Abstract

A semi-blind image restoration algorithm is proposed based on reduced non-convex approximation of Luminita Vese and Tony Chan's (C-V) denoising model. Compared with C-V denoising model, we modify the fidelity term and add a term on point spread function (PSF). The function depends on two variables: the image function to be restored <i>u</i> and the standard deviation of Gaussian kernel to be estimated <i>σ</i>. Then the problems consist in solving a system with two coupled equations. Compared with the Leah Bar's semi-blind image restoration model which must solve three coupled equations, our method only needs to solve two equations. Furthermore, the estimation of <i>f</i> by our algorithm is superior to Leah Bar's algorithm. The experimental results demonstrate that the proposed method is effective.

© 2008 Chinese Optics Letters

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  1. Y.-L. You and M. Kaveh, IEEE Trans. Image Processing 8, 396 (1999).
  2. Y. Liang, C. Rao, M. Li, and Z. Geng, Chin. Opt. Lett. 4, 187 (2006).
  3. Q. Li, S. Liao, H. Wei, and M. Shen. Chin. Opt. Lett. 5, 201 (2007).
  4. T. F. Chan and C.-K. Wong, IEEE Trans. Image Processing 7, 370 (1998).
  5. L. Bar, N. Sochen, and N. Kiryati, IEEE Trans. Image Processing 15, 483 (2006).
  6. J. H. Money and S. H. Kang, "Total variation semi-blind deconvolution using shock filters" (2006). http://www.cs.nccu.edu/~jmoney/semi_deblur.pdf.
  7. L. Vese and T. F. Chan, "Reduced non-convex functional approximations for image restoration & segmentation" UCLA CAM Reports 97-56 (1997). http://www.math.ucla.edu/applied/cam/index.shtml.
  8. D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, 577 (1989).
  9. C. R. Vogel and M. E. Oman, IEEE Trans. Image Processing 7, 813 (1998).
  10. Y. L. You and M. Kaveh, IEEE Trans. Image Processing 5, 416 (1996).

2007 (1)

Q. Li, S. Liao, H. Wei, and M. Shen. Chin. Opt. Lett. 5, 201 (2007).

2006 (2)

L. Bar, N. Sochen, and N. Kiryati, IEEE Trans. Image Processing 15, 483 (2006).

Y. Liang, C. Rao, M. Li, and Z. Geng, Chin. Opt. Lett. 4, 187 (2006).

1999 (1)

Y.-L. You and M. Kaveh, IEEE Trans. Image Processing 8, 396 (1999).

1998 (2)

C. R. Vogel and M. E. Oman, IEEE Trans. Image Processing 7, 813 (1998).

T. F. Chan and C.-K. Wong, IEEE Trans. Image Processing 7, 370 (1998).

1996 (1)

Y. L. You and M. Kaveh, IEEE Trans. Image Processing 5, 416 (1996).

1989 (1)

D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, 577 (1989).

Bar, L.

L. Bar, N. Sochen, and N. Kiryati, IEEE Trans. Image Processing 15, 483 (2006).

Chan, T. F.

T. F. Chan and C.-K. Wong, IEEE Trans. Image Processing 7, 370 (1998).

Geng, Z.

Kaveh, M.

Y.-L. You and M. Kaveh, IEEE Trans. Image Processing 8, 396 (1999).

Y. L. You and M. Kaveh, IEEE Trans. Image Processing 5, 416 (1996).

Kiryati, N.

L. Bar, N. Sochen, and N. Kiryati, IEEE Trans. Image Processing 15, 483 (2006).

Li, M.

Li, Q.

Q. Li, S. Liao, H. Wei, and M. Shen. Chin. Opt. Lett. 5, 201 (2007).

Liang, Y.

Liao, S.

Q. Li, S. Liao, H. Wei, and M. Shen. Chin. Opt. Lett. 5, 201 (2007).

Mumford, D.

D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, 577 (1989).

Oman, M. E.

C. R. Vogel and M. E. Oman, IEEE Trans. Image Processing 7, 813 (1998).

Rao, C.

Shah, J.

D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, 577 (1989).

Sochen, N.

L. Bar, N. Sochen, and N. Kiryati, IEEE Trans. Image Processing 15, 483 (2006).

Vogel, C. R.

C. R. Vogel and M. E. Oman, IEEE Trans. Image Processing 7, 813 (1998).

Wei, H.

Q. Li, S. Liao, H. Wei, and M. Shen. Chin. Opt. Lett. 5, 201 (2007).

Wong, C.-K.

T. F. Chan and C.-K. Wong, IEEE Trans. Image Processing 7, 370 (1998).

You, Y. L.

Y. L. You and M. Kaveh, IEEE Trans. Image Processing 5, 416 (1996).

You, Y.-L.

Y.-L. You and M. Kaveh, IEEE Trans. Image Processing 8, 396 (1999).

and M. Shen. Chin. Opt. Lett. (1)

Q. Li, S. Liao, H. Wei, and M. Shen. Chin. Opt. Lett. 5, 201 (2007).

Chin. Opt. Lett. (1)

Commun. Pure Appl. Math. (1)

D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, 577 (1989).

IEEE Trans. Image Processing (5)

C. R. Vogel and M. E. Oman, IEEE Trans. Image Processing 7, 813 (1998).

Y. L. You and M. Kaveh, IEEE Trans. Image Processing 5, 416 (1996).

Y.-L. You and M. Kaveh, IEEE Trans. Image Processing 8, 396 (1999).

T. F. Chan and C.-K. Wong, IEEE Trans. Image Processing 7, 370 (1998).

L. Bar, N. Sochen, and N. Kiryati, IEEE Trans. Image Processing 15, 483 (2006).

Other (2)

J. H. Money and S. H. Kang, "Total variation semi-blind deconvolution using shock filters" (2006). http://www.cs.nccu.edu/~jmoney/semi_deblur.pdf.

L. Vese and T. F. Chan, "Reduced non-convex functional approximations for image restoration & segmentation" UCLA CAM Reports 97-56 (1997). http://www.math.ucla.edu/applied/cam/index.shtml.

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