Abstract

A method for performing blind deconvolutions on degraded images and data has been developed. The technique uses a power law relation applied to the Fourier transform of the degraded data to extract a filter function. This filter function closely resembles the point-spread function of the system and can be used to restore and enhance higher-frequency content. The process is noniterative and requires only that the point-spread function be space invariant and the transfer function be real. The algorithm has been validated by direct comparisons by use of a pseudoinverse filter with known transfer functions.

© 2001 Optical Society of America

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References

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  1. N. F. Law and D. T. Nguyen, Electron. Lett. 31, 1733 (1995).
  2. S. Barraza-Felix and B. R. Frieden, Appl. Opt. 38, 2232 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  11. Image courtesy of R. J. Hanisch, Space Telescope Science Institute, STScI/NASA, 3700 San Martin Drive, Baltimore, Md. 21218.

1999 (2)

1998 (2)

1995 (1)

N. F. Law and D. T. Nguyen, Electron. Lett. 31, 1733 (1995).

1994 (1)

1993 (1)

O. Shalvi and E. Weinstein, IEEE Trans. Inf. Theory 39, 504 (1993).
[CrossRef]

1967 (1)

Barraza-Felix, S.

Bones, P. J.

Frieden, B. R.

Helstrom, C. W.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Kopeika, N. S.

Lantzman, A.

Law, N. F.

N. F. Law and D. T. Nguyen, Electron. Lett. 31, 1733 (1995).

Milberg, R.

Mor, I.

Nguyen, D. T.

N. F. Law and D. T. Nguyen, Electron. Lett. 31, 1733 (1995).

Satherly, B. L.

Shalvi, O.

O. Shalvi and E. Weinstein, IEEE Trans. Inf. Theory 39, 504 (1993).
[CrossRef]

Slepian, D.

Weinstein, E.

O. Shalvi and E. Weinstein, IEEE Trans. Inf. Theory 39, 504 (1993).
[CrossRef]

Wiener, N.

N. Wiener, The Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications (Wiley, New York, 1949).

Yitzhaky, Y.

Yohaev, S.

Appl. Opt. (3)

Electron. Lett. (1)

N. F. Law and D. T. Nguyen, Electron. Lett. 31, 1733 (1995).

IEEE Trans. Inf. Theory (1)

O. Shalvi and E. Weinstein, IEEE Trans. Inf. Theory 39, 504 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Other (3)

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

N. Wiener, The Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications (Wiley, New York, 1949).

Image courtesy of R. J. Hanisch, Space Telescope Science Institute, STScI/NASA, 3700 San Martin Drive, Baltimore, Md. 21218.

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Figures (3)

Fig. 1
Fig. 1

Top, data produced by implementing a first-order autoregressive model. Upper center, data convolved with a synthetic transfer function. Lower center, restoration of the data by use of the synthetic transfer function and a pseudoinverse filter. Bottom, restoration of the data by use of the SeDDaRa and a pseudoinverse filter.

Fig. 2
Fig. 2

Top, image of Saturn taken from the Hubble Telescope11 before the optical correction in 1993. Center, deconvolution with a measured optical transfer function with a pseudoinverse filter. Bottom, blind deconvolution with the SeDDaRA and a pseudoinverse filter.

Fig. 3
Fig. 3

Top, an out-of-focus image of a bassoon octet taken with a photographic camera and digitized. Bottom, blind deconvolution of the image with the SeDDaRA and a pseudoinverse filter. The restoration removes blur introduced by both the image and the restoration process.

Equations (10)

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

gx,y=fx,y*dx,y+wx,y,
Gu,v=Fu,vDu,v+Wu,v.
SAu,vAu,v2N2.
Du,v=KDSSGu,v-SWu,vα/2,
D1-αu,v=KDSSFα/2u,v,
Du,v=KDSSFα/2u,vSDαu,v,
Du,v=KDSSFu,vD2u,vα/2.
SGu,v-SWu,v=SFu,vD2u,v
xi+1=ρ1xi+ani,
di=σd2ρ2i,

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