Abstract

A blind deconvolution problem is newly stated with the following conditions: the point-spread function is band limited, both the object and the point-spread function are nonnegative, and the solution is to be a diffraction-limited object. A blind deconvolution method was developed that can easily be applied to problems in optics because of the conditions used. The performance of the method is investigated with computer simulations.

© 2003 Optical Society of America

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References

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  1. G. R. Ayers and J. C. Dainty, Opt. Lett. 13, 547 (1988).
    [CrossRef]
  2. R. G. Lane and R. H. T. Bates, J. Opt. Soc. Am. A 4, 180 (1987).
    [CrossRef]
  3. R. G. Lane, J. Opt. Soc. Am. A 9, 1508 (1992).
    [CrossRef]
  4. E. Thiébaut and J.-M. Conan, J. Opt. Soc. Am. A 12, 485 (1995).
    [CrossRef]
  5. Y. Biraud, Astron. Astrophys. 1, 124 (1969).
  6. N. Miura and N. Baba, Opt. Lett. 21, 1174 (1996).
    [CrossRef] [PubMed]
  7. N. Miura and K. Kikuchi, Proc. SPIE 4829, 213 (2002).
  8. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

2002 (1)

N. Miura and K. Kikuchi, Proc. SPIE 4829, 213 (2002).

1996 (1)

1995 (1)

1992 (1)

1988 (1)

1987 (1)

1969 (1)

Y. Biraud, Astron. Astrophys. 1, 124 (1969).

Ayers, G. R.

Baba, N.

Bates, R. H. T.

Biraud, Y.

Y. Biraud, Astron. Astrophys. 1, 124 (1969).

Conan, J.-M.

Dainty, J. C.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Kikuchi, K.

N. Miura and K. Kikuchi, Proc. SPIE 4829, 213 (2002).

Lane, R. G.

Miura, N.

N. Miura and K. Kikuchi, Proc. SPIE 4829, 213 (2002).

N. Miura and N. Baba, Opt. Lett. 21, 1174 (1996).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Thiébaut, E.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Astron. Astrophys. (1)

Y. Biraud, Astron. Astrophys. 1, 124 (1969).

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

Opt. Lett. (2)

Proc. SPIE (1)

N. Miura and K. Kikuchi, Proc. SPIE 4829, 213 (2002).

Other (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

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Figures (4)

Fig. 1
Fig. 1

Effect of a nonnegativity constraint: the total unknown area of both Φu,v and Ψu,v is always smaller than the observed area in Gu,v.

Fig. 2
Fig. 2

The algorithm starts from initial estimates of Φu,v and Ψu,v. The final estimates are obtained through minimizing an errormetric and permit dx,y and px,y to be calculated easily.

Fig. 3
Fig. 3

Demonstration with simulation: (a) object; (b) noisy convolution image; (c), (d) images restored with the present method and with the Ayers–Dainty method, respectively.

Fig. 4
Fig. 4

Dependence of the algorithm on initial estimates: the deviation of the resultant intensity ratios from the true value 0.6 becomes serious for small initial intensity ratios.

Equations (6)

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

ix,y=ox,y*px,y,
gx,y=ix,y*mx,y=dx,y*px,y,
dx,y=ϕx,y2,
px,y=ψx,y2,
Gu,v=Φu,v*Φu,vΨu,v*Ψu,v,
E=uvGu,v-Φu,v*Φu,v×Ψu,v*Ψu,v2.

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