Abstract

Single molecule based superresolution techniques (STORM/PALM) achieve nanometer spatial resolution by integrating the temporal information of the switching dynamics of fluorophores (emitters). When emitter density is low for each frame, they are located to the nanometer resolution. However, when the emitter density rises, causing significant overlapping, it becomes increasingly difficult to accurately locate individual emitters. This is particularly apparent in three dimensional (3D) localization because of the large effective volume of the 3D point spread function (PSF). The inability to precisely locate the emitters at a high density causes poor temporal resolution of localization-based superresolution technique and significantly limits its application in 3D live cell imaging. To address this problem, we developed a 3D high-density superresolution imaging platform that allows us to precisely locate the positions of emitters, even when they are significantly overlapped in three dimensional space. Our platform involves a multi-focus system in combination with astigmatic optics and an 1-Homotopy optimization procedure. To reduce the intrinsic bias introduced by the discrete formulation of compressed sensing, we introduced a debiasing step followed by a 3D weighted centroid procedure, which not only increases the localization accuracy, but also increases the computation speed of image reconstruction. We implemented our algorithms on a graphic processing unit (GPU), which speeds up processing 10 times compared with central processing unit (CPU) implementation. We tested our method with both simulated data and experimental data of fluorescently labeled microtubules and were able to reconstruct a 3D microtubule image with 1000 frames (512×512) acquired within 20 seconds.

© 2015 Optical Society of America

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References

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2014 (6)

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

J. Min, S. J. Holden, L. Carlini, M. Unser, S. Manley, and J. C. Ye, “3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction,” Biomed. Opt. Express 5, 3935–3948 (2014).
[Crossref]

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci. Rep. 4, 5388 (2014).
[Crossref] [PubMed]

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nature Photon. 8, 302–306 (2014).
[Crossref]

A. Tahmasbi, S. Ram, J. Chao, A. V. Abraham, F. W. Tang, E. S. Ward, and R. J. Ober, “Designing the focal plane spacing for multifocal plane microscopy,” Opt. Express 22, 16706–16721 (2014).
[Crossref] [PubMed]

2013 (3)

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]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

H. P. Babcock, J. R. Moffitt, Y. Cao, and X. Zhuang, “Fast compressed sensing analysis for super-resolution imaging using L1-homotopy,” Opt. Express 21, 28583 (2013).
[Crossref]

2012 (5)

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

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref] [PubMed]

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

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Optical Nanoscopy 1, 1–10 (2012).
[Crossref]

I. Izeddin, J. Boulanger, V. Racine, C. Specht, A. Kechkar, D. Nair, A. Triller, D. Choquet, M. Dahan, and J. Sibarita, “Wavelet analysis for single molecule localization microscopy,” Opt. Express 20, 2081–2095 (2012).
[Crossref] [PubMed]

2011 (4)

Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011).
[Crossref]

T. Quan, H. Zhu, X. Liu, Y. Liu, J. Ding, S. Zeng, and Z.-L. Huang, “High-density localization of active molecules using Structured Sparse Model and Bayesian Information Criterion,” Opt. Express 19, 16963–16974 (2011).
[Crossref] [PubMed]

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref] [PubMed]

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

2010 (1)

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

2007 (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

2006 (4)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

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

1991 (1)

1988 (1)

A. Goshtasby, “Image Registration by Local Approximation Methods,” Image Vision Comput. 6, 255–261 (1988).
[Crossref]

Abraham, A. V.

Abrahamsson, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Agard, D. A.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

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]

Babcock, H.

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref] [PubMed]

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Optical Nanoscopy 1, 1–10 (2012).
[Crossref]

Babcock, H. P.

Bargmann, C. I.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Barsic, A.

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci. Rep. 4, 5388 (2014).
[Crossref] [PubMed]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref] [PubMed]

Betzig, E.

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

Bonifacino, J. S.

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

Boulanger, J.

Boyd, S.

M. Grant, S. Boyd, and Y. Ye, “CVX: Matlab software for disciplined convex programming,” http://cvxr.com/cvx/ (2008).

Byars, J. M.

Calderbank, A. R.

Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011).
[Crossref]

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Cao, Y.

Carlini, L.

J. Min, S. J. Holden, L. Carlini, M. Unser, S. Manley, and J. C. Ye, “3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction,” Biomed. Opt. Express 5, 3935–3948 (2014).
[Crossref]

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Chang, H.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Chao, J.

Chen, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Chen, Y.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Chi, Y.

Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011).
[Crossref]

Choquet, D.

Churchman, L. S.

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

Dahan, M.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

I. Izeddin, J. Boulanger, V. Racine, C. Specht, A. Kechkar, D. Nair, A. Triller, D. Choquet, M. Dahan, and J. Sibarita, “Wavelet analysis for single molecule localization microscopy,” Opt. Express 20, 2081–2095 (2012).
[Crossref] [PubMed]

Darzacq, C. D.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Darzacq, X.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Davidson, M. W.

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

Ding, J.

Elnatan, D.

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

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Flyvbjerg, H.

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

Frisken Gibson, S.

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

Goshtasby, A.

A. Goshtasby, “Image Registration by Local Approximation Methods,” Image Vision Comput. 6, 255–261 (1988).
[Crossref]

Grant, M.

M. Grant, S. Boyd, and Y. Ye, “CVX: Matlab software for disciplined convex programming,” http://cvxr.com/cvx/ (2008).

Grover, G.

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci. Rep. 4, 5388 (2014).
[Crossref] [PubMed]

Gu, L.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Gustafsson, M. G. L.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Hajj, B.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Hess, H. F.

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

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

Holden, S.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Holden, S. J.

Huang, B.

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

Huang, F.

Huang, Z.-L.

Izeddin, I.

Ji, W.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nature Photon. 8, 302–306 (2014).
[Crossref]

Kapanidis, A. N.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref] [PubMed]

Katsov, A. Y.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Kechkar, A.

Kirshner, H.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[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]

Lanni, F.

Lidke, K. A.

Lindwasser, O. W.

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

Lippincott-Schwartz, J.

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

Liu, X.

Liu, Y.

Lv, P.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Manley, S.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

J. Min, S. J. Holden, L. Carlini, M. Unser, S. Manley, and J. C. Ye, “3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction,” Biomed. Opt. Express 5, 3935–3948 (2014).
[Crossref]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

Min, J.

J. Min, S. J. Holden, L. Carlini, M. Unser, S. Manley, and J. C. Ye, “3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction,” Biomed. Opt. Express 5, 3935–3948 (2014).
[Crossref]

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Mizuguchi, G.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Moffitt, J. R.

Mortensen, K. I.

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

Mueller, F.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Mukamel, E. A.

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref] [PubMed]

Nair, D.

Nowak, R. D.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Ober, R. J.

Olenych, S.

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

Olivier, N.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Patterson, G. H.

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

Pezeshki, A.

Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011).
[Crossref]

Piestun, R.

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci. Rep. 4, 5388 (2014).
[Crossref] [PubMed]

Quan, T.

Racine, V.

Ram, S.

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref] [PubMed]

Sage, D.

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]

Scharf, L. L.

Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011).
[Crossref]

Schwartz, S. L.

Sheng, Y.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Sibarita, J.

Sigal, Y. M.

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Optical Nanoscopy 1, 1–10 (2012).
[Crossref]

Sougrat, R.

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

Soule, P.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Specht, C.

Spudich, J. A.

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

Stallinga, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Tahmasbi, A.

Tang, F. W.

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

Triller, A.

Unser, M.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

J. Min, S. J. Holden, L. Carlini, M. Unser, S. Manley, and J. C. Ye, “3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction,” Biomed. Opt. Express 5, 3935–3948 (2014).
[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]

Uphoff, S.

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref] [PubMed]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nature Photon. 8, 302–306 (2014).
[Crossref]

Vonesch, C.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Wang, Y.

Ward, E. S.

Wisniewski, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Wright, S. J.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Wu, C.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Xu, T.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Ye, J. C.

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

J. Min, S. J. Holden, L. Carlini, M. Unser, S. Manley, and J. C. Ye, “3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction,” Biomed. Opt. Express 5, 3935–3948 (2014).
[Crossref]

Ye, Y.

M. Grant, S. Boyd, and Y. Ye, “CVX: Matlab software for disciplined convex programming,” http://cvxr.com/cvx/ (2008).

Zeng, S.

Zhang, W.

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

Zhang, Y.

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

Zhu, H.

Zhu, L.

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

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nature Photon. 8, 302–306 (2014).
[Crossref]

H. P. Babcock, J. R. Moffitt, Y. Cao, and X. Zhuang, “Fast compressed sensing analysis for super-resolution imaging using L1-homotopy,” Opt. Express 21, 28583 (2013).
[Crossref]

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref] [PubMed]

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Optical Nanoscopy 1, 1–10 (2012).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref] [PubMed]

Biomed. Opt. Express (2)

Biophys. J. (3)

L. Gu, Y. Sheng, Y. Chen, H. Chang, Y. Zhang, P. Lv, W. Ji, and T. Xu, “High-density 3D single molecular analysis based on compressed sensing,” Biophys. J. 106, 2443–2449 (2014).
[Crossref] [PubMed]

E. A. Mukamel, H. Babcock, and X. Zhuang, “Statistical deconvolution for superresolution fluorescence microscopy,” Biophys. J. 102, 2391–2400 (2012).
[Crossref] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-High Resolution Imaging by Fluorescence Photoactivation Localization Microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

IEEE J. Sel. Top. Signal Process. (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

IEEE Trans. Inf. Theory (1)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

IEEE Trans. Signal Process. (1)

Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011).
[Crossref]

Image Vision Comput. (1)

A. Goshtasby, “Image Registration by Local Approximation Methods,” Image Vision Comput. 6, 255–261 (1988).
[Crossref]

J. Microsc. (1)

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 (1)

Nat. Methods (5)

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

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

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
[Crossref] [PubMed]

S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods 8, 279–280 (2011).
[Crossref] [PubMed]

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

Nature Photon. (1)

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nature Photon. 8, 302–306 (2014).
[Crossref]

Opt. Express (5)

Optical Nanoscopy (1)

H. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Optical Nanoscopy 1, 1–10 (2012).
[Crossref]

Sci. Rep. (2)

A. Barsic, G. Grover, and R. Piestun, “Three-dimensional super-resolution and localization of dense clusters of single molecules,” Sci. Rep. 4, 5388 (2014).
[Crossref] [PubMed]

J. Min, C. Vonesch, H. Kirshner, L. Carlini, N. Olivier, S. Holden, S. Manley, J. C. Ye, and M. Unser, “FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data,” Sci. Rep. 4, 4577 (2014).
[Crossref] [PubMed]

Science (1)

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

Other (1)

M. Grant, S. Boyd, and Y. Ye, “CVX: Matlab software for disciplined convex programming,” http://cvxr.com/cvx/ (2008).

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Figures (9)

Fig. 1
Fig. 1 (a) 3D Multi-focus astigmatism imaging system (3D MACS). (b) Images of an emitter on the three cameras with various z focuses (c) Calibration curves of the PSFs. wx and wy are functions of the focus position z for different cameras.
Fig. 2
Fig. 2 Image registration error distribution. The image from the first camera was used as the reference and the second and third camera images were registered to the first camera image. The standard deviation of the registration error for the second and third cameras are 5.94 nm and 5.54 nm respectively.
Fig. 3
Fig. 3 Comparison of the performance of 3D SACS and 3D MACS at low (a, b) and high density (c, d) of emitters. C1, C2, and C3 label the images formed on the three different cameras. At low emitter density, both 3D SACS and MACS can identify all the emitters with similar accuracy (lower right panel of (a) and lower panel of (b)). We used an ellipsoid to represent the x, y and z locations of an emitter. The center of ellipsoid was determined by the x and y positions and the shape was determined by the z position. Red represents the results from our calculation and white represents the actual location from the simulation. When the emitter density increases (c, d), 3D MACS (lower right panel of (c)) correctly identified all the emitters, while SACS clearly showed ambiguity (lower panel of (d)) with two wrongly detected emitters (colored yellow).
Fig. 4
Fig. 4 Bias at different z locations (a) without and (b) with debiasing step. (c) Localization accuracy increases with debiasing step, particularly for the axial direction (green solid and dashed lines). For the x and y directions, debiasing barely improves the localization accuracy. (d) z localization accuracy improves with the increase of the z sampling factor.
Fig. 5
Fig. 5 (a) The execution time of both 3D MACS and 3D SACS decreases with the increase of epsilon. (b) The x, y, and z direction localization error only slightly increase with the increase of epsilon. The false negative (c) and false discovery rate (d) stay relatively constant as epsilon increases from 1.5 to 2.5.
Fig. 6
Fig. 6 (a) A comparison of the identified emitter densities using 3D SACS, 3D MACS, SF-SEA and MF-SEA methods. (b) False discovery rates of the emitters using the three different methods. (c) XY and (d) Z localization precision at various emitter densities.
Fig. 7
Fig. 7 Change of the execution time as a function of the emitter densities.
Fig. 8
Fig. 8 The XY, XZ, and YZ projection images of (a) simulated spheres, (b) 3-crossinged lines, and (c) 3D stellate with MF-SEA and 3D MACS using 3000 frames. Scale bar: 100 nm.
Fig. 9
Fig. 9 (a) Reconstructed Microtubule image (bar: 1000 nm). (b) Zoom in of the selected region in (a) (bar: 500 nm). (c) Averaged image. (d) One typical raw frame. (e) YZ projection view of the selected region in (b) (bar: 100 nm). (f) Line profile of (e).

Tables (2)

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Algorithm 1 3D Compressed Sensing on STORM

Tables Icon

Algorithm 2 3D Local Debiasing

Equations (6)

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

f ( x , y ) = I 2 π w x w y exp ( ( x x 0 ) 2 2 w x 2 ( y y 0 ) 2 2 w y 2 ) + b ,
w x , y ( z 0 ) = w 0 1 + ( z 0 c d ) 2 + A ( z 0 c d ) 3 + B ( z 0 c d ) 4 ,
y = A x ,
minimize x 1 subject to x 0 y A x 2 ε y 1 ,
min θ m i j ( y m ( i , j ) f θ , m ( i , j ) ) 2 ,
β = y f θ 2 y 1

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