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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28583–28596

Fast compressed sensing analysis for super-resolution imaging using L1-homotopy

Hazen P. Babcock, Jeffrey R. Moffitt, Yunlong Cao, and Xiaowei Zhuang  »View Author Affiliations

Optics Express, Vol. 21, Issue 23, pp. 28583-28596 (2013)

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In super-resolution imaging techniques based on single-molecule switching and localization, the time to acquire a super-resolution image is limited by the maximum density of fluorescent emitters that can be accurately localized per imaging frame. In order to increase the imaging rate, several methods have been recently developed to analyze images with higher emitter densities. One powerful approach uses methods based on compressed sensing to increase the analyzable emitter density per imaging frame by several-fold compared to other reported approaches. However, the computational cost of this approach, which uses interior point methods, is high, and analysis of a typical 40 µm x 40 µm field-of-view super-resolution movie requires thousands of hours on a high-end desktop personal computer. Here, we demonstrate an alternative compressed-sensing algorithm, L1-Homotopy (L1H), which can generate super-resolution image reconstructions that are essentially identical to those derived using interior point methods in one to two orders of magnitude less time depending on the emitter density. Moreover, for an experimental data set with varying emitter density, L1H analysis is ~300-fold faster than interior point methods. This drastic reduction in computational time should allow the compressed sensing approach to be routinely applied to super-resolution image analysis.

© 2013 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(110.2960) Imaging systems : Image analysis
(170.2520) Medical optics and biotechnology : Fluorescence microscopy

ToC Category:
Image Processing

Original Manuscript: September 3, 2013
Revised Manuscript: November 4, 2013
Manuscript Accepted: November 6, 2013
Published: November 13, 2013

Virtual Issues
Vol. 9, Iss. 1 Virtual Journal for Biomedical Optics

Hazen P. Babcock, Jeffrey R. Moffitt, Yunlong Cao, and Xiaowei Zhuang, "Fast compressed sensing analysis for super-resolution imaging using L1-homotopy," Opt. Express 21, 28583-28596 (2013)

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  1. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006). [CrossRef] [PubMed]
  2. 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,” Science313(5793), 1642–1645 (2006). [CrossRef] [PubMed]
  3. S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J.91(11), 4258–4272 (2006). [CrossRef] [PubMed]
  4. H. Shroff, C. G. Galbraith, J. A. Galbraith, and E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods5(5), 417–423 (2008). [CrossRef] [PubMed]
  5. B. Huang, H. P. Babcock, and X. Zhuang, “Breaking the diffraction barrier: Super-resolution imaging of cells,” Cell143(7), 1047–1058 (2010). [CrossRef] [PubMed]
  6. S. A. Jones, S.-H. Shim, J. He, and X. Zhuang, “Fast, three-dimensional super-resolution imaging of live cells,” Nat. Methods8(6), 499–505 (2011). [CrossRef] [PubMed]
  7. R. P. J. Nieuwenhuizen, K. A. Lidke, M. Bates, D. L. Puig, D. Grünwald, S. Stallinga, and B. Rieger, “Measuring image resolution in optical nanoscopy,” Nat. Methods10(6), 557–562 (2013). [CrossRef] [PubMed]
  8. S.-H. Shim, C. Xia, G. Zhong, H. P. Babcock, J. C. Vaughan, B. Huang, X. Wang, C. Xu, G.-Q. Bi, and X. Zhuang, “Super-resolution fluorescence imaging of organelles in live cells with photoswitchable membrane probes,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13978–13983 (2012). [CrossRef] [PubMed]
  9. S. J. Holden, S. Uphoff, and A. N. Kapanidis, “DAOSTORM: an algorithm for high- density super-resolution microscopy,” Nat. Methods8(4), 279–280 (2011). [CrossRef] [PubMed]
  10. F. Huang, S. L. Schwartz, J. M. Byars, and K. A. Lidke, “Simultaneous multiple-emitter fitting for single molecule super-resolution imaging,” Biomed. Opt. Express2(5), 1377–1393 (2011). [CrossRef] [PubMed]
  11. S. Cox, E. Rosten, J. Monypenny, T. Jovanovic-Talisman, D. T. Burnette, J. Lippincott-Schwartz, G. E. Jones, and R. Heintzmann, “Bayesian localization microscopy reveals nanoscale podosome dynamics,” Nat. Methods9(2), 195–200 (2011). [CrossRef] [PubMed]
  12. 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. Express19(18), 16963–16974 (2011). [CrossRef] [PubMed]
  13. H. P. Babcock, Y. M. Sigal, and X. Zhuang, “A high-density 3D localization algorithm for stochastic optical reconstruction microscopy,” Optical Nanoscopy1(1), 6–10 (2012). [CrossRef]
  14. E. A. Mukamel, H. P. Babcock, and X. Zhuang, “Statistical Deconvolution for Superresolution Fluorescence Microscopy,” Biophys. J.102(10), 2391–2400 (2012). [CrossRef] [PubMed]
  15. L. Zhu, W. Zhang, D. Elnatan, and B. Huang, “Faster STORM using compressed sensing,” Nat. Methods9(7), 721–723 (2012). [CrossRef] [PubMed]
  16. M. R. Osborne, B. Presnell, and B. A. Turlach, “A new approach to variable selection in least squares problems,” IMA J. Numer. Anal.20(3), 389–403 (2000). [CrossRef]
  17. D. M. Malioutov, M. Cetin, and A. S. Willsky, “Homotopy continuation for sparse signal representation,” ICASSP5, 733–736 (2005).
  18. D. L. Donoho and Y. Tsaig, “Fast Solution of the L1-norm Minimization Problem When the Solution May be Sparse,” IEEE Trans. Inf. Theory54(11), 4789–4812 (2008). [CrossRef]
  19. A. Y. Yang and S. S. Sastry, “Fast l1-minimization algorithms and an application in robust face recognition: a review,” Proceedings of 2010 IEEE 17th International Conference on Image Processing, 1849–1852 (2010). [CrossRef]
  20. A. Y. Yang, Z. Zhou, A. Ganesh, S. S. Shankar, and Y. Ma, “Fast L1-Minimization Algorithms For Robust Face Recognition,” IEEE Trans. Image Process.22(8), 3234–3246 (2012).
  21. E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput.31(2), 890–912 (2009). [CrossRef]
  22. A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM Journal on Imaging Sciences2(1), 183–202 (2009). [CrossRef]
  23. M. C. Grant and S. P. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.0 beta,” http://cvxr.com/cvx (2013).
  24. M. Bates, B. Huang, G. T. Dempsey, and X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science317(5845), 1749–1753 (2007). [CrossRef] [PubMed]
  25. B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008). [CrossRef] [PubMed]
  26. M. Grant, S. Boyd, and Y. Ye, “CVX: Matlab Software for Disciplined Convex Programming, Version 1.0 beta 3,” Recent Advances in Learning and Control}, 95-110 (2006).
  27. K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010). [CrossRef] [PubMed]

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