Conventional light microscopes have been used for centuries for the study of small length scales down to approximately 250 nm. Images from such a microscope are typically blurred and noisy, and the measurement error in such images can often be well approximated by Gaussian or Poisson noise. In the past, this approximation has been the focus of a multitude of deconvolution techniques in imaging. However, conventional microscopes have an intrinsic physical limit of resolution. Although this limit remained unchallenged for a century, it was broken for the first time in the 1990s with the advent of modern superresolution fluorescence microscopy techniques. Since then, superresolution fluorescence microscopy has become an indispensable tool for studying the structure and dynamics of living organisms. Current experimental advances go to the physical limits of imaging, where discrete quantum effects are predominant. Consequently, this technique is inherently of a non-Gaussian statistical nature, and we argue that recent technological progress also challenges the long-standing Poisson assumption. Thus, analysis and exploitation of the discrete physical mechanisms of fluorescent molecules and light, as well as their distributions in time and space, have become necessary to achieve the highest resolution possible. This article presents an overview of some physical principles underlying modern fluorescence microscopy techniques from a statistical modeling and analysis perspective. To this end, we develop a prototypical model for fluorophore dynamics and use it to discuss statistical methods for image deconvolution and more complicated image reconstruction and enhancement techniques. Several examples are discussed in more detail, including variational multiscale methods for confocal and stimulated emission depletion (STED) microscopy, drift correction for single marker switching (SMS) microscopy, and sparse estimation and background removal for superresolution by polarization angle demodulation (SPoD). We illustrate that such methods benefit from advances in large-scale computing, for example, from recent tools from convex optimization. We argue that in the future, even higher resolutions will require more detailed models that delve into sub-Poissonian statistics.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Abbe E. 1873. Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung. Archiv Mikrosk. 9:413–68 [Google Scholar]
  2. Abramovich F, Silverman BW. 1998. Wavelet decomposition approaches to statistical inverse problems. Biometrika 85:1115–29 [Google Scholar]
  3. Allen RD, David GB, Nomarski G. 1969. The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy. Z. Wiss. Mikrosk. Mikrosk. Tech. 69:193–221 [Google Scholar]
  4. Amos B, McConnell G, Wilson T. 2012. Confocal microscopy. Comprehensive Biophysics EH Egelman 3–23 Amsterdam: Elsevier [Google Scholar]
  5. Antoniadis A, Bigot J. 2006. Poisson inverse problems. Ann. Stat. 34:52132–58 [Google Scholar]
  6. Antoniadis A, Fan J. 2001. Regularization of wavelet approximations. J. Am. Stat. Assoc. 96:455939–67 [Google Scholar]
  7. Bühlmann P, Yu B. 2003. Boosting with the L2 loss: regression and classification. J. Am. Stat. Assoc. 98:462324–39 [Google Scholar]
  8. Babcock H, Sigal YM, Zhuang X. 2012. A high-density 3D localization algorithm for stochastic optical reconstruction microscopy. Opt. Nanosc. 1:11–10 [Google Scholar]
  9. Babcock HP, Moffitt JR, Cao Y, Zhuang X. 2013. Fast compressed sensing analysis for super-resolution imaging using L1-homotopy. Opt. Express 21:2328583–96 [Google Scholar]
  10. Baddeley D, Cannell MB, Soeller C. 2010. Visualization of localization microscopy data. Microsc. Microanal. 16:164–72 [Google Scholar]
  11. Bailey B, Farkas DL, Taylor DL, Lanni F. 1993. Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation. Nature 366:645044–48 [Google Scholar]
  12. Beck A, Teboulle M. 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2:1183–202 [Google Scholar]
  13. Bertero M, Boccacci P, Desiderá G, Vicidomini G. 2009. Image deblurring with Poisson data: from cells to galaxies. Inverse Probl. 25:12123006 [Google Scholar]
  14. Betzig E, Patterson GH, Sougrat R, Lindwasser OW, Olenych S. et al. 2006. Imaging intracellular fluorescent proteins at nanometer resolution. Science 313:57931642–45 [Google Scholar]
  15. Bigot J, Gadat S, Klein T, Marteau C. 2013. Intensity estimation of non-homogeneous Poisson processes from shifted trajectories. Electron. J. Stat. 7:2013881–931 [Google Scholar]
  16. Bissantz N, Dümbgen L, Munk A, Stratmann B. 2009. Convergence analysis of generalized iteratively reweighted least squares algorithms on convex function spaces. SIAM J. Optim. 19:41828–45 [Google Scholar]
  17. Bissantz N, Hohage T, Munk A, Ruymgaart F. 2007. Convergence rates of general regularization methods for statistical inverse problems and applications. SIAM J. Numer. Anal. 45:62610–36 [Google Scholar]
  18. Bissantz N, Mair B, Munk A. 2008. A statistical stopping rule for MLEM reconstructions in PET. IEEE Nucl. Sci. Symp. Conf. Rec. 2008. Dresden, Ger., Oct. 19–254198–200 doi: 10.1109/NSSMIC.2008.4774207
  19. Biteen JS, Thompson MA, Tselentis NK, Bowman GR, Shapiro L, Moerner WE. 2008. Super-resolution imaging in live Caulobacter crescentus cells using photoswitchable EYFP. Nat. Methods 5:11947–49 [Google Scholar]
  20. Born M, Wolf E. 1999. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light Cambridge, UK: Cambridge Univ. Press, 7th ed..
  21. Boysen L, Bruns S, Munk A. 2009. Jump estimation in inverse regression. Electron. J. Stat. 3:1322–59 [Google Scholar]
  22. Brown LD, Cai TT, Zhou HH. 2010. Nonparametric regression in exponential families. Ann. Stat. 38:42005–46 [Google Scholar]
  23. Bugiel I, König K, Wabnitz H. 1989. Investigation of cells by fluorescence laser scanning microscopy with subnanosecond time resolution. Lasers Life Sci. 3:47–53 [Google Scholar]
  24. Candès EJ, Donoho DL. 2002. Recovering edges in ill-posed inverse problems: optimality of curvelet frames. Ann. Stat. 30:3784–842 [Google Scholar]
  25. Candès EJ, Guo F. 2002. New multiscale transforms, minimum total variation synthesis: applications to edge-preserving image reconstruction. Signal Process. 82:111519–43 [Google Scholar]
  26. Candès EJ, Romberg JK, Tao T. 2006. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59:81207–23 [Google Scholar]
  27. Candes EJ, Tao T. 2007. The Dantzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35:62313–51 [Google Scholar]
  28. Cavalier L, Koo JY. 2002. Poisson intensity estimation for tomographic data using a wavelet shrinkage approach. IEEE Trans. Inform. Theory 48:2794–802 [Google Scholar]
  29. Chambolle A, Pock T. 2011. A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40:1120–45 [Google Scholar]
  30. Chesneau C, Fadili J, Starck J-L. 2010. Stein block thresholding for image denoising. Appl. Comput. Harmon. Anal. 28:167–88 [Google Scholar]
  31. Coifman RR, Sowa A. 2000. Combining the calculus of variations and wavelets for image enhancement. Appl. Comput. Harmon. Anal. 9:11–18 [Google Scholar]
  32. Cox S, Rosten E, Monypenny J, Jovanovic-Talisman T, Burnette DT. et al. 2012. Bayesian localization microscopy reveals nanoscale podosome dynamics. Nat. Methods 9:2195–200 [Google Scholar]
  33. Dümbgen L, Piterbarg VI, Zholud D. 2006. On the limit distribution of multiscale test statistics for nonparametric curve estimation. Math. Methods Stat. 15:120–25 [Google Scholar]
  34. Dümbgen L, Spokoiny VG. 2001. Multiscale testing of qualitative hypotheses. Ann. Stat. 29:1124–52 [Google Scholar]
  35. Dümbgen L, Walther G. 2008. Multiscale inference about a density. Ann. Stat. 36:41758–85 [Google Scholar]
  36. Davies PL, Kovac A. 2001. Local extremes, runs, strings and multiresolution. Ann. Stat. 29:11–48 [Google Scholar]
  37. Dertinger T, Colyer R, Iyer G, Weiss S, Enderlein J. 2009. Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). PNAS 106:5222287–92 [Google Scholar]
  38. Dertinger T, Colyer R, Vogel R, Enderlein J, Weiss S. 2010. Achieving increased resolution and more pixels with superresolution optical fluctuation imaging (SOFI). Opt. Express 18:1818875–85 [Google Scholar]
  39. Deschout H, Zanacchi FC, Mlodzianoski M, Diaspro A, Bewersdorf J. et al. 2014. Precisely and accurately localizing single emitters in fluorescence microscopy. Nat. Methods 11:3253–66 [Google Scholar]
  40. Dinh QT, Kyrillidis A, Cevher V. 2014. An inexact proximal path-following algorithm for constrained convex minimization. arXiv:1311.1756 [math.OC]
  41. Dong Y, Hintermüller M, Rincon-Camacho MM. 2011. Automated regularization parameter selection in multi-scale total variation models for image restoration. J. Math. Imaging Vis. 40:182–104 [Google Scholar]
  42. Donoho DL. 1995a. De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41:3613–27 [Google Scholar]
  43. Donoho DL. 1995b. Nonlinear solution of linear inverse problems by wavelet–vaguelette decomposition. Appl. Comput. Harmon. Anal. 2:2101–26 [Google Scholar]
  44. Egner A, Geisler C, von Middendorff C, Bock H, Wenzel D. et al. 2007. Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters. Biophys. J. 93:93285–90 [Google Scholar]
  45. Egner A, Hell SW. 2005. Fluorescence microscopy with super-resolved optical sections. Trends Cell Biol. 15:4207–15 [Google Scholar]
  46. Eisenberg D, Marcotte EM, Xenarios I, Yeates TO. 2000. Protein function in the post-genomic era. Nature 405:6788823–26 [Google Scholar]
  47. Enderlein J, Boehmer M. 2003. Influence of interface dipole interactions on the effciency of fluorescence light collection near surfaces. Opt. Lett. 28:11941–43 [Google Scholar]
  48. Fan J. 1991. On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Stat. 19:31257–72 [Google Scholar]
  49. Fölling J, Belov V, Kunetsky R, Medda R, Schönle A. et al. 2007. Photochromic rhodamines provide nanoscopy with optical sectioning. Angew. Chem. Int. Ed. 46:336266–70 [Google Scholar]
  50. Fölling J, Bossi M, Bock H, Medda R, Wfoeliurm CA. et al. 2008. Fluorescence nanoscopy by ground-state depletion and single-molecule return. Nat. Methods 5:11943–45 [Google Scholar]
  51. Fornasier M, Rauhut H, Ward R. 2011. Low-rank matrix recovery via iteratively reweighted least squares minimization. SIAM J. Optim. 21:41614–40 [Google Scholar]
  52. Freimann R, Pentz S, Horler H. 1997. Development of a standing-wave fluorescence microscope with high nodal plane flatness. J. Microsc. 187:3193–200 [Google Scholar]
  53. Frick K, Marnitz P, Munk A. 2012a. Shape-constrained regularization by statistical multiresolution for inverse problems: asymptotic analysis. Inverse Probl. 28:6065006 [Google Scholar]
  54. Frick K, Marnitz P, Munk A. 2012b. Statistical multiresolution Dantzig estimation in imaging: fundamental concepts and algorithmic framework. Electron. J. Stat. 6:231–68 [Google Scholar]
  55. Frick K, Marnitz P, Munk A. 2013. Statistical multiresolution estimation for variational imaging: with an application in Poisson-biophotonics. J. Math. Imaging Vis. 46:3370–87 [Google Scholar]
  56. Frick K, Munk A, Sieling H. 2014. Multiscale change point inference. J. R. Stat. Soc. B 76:3495–580 [Google Scholar]
  57. Frick S, Hohage T, Munk A. 2014. Asymptotic laws for change point estimation in inverse regression. Stat. Sin. 24:555–75 [Google Scholar]
  58. Geisler C, Hotz T, Schánle A, Hell SW, Munk A, Egner A. 2012. Drift estimation for single marker switching based imaging schemes. Opt. Express 20:77274–89 [Google Scholar]
  59. Goldenshluger A, Tsybakov A, Zeevi A. 2006. Optimal change-point estimation from indirect observations. Ann. Stat. 34:1350–72 [Google Scholar]
  60. Goodman JW. 1996. Introduction to Fourier Optics New York: McGraw-Hill, 2nd ed..
  61. Gould TJ, Hess ST, Bewersdorf J. 2012. Optical nanoscopy: from acquisition to analysis. Annu. Rev. Biomed. Eng. 14:231–54 [Google Scholar]
  62. Grasmair M, Haltmeier M, Scherzer O. 2011. The residual method for regularizing ill-posed problems. Appl. Math. Comput. 218:62693–710 [Google Scholar]
  63. Gustafsson MGL. 2000. Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy. J. Microsc. 198:282–87 [Google Scholar]
  64. Gustafsson MGL. 2005. Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution. PNAS 102:3713081–86 [Google Scholar]
  65. Gustafsson MGL, Agard DA, Sedat JW. 1995. Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective lenses. Proc. SPIE2412147–56
  66. Gustafsson MGL, Shao L, Carlton PM, Wang CJR, Golubovskaya IN. et al. 2008. Three-dimensional resolution doubling in wide-field fluorescence microscopy by structured illumination. Biophys. J. 94:124957–70 [Google Scholar]
  67. Hafi N, Grunwald M, van den Heuvel LS, Aspelmeier T, Chen J-H. et al. 2014. Fluorescence nanoscopy by polarization modulation and polarization angle narrowing. Nat. Methods 11:4579–84 [Google Scholar]
  68. Harke B, Keller J, Ullal CK, Westphal V, Schönle A, Hell SW. 2008. Resolution scaling in STED microscopy. Opt. Express 16:64154–62 [Google Scholar]
  69. Harremoës P, Johnson O, Kontoyiannis I. 2010. Thinning, entropy, and the law of thin numbers. IEEE Trans. Inf. Theory 56:94228–44 [Google Scholar]
  70. Hartmann A, Huckemann S, Dannemann J, Laitenberger O, Geisler C. et al. 2014. Drift estimation in sparse sequential dynamic imaging: with application to nanoscale fluorescence microscopy. arXiv:1403.1389 [stat.ME]
  71. Hashorva E, Kabluchko Z, Wübker A. 2012. Extremes of independent chi-square random vectors. Extremes 15:135–42 [Google Scholar]
  72. Hebert T, Leahy R, Singh M. 1988. Fast MLE for SPECT using an intermediate polar representation and a stopping criterion. IEEE Trans. Nucl. Sci. 35:1615–19 [Google Scholar]
  73. Heilemann M, Dedecker P, Hofkens J, Sauer M. 2009. Photoswitches: key molecules for subdiffraction-resolution fluorescence imaging and molecular quantification. Laser Photon. Rev. 3:1–2180–202 [Google Scholar]
  74. Heilemann M, van de Linde S, Schüttpelz M, Kasper R, Seefeldt B. et al. 2008. Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes. Angew. Chem. Int. Ed. 47:336172–76 [Google Scholar]
  75. Heilemann M. 2010. Fluorescence microscopy beyond the diffraction limit. J. Biotechnol. 149:4243–51 [Google Scholar]
  76. Heintzmann R, Jovin TM, Cremer C. 2002. Saturated patterned excitation microscopy—a concept for optical resolution improvement. J. Opt. Soc. Am. A 19:81599–609 [Google Scholar]
  77. Hell SW, Kroug M. 1995. Ground-state-depletion fluorescence microscopy: a concept for breaking the diffraction resolution limit. Appl. Phys. B 60:5495–97 [Google Scholar]
  78. Hell SW, Stelzer EHK. 1992. Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation. Opt. Commun. 93:277–82 [Google Scholar]
  79. Hell SW, Wichmann J. 1994. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 19:11780–82 [Google Scholar]
  80. Hell SW. 2003. Toward fluorescence nanoscopy. Nat. Biotechnol. 21:111347–55 [Google Scholar]
  81. Hell SW. 2009. Microscopy and its focal switch. Nat. Methods 6:124–32 [Google Scholar]
  82. Hess ST, Girirajan TPK, Mason MD. 2006. Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. Biophys. J. 91:114258–72 [Google Scholar]
  83. Hohage T, Werner F. 2013. Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data. Numer. Math. 123:4745–79 [Google Scholar]
  84. Huang B, Bates M, Zhuang X. 2009. Super-resolution fluorescence microscopy. Annu. Rev. Biochem. 78:993–1016 [Google Scholar]
  85. Huang F, Schwartz SL, Byars JM, Lidke KA. 2011. Simultaneous multiple-emitter fitting for single molecule super-resolution imaging. Biomed. Opt. Express 2:51377–93 [Google Scholar]
  86. Hughes J, Fricks J, Hancock W. 2010. Likelihood inference for particle location in fluorescence microscopy. Ann. Appl. Stat. 4:2830–48 [Google Scholar]
  87. Johnstone IM, Paul D. 2014. Adaptation in some linear inverse problems. Stat 3:1187–99 [Google Scholar]
  88. Jost A, Heintzmann R. 2013. Superresolution multidimensional imaging with structured illumination microscopy. Annu. Rev. Mater. Res. 43:261–82 [Google Scholar]
  89. Kabluchko Z, Munk A. 2008. Exact convergence rate for the maximum of standardized Gaussian increments. Electron. Comm. Probab. 13:302–10 [Google Scholar]
  90. Kabluchko Z, Wang Y. 2014. Limiting distribution for the maximal standardized increment of a random walk. Stoch. Process. Appl. 124:92824–67 [Google Scholar]
  91. Kabluchko Z. 2011. Extremes of the standardized Gaussian noise. Stoch. Process. Appl. 121:3515–33 [Google Scholar]
  92. Kalifa J, Mallat S. 2003. Thresholding estimators for linear inverse problems and deconvolutions. Ann. Stat. 31:158–109 [Google Scholar]
  93. Karadaglić D, Wilson T. 2008. Image formation in structured illumination wide-field fluorescence microscopy. Micron 39:7808–18 [Google Scholar]
  94. Kawata S, Inouye Y, Verma P. 2009. Plasmonics for near-field nano-imaging and superlensing. Nat. Photon. 3:7388–94 [Google Scholar]
  95. Kittel RJ, Wichmann C, Rasse TM, Fouquet W, Schmidt M. et al. 2006. Bruchpilot promotes active zone assembly, Ca2+ channel clustering, and vesicle release. Science 312:57761051–54 [Google Scholar]
  96. Klar TA, Jakobs S, Dyba M, Egner A, Hell SW. 2000. Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission. PNAS 97:158206–10 [Google Scholar]
  97. LaRiccia VN, Eggermont PPB. 2009. Maximum Penalized Likelihood Estimation 2 Regression New York: Springer
  98. Lichtman JW, Conchello J-A. 2005. Fluorescence microscopy. Nat. Methods 2:12910–19 [Google Scholar]
  99. Lucy LB. 1974. An iterative technique for the rectification of observed distributions. Astron. J. 79:745 [Google Scholar]
  100. Magde D, Elson E, Webb WW. 1972. Thermodynamic fluctuations in a reacting system—measurement by fluorescence correlation spectroscopy. Phys. Rev. Lett. 29:705–8 [Google Scholar]
  101. Malgouyres F. 2002. Minimizing the total variation under a general convex constraint for image restoration. IEEE Trans. Image Process. 11:121450–56 [Google Scholar]
  102. Masters BR. 2010. The development of fluorescence microscopy. Encyclopedia of Life Sciences. Chichester, UK: John Wiley & Sons [Google Scholar]
  103. Meister A. 2009. Deconvolution Problems in Nonparametric Statistics Berlin/Heidelberg: Springer
  104. Minsky M. 1961. Microscopy apparatus. US Patent No. 3013467
  105. Mlodzianoski MJ, Schreiner JM, Callahan SP, Smolková K, Dlasková A. et al. 2011. Sample drift correction in 3D fluorescence photoactivation localization microscopy. Opt. Express 19:1615009–19 [Google Scholar]
  106. Mukamel EA, Babcock H, Zhuang X. 2012. Statistical deconvolution for superresolution fluorescence microscopy. Biophys. J. 102:102391–400 [Google Scholar]
  107. Munk A, Pricop M. 2010. On the self-regularization property of the EM algorithm for Poisson inverse problems. Statistical Modelling and Regression Structures T Kneib, G Tutz 431–48 Heidelberg, Ger: Physica [Google Scholar]
  108. Nagorni M, Hell SW. 2001. Coherent use of opposing lenses for axial resolution increase. II. Power and limitation of nonlinear image restoration. J. Opt. Soc. Am. A 18:149–54 [Google Scholar]
  109. Nowak RD, Kolaczyk ED. 2000. A statistical multiscale framework for Poisson inverse problems. IEEE Trans. Inf. Theory 46:51811–25 [Google Scholar]
  110. Pawley JB. 2006. Handbook of Biological Confocal Microscopy New York: Springer, 3rd ed..
  111. Pendry JB. 2000. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85:3966–69 [Google Scholar]
  112. Pohl DW, Denk W, Lanz M. 1984. Optical stethoscopy: image recording with resolution λ/20. Appl. Phys. Lett 44:7651–53 [Google Scholar]
  113. Quan T, Zhu H, Liu X, Liu Y, Ding J. et al. 2011. High-density localization of active molecules using Structured Sparse Model and Bayesian Information Criterion. Opt. Express 19:1816963–74 [Google Scholar]
  114. Richardson WH. 1972. Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62:155–59 [Google Scholar]
  115. Rivera C, Walther G. 2013. Optimal detection of a jump in the intensity of a Poisson process or in a density with likelihood ratio statistics. Scand. J. Stat. 40:4752–69 [Google Scholar]
  116. Rust MJ, Bates M, Zhuang X. 2006. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods 3:10793–96 [Google Scholar]
  117. Sakdinawat A, Attwood D. 2010. Nanoscale X-ray imaging. Nat. Photon. 4:12840–48 [Google Scholar]
  118. Schmidt R, Wurm CA, Jakobs S, Engelhardt J, Egner A, Hell SW. 2008. Spherical nanosized focal spot unravels the interior of cells. Nat. Methods 5:6539–44 [Google Scholar]
  119. Schmidt-Hieber J, Munk A, Dümbgen L. 2013. Multiscale methods for shape constraints in deconvolution: confidence statements for qualitative features. Ann. Stat. 41:31299–328 [Google Scholar]
  120. Sharonov A, Hochstrasser RM. 2006. Wide-field subdiffraction imaging by accumulated binding of diffusing probes. PNAS 103:5018911–16 [Google Scholar]
  121. Shroff H, Galbraith CG, Galbraith JA, Betzig E. 2008. Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics. Nat. Methods 5:5417–23 [Google Scholar]
  122. Silverman BW, Jones MC, Wilson JD, Nychka DW. 1990. A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography. J. R. Stat. Soc. B 52:2271–324 [Google Scholar]
  123. Spence JCH. 2013. High-Resolution Electron Microscopy Oxford, UK: Oxford Univ. Press, 4th ed..
  124. Stryer L. 1978. Fluorescence energy transfer as a spectroscopic ruler. Annu. Rev. Biochem. 47:819–46 [Google Scholar]
  125. Thompson RE, Larson DR, Webb WW. 2002. Precise nanometer localization analysis for individual fluorescent probes. Biophys. J. 82:52775–83 [Google Scholar]
  126. Tibshirani R. 1996. Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58:1267–88 [Google Scholar]
  127. Vardi Y, Lee D. 1993. From image deblurring to optimal investments: maximum likelihood solutions for positive linear inverse problems. J. R. Stat. Soc. B 55:3569–612 [Google Scholar]
  128. Vardi Y, Shepp LA, Kaufman L. 1985. A statistical model for positron emission tomography. J. Am. Stat. Assoc. 80:8–20 [Google Scholar]
  129. Veklerov E, Llacer J. 1987. Stopping rule for the MLE algorithm based on statistical hypothesis testing. IEEE Trans. Med. Imaging 6:4313–19 [Google Scholar]
  130. White J, Stelzer E. 1999. Photobleaching GFP reveals protein dynamics inside live cells. Trends Cell Biol. 9:261–65 [Google Scholar]
  131. Xu K, Zhong G, Zhuang X. 2013. Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons. Science 339:6118452–56 [Google Scholar]
  132. Zernike F. 1955. How I discovered phase contrast. Science 121:3141345–49 [Google Scholar]
  133. Zhang B, Fadili JM, Starck JL. 2008. Wavelets, ridgelets, and curvelets for Poisson noise removal. IEEE Trans. Image Process. 17:71093–108 [Google Scholar]
  134. Zhu L, Zhang W, Elnatan D, Huang B. 2012. Faster STORM using compressed sensing. Nat. Methods 9:7721–23 [Google Scholar]

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error