OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 22, Iss. 4 — Apr. 1, 2005
  • pp: 616–624

Signal recovery from autocorrelation and cross-correlation data

Timothy J. Schulz and David G. Voelz  »View Author Affiliations

JOSA A, Vol. 22, Issue 4, pp. 616-624 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (396 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A signal recovery technique is motivated and derived for the recovery of several nonnegative signals from measurements of their autocorrelation and cross-correlation functions. The iterative technique is shown to preserve nonnegativity of the signal estimates and to produce a sequence of estimates whose correlations better approximate the measured correlations as the iterations proceed. The method is demonstrated on simulated data for active imaging with dual-frequency or dual-polarization illumination.

© 2005 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(110.0110) Imaging systems : Imaging systems

Original Manuscript: June 22, 2004
Manuscript Accepted: September 22, 2004
Published: April 1, 2005

Timothy J. Schulz and David G. Voelz, "Signal recovery from autocorrelation and cross-correlation data," J. Opt. Soc. Am. A 22, 616-624 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  2. T. J. Schulz, D. L. Snyder, “Image recovery from correlations,” J. Opt. Soc. Am. A 9, 1266–1272 (1992). [CrossRef]
  3. G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its application,” Opt. Lett. 13, 547–549 (1988). [CrossRef]
  4. T. J. Holmes, “Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach,” J. Opt. Soc. Am. A 9, 1052–1061 (1992). [CrossRef] [PubMed]
  5. T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993). [CrossRef]
  6. J. C. Dainty, J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Applications, H. Stark, ed. (Academic, New York, 1987), pp. 231–275.
  7. T. Isernia, V. Pascazio, R. Pierri, G. Schirinzi, “Image reconstruction from Fourier transform magnitude with applications to synthetic aperture radar imaging,” J. Opt. Soc. Am. A 13, 922–934 (1996). [CrossRef]
  8. B. R. Hunt, T. L. Overman, P. Gough, “Image reconstruction from pairs of Fourier-transform magnitude,” Opt. Lett. 23, 1123–1125 (1998). [CrossRef]
  9. M. C. Roggemann, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  10. R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imagingtechnique utilizing two speckle fields: root reconstructors,” J. Opt. Soc. Am. A 19, 444–457 (2002). [CrossRef]
  11. R. B. Holmes, K. Hughes, P. Fairchild, B. Spivey, A. Smith, “Description and simulation of an active imaging technique utilizing two speckle fields: iterative reconstructors,” J. Opt. Soc. Am. A 19, 458–471 (2002). [CrossRef]
  12. D. G. Voelz, J. F. Belsher, L. Ulibarri, V. Gamiz, “Ground-to-space laser imaging: review 2001,” in Free-Space Laser Communication and Laser Imaging, D. G. Voelz, J. C. Ricklin, eds., Proc. SPIE4489, 35–47 (2002). [CrossRef]
  13. J. R. Fienup, P. S. Idell, “Imaging correlography with sparse arrays of detectors,” Opt. Eng. 27, 778–784 (1988). [CrossRef]
  14. D. G. Voelz, J. D. Gonglewski, P. S. Idell, “Image synthesis from nonimaged laser-speckle patterns: comparison of theory, computer simulation, and laboratory results,” Appl. Opt. 30, 3333–3344 (1991). [CrossRef] [PubMed]
  15. L. K. Jones, C. L. Byrne, “General entropy criteria for inverse problems, with applications to data compression, pattern classification, and cluster analysis,” IEEE Trans. Inf. Theory 36, 23–30 (1990). [CrossRef]
  16. I. Csiszar, “Why least squares and maximum entropy?—An axiomatic approach to inverse problems,” Ann. Stat. 19, 2033–2066 (1991). [CrossRef]
  17. A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B Methodol. 39, 1–37 (1977) (with discussion).
  18. G. J. McLachlan, T. Krishnan, The EM Algorithm and Extensions (Wiley, New York, 1997).
  19. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Heidelberg, Germany, 1984).
  20. J. M. Geary, Introduction to Wavefront Sensors, Vol. TT 18 of Tutorial Texts in Optical Engineering (SPIE, Bellingham, Wash., 1995).
  21. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  22. D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer-Verlag, New York, 1991).

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited