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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 2 — Feb. 1, 2012

Sampling and processing for compressive holography [Invited]

Sehoon Lim, Daniel L. Marks, and David J. Brady  »View Author Affiliations

Applied Optics, Vol. 50, Issue 34, pp. H75-H86 (2011)

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Compressive holography applies sparsity priors to data acquired by digital holography to infer a small number of object features or basis vectors from a slightly larger number of discrete measurements. Compressive holography may be applied to reconstruct three-dimensional (3D) images from two-dimensional (2D) measurements or to reconstruct 2D images from sparse apertures. This paper is a tutorial covering practical compressive holography procedures, including field propagation, reference filtering, and inverse problems in compressive holography. We present as examples 3D tomography from a 2D hologram, 2D image reconstruction from a sparse aperture, and diffuse object estimation from diverse speckle realizations.

© 2011 Optical Society of America

OCIS Codes
(100.6950) Image processing : Tomographic image processing
(110.6150) Imaging systems : Speckle imaging
(110.1758) Imaging systems : Computational imaging
(090.1995) Holography : Digital holography

ToC Category:
Invited ISP Papers

Original Manuscript: August 15, 2011
Revised Manuscript: September 3, 2011
Manuscript Accepted: September 7, 2011
Published: November 10, 2011

Virtual Issues
Vol. 7, Iss. 2 Virtual Journal for Biomedical Optics
Digital Holography and 3D Imaging 2011 (2011) Applied Optics

Sehoon Lim, Daniel L. Marks, and David J. Brady, "Sampling and processing for compressive holography [Invited]," Appl. Opt. 50, H75-H86 (2011)

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  1. W. Jueptner and U. Schnars, Digital Holography (Springer-Verlag, 2005).
  2. E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006). [CrossRef]
  3. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006). [CrossRef]
  4. M. A. Neifeld and P. Shankar, “Feature-specific imaging,” Appl. Opt. 42, 3379–3389 (2003). [CrossRef] [PubMed]
  5. D. J. Brady, N. Pitsianis, X. Sun, and P. Potuluri, “Compressive sampling and signal inference,” U.S. patent 7,283,231(16 October 2007).
  6. 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]
  7. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A 27, 1630–1637 (2010). [CrossRef]
  8. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049(2009). [CrossRef] [PubMed]
  9. J. Hahn, S. Lim, K. Choi, R. Horisaki, and D. J. Brady, “Video-rate compressive holographic microscopic tomography,” Opt. Express 19, 7289–7298 (2011). [CrossRef] [PubMed]
  10. C. F. Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, “Millimeter-wave compressive holography,” Appl. Opt. 49, E67–E82 (2010). [CrossRef] [PubMed]
  11. K. Choi, R. Horisaki, J. Hahn, S. Lim, D. L. Marks, T. J. Schulz, and D. J. Brady, “Compressive holography of diffuse objects,” Appl. Opt. 49, H1–H10 (2010). [CrossRef] [PubMed]
  12. L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009). [CrossRef] [PubMed]
  13. C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27, 1856–1862 (2010). [CrossRef]
  14. M. M. Marim, M. Atlan, E. Angelini, and J.-C. Olivo-Marin, “Compressed sensing with off-axis frequency-shifting holography,” Opt. Lett. 35, 871–873 (2010). [CrossRef] [PubMed]
  15. M. Marim, E. Angelini, J.-C. Olivo-Marin, and M. Atlan, “Off-axis compressed holographic microscopy in low-light conditions,” Opt. Lett. 36, 79–81 (2011). [CrossRef] [PubMed]
  16. Y. Rivenson, A. Stern, and B. Javidi, “Compressive fresnel holography,” IEEE J. Display Technol. 6, 506–509 (2010). [CrossRef]
  17. Y. Rivenson, A. Stern, and J. Rosen, “Compressive multiple view projection incoherent holography,” Opt. Express 19, 6109–6118 (2011). [CrossRef] [PubMed]
  18. Q. Xu, K. Shi, H. Li, K. Choi, R. Horisaki, D. Brady, D. Psaltis, and Z. Liu, “Inline holographic coherent anti-Stokes Raman microscopy,” Opt. Express 18, 8213–8219 (2010). [CrossRef] [PubMed]
  19. Z. Xu and E. Y. Lam, “Image reconstruction using spectroscopic and hyperspectral information for compressive terahertz imaging,” J. Opt. Soc. Am. A 27, 1638–1646 (2010). [CrossRef]
  20. A. F. Coskun, I. Sencan, T.-W. Su, and A. Ozcan, “Lensless wide-field fluorescent imaging on a chip using compressive decoding of sparse objects,” Opt. Express 18, 10510–10523(2010). [CrossRef] [PubMed]
  21. M. Suezen, A. Giannoula, and T. Durduran, “Compressed sensing in diffuse optical tomography,” Opt. Express 18, 23676–23690 (2010). [CrossRef]
  22. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962). [CrossRef]
  23. E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008). [CrossRef]
  24. U. Schnars and W. Juptner, Digital Holography, Digital Hologram Recording, Numerical Reconstruction and Related Techniques (Springer, 2005).
  25. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts and Company, 2005).
  26. U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85–R101 (2002). [CrossRef]
  27. D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009). [CrossRef]
  28. T. Kreis, M. Adams, and W. Juptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997). [CrossRef]
  29. D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948). [CrossRef] [PubMed]
  30. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268(1992). [CrossRef]
  31. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004(2007). [CrossRef] [PubMed]
  32. J. W. Goodman, Speckle Phenomena in Optics, Theory and Applications (Roberts and Company, 2007).
  33. T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing (Prentice-Hall, 2000).
  34. J. Tropp, “Just relax: convex programming methods for identifying sparse signals in noise,” IEEE Trans. Inf. Theory 52, 1030–1051 (2006). [CrossRef]
  35. S. Lim, K. Choi, J. Hahn, D. L. Marks, and D. J. Brady, “Image-based registration for synthetic aperture holography,” Opt. Express 19, 11716–11731 (2011). [CrossRef] [PubMed]
  36. A. R. Thompson, J. M. Moran, and J. G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley, 2001). [CrossRef]

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