Abstract

We propose non-negative matrix factorisation with iterative restarts (iNMF) to model a noisy dataset of highly overlapping fluorophores with intermittent intensities. We can recover high-resolution images of individual sources from the optimised model, despite their high mutual overlap in the original data. Each source can have an arbitrary, unknown shape of the PSF and blinking behaviour. This allows us to use quantum dots as bright and stable fluorophores for localisation microscopy. We compare the iNMF results to CSSTORM, 3B and bSOFI. iNMF shows superior performance in the challenging task of super-resolution imaging using quantum dots. We can also retrieve axial localisation of the sources from the shape of the recovered PSF.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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  26. D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
    [Crossref]

2014 (1)

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

2013 (2)

A. Barsic and R. Piestun, “Super-resolution of dense nanoscale emitters beyond the diffraction limit using spatial and temporal information,” Appl. Phys. Lett. 102(23), 231103 (2013).
[Crossref]

N. Olivier, D. Keller, P. Gonczy, and S. Manley, “Resolution doubling in 3D-STORM imaging through improved buffers,” PLoS One 8(7), 69004 (2013).
[Crossref]

2012 (2)

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

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

2011 (5)

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
[Crossref]

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (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]

F. Huang, S. L. Schwartz, J. M. Byars, K. A. Lidke, and F. Huang, “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” Biomed. Opt. Express 2(5), 1377–1393 (2011).
[Crossref] [PubMed]

2009 (4)

T. Dertinger, R. Colyera, G. Iyera, S. Weissa, and J. Enderleind, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Supporting Information,” PNAS 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

M. Everingham, L. Gool, C. K. I. Williams, J. Winn, and A. Zisserman, “The Pascal Visual Object Classes (VOC) Challenge,” Int. J. Comput. Vis. 88(2), 303–338 (2009).
[Crossref]

A. R. Small, “Theoretical limits on errors and acquisition rates in localizing switchable fluorophores,” Biophys. J. 96(2), 16–18 (2009).
[Crossref]

F. D. Stefani, J. P. Hoogenboom, and E. Barkai, “Beyond quantum jumps: blinking nanoscale light emitters,” Phys. Today 62(2), 34 (2009).
[Crossref]

2008 (1)

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5(9), 763–775 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (1)

2004 (1)

P. O. Hoyer, “Non-negative matrix factorization with sparseness constraints,” J. Mach. Learn. Res. 5, 1457–1469 (2004).

2001 (1)

D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” Adv. Neural Inf. Process. Syst. 13, 556–562 (2001).

2000 (1)

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4–5), 411–430 (2000).
[Crossref] [PubMed]

Baddeley, D.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
[Crossref]

Barkai, E.

F. D. Stefani, J. P. Hoogenboom, and E. Barkai, “Beyond quantum jumps: blinking nanoscale light emitters,” Phys. Today 62(2), 34 (2009).
[Crossref]

Barsic, A.

A. Barsic and R. Piestun, “Super-resolution of dense nanoscale emitters beyond the diffraction limit using spatial and temporal information,” Appl. Phys. Lett. 102(23), 231103 (2013).
[Crossref]

Berclaz, C.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

Bocchio, N. L.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

Burnette, D. T.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Byars, J. M.

Cannell, M. B.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
[Crossref]

Cavaliere-Jaricot, S.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5(9), 763–775 (2008).
[Crossref] [PubMed]

Colyera, R.

T. Dertinger, R. Colyera, G. Iyera, S. Weissa, and J. Enderleind, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Supporting Information,” PNAS 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Cox, S.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Davidson, M. W.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Dellagiacoma, C.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

Dertinger, T.

T. Dertinger, R. Colyera, G. Iyera, S. Weissa, and J. Enderleind, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Supporting Information,” PNAS 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Elnatan, D.

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

Enderleind, J.

T. Dertinger, R. Colyera, G. Iyera, S. Weissa, and J. Enderleind, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Supporting Information,” PNAS 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Everingham, M.

M. Everingham, L. Gool, C. K. I. Williams, J. Winn, and A. Zisserman, “The Pascal Visual Object Classes (VOC) Challenge,” Int. J. Comput. Vis. 88(2), 303–338 (2009).
[Crossref]

Geissbuehler, S.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

Ghitani, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Gonczy, P.

N. Olivier, D. Keller, P. Gonczy, and S. Manley, “Resolution doubling in 3D-STORM imaging through improved buffers,” PLoS One 8(7), 69004 (2013).
[Crossref]

Gool, L.

M. Everingham, L. Gool, C. K. I. Williams, J. Winn, and A. Zisserman, “The Pascal Visual Object Classes (VOC) Challenge,” Int. J. Comput. Vis. 88(2), 303–338 (2009).
[Crossref]

Grabolle, M.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5(9), 763–775 (2008).
[Crossref] [PubMed]

Heintzmann, R.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution by localization of quantum dots using blinking statistics,” Opt. Express 13(18), 7052 (2005).
[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]

Hoogenboom, J. P.

F. D. Stefani, J. P. Hoogenboom, and E. Barkai, “Beyond quantum jumps: blinking nanoscale light emitters,” Phys. Today 62(2), 34 (2009).
[Crossref]

Hoyer, P. O.

P. O. Hoyer, “Non-negative matrix factorization with sparseness constraints,” J. Mach. Learn. Res. 5, 1457–1469 (2004).

Huang, B.

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

Huang, F.

Hyvärinen, A.

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4–5), 411–430 (2000).
[Crossref] [PubMed]

Iyera, G.

T. Dertinger, R. Colyera, G. Iyera, S. Weissa, and J. Enderleind, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Supporting Information,” PNAS 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Jones, G. E.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Jovanovic-Talisman, T.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Jovin, T. M.

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]

Keller, D.

N. Olivier, D. Keller, P. Gonczy, and S. Manley, “Resolution doubling in 3D-STORM imaging through improved buffers,” PLoS One 8(7), 69004 (2013).
[Crossref]

Kim, J.

J. Kim and H. Park, “Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons,” 2008 Eighth IEEE International Conference on Data Mining (2008), pp. 353–362.

Lasser, T.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

Lee, D. D.

D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” Adv. Neural Inf. Process. Syst. 13, 556–562 (2001).

Leutenegger, M.

S. Geissbuehler, N. L. Bocchio, C. Dellagiacoma, C. Berclaz, M. Leutenegger, and T. Lasser, “Mapping molecular statistics with balanced super-resolution optical fluctuation imaging (bSOFI),” Opt. Nanoscopy 1(1), 4 (2012).
[Crossref]

Lidke, K. A.

Lippincott-Schwartz, J.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Mandula, O.

O. Mandula, “Super-resolution methods for fluorescence microscopy,” PhD thesis, University of Edinburgh (2012).

Manley, S.

N. Olivier, D. Keller, P. Gonczy, and S. Manley, “Resolution doubling in 3D-STORM imaging through improved buffers,” PLoS One 8(7), 69004 (2013).
[Crossref]

Monypenny, J.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Nann, T.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5(9), 763–775 (2008).
[Crossref] [PubMed]

Nitschke, R.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5(9), 763–775 (2008).
[Crossref] [PubMed]

Oja, E.

A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Netw. 13(4–5), 411–430 (2000).
[Crossref] [PubMed]

Olivier, N.

N. Olivier, D. Keller, P. Gonczy, and S. Manley, “Resolution doubling in 3D-STORM imaging through improved buffers,” PLoS One 8(7), 69004 (2013).
[Crossref]

Olivo-Marin, J.-C.

Park, H.

J. Kim and H. Park, “Toward Faster Nonnegative Matrix Factorization: A New Algorithm and Comparisons,” 2008 Eighth IEEE International Conference on Data Mining (2008), pp. 353–362.

Piestun, R.

A. Barsic and R. Piestun, “Super-resolution of dense nanoscale emitters beyond the diffraction limit using spatial and temporal information,” Appl. Phys. Lett. 102(23), 231103 (2013).
[Crossref]

Resch-Genger, U.

U. Resch-Genger, M. Grabolle, S. Cavaliere-Jaricot, R. Nitschke, and T. Nann, “Quantum dots versus organic dyes as fluorescent labels,” Nat. Methods 5(9), 763–775 (2008).
[Crossref] [PubMed]

Rieger, B.

Rosten, E.

S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods 9(2), 195–200, (2011).
[Crossref] [PubMed]

Schwartz, S. L.

Seung, H. S.

D. D. Lee and H. S. Seung, “Algorithms for non-negative matrix factorization,” Adv. Neural Inf. Process. Syst. 13, 556–562 (2001).

Shroff, H.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Small, A.

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

Small, A. R.

A. R. Small, “Theoretical limits on errors and acquisition rates in localizing switchable fluorophores,” Biophys. J. 96(2), 16–18 (2009).
[Crossref]

Soeller, C.

D. Baddeley, M. B. Cannell, and C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4(6), 589–598 (2011).
[Crossref]

Stahlheber, S.

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref] [PubMed]

Stefani, F. D.

F. D. Stefani, J. P. Hoogenboom, and E. Barkai, “Beyond quantum jumps: blinking nanoscale light emitters,” Phys. Today 62(2), 34 (2009).
[Crossref]

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]

Vaziri, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Weissa, S.

T. Dertinger, R. Colyera, G. Iyera, S. Weissa, and J. Enderleind, “Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Supporting Information,” PNAS 106(52), 22287–22292 (2009).
[Crossref] [PubMed]

Williams, C. K. I.

M. Everingham, L. Gool, C. K. I. Williams, J. Winn, and A. Zisserman, “The Pascal Visual Object Classes (VOC) Challenge,” Int. J. Comput. Vis. 88(2), 303–338 (2009).
[Crossref]

Winn, J.

M. Everingham, L. Gool, C. K. I. Williams, J. Winn, and A. Zisserman, “The Pascal Visual Object Classes (VOC) Challenge,” Int. J. Comput. Vis. 88(2), 303–338 (2009).
[Crossref]

York, A. G.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, and H. Shroff, “Confined activation and subdiffractive localization enables whole-cell PALM with genetically expressed probes,” Nat. Methods 8(4), 327–333 (2011).
[Crossref] [PubMed]

Zerubia, J.

Zhang, B.

Zhang, W.

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

Zhu, L.

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

Zisserman, A.

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Figures (7)

Fig. 1:
Fig. 1:

(a) Illustration of NMF. Each frame in the dataset d(x, t) is described as the sum of K individual PSFs wk(x) with appropriate intensity hk(t). (b) iNMF algorithm applied to a single patch.

Fig. 2:
Fig. 2:

(a–b) Classification of true positives (TP), false positives (FP) and false negatives (FN) from the true (red dot) and estimated (green cross) locations. (c) Example of the precision P(li) (blue) and recall R(li) (green) curve against the confidence levels li for one iNMF evaluation. (d) The precision/recall curve P(R) (blue) with interpolated precision Pinterp() (red) reducing the wiggles. The average precision (green dashed line) was estimated from averaging of the red curve.

Fig. 3:
Fig. 3:

Simulated data of randomly scattered emitters. (a) Average precision which summarises both localisation precision and the ability to recover the individual sources (higher values are better). Error bars show standard deviation for repeated simulations. (b–c) Red dots in the wide-field (WF) image show the true positions of the emitters. Green crosses are the identified locations for iNMF (visualisation of one run of iNMF), CSSTORM, bSOFI and 3B reconstructions. Red circles indicate the threshold distance r from the true locations. A green cross within a red circle was counted as a true positive (TP). A green cross outside a red circle was counted as false positive (FP). Red circle without any green cross inside was counted as a false negative (FN). Red arrows point to close unresolved sources. Green arrow point at sources resolved only in the iNMF reconstruction. Blue arrows show where multiple emitters were approximated by a single source in the iNMF image.

Fig. 4:
Fig. 4:

Comparison of wide field (WF), iNMF, CSSTORM, bSOFI and 3B techniques. (a) Reconstruction of a simulated structure. The true sources’ positions are indicated as red dots in the WF image. The red arrows point at sub-resolution double line structure recovered with iNMF, CSSTORM and bSOFI. The green arrows point to a sub-resolution hole visible only in the iNMF image. The blue arrows show the area where 3B and CSSTORM failed to resolve the double line of the artificial specimen. (b) Tubulin structure labelled with QDs. Scale bars 400nm.

Fig. 5:
Fig. 5:

iNMF reconstructed images. (a) Tubulin labelled with QDs. Red dashed box shows the region used for comparison of the methods in Fig. 4(b). (b) Tubulin labelled with Alexa 647. Scale bars 500nm.

Fig. 6:
Fig. 6:

Recovery of the different PSFs. (a) Movie of blinking QDs randomly scattered on an out-of-focus plane. 103 frames in total. (b) Individual PSFs wk recovered with iNMF (K = 22). The bars under each frame show the mean intensity of the source. (c) wk recovered with ICA (K = 22). Blue colour indicate the pixels with negative values. Scale bars 1μm.

Fig. 7:
Fig. 7:

(a) A neurone with neurotransmitter receptor subunits labeled with QD605. Inset in the upper right corner shows the PSF obtained from measurement of the axial profile of a fluorescence bead (WF), iNMF reconstructed region of low QD density taken at different axial positions (iNMF) and simulated PSF (Sim) used for localisation. The axial localisation is colour-coded (colorbar with corresponding PSF slices) with transparency proportional to the mean brightness of each estimated source. Data were kindly provided by Anja Huss. (b) Simulated data with PRILM [26] tailored PSF. Experimental PSF (shown on the left) has been used for data simulations. Data kindly provided by David Baddeley. The PSFs are shown on the same scale as the large images.

Equations (10)

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d ( x , t ) k = 1 K w k ( x ) h k ( t ) ,
D × WH ,
w x k = x x k t = 1 T h k t [ ( D WH ) H ] x k h k t = h k t x = 1 N w x k [ W ( D WH ) ] k t .
log p ( D | W , H ) = x t ( d x t log k = 1 K w x k h k t k = 1 K w x k h k t ) + const . ,
W j + 1 ( W j , H j , D ) H j + 1 ( W j + 1 , H j , D ) ,
b k = mean t ( h k t ) ,
P ( l i ) = TP ( l i ) TP ( l i ) + FP ( l i )
R ( l i ) = TP ( l i ) TP ( l i ) + FN ( l i ) .
P interp ( R ˜ ) = max R ; R R ˜ P ( R ) .
AP = 1 11 R ˜ P interp ( R ˜ ) .

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