Abstract

We propose and simulate an iterative maximum-likelihood image reconstruction method that uses multiple images taken through the turbulent atmosphere under photon-limited conditions. The method assumes that the point-spread function corresponding to each image has been measured by a guide star or other technique. Although a guide star is still required, wavefront correction is achieved through postprocessing instead of by the mechanical methods currently used with adaptive optics. A restored image of greatly increased quality was found to be produced after only 10 iterations. Additional iterations continued to reduce the mean-square error.

© 1998 Optical Society of America

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References

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    [CrossRef]

1996 (1)

D. R. Gerwe, M. A. Plonus, and B. H. Elsebelgy, Proc. SPIE 2748, 258 (1996).
[CrossRef]

1995 (1)

1994 (2)

1991 (1)

1990 (1)

K. T. Lay and A. K. Katsaggelos, Opt. Eng. 29, 436 (1990).
[CrossRef]

1982 (1)

L. A. Shepp and Y. Vardi, IEEE Trans. Med. Image. MI-1, 113 (1982).
[CrossRef]

1977 (1)

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

Dayton, D.

D. Dayton and S. Sandven, Proc. SPIE 2312, 347 (1994).
[CrossRef]

Dempster, A. P.

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

Elsebelgy, B. H.

D. R. Gerwe, M. A. Plonus, and B. H. Elsebelgy, Proc. SPIE 2748, 258 (1996).
[CrossRef]

Fried, D. L.

Gardner, C. S.

Gavel, D. T.

Gerwe, D. R.

D. R. Gerwe, M. A. Plonus, and B. H. Elsebelgy, Proc. SPIE 2748, 258 (1996).
[CrossRef]

Katsaggelos, A. K.

K. T. Lay and A. K. Katsaggelos, Opt. Eng. 29, 436 (1990).
[CrossRef]

Laird, N. M.

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

Lay, K. T.

K. T. Lay and A. K. Katsaggelos, Opt. Eng. 29, 436 (1990).
[CrossRef]

Morris, J. R.

Plonus, M. A.

D. R. Gerwe, M. A. Plonus, and B. H. Elsebelgy, Proc. SPIE 2748, 258 (1996).
[CrossRef]

Rubin, D. B.

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

Sandven, S.

D. Dayton and S. Sandven, Proc. SPIE 2312, 347 (1994).
[CrossRef]

Shepp, L. A.

L. A. Shepp and Y. Vardi, IEEE Trans. Med. Image. MI-1, 113 (1982).
[CrossRef]

Vardi, Y.

L. A. Shepp and Y. Vardi, IEEE Trans. Med. Image. MI-1, 113 (1982).
[CrossRef]

Vernon, R. G.

Welsh, B.

IEEE Trans. Med. Image. (1)

L. A. Shepp and Y. Vardi, IEEE Trans. Med. Image. MI-1, 113 (1982).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

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

Opt. Eng. (1)

K. T. Lay and A. K. Katsaggelos, Opt. Eng. 29, 436 (1990).
[CrossRef]

Proc. SPIE (2)

D. R. Gerwe, M. A. Plonus, and B. H. Elsebelgy, Proc. SPIE 2748, 258 (1996).
[CrossRef]

D. Dayton and S. Sandven, Proc. SPIE 2312, 347 (1994).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Sequence of images of stellar objects to be viewed, and corresponding image sequence of a guide star, captured with two shuttered CCD arrays. The light from the guide star is separated by a dichroic mirror, with any remaining laser light absorbed by a narrow-band filter.

Fig. 2
Fig. 2

The probability that a photon emitted within object cell Oj during exposure time t will be detected at detector cell Ii is given by element pjit of the discretized anisoplanatic point-spread function.

Fig. 3
Fig. 3

Left, sample of the computer-generated point-spread functions used in the simulations; right, example of the simulated noisy exposures. Only the center 64×64 pixels of each image are shown.

Fig. 4
Fig. 4

Quality of the restored image after 2, 10, and 100 iterations made with 100 exposures. The images at the right are the same as those at the left but with the intensity brightened by a gamma factor of 3.5 to enhance the contrast and make the dim features visible. Only the center 64×64 pixels are shown.

Fig. 5
Fig. 5

Error of the estimated image as a function of number of iterations for the numbers of noisy images shown by the curves. The measure of error used is MSE=jλjq-λj21/2/jλj2, where λjq is the current estimate of the true emission rate λj.

Equations (5)

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

f(s|λ, p)=jitexp-λjitλjisjit/sjit!,
log f(s|λq+1, p)|λq, p, I.
jit-λjitq+1+Iitλjitqjλjitqlog λjitq+1-sjit!|λq, p, I,
λjq+1=λjqitPjititIitjλjpjitpjit.
f[s|ϕλ]=bsexpϕλ·tsT/aϕλ,

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