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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: Franco Gori
  • Vol. 29, Iss. 3 — Mar. 1, 2012
  • pp: 331–343

Experimental results for improving the matrix condition using a hybrid optical system

Iftach Klapp and David Mendlovic  »View Author Affiliations


JOSA A, Vol. 29, Issue 3, pp. 331-343 (2012)
http://dx.doi.org/10.1364/JOSAA.29.000331


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Abstract

We present preliminary experimental results for implementing the “blurred trajectories” method on three parallel optics (PO) systems. The “main” system and “auxiliary” optics were simple laboratory graded lenses attached to an iris diaphragm. When applying the blurred trajectories method we first show an improvement in the matrix condition, as the matrix condition number decreased in a range of factors of 3 to 418 relative to the main system. Following that, image restoration by weak regularization was performed so that the system matrix condition dominated the restoration process. It was shown that the restoration results of the PO are better than those of the main system and the auxiliary optics separately. In addition, the quality of the restoration follows the system’s matrix condition. The improvement in the matrix condition achieved by the PO system improved the immunity to detection noise. Finally, a comparison to Wiener filtering restoration shows that it is also generally inferior to the proposed method.

© 2012 Optical Society of America

OCIS Codes
(070.6110) Fourier optics and signal processing : Spatial filtering
(080.1010) Geometric optics : Aberrations (global)
(100.3190) Image processing : Inverse problems
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: August 16, 2011
Revised Manuscript: November 29, 2011
Manuscript Accepted: November 29, 2011
Published: February 21, 2012

Citation
Iftach Klapp and David Mendlovic, "Experimental results for improving the matrix condition using a hybrid optical system," J. Opt. Soc. Am. A 29, 331-343 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-3-331


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References

  1. A. A. Sawchuk and M. J. Peyrovian, “Restoration of astigmatism and curvature of field,” J. Opt. Soc. Am. 65, 712–715 (1975). [CrossRef]
  2. M. P. Ekstrom, “A spectral characterization of the ill conditioning in numerical deconvolution,” IEEE Trans. Audio Electroacoust. 21, 344–348 (1973). [CrossRef]
  3. P. C. Hansen and J. G. Nagy, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006), Chap. 1.4.
  4. I. Klapp and D. Mendlovic, “Improvement of matrix condition of hybrid, space variant optics by the means of parallel optics design,” Opt. Express 17, 11673–11689(2009). [CrossRef]
  5. J. H. Wilkinson, Rounding Errors in Algebraic Processes (Her Majesty’s Stationery Office, 1963), Chap. 3, p. 91.
  6. M. Sabbarao, Y. Kang, S. Dutta, and X. Tue, “Localized and computationally efficient approach to shift-variant image deblurring,” in Proceedings of IEEE International Conference on Image Processing, 2008 (ICIP 2008) (IEEE, 2008), pp. 657–660.
  7. Y. Yoo, S. Jun, J. Shin, and J. Paik, “Regularized iterative restoration of combined optical and color filter array degradation,” in Second International Conference on Future Generation Communication and Networking Symposia, 2008 (FGCNS 2008) (IEEE, 2008), pp. 197–202.
  8. L. Deng and R. Lu, “A blind image restoration method based on genetic algorithm and the fuzzy control,” in International Conference on Audio, Language and Image Processing, 2008 (ICALIP 2008) (IEEE, 2008), pp. 330–334.
  9. T. A. Cheema, I. M. Qureshi, and A. Hussain, “Blind Image deconvolution using space-variant neural network approach,” Electron. Lett. 41, 308–309 (2005). [CrossRef]
  10. M. Kieweg, H. Gross, T. Sievers, and L. Müller, “Ill-posedness of space variant image deconvolution,” Proc. SPIE 7800, 78000K (2010). [CrossRef]
  11. T. Ito, H. Hoshino, Y. Fujii, and N. Ohta, “Measurements of space variant PSF and its application to restoring severely degraded images,” in Proceedings of ICROS-SICE International Joint Conference 2009 (IEEE, 2009), pp. 2301–2304.
  12. M. Rerabek and P. Pata, “The space variant PSF for deconvolution of wide field astronomical images,” Proc. SPIE 7015, 70152G (2008). [CrossRef]
  13. M. K. Singh, U. S. Tiwary, and Y. Kim, “An adaptively accelerated Lucy-Richardson method for image deblurring,” EURASIP J. Adv. Signal Process. V2008, 365021 (2008).
  14. H. C. Andrews and C. L. Paterson, “Singular value decomposition and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976). [CrossRef]
  15. I. Klapp and D. Mendlovic, “Optical design for improving matrix condition,” in Signal Recovery and SynthesisOSA Technical Digest (CD) (Optical Society of America, 2009), paper STuA7.
  16. I. Klapp, N. Sochen, and D. Mendlovic, “Trajectories in parallel optics,” J. Opt. Soc. Am. A 28, 2014–2025 (2011). [CrossRef]
  17. I. Klapp and D. Mendlovic, “Trajectories by a blurred auxiliary lens,” J. Opt. Soc. Am. A 28, 1796–1804 (2011). [CrossRef]
  18. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998), Chap. 18.
  19. G. H. Golob and C. F. Van-Loan, Matrix Computations (North Oxford Academic, 1983).
  20. S. Kavusi, H. Kakavand, and A. El Gamal, “Quantitative study of high dynamic range sigma delta-based focal plane array architectures, Proc. SPIE 5406, 341–350 (2004). [CrossRef]
  21. X. Liu, “CMOS image sensors dynamic range and SNR enhancement via statistical signal processing,” Ph.D. dissertation (Stanford, 2002).
  22. N. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322–336 (1992). [CrossRef]
  23. A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, 1989), Chap. 3.6.
  24. M. Elad, “Introduction to image processing,” Lecture Notes (Technion, 1999) (in Hebrew). http://www.cs.technion.ac.il/~elad/publications/Various/Book_ImageProcessing.pdf .
  25. M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.24–41 (1997). [CrossRef]
  26. I. Klapp and D. Mendlovic, “Optical design for improving the matrix condition—experiment,” in Frontiers in OpticsOSA Technical Digest (CD) (Optical Society of America, 2010), paper FTuD5.

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