Abstract

This paper discusses questions associated with the added noise of blurred and/or defocused images. The sequence of filtering the noise on such images—before eliminating the blurring/defocusing, or after it—is analyzed. The concepts of preliminary and subsequent filtering of noise are introduced. The blurring/defocusing of a series of images was eliminated by the methods of parametric Wiener filtering and Tikhonov regularization, while the noise was filtered out by the methods of adaptive Wiener filtering and median filtering.

© 2013 Optical Society of America

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  1. J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, Englewood Cliffs, NJ, 1990).
  2. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, NJ, 2002; Tekhnosfera, Moscow, 2006).
  3. R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice Hall, Upper Saddle River, NJ, 2004; Tekhnosfera, Moscow, 2006).
  4. V. D’yakonov and I. Abramenkova, MATLAB. Signal and Image Processing (Piter, St. Petersburg, 2002).
  5. V. S. Sizikov, Inverse Applied Problems in MATLAB (Lan’, St. Petersburg, 2011).
  6. V. S. Sizikov, Integral Equations and MATLAB in Problems of Tomography, Iconics, and Spectroscopy (LAP, Saarbrücken, 2011).
  7. V. S. Sizikov and I. A. Belov, “Reconstruction of blurred and out-of-focus images by regularization,” Opt. Zh. 67, No. 4, 60 (2000) [J. Opt. Technol.67, 351 (2000)].
  8. V. S. Sizikov, Mathematical Methods of Processing the Results of Measurements (Politekhnika, St. Petersburg, 2001).
  9. V. S. Sizikov, M. V. Rimskikh, and R. K. Mirdzhamolov, “Reconstructing blurred noisy images without using boundary conditions,” Opt. Zh. 76, No. 5, 38 (2009) [J. Opt. Technol.76, 279 (2009)].
  10. V. S. Sizikov, “The truncation–blurring–rotation technique for reconstructing distorted images,” Opt. Zh. 78, No. 5, 18 (2011) [J. Opt. Technol.78, 298 (2011)].
  11. R. A. Ékzemplyarov and V. S. Sizikov, “Eliminating blurring and defocusing of images with preliminary noise filtering in MatLab,” in Materials of the International Conference, Thirty-Nine Weeks of SPbGPU, part XIII (IMOP), ed. A. I. Rudskii (SPbGPU, St. Petersburg, 2010), pp. 223–225.
  12. Yu. P. Petrov and V. S. Sizikov, Well-Posed, Ill-Posed, and Intermediate Problems with Applications (VSP, Leiden, 2005).
  13. A. V. Gorshkov, “Improving the resolution of images when processing the data of a physical experiment and imposing an unknown instrumental function using the REIMAGE software package,” Prib. Tekh. Eksp. No. 2, 68 (1995).
  14. M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
    [CrossRef]
  15. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996).
  16. A. F. Verlan’ and V. S. Sizikov, Integral Equations: Methods, Algorithms, Programs (Naukov Dumka, Kiev, 1986).
  17. Yu. E. Voskobonikov and V. A. Litasov, “Stable algorithm for reconstructing an image with an inaccurately specified spread function,” Avtometriya 42, No. 6, 3 (2006).
  18. V. N. Ostrikov and O. V. Plakhotnikov, “Identifying the point-spread function of an observation channel from a calibrating image by the method of least squares,” Opt. Zh. 73, No. 2, 26 (2006) [J. Opt. Technol.73, 91 (2006)].
  19. D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

2006 (3)

M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
[CrossRef]

Yu. E. Voskobonikov and V. A. Litasov, “Stable algorithm for reconstructing an image with an inaccurately specified spread function,” Avtometriya 42, No. 6, 3 (2006).

D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

1995 (1)

A. V. Gorshkov, “Improving the resolution of images when processing the data of a physical experiment and imposing an unknown instrumental function using the REIMAGE software package,” Prib. Tekh. Eksp. No. 2, 68 (1995).

Abramenkova, I.

V. D’yakonov and I. Abramenkova, MATLAB. Signal and Image Processing (Piter, St. Petersburg, 2002).

Belov, I. A.

V. S. Sizikov and I. A. Belov, “Reconstruction of blurred and out-of-focus images by regularization,” Opt. Zh. 67, No. 4, 60 (2000) [J. Opt. Technol.67, 351 (2000)].

D’yakonov, V.

V. D’yakonov and I. Abramenkova, MATLAB. Signal and Image Processing (Piter, St. Petersburg, 2002).

Donatelli, M.

M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
[CrossRef]

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice Hall, Upper Saddle River, NJ, 2004; Tekhnosfera, Moscow, 2006).

Ékzemplyarov, R. A.

R. A. Ékzemplyarov and V. S. Sizikov, “Eliminating blurring and defocusing of images with preliminary noise filtering in MatLab,” in Materials of the International Conference, Thirty-Nine Weeks of SPbGPU, part XIII (IMOP), ed. A. I. Rudskii (SPbGPU, St. Petersburg, 2010), pp. 223–225.

Engl, H. W.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996).

Estatico, C.

M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice Hall, Upper Saddle River, NJ, 2004; Tekhnosfera, Moscow, 2006).

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, NJ, 2002; Tekhnosfera, Moscow, 2006).

Gorshkov, A. V.

A. V. Gorshkov, “Improving the resolution of images when processing the data of a physical experiment and imposing an unknown instrumental function using the REIMAGE software package,” Prib. Tekh. Eksp. No. 2, 68 (1995).

Hanke, M.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996).

Lim, J. S.

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, Englewood Cliffs, NJ, 1990).

Litasov, V. A.

Yu. E. Voskobonikov and V. A. Litasov, “Stable algorithm for reconstructing an image with an inaccurately specified spread function,” Avtometriya 42, No. 6, 3 (2006).

Martinelli, A.

M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
[CrossRef]

Mirdzhamolov, R. K.

V. S. Sizikov, M. V. Rimskikh, and R. K. Mirdzhamolov, “Reconstructing blurred noisy images without using boundary conditions,” Opt. Zh. 76, No. 5, 38 (2009) [J. Opt. Technol.76, 279 (2009)].

Neubauer, A.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996).

Ostrikov, V. N.

V. N. Ostrikov and O. V. Plakhotnikov, “Identifying the point-spread function of an observation channel from a calibrating image by the method of least squares,” Opt. Zh. 73, No. 2, 26 (2006) [J. Opt. Technol.73, 91 (2006)].

Petrov, Yu. P.

Yu. P. Petrov and V. S. Sizikov, Well-Posed, Ill-Posed, and Intermediate Problems with Applications (VSP, Leiden, 2005).

Plakhotnikov, O. V.

V. N. Ostrikov and O. V. Plakhotnikov, “Identifying the point-spread function of an observation channel from a calibrating image by the method of least squares,” Opt. Zh. 73, No. 2, 26 (2006) [J. Opt. Technol.73, 91 (2006)].

Rimskikh, M. V.

V. S. Sizikov, M. V. Rimskikh, and R. K. Mirdzhamolov, “Reconstructing blurred noisy images without using boundary conditions,” Opt. Zh. 76, No. 5, 38 (2009) [J. Opt. Technol.76, 279 (2009)].

Serra-Capizzano, S.

M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
[CrossRef]

Shchekotin, D. S.

D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

Shempliner, V. V.

D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

Sizikov, V. S.

V. S. Sizikov, “The truncation–blurring–rotation technique for reconstructing distorted images,” Opt. Zh. 78, No. 5, 18 (2011) [J. Opt. Technol.78, 298 (2011)].

V. S. Sizikov, M. V. Rimskikh, and R. K. Mirdzhamolov, “Reconstructing blurred noisy images without using boundary conditions,” Opt. Zh. 76, No. 5, 38 (2009) [J. Opt. Technol.76, 279 (2009)].

D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

V. S. Sizikov and I. A. Belov, “Reconstruction of blurred and out-of-focus images by regularization,” Opt. Zh. 67, No. 4, 60 (2000) [J. Opt. Technol.67, 351 (2000)].

R. A. Ékzemplyarov and V. S. Sizikov, “Eliminating blurring and defocusing of images with preliminary noise filtering in MatLab,” in Materials of the International Conference, Thirty-Nine Weeks of SPbGPU, part XIII (IMOP), ed. A. I. Rudskii (SPbGPU, St. Petersburg, 2010), pp. 223–225.

V. S. Sizikov, Mathematical Methods of Processing the Results of Measurements (Politekhnika, St. Petersburg, 2001).

V. S. Sizikov, Integral Equations and MATLAB in Problems of Tomography, Iconics, and Spectroscopy (LAP, Saarbrücken, 2011).

A. F. Verlan’ and V. S. Sizikov, Integral Equations: Methods, Algorithms, Programs (Naukov Dumka, Kiev, 1986).

Yu. P. Petrov and V. S. Sizikov, Well-Posed, Ill-Posed, and Intermediate Problems with Applications (VSP, Leiden, 2005).

V. S. Sizikov, Inverse Applied Problems in MATLAB (Lan’, St. Petersburg, 2011).

Verlan’, A. F.

A. F. Verlan’ and V. S. Sizikov, Integral Equations: Methods, Algorithms, Programs (Naukov Dumka, Kiev, 1986).

Voskobonikov, Yu. E.

Yu. E. Voskobonikov and V. A. Litasov, “Stable algorithm for reconstructing an image with an inaccurately specified spread function,” Avtometriya 42, No. 6, 3 (2006).

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, NJ, 2002; Tekhnosfera, Moscow, 2006).

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice Hall, Upper Saddle River, NJ, 2004; Tekhnosfera, Moscow, 2006).

Zakharov, D. D.

D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

Avtometriya (1)

Yu. E. Voskobonikov and V. A. Litasov, “Stable algorithm for reconstructing an image with an inaccurately specified spread function,” Avtometriya 42, No. 6, 3 (2006).

Inverse Probl. (1)

M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved image deblurring with anti-reflective boundary conditions and re-blurring,” Inverse Probl. 22, 2035 (2006).
[CrossRef]

Nauchno-Tekhn. Vest. ITMO (1)

D. D. Zakharov, V. S. Sizikov, V. V. Shempliner, and D. S. Shchekotin, “New methods for eliminating artefacts on tomographic and other images,” Nauchno-Tekhn. Vest. ITMO 32, 138 (2006).

Opt. Zh. J. Opt. Technol. (4)

V. N. Ostrikov and O. V. Plakhotnikov, “Identifying the point-spread function of an observation channel from a calibrating image by the method of least squares,” Opt. Zh. 73, No. 2, 26 (2006) [J. Opt. Technol.73, 91 (2006)].

V. S. Sizikov and I. A. Belov, “Reconstruction of blurred and out-of-focus images by regularization,” Opt. Zh. 67, No. 4, 60 (2000) [J. Opt. Technol.67, 351 (2000)].

V. S. Sizikov, M. V. Rimskikh, and R. K. Mirdzhamolov, “Reconstructing blurred noisy images without using boundary conditions,” Opt. Zh. 76, No. 5, 38 (2009) [J. Opt. Technol.76, 279 (2009)].

V. S. Sizikov, “The truncation–blurring–rotation technique for reconstructing distorted images,” Opt. Zh. 78, No. 5, 18 (2011) [J. Opt. Technol.78, 298 (2011)].

Prib. Tekh. Eksp. (1)

A. V. Gorshkov, “Improving the resolution of images when processing the data of a physical experiment and imposing an unknown instrumental function using the REIMAGE software package,” Prib. Tekh. Eksp. No. 2, 68 (1995).

Other (11)

V. S. Sizikov, Mathematical Methods of Processing the Results of Measurements (Politekhnika, St. Petersburg, 2001).

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, Dordrecht, 1996).

A. F. Verlan’ and V. S. Sizikov, Integral Equations: Methods, Algorithms, Programs (Naukov Dumka, Kiev, 1986).

R. A. Ékzemplyarov and V. S. Sizikov, “Eliminating blurring and defocusing of images with preliminary noise filtering in MatLab,” in Materials of the International Conference, Thirty-Nine Weeks of SPbGPU, part XIII (IMOP), ed. A. I. Rudskii (SPbGPU, St. Petersburg, 2010), pp. 223–225.

Yu. P. Petrov and V. S. Sizikov, Well-Posed, Ill-Posed, and Intermediate Problems with Applications (VSP, Leiden, 2005).

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, Englewood Cliffs, NJ, 1990).

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice Hall, Upper Saddle River, NJ, 2002; Tekhnosfera, Moscow, 2006).

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB (Prentice Hall, Upper Saddle River, NJ, 2004; Tekhnosfera, Moscow, 2006).

V. D’yakonov and I. Abramenkova, MATLAB. Signal and Image Processing (Piter, St. Petersburg, 2002).

V. S. Sizikov, Inverse Applied Problems in MATLAB (Lan’, St. Petersburg, 2011).

V. S. Sizikov, Integral Equations and MATLAB in Problems of Tomography, Iconics, and Spectroscopy (LAP, Saarbrücken, 2011).

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