Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 298689, 18 pages
http://dx.doi.org/10.1155/2015/298689
Research Article

Application of the Least Squares Solutions in Image Deblurring

1Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
2Faculty of Computer Science, Goce Delčev University, Goce Delčev 89, 2000 Štip, Macedonia
3Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
4Department of Statistics, Athens University of Economics and Business, 76 Patission Street, 10434 Athens, Greece

Received 2 September 2014; Revised 20 January 2015; Accepted 28 January 2015

Academic Editor: Joao B. R. Do Val

Copyright © 2015 Predrag S. Stanimirović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Processing Magazine, vol. 14, no. 2, pp. 24–41, 1997. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Bovik, The Essential Guide to the Image Processing, Academic Press, New York, NY, USA, 2009.
  3. S. Esedoglu and S. J. Osher, “Decomposition of images by the anisotropic Rudin-Osher-Fatemi model,” Communications on Pure and Applied Mathematics, vol. 57, no. 12, pp. 1609–1626, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice Hall, 3rd edition, 2007.
  5. P. C. Hansen, J. G. Nagy, and D. O'Leary, Deblurring Images: Matrices, Spectra, and Filtering, SIAM, Philadelphia, Pa, USA, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. Kundur and D. Hatzinakos, “Blind image deconvolution: an algorithmic approach to practical image restoration,” IEEE Signal Processing Magazine, vol. 13, no. 3, pp. 43–64, 1996. View at Google Scholar · View at Scopus
  7. S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Processing Magazine, vol. 20, no. 3, pp. 21–36, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. J. van de Weijer and R. van den Boomgaard, “Least squares and robust estimation of local image structure,” International Journal of Computer Vision, vol. 64, no. 2-3, pp. 143–155, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. P. S. Stanimirović, S. Chountasis, D. Pappas, and I. Stojanović, “Removal of blur in images based on least squares solutions,” Mathematical Methods in the Applied Sciences, vol. 36, no. 17, pp. 2280–2296, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Stanimirović, I. Stojanović, S. Chountasis, and D. Pappas, “Image deblurring process based on separable restoration methods,” Computational and Applied Mathematics, vol. 33, no. 2, pp. 301–323, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Mathematical Problems in Engineering, vol. 2009, Article ID 170724, 12 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Mathematical Problems in Engineering, vol. 2010, Article ID 750352, 14 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Chountasis, V. N. Katsikis, and D. Pappas, “Image reconstruction methods for MATLAB users—a Moore-Penrose inverse approach,” in MATLAB—A Fundamental Tool for Scientific Computing and Engineering Applications: Volume 1, InTech, 2012. View at Publisher · View at Google Scholar
  14. P. J. Maher, “Some operator inequalities concerning generalized inverses,” Illinois Journal of Mathematics, vol. 34, no. 3, pp. 503–514, 1990. View at Google Scholar · View at MathSciNet
  15. R. Penrose, “A generalized inverse for matrices,” Proceedings of the Cambridge Philosophical Society, vol. 51, pp. 406–413, 1955. View at Google Scholar · View at MathSciNet
  16. B. H. Shakibaei and J. Flusser, “Image deconvolution in the moment domain,” in Moments and Moment Invariants—Theory and Applications, vol. 1, pp. 111–125, GCSRL, 2014. View at Google Scholar
  17. S. A. Dudani, K. J. Breeding, and R. B. McGhee, “Aircraft identification by moment invariants,” IEEE Transactions on Computers, vol. 26, no. 1, pp. 39–46, 1977. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Milanfar, W. C. Karl, and A. S. Willsky, “A moment-based variational approach to tomographic reconstruction,” IEEE Transactions on Image Processing, vol. 5, no. 3, pp. 459–470, 1996. View at Publisher · View at Google Scholar · View at Scopus
  19. T. B. Nguyen and B. J. Oommen, “Moment-preserving piecewise linear approximations of signals and images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 1, pp. 84–91, 1997. View at Publisher · View at Google Scholar
  20. M. R. Teague, “Image analysis via the general theory of moments,” Journal of the Optical Society of America, vol. 70, no. 8, pp. 920–930, 1980. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. M. Sonka, V. Hlavac, and R. Boyle, Image Processing, Analysis and Machine Vision, Cengage Learning, Stamford, Conn, USA, 2014.
  22. R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulence media,” Journal of the Optical Society of America, vol. 54, no. 1, pp. 52–60, 1964. View at Publisher · View at Google Scholar