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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 6 — Mar. 12, 2012
  • pp: 5942–5954

Solving inverse problems for optical scanning holography using an adaptively iterative shrinkage-thresholding algorithm

Fengjun Zhao, Xiaochao Qu, Xin Zhang, Ting-Chung Poon, Taegeun Kim, You Seok Kim, and Jimin Liang  »View Author Affiliations

Optics Express, Vol. 20, Issue 6, pp. 5942-5954 (2012)

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Optical scanning holography (OSH) records a three-dimensional object into a two-dimensional hologram through two-dimensional optical scanning. The recovery of sectional images from the hologram, termed as an inverse problem, has been previously implemented by conventional methods as well as the use of l 2 norm. However, conventional methods require time consuming processing of section by section without eliminating the defocus noise and the l 2 norm method often suffers from the drawback of over-smoothing. Moreover, these methods require the whole hologram data (real and imaginary parts) to eliminate the twin image noise, whose computation complexity and the sophisticated post-processing are far from desirable. To handle these difficulties, an adaptively iterative shrinkage-thresholding (AIST) algorithm, characterized by fast computation and adaptive iteration, is proposed in this paper. Using only a half hologram data, the proposed method obtained satisfied on-axis reconstruction free of twin image noise. The experiments of multi-planar reconstruction and improvement of depth of focus further validate the feasibility and flexibility of our proposed AIST algorithm.

© 2012 OSA

OCIS Codes
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(180.6900) Microscopy : Three-dimensional microscopy
(090.1995) Holography : Digital holography

ToC Category:
Image Processing

Original Manuscript: December 19, 2011
Revised Manuscript: February 14, 2012
Manuscript Accepted: February 20, 2012
Published: February 27, 2012

Virtual Issues
Vol. 7, Iss. 5 Virtual Journal for Biomedical Optics

Fengjun Zhao, Xiaochao Qu, Xin Zhang, Ting-Chung Poon, Taegeun Kim, You Seok Kim, and Jimin Liang, "Solving inverse problems for optical scanning holography using an adaptively iterative shrinkage-thresholding algorithm," Opt. Express 20, 5942-5954 (2012)

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  1. T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A2(4), 521–527 (1985). [CrossRef]
  2. B. D. Duncan and T.-C. Poon, “Gaussian beam analysis of optical scanning holography,” J. Opt. Soc. Am. A9(2), 229–236 (1992). [CrossRef]
  3. J. Swoger, M. Martínez-Corral, J. Huisken, and E. H. Stelzer, “Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy,” J. Opt. Soc. Am. A19(9), 1910–1918 (2002). [CrossRef] [PubMed]
  4. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt.48(34), H113–H119 (2009). [CrossRef] [PubMed]
  5. G. Indebetouw and W. Zhong, “Scanning holographic microscopy of three-dimensional fluorescent specimens,” J. Opt. Soc. Am. A23(7), 1699–1707 (2006). [CrossRef] [PubMed]
  6. G. Indebetouw, A. El Maghnouji, and R. Foster, “Scanning holographic microscopy with transverse resolution exceeding the Rayleigh limit and extended depth of focus,” J. Opt. Soc. Am. A22(5), 892–898 (2005). [CrossRef] [PubMed]
  7. T. Kim, “Optical sectioning by optical scanning holography and a Wiener filter,” Appl. Opt.45(5), 872–879 (2006). [CrossRef] [PubMed]
  8. H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt.47(19), D164–D175 (2008). [CrossRef] [PubMed]
  9. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express16(22), 17215–17226 (2008). [CrossRef] [PubMed]
  10. X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett.34(20), 3098–3100 (2009). [CrossRef] [PubMed]
  11. S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularizedleast squares,” IEEE J. Sel. Top. Signal Process.1(4), 606–617 (2007). [CrossRef]
  12. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A27(7), 1630–1637 (2010). [CrossRef] [PubMed]
  13. S. Wei and H. Xu, “Staircasing reduction model applied to total variation based image reconstruction,”in 17th European Signal Processing Conference (EUSIPCO, Glasgow, Scotland, 2009), pp. 2579–2583.
  14. I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm,” IEEE Trans. Signal Process.45(3), 600–616 (1997). [CrossRef]
  15. Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express17(10), 8062–8080 (2009). [CrossRef] [PubMed]
  16. Q. Zhang, H. Zhao, D. Chen, X. Qu, X. Chen, X. He, W. Li, Z. Hu, J. Liu, J. Liang, and J. Tian, “Source sparsity based primal-dual interior-point method for three-dimensional bioluminescence tomography,” Opt. Commun.284(24), 5871–5876 (2011). [CrossRef]
  17. X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express18(24), 24825–24841 (2010). [CrossRef] [PubMed]
  18. D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express18(8), 8630–8646 (2010). [CrossRef] [PubMed]
  19. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, New York, 2007).
  20. X. Zhang, E. Y. Lam, and T.-C. Poon, “Fast iterative sectional image reconstruction in optical scanning holography,” in Digital Holography and Three-Dimensional Imaging, Technical Digest (CD) (Optical Society of America, 2009), paper DMA3.
  21. S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM Rev.43(1), 129–159 (2001). [CrossRef]
  22. E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math.59(8), 1207–1223 (2006). [CrossRef]
  23. A. Yang, A. Ganesh, S. Sastry, and Y. Ma, “Fast L1-minimization algorithms and an application in robust face recognition: a review,” in proceedings of IEEE International Conference on Image Processing, (Institute of Electrical and Electronics Engineers, California, 2010), pp. 1849–1852.
  24. S. J. Wright, R. D. Nowak, and M. A. Figueiredo, “Sparse Reconstruction by Separable Approximation,” IEEET, Signal Process.57, 2479–2493 (2009).
  25. I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math.57(11), 1413–1457 (2004). [CrossRef]
  26. P. Combettes and V. Wajs, “Signal recovery by proximal forward backward splitting,” Multiscale Model. Simul.4(4), 1168–1200 (2005). [CrossRef]
  27. E. Hale, W. Yin, and Y. Zhang, “A fixed-point continuation method for L1-regularized minimization with applications to compressed sensing,” Tech. Rep. TR07–07 (Rice Univ., Houston, TX, 2007).
  28. Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett.9(3), 81–84 (2002). [CrossRef]

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