Z5, Z6) and primary spherical aberration (Z11). (a) Axial position estimates of CNNs trained with (blue) and without (red) varying aberrations. (b) Estimated content of astigmatism. The orange line marks the value applied by the SLM. (c) Estimated content of primary spherical aberration.
Fig. 8
Fig. 8 Test of the phase retrieval routine. (a) Zernike modes retrieved after an initial run. (b) Results of a second run, after Z11=−0.5 rad has been applied with the SLM. (c) The difference between the bar plots shown in (a) and (b) yields a value of Z11=−0.54.
Fig. 9
Fig. 9 Comparison of phase retrieval results obtained with (blue bars) and without (red bars) considering the measured objective transmission function. The main differences concern spherical aberration and astigmatism terms.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

P k ( n k | μ θ , k ) = e μ θ , k μ θ , k n k n k ! .
θ ^ = arg min θ k ( μ θ , k n k ln ( μ θ , k ) ) .
Φ = i = 2 37 a i Z i + a 56 Z 56 ,
E = i = 1 n x j = 1 n y k = 1 n z | I sim ( i , j , k ) I exp ( i , j , k ) | ,
FI m , n = k = 1 K 1 μ θ , k Δ μ θ , k Δ θ m Δ μ θ , k Δ θ n ,