OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 27269–27276

Two-kernel image deconvolution

V. Gorelik  »View Author Affiliations

Optics Express, Vol. 21, Issue 22, pp. 27269-27276 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (928 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A method for deconvolution of the true image of an object from two recorded images is proposed. These two images have to be made by an imaging system with two different but interconnected kernels. The method is formulated as a system of Fredholm equations of the first kind reduced to a single functional equation in Fourier space. The kernels of the system and the true image of an object are found from the same recorded images.

© 2013 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing

ToC Category:
Image Processing

Original Manuscript: May 20, 2013
Manuscript Accepted: October 23, 2013
Published: November 1, 2013

V. Gorelik, "Two-kernel image deconvolution," Opt. Express 21, 27269-27276 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Demenikov and A. R. Harvey, “Parametric blind-deconvolution algorithm to remove image artifacts in hybrid imaging systems,” Opt. Express18(17), 18035–18040 (2010). [PubMed]
  2. W. Dong, H. Feng, Z. Xu, and Q. Li, “A piecewise local regularized Richardson–Lucy algorithm for remote sensing image deconvolution,” Opt. Laser Technol.43(5), 926–933 (2011). [CrossRef]
  3. N. Wiener, The Extrapolation, Interpolation and Smoothing of Stationary Time series (John Wiley & Sons, 1949).
  4. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am.62(1), 55–59 (1972). [CrossRef]
  5. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J.79, 745–754 (1974). [CrossRef]
  6. A. N. Tikhonov and V. Y. Arsenin, Methods for Solution of Incorrect Problems (Nauka, 1986).
  7. V. A. Gorelik, “Method of recovering the fine structure of a spectrum without measuring the instrument function of the spectrometer,” Tech. Phys.39, 444–446 (1994).
  8. V. A. Gorelik and A. V. Yakovenko, “Fine structure extraction without analyser function measurement,” J. Elec. Spec. Rel. Phenom.73(1), R1–R3 (1995). [CrossRef]
  9. R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photography: motion deblurring using fluttered shutter,” ACM Trans. Graph.25(3), 795–804 (2006). [CrossRef]
  10. A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph.26(3), 69 (2007). [CrossRef]
  11. Y. Y. Schechner and N. Kiryati, “Depth from Defocus vs. Stereo: How Different Really Are They?” Int. J. Comput. Vis.39(2), 141–162 (2000). [CrossRef]
  12. D. Rajan and S. Chaudhuri, “Simultaneous Estimation of Super-Resolved Scene and Depth Map from Low Resolution Defocused Observations,” IEEE Trans. Pattern Anal. Mach. Intell.25(9), 1102–1117 (2003). [CrossRef]
  13. P. Favaro, S. Soatto, M. Burger, and S. J. Osher, “Shape from defocus via Diffusion,” IEEE Trans. Pattern Anal. Mach. Intell.30(3), 518–531 (2008). [CrossRef] [PubMed]
  14. J. K. Doylend, M. J. R. Heck, J. T. Bovington, J. D. Peters, L. A. Coldren, and J. E. Bowers, “Two-dimensional free-space beam steering with an optical phased array on silicon-on-insulator,” Opt. Express19(22), 21595–21604 (2011). [CrossRef] [PubMed]
  15. A. R. Vasishtha, Complex Analysis, 11th ed. (Krishna Prakashan Media, 2010).
  16. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, 1992), Chap. 13.

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited