Abstract

A proper estimation of realistic point-spread function (PSF) in optical microscopy can significantly improve the deconvolution performance and assist the microscope calibration process. In this work, by exemplifying 3D wide-field fluorescence microscopy, we propose an approach for estimating the spherically aberrated PSF of a microscope, directly from the observed samples. The PSF, expressed as a linear combination of 4 basis functions, is obtained directly from the acquired image by minimizing a novel criterion, which is derived from the noise statistics in the microscope. We demonstrate the effectiveness of the PSF approximation model and of our estimation method using both simulations and real experiments that were carried out on quantum dots. The principle of our PSF estimation approach is sufficiently flexible to be generalized non-spherical aberrations and other microscope modalities.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
    [Crossref] [PubMed]
  2. P. Theer, C. Mongis, and M. Knop, “PSFj: know your fluorescence microscope,” Nat. Methods 11, 981–982 (2014).
    [Crossref] [PubMed]
  3. P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23, 32–45 (2006).
    [Crossref]
  4. D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
    [Crossref] [PubMed]
  5. J. Li, F. Luisier, and T. Blu, “PURE-LET deconvolution of 3D fluorescence microscopy images,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2017), pp. 723–727.
  6. W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).
    [Crossref]
  7. J. W. Shaevitz and D. A. Fletcher, “Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function,” J. Opt. Soc. Am. A 24, 2622–2627 (2007).
    [Crossref]
  8. S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 9, 154–166 (1992).
    [Crossref] [PubMed]
  9. M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Cambridge University, 1999).
    [Crossref]
  10. P. Török and P. Varga, “Electromagnetic diffraction of light focused through a stratified medium,” Appl. Opt. 36, 2305–2312 (1997).
    [Crossref] [PubMed]
  11. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” P. Roy. Soc. Lond. A Mat. 253, 358–379 (1959).
    [Crossref]
  12. A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11, 267–279 (2014).
    [Crossref] [PubMed]
  13. D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
    [Crossref] [PubMed]
  14. Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .
  15. H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
    [Crossref] [PubMed]
  16. L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
    [Crossref] [PubMed]
  17. E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J. W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A 24, 1580–1600 (2007).
    [Crossref]
  18. T. Kenig, Z. Kam, and A. Feuer, “Blind image deconvolution using machine learning for three-dimensional microscopy,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2191–2204 (2010).
    [Crossref] [PubMed]
  19. M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.
  20. J. Markham and J.-A. Conchello, “Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur,” J. Opt. Soc. Am. A 16, 2377–2391 (1999).
    [Crossref]
  21. P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for thin-layered confocal imaging,” Appl. Opt. 48, 4437–4448 (2009).
    [Crossref] [PubMed]
  22. F. Soulez, L. Denis, Y. Tourneur, and É. Thiébaut, “Blind deconvolution of 3D data in wide field fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2012), pp. 1735–1738.
  23. F. Xue and T. Blu, “A novel SURE-based criterion for parametric PSF estimation,” IEEE Trans. Image Process. 24, 595–607 (2015).
    [Crossref]
  24. J. Li, F. Xue, and T. Blu, “Gaussian blur estimation for photon-limited images,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2017), pp. 495–499.
  25. F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process. 20, 696–708 (2011).
    [Crossref]
  26. Y. Hiraoka, J. W. Sedat, and D. A. Agard, “Determination of three-dimensional imaging properties of a light microscope system. partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
    [Crossref] [PubMed]
  27. C. Preza and J.-A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
    [Crossref]
  28. J. Kim, S. An, S. Ahn, and B. Kim, “Depth-variant deconvolution of 3D widefield fluorescence microscopy using the penalized maximum likelihood estimation method,” Opt. Express 21, 27668–27681 (2013).
    [Crossref]
  29. F. Aguet, D. Van De Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005).
    [Crossref] [PubMed]
  30. H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249, 13–25 (2013).
    [Crossref]
  31. S. Liu, E. B. Kromann, W. D. Krueger, J. Bewersdorf, and K. A. Lidke, “Three dimensional single molecule localization using a phase retrieved pupil function,” Opt. Express 21, 29462–29487 (2013).
    [Crossref]
  32. J. Huang, M. Sun, K. Gumpper, Y. Chi, and J. Ma, “3D multifocus astigmatism and compressed sensing (3D MACS) based superresolution reconstruction,” Biomed. Opt. Express 6, 902–917 (2015).
    [Crossref] [PubMed]
  33. M. Štefko, B. Ottino, K. M. Douglass, and S. Manley, “Design principles for autonomous illumination control in localization microscopy,” bioRxiv 295519; doi: https://doi.org/10.1101/295519 .
  34. J. Li, F. Xue, and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy,” J. Opt. Soc. Am. A 34, 1029–1034 (2017).
    [Crossref]
  35. C. Smith, M. Huisman, M. Siemons, D. Grünwald, and S. Stallinga, “Simultaneous measurement of emission color and 3d position of single molecules,” Opt. Express 24, 4996–5013 (2016).
    [Crossref] [PubMed]
  36. O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
    [Crossref]
  37. F. Aguet, “Super-resolution fluorescence microscopy based on physical models,” Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne (2009).
  38. M. Arigovindan, J. Shaevitz, J. McGowan, J. W. Sedat, and D. A. Agard, “A parallel product-convolution approach for representing depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt. Express 18, 6461–6476 (2010).
    [Crossref] [PubMed]
  39. B. Kim and T. Naemura, “Blind depth-variant deconvolution of 3D data in wide-field fluorescence microscopy,” Sci. Rep. 5, 9894 (2015).
    [Crossref] [PubMed]
  40. N. Patwary and C. Preza, “Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions,” Biomed. Opt. Express 6, 3826–3841 (2015).
    [Crossref] [PubMed]
  41. C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
    [Crossref]
  42. J. Li, F. Luisier, and T. Blu, “PURE-LET Image Deconvolution,” IEEE Trans. Image Process. 27, 92–105 (2018).
    [Crossref]
  43. J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
    [Crossref]
  44. J. Li, F. Xue, and T. Blu, “Accurate 3D PSF estimation from a wide-field microscopy image,” in Proceedings of IEEE International Symposium on Biomedical Imaging, (IEEE, 2018), pp. 501–504.
  45. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46, 1819–1829 (2007).
    [Crossref] [PubMed]
  46. S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
    [Crossref]
  47. S. Dmitrieff and F. Nédélec, “ConfocalGN: A minimalistic confocal image generator,” SoftwareX 6, 243–247 (2017).
    [Crossref]
  48. D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).
  49. J.-S. Lee, T.-L. E. Wee, and C. M. Brown, “Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging,” J. Biomol. Tech. 25, 31 (2014).
    [Crossref] [PubMed]
  50. 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]

2018 (2)

2017 (4)

J. Li, F. Xue, and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy,” J. Opt. Soc. Am. A 34, 1029–1034 (2017).
[Crossref]

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[Crossref] [PubMed]

S. Dmitrieff and F. Nédélec, “ConfocalGN: A minimalistic confocal image generator,” SoftwareX 6, 243–247 (2017).
[Crossref]

2016 (1)

2015 (5)

B. Kim and T. Naemura, “Blind depth-variant deconvolution of 3D data in wide-field fluorescence microscopy,” Sci. Rep. 5, 9894 (2015).
[Crossref] [PubMed]

J. Huang, M. Sun, K. Gumpper, Y. Chi, and J. Ma, “3D multifocus astigmatism and compressed sensing (3D MACS) based superresolution reconstruction,” Biomed. Opt. Express 6, 902–917 (2015).
[Crossref] [PubMed]

N. Patwary and C. Preza, “Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions,” Biomed. Opt. Express 6, 3826–3841 (2015).
[Crossref] [PubMed]

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

F. Xue and T. Blu, “A novel SURE-based criterion for parametric PSF estimation,” IEEE Trans. Image Process. 24, 595–607 (2015).
[Crossref]

2014 (4)

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
[Crossref] [PubMed]

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

P. Theer, C. Mongis, and M. Knop, “PSFj: know your fluorescence microscope,” Nat. Methods 11, 981–982 (2014).
[Crossref] [PubMed]

J.-S. Lee, T.-L. E. Wee, and C. M. Brown, “Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging,” J. Biomol. Tech. 25, 31 (2014).
[Crossref] [PubMed]

2013 (3)

2011 (2)

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process. 20, 696–708 (2011).
[Crossref]

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

2010 (3)

T. Kenig, Z. Kam, and A. Feuer, “Blind image deconvolution using machine learning for three-dimensional microscopy,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2191–2204 (2010).
[Crossref] [PubMed]

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

M. Arigovindan, J. Shaevitz, J. McGowan, J. W. Sedat, and D. A. Agard, “A parallel product-convolution approach for representing depth varying point spread functions in 3D widefield microscopy based on principal component analysis,” Opt. Express 18, 6461–6476 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (3)

2006 (2)

C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
[Crossref]

P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23, 32–45 (2006).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
[Crossref]

2001 (1)

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).
[Crossref]

1999 (1)

1997 (1)

1995 (1)

D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).

1993 (1)

S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

1992 (1)

1990 (1)

Y. Hiraoka, J. W. Sedat, and D. A. Agard, “Determination of three-dimensional imaging properties of a light microscope system. partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[Crossref] [PubMed]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” P. Roy. Soc. Lond. A Mat. 253, 358–379 (1959).
[Crossref]

Agard, D. A.

Aguet, F.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249, 13–25 (2013).
[Crossref]

C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
[Crossref]

F. Aguet, D. Van De Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005).
[Crossref] [PubMed]

F. Aguet, “Super-resolution fluorescence microscopy based on physical models,” Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne (2009).

Ahn, S.

Algorithm, R. L.

D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).

An, S.

Arigovindan, M.

Babcock, H. P.

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[Crossref] [PubMed]

Betzig, E.

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
[Crossref] [PubMed]

Bewersdorf, J.

Blanc-Féraud, L.

Blu, T.

J. Li, F. Luisier, and T. Blu, “PURE-LET Image Deconvolution,” IEEE Trans. Image Process. 27, 92–105 (2018).
[Crossref]

J. Li, F. Xue, and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy,” J. Opt. Soc. Am. A 34, 1029–1034 (2017).
[Crossref]

F. Xue and T. Blu, “A novel SURE-based criterion for parametric PSF estimation,” IEEE Trans. Image Process. 24, 595–607 (2015).
[Crossref]

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process. 20, 696–708 (2011).
[Crossref]

J. Li, F. Xue, and T. Blu, “Accurate 3D PSF estimation from a wide-field microscopy image,” in Proceedings of IEEE International Symposium on Biomedical Imaging, (IEEE, 2018), pp. 501–504.

J. Li, F. Xue, and T. Blu, “Gaussian blur estimation for photon-limited images,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2017), pp. 495–499.

J. Li, F. Luisier, and T. Blu, “PURE-LET deconvolution of 3D fluorescence microscopy images,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2017), pp. 723–727.

Born, M.

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Cambridge University, 1999).
[Crossref]

Boulanger, J.

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

Bouthemy, P.

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

Brinicombe, A. M.

D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).

Brown, C. M.

J.-S. Lee, T.-L. E. Wee, and C. M. Brown, “Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging,” J. Biomol. Tech. 25, 31 (2014).
[Crossref] [PubMed]

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Brox, T.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Chen, B.-C.

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
[Crossref] [PubMed]

Chi, Y.

Cole, R. W.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Conchello, J.-A.

Cremer, C.

S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Denis, L.

F. Soulez, L. Denis, Y. Tourneur, and É. Thiébaut, “Blind deconvolution of 3D data in wide field fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2012), pp. 1735–1738.

Dmitrieff, S.

S. Dmitrieff and F. Nédélec, “ConfocalGN: A minimalistic confocal image generator,” SoftwareX 6, 243–247 (2017).
[Crossref]

Donati, L.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Douglass, K. M.

M. Štefko, B. Ottino, K. M. Douglass, and S. Manley, “Design principles for autonomous illumination control in localization microscopy,” bioRxiv 295519; doi: https://doi.org/10.1101/295519 .

Elbau, P.

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

Ellenberg, J.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Feuer, A.

T. Kenig, Z. Kam, and A. Feuer, “Blind image deconvolution using machine learning for three-dimensional microscopy,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2191–2204 (2010).
[Crossref] [PubMed]

Fish, D. A.

D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).

Fletcher, D. A.

Fortun, D.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Gao, L.

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
[Crossref] [PubMed]

Gibson, S. F.

Grünwald, D.

Guiet, R.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Gumpper, K.

Haase, S.

Haeberlé, O.

O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
[Crossref]

Hell, S.

S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Heun, P.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Hiraoka, Y.

Y. Hiraoka, J. W. Sedat, and D. A. Agard, “Determination of three-dimensional imaging properties of a light microscope system. partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[Crossref] [PubMed]

Hoess, P.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Hom, E. F. Y.

Huang, J.

Huisman, M.

Hulleman, C.

Jinadasa, T.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Kam, Z.

T. Kenig, Z. Kam, and A. Feuer, “Blind image deconvolution using machine learning for three-dimensional microscopy,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2191–2204 (2010).
[Crossref] [PubMed]

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for thin-layered confocal imaging,” Appl. Opt. 48, 4437–4448 (2009).
[Crossref] [PubMed]

Kenig, T.

T. Kenig, Z. Kam, and A. Feuer, “Blind image deconvolution using machine learning for three-dimensional microscopy,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2191–2204 (2010).
[Crossref] [PubMed]

Kervrann, C.

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

Keuper, M.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Kim, B.

Kim, J.

Kirshner, H.

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249, 13–25 (2013).
[Crossref]

Knop, M.

P. Theer, C. Mongis, and M. Knop, “PSFj: know your fluorescence microscope,” Nat. Methods 11, 981–982 (2014).
[Crossref] [PubMed]

Kromann, E. B.

Krueger, W. D.

Lanni, F.

Lee, J.-S.

J.-S. Lee, T.-L. E. Wee, and C. M. Brown, “Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging,” J. Biomol. Tech. 25, 31 (2014).
[Crossref] [PubMed]

Lee, T. K.

Li, J.

J. Li, F. Luisier, and T. Blu, “PURE-LET Image Deconvolution,” IEEE Trans. Image Process. 27, 92–105 (2018).
[Crossref]

J. Li, F. Xue, and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy,” J. Opt. Soc. Am. A 34, 1029–1034 (2017).
[Crossref]

J. Li, F. Xue, and T. Blu, “Accurate 3D PSF estimation from a wide-field microscopy image,” in Proceedings of IEEE International Symposium on Biomedical Imaging, (IEEE, 2018), pp. 501–504.

J. Li, F. Xue, and T. Blu, “Gaussian blur estimation for photon-limited images,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2017), pp. 495–499.

J. Li, F. Luisier, and T. Blu, “PURE-LET deconvolution of 3D fluorescence microscopy images,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2017), pp. 723–727.

Li, Y.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Lidke, K. A.

Liu, S.

Luisier, F.

J. Li, F. Luisier, and T. Blu, “PURE-LET Image Deconvolution,” IEEE Trans. Image Process. 27, 92–105 (2018).
[Crossref]

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process. 20, 696–708 (2011).
[Crossref]

J. Li, F. Luisier, and T. Blu, “PURE-LET deconvolution of 3D fluorescence microscopy images,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2017), pp. 723–727.

Ma, J.

Manley, S.

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

M. Štefko, B. Ottino, K. M. Douglass, and S. Manley, “Design principles for autonomous illumination control in localization microscopy,” bioRxiv 295519; doi: https://doi.org/10.1101/295519 .

Marchis, F.

Markham, J.

Matti, U.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

McGowan, J.

Min, J.

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

Mongis, C.

P. Theer, C. Mongis, and M. Knop, “PSFj: know your fluorescence microscope,” Nat. Methods 11, 981–982 (2014).
[Crossref] [PubMed]

Mund, M.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Naemura, T.

B. Kim and T. Naemura, “Blind depth-variant deconvolution of 3D data in wide-field fluorescence microscopy,” Sci. Rep. 5, 9894 (2015).
[Crossref] [PubMed]

Nédélec, F.

S. Dmitrieff and F. Nédélec, “ConfocalGN: A minimalistic confocal image generator,” SoftwareX 6, 243–247 (2017).
[Crossref]

Nehorai, A.

P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23, 32–45 (2006).
[Crossref]

Nijmeijer, B.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Olivo-Marin, J.-C.

Ottino, B.

M. Štefko, B. Ottino, K. M. Douglass, and S. Manley, “Design principles for autonomous illumination control in localization microscopy,” bioRxiv 295519; doi: https://doi.org/10.1101/295519 .

Padeken, J.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Pankajakshan, P.

Patwary, N.

Pengo, T.

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

Pike, E. R.

D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).

Preza, C.

Reiner, G.

S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” P. Roy. Soc. Lond. A Mat. 253, 358–379 (1959).
[Crossref]

Ries, J.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Ronneberger, O.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Sabinina, V. J.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Sage, D.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249, 13–25 (2013).
[Crossref]

Salamero, J.

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

Sarder, P.

P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23, 32–45 (2006).
[Crossref]

Schaefer, L. H.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).
[Crossref]

Schmidt, T.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Schmit, G.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Schoen, I.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

Sedat, J. W.

Seitz, A.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Shaevitz, J.

Shaevitz, J. W.

Shao, L.

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
[Crossref] [PubMed]

Sibarita, J.-B.

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

Siemons, M.

Small, A.

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

Smith, C.

Soulez, F.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

F. Soulez, L. Denis, Y. Tourneur, and É. Thiébaut, “Blind deconvolution of 3D data in wide field fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2012), pp. 1735–1738.

Stahlheber, S.

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

Stallinga, S.

Štefko, M.

M. Štefko, B. Ottino, K. M. Douglass, and S. Manley, “Design principles for autonomous illumination control in localization microscopy,” bioRxiv 295519; doi: https://doi.org/10.1101/295519 .

Stelzer, E. H.

S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

Stuurman, N.

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

Sun, M.

Swedlow, J. R.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).
[Crossref]

Temerinac-Ott, M.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Theer, P.

P. Theer, C. Mongis, and M. Knop, “PSFj: know your fluorescence microscope,” Nat. Methods 11, 981–982 (2014).
[Crossref] [PubMed]

Thiébaut, É.

F. Soulez, L. Denis, Y. Tourneur, and É. Thiébaut, “Blind deconvolution of 3D data in wide field fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2012), pp. 1735–1738.

Thorsen, R.

Török, P.

Tourneur, Y.

F. Soulez, L. Denis, Y. Tourneur, and É. Thiébaut, “Blind deconvolution of 3D data in wide field fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2012), pp. 1735–1738.

Unser, M.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249, 13–25 (2013).
[Crossref]

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process. 20, 696–708 (2011).
[Crossref]

C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
[Crossref]

F. Aguet, D. Van De Ville, and M. Unser, “A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles,” Opt. Express 13, 10503–10522 (2005).
[Crossref] [PubMed]

Van De Ville, D.

Varga, P.

Vonesch, C.

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
[Crossref]

Vonesch, J.-L.

C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
[Crossref]

Walker, J. G.

D. A. Fish, A. M. Brinicombe, E. R. Pike, J. G. Walker, and R. L. Algorithm, “Blind deconvolution by means of the Richardson-Lucy algorithm,” Appl. Opt. 12, 58–65 (1995).

Wallace, W.

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).
[Crossref]

Wee, T.-L. E.

J.-S. Lee, T.-L. E. Wee, and C. M. Brown, “Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging,” J. Biomol. Tech. 25, 31 (2014).
[Crossref] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” P. Roy. Soc. Lond. A Mat. 253, 358–379 (1959).
[Crossref]

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Cambridge University, 1999).
[Crossref]

Xue, F.

J. Li, F. Xue, and T. Blu, “Fast and accurate three-dimensional point spread function computation for fluorescence microscopy,” J. Opt. Soc. Am. A 34, 1029–1034 (2017).
[Crossref]

F. Xue and T. Blu, “A novel SURE-based criterion for parametric PSF estimation,” IEEE Trans. Image Process. 24, 595–607 (2015).
[Crossref]

J. Li, F. Xue, and T. Blu, “Gaussian blur estimation for photon-limited images,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2017), pp. 495–499.

J. Li, F. Xue, and T. Blu, “Accurate 3D PSF estimation from a wide-field microscopy image,” in Proceedings of IEEE International Symposium on Biomedical Imaging, (IEEE, 2018), pp. 501–504.

Zerubia, J.

Zhang, B.

Zhuang, X.

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[Crossref] [PubMed]

Appl. Opt. (4)

Biomed. Opt. Express (2)

Biophys. J. (1)

Y. Hiraoka, J. W. Sedat, and D. A. Agard, “Determination of three-dimensional imaging properties of a light microscope system. partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[Crossref] [PubMed]

Biotechniques (1)

W. Wallace, L. H. Schaefer, and J. R. Swedlow, “A workingperson’s guide to deconvolution in light microscopy,” Biotechniques 31, 1076–1097 (2001).
[Crossref]

IEEE Signal Process. Mag. (2)

P. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Signal Process. Mag. 23, 32–45 (2006).
[Crossref]

C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, “The colored revolution of bioimaging,” IEEE Signal Process. Mag. 23, 20–31 (2006).
[Crossref]

IEEE Trans. Image Process. (3)

J. Li, F. Luisier, and T. Blu, “PURE-LET Image Deconvolution,” IEEE Trans. Image Process. 27, 92–105 (2018).
[Crossref]

F. Luisier, T. Blu, and M. Unser, “Image denoising in mixed Poisson-Gaussian noise,” IEEE Trans. Image Process. 20, 696–708 (2011).
[Crossref]

F. Xue and T. Blu, “A novel SURE-based criterion for parametric PSF estimation,” IEEE Trans. Image Process. 24, 595–607 (2015).
[Crossref]

IEEE Trans. Med. Imag. (1)

J. Boulanger, C. Kervrann, P. Bouthemy, P. Elbau, J.-B. Sibarita, and J. Salamero, “Patch-based nonlocal functional for denoising fluorescence microscopy image sequences,” IEEE Trans. Med. Imag. 29, 442–454 (2010).
[Crossref]

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

T. Kenig, Z. Kam, and A. Feuer, “Blind image deconvolution using machine learning for three-dimensional microscopy,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 2191–2204 (2010).
[Crossref] [PubMed]

J. Biomol. Tech. (1)

J.-S. Lee, T.-L. E. Wee, and C. M. Brown, “Calibration of wide-field deconvolution microscopy for quantitative fluorescence imaging,” J. Biomol. Tech. 25, 31 (2014).
[Crossref] [PubMed]

J. Microsc. (2)

S. Hell, G. Reiner, C. Cremer, and E. H. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[Crossref]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc. 249, 13–25 (2013).
[Crossref]

J. Opt. Soc. Am. A (6)

Methods (1)

D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, and M. Unser, “Deconvolutionlab2: An open-source software for deconvolution microscopy,” Methods 115, 28–41 (2017).
[Crossref] [PubMed]

Nat. Methods (3)

P. Theer, C. Mongis, and M. Knop, “PSFj: know your fluorescence microscope,” Nat. Methods 11, 981–982 (2014).
[Crossref] [PubMed]

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

D. Sage, H. Kirshner, T. Pengo, N. Stuurman, J. Min, S. Manley, and M. Unser, “Quantitative evaluation of software packages for single-molecule localization microscopy,” Nat. Methods 12, 717–724 (2015).
[Crossref] [PubMed]

Nat. Protoc. (2)

L. Gao, L. Shao, B.-C. Chen, and E. Betzig, “3D live fluorescence imaging of cellular dynamics using Bessel beam plane illumination microscopy,” Nat. Protoc. 9, 1083–1101 (2014).
[Crossref] [PubMed]

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Opt. Commun. (1)

O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
[Crossref]

Opt. Express (6)

P. Roy. Soc. Lond. A Mat. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. structure of the image field in an aplanatic system,” P. Roy. Soc. Lond. A Mat. 253, 358–379 (1959).
[Crossref]

Sci. Rep. (2)

H. P. Babcock and X. Zhuang, “Analyzing single molecule localization microscopy data using cubic splines,” Sci. Rep. 7, 552 (2017).
[Crossref] [PubMed]

B. Kim and T. Naemura, “Blind depth-variant deconvolution of 3D data in wide-field fluorescence microscopy,” Sci. Rep. 5, 9894 (2015).
[Crossref] [PubMed]

SoftwareX (1)

S. Dmitrieff and F. Nédélec, “ConfocalGN: A minimalistic confocal image generator,” SoftwareX 6, 243–247 (2017).
[Crossref]

Other (9)

F. Aguet, “Super-resolution fluorescence microscopy based on physical models,” Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne (2009).

J. Li, F. Xue, and T. Blu, “Accurate 3D PSF estimation from a wide-field microscopy image,” in Proceedings of IEEE International Symposium on Biomedical Imaging, (IEEE, 2018), pp. 501–504.

M. Keuper, T. Schmidt, M. Temerinac-Ott, J. Padeken, P. Heun, O. Ronneberger, and T. Brox, “Blind deconvolution of widefield fluorescence microscopic data by regularization of the optical transfer function (OTF),” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2013), pp. 2179–2186.

Y. Li, M. Mund, P. Hoess, U. Matti, B. Nijmeijer, V. J. Sabinina, J. Ellenberg, I. Schoen, and J. Ries, “Fast, robust and precise 3d localization for arbitrary point spread functions,” bioRxiv 172643; doi: https://doi.org/10.1101/172643 .

J. Li, F. Luisier, and T. Blu, “PURE-LET deconvolution of 3D fluorescence microscopy images,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2017), pp. 723–727.

M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Cambridge University, 1999).
[Crossref]

J. Li, F. Xue, and T. Blu, “Gaussian blur estimation for photon-limited images,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2017), pp. 495–499.

M. Štefko, B. Ottino, K. M. Douglass, and S. Manley, “Design principles for autonomous illumination control in localization microscopy,” bioRxiv 295519; doi: https://doi.org/10.1101/295519 .

F. Soulez, L. Denis, Y. Tourneur, and É. Thiébaut, “Blind deconvolution of 3D data in wide field fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2012), pp. 1735–1738.

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Figures (8)

Fig. 1
Fig. 1 (a) Reliability of blur-PURE as an estimate of the blur-MSE: a typical example of the Bars image degraded by a PSF and various noise parameters (α = 0.02, σ2 ∈ [0, 25]). The values of the blur-PURE for various values of σ closely match those of the blur-MSE, which confirms that the blur-PURE is an accurate substitute to the blur-MSE in practice. 3D rendering of the blurred noisy image when σ2 = 16 is shown at the right bottom. See details of the experimental setting in Section 5.1. (b) and (c) show the z and x profiles of band-indicators (true frequency responses of UH0,μ and approximated Uapp), respectively.
Fig. 2
Fig. 2 The scheme diagram of the proposed PSF estimation approach. With the help of the 4-basis PSF approximation model, the band-indicator Uapp is firstly estimated by minimizing the blur-PURE in Theorem 1, and then the estimated PSF HEst is obtained by an iterative optimization algorithm in Eq. (4).
Fig. 3
Fig. 3 (a) Determination of the optimal η in the sense of minimal RSE: typical examples of three different focus positions zp = 0, 500 nm and 1000 nm. Other settings: λ = 395 nm, NA = 1.4, ns = 1.38, ni = 1.515. The estimated value is η = 0, 529.10 nm and 1025.07 nm, respectively. (b) The scatter plot between the true zp and the estimated η. The ideal relation is indicated by solid red line.
Fig. 4
Fig. 4 Evaluation of the proposed approximation model on simulated PSFs. (a) Plot of the mean RSE between the theoretical and fitted PSFs over different wavelengths λ. (b) Axial intensity profile of typical PSFs (λ = 395nm, zp = 500 nm) generated by the complete Gibson-Lanni model (the black curve) and fitting (the dashed red curve). The focal shift can be observed. The fitted PSF closely matches the ground truth PSF (RSE = 0.48%). (c) xz section of the theoretical PSF. Note the non-symmetric pattern caused by the refractive index mismatch. The degraded PSFs in (d) and (f) are fitted by the proposed approximation model in Eq. (2) resulting in (e) and (g), respectively. Images have been cropped and rescaled for visualization purpose.
Fig. 5
Fig. 5 A practical example. The xy (a) and yz (b) sections of the experimental PSF. (c–d) The xy and yz sections of the fitted PSF by the proposed approximation model in Eq. (2). The focus indicator (parameter η) is estimated to be 1.855 μm. The mismatch between the refractive indices of the sample and immersion medium contributes to an axially asymmetric PSF. Scale bar: 0.5 μm.
Fig. 6
Fig. 6 Comparison results of PSF estimations in the high noise conditions (α = 0.2, σ = 0.02). (a) zp = 0 μm; (b) zp = 2 μm. Other settings: λ = 622 nm, NA = 1.4, ni = 1.33 and ns = 1.46. Locators (orange line) indicate the location of displayed sections (z = 0). Images have been cropped and rescaled for visualization purpose.
Fig. 7
Fig. 7 The PSF estimation results of experimental data from Qdots. (a–b) the xy and zy sections of the estimated PSF. (c) the z profile of the PSF estimated with our algorithm (described in Section 3), compared to the z profiles of the experimental and fitted PSFs (same conditions as in Fig. 5).
Fig. 8
Fig. 8 Deconvolution results of experimental Qdots data. (a) raw image (256 × 256 × 113 voxels); (b) and (c) restored images by the Richardson-Lucy algorithm and PURE-LET algorithm [5] with the measured PSF, respectively; (d) restored image by the blind-RL algorithm; (e) restored image by the EpiDEMIC plugin; (f) restored image by the PURE-LET algorithm with the PSF estimated by our approach (described in Section 3). Locators (yellow line) indicate the location of displayed sections (z = 0). Zoomed-in regions (×2) show the resolution improvement of our method in (f). Also note the significant reduction of out-of-focus blur in the xz plane. Scale bar: 1μm.

Tables (1)

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Table 1 RSE (%) comparison of the PSF estimation accuracy with other approaches under different scenarios. The results have been averaged over 5 random initializations.

Equations (8)

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f m ( ρ , z ; η , p , q ) = z p m 2 ρ 2 + η q m 2 ρ 2 ,
h app ( r ; c , η ) = m = 1 4 c m h m ( r ; η ) ,
h m ( r ; η ) = | A 0 min ( NA , p m , q m ) exp ( i K f m ( ρ , z ; η , p , q ) ) J 0 ( K r ρ ) ρ d ρ | 2 ,
Y = α 𝒫 ( H 0 X α ) + 𝒩 ( 0 , σ 2 I ) ,
1 N U Y 2 + 1 N Y 2 α N 1 T Y 2 N n = 1 N Y T U ( Y α e n ) + 2 σ 2 N Tr ( U ) σ 2 blur PURE 1 N U Y H 0 X 2 ,
H ( k ) = arg min H = m c m H m HW H ( k 1 ) U app 2 2 ,
W H ( k 1 ) = H ( k 1 ) + ( H ( k 1 ) ) T 2 ( ( H ( k 1 ) ) T H ( k 1 ) + μ P ) 1 ,
RSE ( h app , h 0 ) = h app , h 0 2 2 h 0 2 2 × 100 % ,

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