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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 15 — Jul. 29, 2013
  • pp: 18125–18137

Sparse ACEKF for phase reconstruction

Zhong Jingshan, Justin Dauwels, Manuel A. Vázquez, and Laura Waller  »View Author Affiliations


Optics Express, Vol. 21, Issue 15, pp. 18125-18137 (2013)
http://dx.doi.org/10.1364/OE.21.018125


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Abstract

We propose a novel low-complexity recursive filter to efficiently recover quantitative phase from a series of noisy intensity images taken through focus. We first transform the wave propagation equation and nonlinear observation model (intensity measurement) into a complex augmented state space model. From the state space model, we derive a sparse augmented complex extended Kalman filter (ACEKF) to infer the complex optical field (amplitude and phase), and find that it converges under mild conditions. Our proposed method has a computational complexity of NzN logN and storage requirement of 𝒪(N), compared with the original ACEKF method, which has a computational complexity of 𝒪(NzN3) and storage requirement of 𝒪(N2), where Nz is the number of images and N is the number of pixels in each image. Thus, it is efficient, robust and recursive, and may be feasible for real-time phase recovery applications with high resolution images.

© 2013 OSA

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.5070) Image processing : Phase retrieval

ToC Category:
Image Processing

History
Original Manuscript: April 4, 2013
Revised Manuscript: June 6, 2013
Manuscript Accepted: July 2, 2013
Published: July 22, 2013

Citation
Zhong Jingshan, Justin Dauwels, Manuel A. Vázquez, and Laura Waller, "Sparse ACEKF for phase reconstruction," Opt. Express 21, 18125-18137 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-15-18125


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References

  1. L. Waller, M. Tsang, S. Ponda, S. Yang, and G. Barbastathis, “Phase and amplitude imaging from noisy images by Kalman filtering,” Opt. Express19, 2805–2814 (2011). [CrossRef] [PubMed]
  2. L. Waller, Y. Luo, S. Y. Yang, and G. Barbastathis, “Transport of intensity phase imaging in a volume holographic microscope,” Opt. Lett.35, 2961–2963 (2010). [CrossRef] [PubMed]
  3. S. S. Gorthi and E. Schonbrun, “Phase imaging flow cytometry using a focus-stack collecting microscope,” Opt. Lett.37, 707–709 (2012). [CrossRef] [PubMed]
  4. R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik35, 237–246 (1972).
  5. J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]
  6. G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett.30, 833–835 (2005). [CrossRef] [PubMed]
  7. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun.49, 6–10 (1984). [CrossRef]
  8. M. Soto and E. Acosta, “Improved phase imaging from intensity measurements in multiple planes,” Appl. Opt.46, 7978–7981 (2007). [CrossRef] [PubMed]
  9. L. Waller, L. Tian, and G. Barbastathis, “Transport of intensity phase-amplitude imaging with higher order intensity derivatives,” Opt. Express18, 12552–12561 (2010). [CrossRef] [PubMed]
  10. R. Paxman, T. Schulz, and J. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A9, 1072–1085 (1992). [CrossRef]
  11. R. Paxman and J. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity,” J. Opt. Soc. Am. A5, 914–923 (1988). [CrossRef]
  12. Z. Jingshan, J. Dauwels, M. A. Vázquez, and L. Waller, “Efficient Gaussian inference algorithms for phase imaging,” Proc. IEEE ICASSP2012 pp. 25–30.
  13. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  14. D. H. Dini and D. P. Mandic, “Class of widely linear complex Kalman filters,” IEEE Trans. Neural Netw. Learn. Syst.23, 775–786 (2012). [CrossRef]
  15. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal of basic Engineering82, 35–45 (1960). [CrossRef]
  16. K. Reif, S. Gunther, E. Yaz, and R. Unbehauen, “Stochastic stability of the discrete-time extended Kalman filter,” IEEE Trans. Autom. Control44, 714–728 (1999). [CrossRef]
  17. T. Lefebvre, H. Bruyninckx, and J. D. Schutter, “Kalman filters for nonlinear systems: a comparison of performance,” Internat. J. Control77, 639–653 (2004). [CrossRef]
  18. A. J. Krener, “The convergence of the extended Kalman filter,” in “Directions in mathematical systems theory and optimization,” (Springer, 2003), pp. 173–182. [CrossRef]
  19. D. J. Lee, M. C. Roggemann, and B. M. Welsh, “Cramér-Rao analysis of phase-diverse wave-front sensing,” J. Opt. Soc. Am. A16, 1005–1015 (1999). [CrossRef]

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