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Deblurring Space-Variant Blur by Adding Noisy Image

  • Iftach Klapp
  • Nir Sochen
  • David Mendlovic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)

Abstract

Imaging restoration is an essential step in hybrid optical and image processing system which relays on poor optics. The poor optics makes the blur ill-conditioned and turns the deblurring process difficult and unstable. Recently the idea of parallel optics (PO) was introduced. In the parallel optics setup the optical system is composed of a main system and an auxiliary system. The auxiliary system is designed to improve the stability of the deblurring process by improving the condition number of the blurring operator. In this paper we show that in one such system the post processing acts as a noise filter hence allows to work with noisy data in the auxiliary channel. Using the singular value decomposition we derive analytical limit for the difference in SNR requirements of the auxiliary channel relative to that of the main channel. The gap between the SNR requirements of the two systems is analyzed theoretically and proved to be as large as 27.68 [db]. Image restoration comparison on simulations is performed between a blurred/noisy pair with average SNR gap of 20 [db] and a system without an auxiliary system. The average Mean Square Error Improvement Factor (MSEIF) achieved by the blurred/noisy pair, was 13.9 [db] higher than the system without a noisy auxiliary system.

Keywords

deblurring parallel optics blurred and noisy image pair 

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References

  1. 1.
    Dowski, E.R., Chathey, T.: Extended depth of field through wave-front coding. App. Opt. 34(11), 1859 (1995)CrossRefGoogle Scholar
  2. 2.
    Demenikov, M., Findlay, E., Harvey, A.R.: Miniaturization of zoom lenses with a single moving element. Opt. Express 17(8), 6118 (2009)CrossRefGoogle Scholar
  3. 3.
    Shabtay, G., Goldenberg, E., Dery, E.: Imaging system with improved image quality and associated methods US patent 2009/122150 A1Google Scholar
  4. 4.
    Guichard, F., et al.: Extended depth-of-field using sharpness transport across color channels. In: Proc. SPIE 7250, 72500N (2009)Google Scholar
  5. 5.
    Muyo, G., et al.: Infrared imaging with a wavefront-coded singlet lens. Opt. Express 17(23), 21118 (2009)CrossRefGoogle Scholar
  6. 6.
    Nitta, K., et al.: Image reconstruction for thin observation module by bound optics by using the iterative backprojection method. App. Opt. 45(13), 2893–2900 (2006)CrossRefGoogle Scholar
  7. 7.
    Duparr, J.W., et al.: Ultra thin camera based on artificial apposition compound eyes, http://www.suss-microoptics.com/downloads/Publications/MOC-04.pdf
  8. 8.
    Ng, R., et al.: Light field photography with hand held Plenoptic camera, Stanford Tech Report CTSR 2005-02Google Scholar
  9. 9.
    Kidjer, M.J.: Principles of lens design. In: SPIE Proc., CR4, pp. 30–52 (1992)Google Scholar
  10. 10.
    Klapp, I., Mendlovic, D.: Improvement of matrix condition of Hybrid, space variant optics by the means of Parallel Optics design. Opt. Express 17, 11673–11689 (2009)CrossRefGoogle Scholar
  11. 11.
    Klapp, I., Mendlovic, D.: Trajectories in Parallel Optics (submitted to JOSA)Google Scholar
  12. 12.
    Klapp, I., Mendlovic, D.: Optical Design for Improving Matrix Condition, SRS, OSA (2009) paper STuA7Google Scholar
  13. 13.
    Kopeika, N.S.: A system Engineering approach to imaging, pp. 517–520 (SPIE, 1998)Google Scholar
  14. 14.
    Jain, A.K.: Fundamentals of digital image processing, p. 59. Prentice Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  15. 15.
    Klapp, I., Mendlovic, D.: Blurred/noisy image pairs in Parallel Optics (to be submitted)Google Scholar
  16. 16.
    Bertero, M., Boccacci, P.: Introduction to inverse problems in imaging (IOP, 1998). Waterman, M.S.: Identification of Common Molecular SubsequencesGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Iftach Klapp
    • 1
  • Nir Sochen
    • 2
  • David Mendlovic
    • 1
  1. 1.Department of Physical ElectronicsTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsTel-Aviv UniversityTel-AvivIsrael

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