OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 11 — Aug. 25, 2010

Edge-preserving sectional image reconstruction in optical scanning holography

Xin Zhang and Edmund Y. Lam  »View Author Affiliations


JOSA A, Vol. 27, Issue 7, pp. 1630-1637 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001630


View Full Text Article

Enhanced HTML    Acrobat PDF (584 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Optical scanning holography (OSH) enables us to capture the three-dimensional information of an object, and a post-processing step known as sectional image reconstruction allows us to view its two-dimensional cross-section. Previous methods often produce reconstructed images that have blurry edges. In this paper, we argue that the hologram’s two-dimensional Fourier transform maps into a semi-spherical surface in the three-dimensional frequency domain of the object, a relationship akin to the Fourier diffraction theorem used in diffraction tomography. Thus, the sectional image reconstruction task is an ill-posed inverse problem, and here we make use of the total variation regularization with a nonnegative constraint and solve it with a gradient projection algorithm. Both simulated and experimental holograms are used to verify that edge-preserving reconstruction is achieved, and the axial distance between sections is reduced compared with previous regularization methods.

© 2010 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(180.6900) Microscopy : Three-dimensional microscopy
(110.1758) Imaging systems : Computational imaging
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: March 25, 2010
Revised Manuscript: May 19, 2010
Manuscript Accepted: May 21, 2010
Published: June 16, 2010

Virtual Issues
Vol. 5, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Xin Zhang and Edmund Y. Lam, "Edge-preserving sectional image reconstruction in optical scanning holography," J. Opt. Soc. Am. A 27, 1630-1637 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-27-7-1630


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T.-C. Poon, “Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis,” J. Opt. Soc. Am. A 2, 521–527 (1985). [CrossRef]
  2. J. Swoger, M. Martínez-Corral, J. Huisken, and E. Stelzer, “Optical scanning holography as a technique for high-resolution three-dimensional biological microscopy,” J. Opt. Soc. Am. A 19, 1910–1918 (2002). [CrossRef]
  3. U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer-Verlag, 2005).
  4. T.-C. Poon, Digital Holography and Three-Dimensional Display: Principles and Applications (Springer, 2006). [CrossRef]
  5. X. Zhang, E. Y. Lam, and T.-C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008). [CrossRef] [PubMed]
  6. T. Kim, “Optical sectioning by optical scanning holography and a Wiener filter,” Appl. Opt. 45, 872–879 (2006). [CrossRef] [PubMed]
  7. 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, D164–D175 (2008). [CrossRef] [PubMed]
  8. S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007). [CrossRef]
  9. G. Indebetouw, “Properties of a scanning holographic microscopy: Improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002). [CrossRef]
  10. R. K. Mueller, M. Kaveh, and G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979). [CrossRef]
  11. A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. GE-22, 3–13 (1984). [CrossRef]
  12. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982). [CrossRef] [PubMed]
  13. P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338–2347 (2005). [CrossRef]
  14. S. J. LaRoque, E. Y. Sidky, and X. Pan, “Accurate image reconstruction from few-view and limited-angle data in diffraction tomography,” J. Opt. Soc. Am. A 25, 1772–1782 (2008). [CrossRef]
  15. G. Indebetouw, P. Klysubun, T. Kim, and T.-C. Poon, “Imaging properties of scanning holographic microscopy,” J. Opt. Soc. Am. A 17, 380–390 (2000). [CrossRef]
  16. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer-Verlag, 2007). [CrossRef]
  17. 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, H113–H119 (2009). [CrossRef] [PubMed]
  18. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005),
  19. G. Indebetouw and W. Zhong, “Scanning holographic microscopy of three-dimensional fluorescent specimens,” J. Opt. Soc. Am. A 23, 1699–1707 (2006). [CrossRef]
  20. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969). [CrossRef]
  21. C. L. Matson and H. Liu, “The Fourier diffraction theorem for turbid media,” in “Advances in Optical Imaging and Photon Migration,” J.Fujimoto and M.Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics (Optical Society of America, 1998) p. ATuD14.
  22. R. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, 1999),
  23. A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. BME-30, 377–386 (1983). [CrossRef]
  24. Y. Zou and X. Pan, “Image reconstruction on PI-lines by use of filtered backprojection in helical cone-beam CT,” Phys. Med. Biol. 49, 2717–2731 (2004). [CrossRef] [PubMed]
  25. T. Chan and J. Shen, Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods (SIAM, 2005).
  26. E. 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]
  27. R. Gonzalez and R. Woods, Digital Image Processing, 3rd ed. (Pearson Prentice Hall, 2008).
  28. Y. Li and F. Santosa, “A computational algorithm for minimizing total variation in image restoration,” IEEE Trans. Image Process. 5, 987–995 (1996). [CrossRef] [PubMed]
  29. D. Strong and T. Chan, “Edge-preserving and scale-dependent properties of total variation regularization,” Inverse Probl. 19, S165–S187 (2003). [CrossRef]
  30. M. K. Ng, H. Shen, E. Lam, and L. Zhang, “A total variation regularization based super-resolution reconstruction algorithm for digital video,” EURASIP Journal on Advances in Signal Processing 2007, 1–16 (2007). Article ID 74585. [CrossRef]
  31. E. Candès and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006). [CrossRef]
  32. E. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008). [CrossRef]
  33. 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 (DH), OSA Technical Digest (CD) (Optical Society of America, 2009), paper DMA3.
  34. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge Univ. Press, Cambridge, 2004).
  35. G. Indebetouw, “A posteriori quasi-sectioning of the three-dimensional reconstructions of scanning holographic microscopy,” J. Opt. Soc. Am. A 23, 2657–2661 (2006). [CrossRef]
  36. 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, 3098–3100 (2009). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited