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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 10 — Oct. 1, 2008
  • pp: 2600–2607

Reconstruction of compact binary images from limited Fourier amplitude data

V. L. Lo and R. P. Millane  »View Author Affiliations


JOSA A, Vol. 25, Issue 10, pp. 2600-2607 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002600


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Abstract

The problem of reconstructing a binary image from undersampled Fourier amplitude data is considered. This problem maps to an image reconstruction problem in x-ray crystallography. The binary constraint is sufficient to overcome the undersampling and enforce uniqueness, but is insufficient in the case of the additional loss of data that can occur in practice. An iterative projection algorithm is developed that uses binary, connectivity, and compactness constraints to solve the image reconstruction problem. Simulations show the utility of the reconstruction algorithm.

© 2008 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(110.1758) Imaging systems : Computational imaging

ToC Category:
Image Processing

History
Original Manuscript: May 2, 2008
Revised Manuscript: August 22, 2008
Manuscript Accepted: August 24, 2008
Published: September 25, 2008

Citation
V. L. Lo and R. P. Millane, "Reconstruction of compact binary images from limited Fourier amplitude data," J. Opt. Soc. Am. A 25, 2600-2607 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-10-2600


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References

  1. R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394-411 (1990). [CrossRef]
  2. J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H.Stark, ed. (Academic, 1987), pp. 231-275.
  3. M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature (London) 442, 63-66 (2006). [CrossRef]
  4. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. R. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179-1200 (2006). [CrossRef]
  5. P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. 62, 248-261 (2006). [CrossRef]
  6. R. H. T. Bates, “Uniqueness of solutions of two-dimensional Fourier phase problems for localized and positive images,” Comput. Vis. Graph. Image Process. 2, 205-217 (1984). [CrossRef]
  7. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237-246 (1972).
  8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  9. A. Levi and H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932-943 (1984). [CrossRef]
  10. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40-55 (2003). [CrossRef]
  11. R. P. Millane, “Iterative projection algorithms for solving inverse problems,” in Proc. Oceans 2003 (IEEE, 2003), CD-ROM, pp. 2714-2719.
  12. D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. 21, 37-50 (2005). [CrossRef]
  13. J. Drenth, Principles of X-ray Crystallography (Springer-Verlag, 1994).
  14. C. W. Carter, K. V. Crumley, D. E. Coleman, F. Hage, and G. Bricogne, “Direct phase determination for the molecular envelope of tryptophanyl-tRNA synthetase from Bacillus stearothermophilus by x-ray contrast variation,” Acta Crystallogr. 46, 57-68 (1990). [CrossRef]
  15. R. Fourme, W. Shepard, R. Kahn, G. l'Hermite, and I. L. de La Sierra, “The multiwavelength anomalous solvent contrast (MASC) method in macromolecular crystallography,” J. Synchrotron Radiat. 2, 36-48 (1995). [CrossRef] [PubMed]
  16. R. P. Millane and W. J. Stroud, “Reconstructing symmetric images from their undersampled Fourier intensities,” J. Opt. Soc. Am. A 14, 568-579 (1997). [CrossRef]
  17. V. Elser, I. Rankenburg, and P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. U.S.A. 104, 418-423 (2007). [CrossRef] [PubMed]
  18. V. Elser and R. P. Millane, “Reconstruction of an object from its symmetry-averaged diffraction pattern,” Acta Crystallogr. 64, 273-279 (2008). [CrossRef]

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