OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 5 — May. 1, 2004
  • pp: 737–750

Penalized-likelihood image reconstruction for digital holography

Saowapak Sotthivirat and Jeffrey A. Fessler  »View Author Affiliations


JOSA A, Vol. 21, Issue 5, pp. 737-750 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000737


View Full Text Article

Enhanced HTML    Acrobat PDF (828 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.

© 2004 Optical Society of America

OCIS Codes
(090.0090) Holography : Holography
(090.1760) Holography : Computer holography
(100.0100) Image processing : Image processing
(100.2000) Image processing : Digital image processing
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems

History
Original Manuscript: March 10, 2003
Revised Manuscript: December 16, 2004
Manuscript Accepted: December 16, 2004
Published: May 1, 2004

Citation
Saowapak Sotthivirat and Jeffrey A. Fessler, "Penalized-likelihood image reconstruction for digital holography," J. Opt. Soc. Am. A 21, 737-750 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-5-737


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  2. D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948). [CrossRef]
  3. E. N. Leith, J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962). [CrossRef]
  4. H. Chen, M. Shih, E. Arons, E. Leith, J. Lopez, D. Dilworth, P. C. Sun, “Electronic holographic imaging through living human tissue,” Appl. Opt. 33, 3630–3632 (1994). [CrossRef] [PubMed]
  5. E. Leith, H. Chen, Y. Chen, D. Dilworth, J. Lopez, R. Masri, J. Rudd, J. Valdmanis, “Electronic holography and speckle methods for imaging through tissue using femtosecond gated pulses,” Appl. Opt. 30, 4204–4210 (1991). [CrossRef] [PubMed]
  6. Y. Takaki, H. Ohzu, “Fast numerical reconstruction technique for high-resolution hybrid holographic microscopy,” Appl. Opt. 38, 2204–2211 (1999). [CrossRef]
  7. Y. Takaki, H. Kawai, H. Ohzu, “Hybrid holographic mi- croscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999). [CrossRef]
  8. E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrasting imaging,” Opt. Lett. 24, 291–293 (1999). [CrossRef]
  9. E. Cuche, P. Marquet, C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000). [CrossRef]
  10. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997). [CrossRef] [PubMed]
  11. S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, “Wave front reconstruction of Fresnel off-axis holograms with compensation of aberrations by means of phase-shifting digital holography,” Opt. Lasers Eng. 37, 331–340 (2002). [CrossRef]
  12. M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel non-diffractive reconstruction method for digital holographic microscopy,” in Proceedings of the IEEE International Symposium on Biomedical Imaging (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 625–628.
  13. C. A. Bouman, K. Sauer, “A unified approach statistical tomography using coordinate descent optimization,” IEEE Trans. Image Process. 5, 480–492 (1996). [CrossRef]
  14. H. Erdoğan, J. A. Fessler, “Monotonic algorithms for transmission tomography,” IEEE Trans. Med. Imaging 18, 801–814 (1999). [CrossRef] [PubMed]
  15. J. A. Conchello, “Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images,” J. Opt. Soc. Am. A 15, 2609–2619 (1998). [CrossRef]
  16. T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988). [CrossRef]
  17. M. Çetin, W. C. Karl, A. S. Willsky, “Edge-preserving image reconstruction for coherent imaging applications,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 481–484.
  18. B. W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman & Hall, New York, 1986).
  19. J. A. Fessler, A. O. Hero, “Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms,” IEEE Trans. Image Process. 4, 1417–1429 (1995). [CrossRef] [PubMed]
  20. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).
  21. J. L. Marroquin, M. Tapia, “Parallel algorithms for phase unwrapping based on Markov random field models,” J. Opt. Soc. Am. A 12, 2578–2585 (1995). [CrossRef]
  22. W. Kim, M. H. Hayes, “Phase retrieval using two Fourier-transform intensities,” J. Opt. Soc. Am. A 7, 441–449 (1990). [CrossRef]
  23. S. Sotthivirat, J. A. Fessler, “Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms,” IEEE Trans. Image Process. 11, 306–317 (2002). [CrossRef]
  24. E. Arons, E. Leith, “Coherence confocal-imaging system for enhanced depth discrimination in transmitted light,” Appl. Opt. 35, 2499–2506 (1996). [CrossRef]
  25. P.-C. Sun, E. N. Leith, “Broad-source image plane holography as a confocal imaging process,” Appl. Opt. 33, 597–602 (1994). [CrossRef] [PubMed]
  26. Y. Censor, “Finite series expansion reconstruction methods,” Proc. IEEE 71, 409–419 (1983). [CrossRef]
  27. D. L. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993). [CrossRef] [PubMed]
  28. M. Cetin, W. C. Karl, A. S. Willsky, “Edge-preserving image reconstruction for coherent imaging applications,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 481–484.
  29. M. Çetin, W. C. Karl, “Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization,” IEEE Trans. Image Process. 10, 623–631 (2001). [CrossRef]
  30. K. Lange, “Convergence of EM image reconstruction algo-rithms with Gibbs smoothing,” IEEE Trans. Med. Imaging 9, 439–446 (1990). [CrossRef]
  31. J. A. Fessler, “Grouped coordinate descent algorithms for robust edge-preserving image restoration,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 184–194 (1997). [CrossRef]
  32. P. J. Huber, Robust Statistics (Wiley, New York, 1981).
  33. J. A. Fessler, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imaging 16, 166–175 (1997). [CrossRef] [PubMed]
  34. A. R. De Pierro, “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography,” IEEE Trans. Med. Imaging 14, 132–137 (1995). [CrossRef] [PubMed]
  35. S. Sotthivirat, “Statistical image recovery techniques for optical imaging systems,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 2003).

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