Abstract

A simple iterative technique has been developed for blind deconvolution of two convolved functions. The method is described, and a number of results obtained from a computational implementation are presented. Some further possible applications are indicated.

© 1988 Optical Society of America

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References

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  1. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  2. C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967).
    [CrossRef]
  3. C. E. Morris, M. A. Richards, M. H. Hayes, J. Opt. Soc. Am. A 4, 200 (1987).
    [CrossRef]
  4. T. G. Stockham, T. M. Cannon, R. B. Ingebretson, Proc. IEEE 63, 678 (1975).
    [CrossRef]
  5. R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).
  6. R. W. Gerchberg, Opt. Acta 21, 709 (1974).
    [CrossRef]
  7. J. R. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]
  8. R. G. Lane, R. H. T. Bates, Opt. Commun. 63, 11 (1987).
    [CrossRef]
  9. R. G. Lane, R. H. T. Bates, J. Opt. Soc. Am. A 4, 180 (1987).
    [CrossRef]
  10. A. W. Lohmann, G. P. Weigelt, B. Wirnitzer, Appl. Opt. 22, 4028 (1983).
    [CrossRef] [PubMed]
  11. K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).
  12. A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

1987 (3)

1983 (1)

1978 (1)

1975 (1)

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, Proc. IEEE 63, 678 (1975).
[CrossRef]

1974 (2)

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

R. W. Gerchberg, Opt. Acta 21, 709 (1974).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

1970 (1)

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

1967 (1)

Bates, R. H. T.

R. G. Lane, R. H. T. Bates, Opt. Commun. 63, 11 (1987).
[CrossRef]

R. G. Lane, R. H. T. Bates, J. Opt. Soc. Am. A 4, 180 (1987).
[CrossRef]

Cannon, T. M.

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, Proc. IEEE 63, 678 (1975).
[CrossRef]

Fienup, J. R.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Gerchberg, R. W.

R. W. Gerchberg, Opt. Acta 21, 709 (1974).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Hayes, M. H.

Helstrom, C. W.

Ingebretson, R. B.

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, Proc. IEEE 63, 678 (1975).
[CrossRef]

Knox, K. T.

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

Labeyrie, A.

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Lane, R. G.

R. G. Lane, R. H. T. Bates, Opt. Commun. 63, 11 (1987).
[CrossRef]

R. G. Lane, R. H. T. Bates, J. Opt. Soc. Am. A 4, 180 (1987).
[CrossRef]

Lohmann, A. W.

Morris, C. E.

Richards, M. A.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Stockham, T. G.

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, Proc. IEEE 63, 678 (1975).
[CrossRef]

Thompson, B. J.

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

Weigelt, G. P.

Wirnitzer, B.

Appl. Opt. (1)

Astron. Astrophys. (1)

A. Labeyrie, Astron. Astrophys. 6, 85 (1970).

Astron. J. (1)

K. T. Knox, B. J. Thompson, Astron. J. 193, L45 (1974).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

R. W. Gerchberg, Opt. Acta 21, 709 (1974).
[CrossRef]

Opt. Commun. (1)

R. G. Lane, R. H. T. Bates, Opt. Commun. 63, 11 (1987).
[CrossRef]

Opt. Lett. (1)

Optik (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Proc. IEEE (1)

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, Proc. IEEE 63, 678 (1975).
[CrossRef]

Other (1)

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

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Figures (3)

Fig. 1
Fig. 1

General deconvolution algorithm.

Fig. 2
Fig. 2

Simple example of deconvolution algorithm results.

Fig. 3
Fig. 3

Example of deconvolving a computer-generated speckle image.

Equations (7)

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c ( x ) = - + f ( x 1 ) g ( x - x 1 ) d x 1 .
C ( u ) = F ( u ) G ( u ) .
f ˜ i ( x ) = f i ( x ) , f i ( x ) 0 , f ˜ i ( x ) = 0 , otherwise , E = - + [ f i ( x ) - f ˜ i ( x ) ] d x ,
f ˜ i ( x ) = f ˜ i ( x ) + E / N ,
F i + 1 ( u ) = F ˜ i ( u ) ;
F i + 1 ( u ) = ( 1 - β ) F ˜ i ( u ) + β C ( u ) G ˜ i ( u ) ,
1 F i + 1 ( u ) = ( 1 - β ) F ˜ i ( u ) + β G ˜ i ( u ) C ( u ) ,

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