Abstract

We present a maximum likelihood (ML) deconvolution algorithm with bandwidth and total variation (TV) constraints for degraded image due to atmospheric turbulence. The bandwidth limit function is estimated in view of optical system parameters and Fourier optical theory. With the aid of bandwidth and TV minimization as compelling constraints, the algorithm can not only suppress noise effectively but also restrict the bandwidth of point-spread function (PSF) that may lead to trivial solution. Compared with the conventional ML method, the proposed algorithm is able to restore a noise-free image, and the detailed texture is better than that of ML.

© 2007 Optical Society of America

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References

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    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
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    [CrossRef]
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  11. M. G. Kang, A. K. Katsaggelos, IEEE Trans. Image Process. 4, 594 (1995).
    [CrossRef]
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    [CrossRef]

2006 (1)

1998 (1)

P. Magain, F. Courbin, and S. Sohy, Astron. Astrophys. 494, 472 (1998).

1995 (1)

M. G. Kang, A. K. Katsaggelos, IEEE Trans. Image Process. 4, 594 (1995).
[CrossRef]

1994 (2)

E. M. Johansson and D. T. Gacel, Proc. SPIE 2200, 372 (1994).
[CrossRef]

F. Tsumuraya, N. Miura, and N. Baba, Astron. Astrophys. 282, 699 (1994).

1993 (1)

T. J. Schulz, J. Opt. Soc. Am. 10, 1064 (1993).
[CrossRef]

1992 (1)

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

1977 (1)

A. P. Dempster, N. M. Laird, and D. B. Rudin, J. R. Stat. Soc. Ser. B 39, 1 (1977).

1974 (1)

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

1972 (1)

Astron. Astrophys. (2)

F. Tsumuraya, N. Miura, and N. Baba, Astron. Astrophys. 282, 699 (1994).

P. Magain, F. Courbin, and S. Sohy, Astron. Astrophys. 494, 472 (1998).

Astron. J. (1)

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

IEEE Trans. Image Process. (1)

M. G. Kang, A. K. Katsaggelos, IEEE Trans. Image Process. 4, 594 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

T. J. Schulz, J. Opt. Soc. Am. 10, 1064 (1993).
[CrossRef]

W. H. Richardson, J. Opt. Soc. Am. 62, 55 (1972).
[CrossRef]

J. R. Stat. Soc. Ser. B (1)

A. P. Dempster, N. M. Laird, and D. B. Rudin, J. R. Stat. Soc. Ser. B 39, 1 (1977).

Opt. Lett. (1)

Physica D (1)

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

Proc. SPIE (1)

E. M. Johansson and D. T. Gacel, Proc. SPIE 2200, 372 (1994).
[CrossRef]

Other (2)

D. G. Luenberger, Optimization by Vector Space Methods (Wiley, 1969).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (2)

Fig. 1
Fig. 1

Original Saturn object image and simulated turbulence short-exposure image.

Fig. 2
Fig. 2

Deconvolution results with the ML and MML algorithms.

Equations (12)

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g ( x ) = f ( x ) h ( x ) + η ( x ) ,
N d = ( 2.44 λ l D ) 1 N u ,
N c = 2 N N d = ( D 1.22 λ l ) N u N .
h ̂ ( x ) = h ( x ) p ( x ) ,
p ( x ) = IFFT ( P ( u ) ) ,
P ( u ) = { 1 , u N c 2 0 , u > N c 2 .
Pr ( { g k } f , { h k } ) = k = 1 K i k g k g k ! exp ( i k ) ,
L ( f , { h k } ) = k y x h ( y x ) f ( x ) + k y ( g k ln x h k ( y x ) f ( x ) ) ,
TV ( f ) = x f ( x ) ,
L TV ( f , { h k } ) = L ( f , { h k } ) α T V ( f ) + λ ( 1 f ) ,
f n ( x ) = f n 1 ( x ) k y h ̂ k n 1 ( y x ) g k ( y ) i k n 1 ( x ) α f n 1 ( x ) f n 1 ( x ) + λ ,
h k n ( x ) = h ̂ k n 1 ( x ) y f n 1 ( y x ) i k n 1 ( x ) g k ( y ) .

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