Abstract

A blind deconvolution algorithm with spatially adaptive total variation regularization is introduced. The spatial information in different image regions is incorporated into regularization by using the edge indicator called difference eigenvalue to distinguish edges from flat areas. The proposed algorithm can effectively reduce the noise in flat regions as well as preserve the edge and detailed information. Moreover, it becomes more robust with the change of the regularization parameter. Comparative results on simulated and real degraded images are reported.

© 2012 Optical Society of America

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References

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2009

2008

2007

2006

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

1998

R. A. Carmona and S. Zhong, IEEE Trans. Image Process. 7, 353 (1998).
[CrossRef]

1996

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

1995

1992

L. I. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

1974

L. B. Lucy, Astron. J. 79, 745 (1974).
[CrossRef]

1972

Blanc-Féraud, L.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Brinicombe, A. M.

Cai, H.

H. Tian, H. Cai, J. Lai, and X. Xu, in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3357.

Carmona, R. A.

R. A. Carmona and S. Zhong, IEEE Trans. Image Process. 7, 353 (1998).
[CrossRef]

Dey, N.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Fish, D. A.

Hatzinakos, D.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

He, G.

Kam, Z.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Kundur, D.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

Lai, J.

H. Tian, H. Cai, J. Lai, and X. Xu, in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3357.

Lam, E.

Lu, Y.

Lucy, L. B.

L. B. Lucy, Astron. J. 79, 745 (1974).
[CrossRef]

Olivo-Marin, J. C.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Pike, E. R.

Richardson, W. H.

Roux, P.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Tian, H.

H. Tian, H. Cai, J. Lai, and X. Xu, in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3357.

Walker, J. G.

Wu, Q.

Xu, X.

H. Tian, H. Cai, J. Lai, and X. Xu, in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3357.

Xu, Z.

Zerubia, J.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Zhang, J.

Zhang, Q.

Zhong, S.

R. A. Carmona and S. Zhong, IEEE Trans. Image Process. 7, 353 (1998).
[CrossRef]

Zhu, H.

Zimmer, C.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Astron. J.

L. B. Lucy, Astron. J. 79, 745 (1974).
[CrossRef]

IEEE Signal Process. Mag.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

IEEE Trans. Image Process.

R. A. Carmona and S. Zhong, IEEE Trans. Image Process. 7, 353 (1998).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Microsc. Res. Tech.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Opt. Lett.

Physica D

L. I. Rudin, S. Osher, and E. Fatemi, Physica D 60, 259 (1992).
[CrossRef]

Other

H. Tian, H. Cai, J. Lai, and X. Xu, in IEEE International Conference on Image Processing (IEEE, 2011), pp. 3357.

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Figures (4)

Fig. 1.
Fig. 1.

Restoration of a simulated degraded image. (a) Original circuit image; (b) blurred and noisy image; (c) image restored by RLTV; and (d) image restored by RLSATV.

Fig. 2.
Fig. 2.

NMSE versus regularization parameter λ of RLTV and RLSATV for the circuit image.

Fig. 3.
Fig. 3.

NMSE versus the iteration number of the three methods for the circuit image with λ=0.0155.

Fig. 4.
Fig. 4.

Restoration of a real degraded image. (a) Real degraded image, (b) image restored by RLTV, (c) image restored by RLSATV, and (d) RESE versus iteration number.

Tables (1)

Tables Icon

Table 1. NMSE of Degraded Image and the Best Restored Image (with the Lowest NMSE) by Different Algorithms

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

i(x)=h(x)*o(x)+n(x),
P(i|o,h)=x[(h*o)(x)]i(x)exp((h*o)(x))i(x)!.
J1(o)=x(i(x)log[(h*o)(x)]+(h*o)(x)).
J2(o)=x(i(x)log[(h*o)(x)]+(h*o)(x))+λx|o(x)|.
Jρ=[j11j12j12j22]=[ox1x1*Gρox1x2*Gρox1x2*Gρox2x2*Gρ],
λ1,2=12[(j11+j22)±(j11j22)2+4j122].
D(x)=(λ1λ2)λ1w(o(x1,x2)),
w(o(x1,x2))=σ(x1,x2)min(σ)max(σ)min(σ),
σ(x1,x2)=19i=11j=11[o(x1+i,x2+j)o(x1,x2)].
SATV=x11+βD(x)|o(x)|,
L(o,h)=x{i(x)log(h*o)(x)+(h*o)(x)+λ1+βD(x)|o(x)|}.
ht(n+1)(x)=h(n)(x){o(n)(x)*[i(x)h(n)(x)*o(n)(x)]},h(n+1)(x)=h(n+1)(x)xht(n+1)(x),
o(n+1)(x)=o(n)(x){h(n+1)(x)*[i(x)h(n+1)(x)*o(n)(x)]}×11λ1+βD(x)div(o(n)(x)|o(n)(x)|).

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