Abstract

A blind deconvolution method is applied to the recovery of atmospherically degraded solar images. The method consists of an iterative deconvolution algorithm that uses several partial images segmented from each of multiple frames. It is shown that the algorithm decreases a specified error metric, allows a unique solution, and reduces contamination originally existing in solar images observed with a limited field of view. Artificial contamination introduced into the partial images by segmentation is calibrated with the use of estimates of an object and a point-spread function at the previous iteration. Computer simulation demonstrates successful reconstruction for a low-contrast degraded image and the expected behavior of an error metric. High-resolution images are reconstructed from observed solar images.

© 1995 Optical Society of America

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References

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  1. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).
  2. J. C. Dainty, “Stellar speckle interferometry,” in Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.
    [CrossRef]
  3. O. von der Luhe, “Speckle imaging of solar small scale structure I. Methods,” Astron. Astrophys. 268, 374–390 (1993); O. von der Luhe, “Speckle imaging of solar small scale structure II: Study of small scale structure in active regions,” Astron. Astrophys. 281, 889–910 (1994).
  4. J. H. Seldin, R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” in Image Reconstruction and Restoration, Timothy J. Schulz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2302, 2302–2319 (1994).
    [CrossRef]
  5. N. Baba, H. Tomita, N. Miura, “Iterative reconstruction method in phase-diversity imaging,” Appl. Opt. 33, 4428–4433 (1994); N. Baba, H. Tomita, N. Miura, “Phase diversity imaging through atmospheric turbulence,” Opt. Rev. 1, 308–310 (1994).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. P. Nisenson, “Single speckle frame imaging using Ayers–Dainty blind deconvolution,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 299–308.
  9. N. Miura, S. Kuwamura, N. Baba, S. Isobe, M. Noguchi, “Parallel scheme of the iterative blind deconvolution method for stellar image reconstruction,” Appl. Opt. 32, 6514–6520 (1993).
    [CrossRef] [PubMed]
  10. N. Miura, K. Ohsawa, N. Baba, “Single-frame blind deconvolution by means of frame segmentation,” Opt. Lett. 19, 695–698 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
    [CrossRef]
  13. T. J. Holmes, “Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach,” J. Opt. Soc. Am. A 9, 1052–1061 (1992).
    [CrossRef] [PubMed]
  14. S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
    [CrossRef]
  15. T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
    [CrossRef]
  16. B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. Soc. Photo-Opt. Instrum. Eng.74, 225–233 (1976).
    [CrossRef]

1994

1993

O. von der Luhe, “Speckle imaging of solar small scale structure I. Methods,” Astron. Astrophys. 268, 374–390 (1993); O. von der Luhe, “Speckle imaging of solar small scale structure II: Study of small scale structure in active regions,” Astron. Astrophys. 281, 889–910 (1994).

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
[CrossRef]

N. Miura, S. Kuwamura, N. Baba, S. Isobe, M. Noguchi, “Parallel scheme of the iterative blind deconvolution method for stellar image reconstruction,” Appl. Opt. 32, 6514–6520 (1993).
[CrossRef] [PubMed]

1992

1988

1970

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).

Acton, D. S.

Ayers, G. R.

Baba, N.

Christou, J. C.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

Dainty, J. C.

G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13, 547–549 (1988).
[CrossRef] [PubMed]

J. C. Dainty, “Stellar speckle interferometry,” in Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.
[CrossRef]

Holmes, T. J.

Isobe, S.

Jefferies, S. M.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

Kuwamura, S.

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lane, R. G.

McGlamery, B. L.

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. Soc. Photo-Opt. Instrum. Eng.74, 225–233 (1976).
[CrossRef]

Miura, N.

Nisenson, P.

P. Nisenson, “Single speckle frame imaging using Ayers–Dainty blind deconvolution,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 299–308.

Noguchi, M.

Ohsawa, K.

N. Miura, K. Ohsawa, N. Baba, “Single-frame blind deconvolution by means of frame segmentation,” Opt. Lett. 19, 695–698 (1994).
[CrossRef] [PubMed]

N. Miura, K. Ohsawa, N. Baba, “Parallel blind deconvolution applied to solar images,” Opt. Rev. 1, 208–210 (1994).
[CrossRef]

Paxman, R. G.

J. H. Seldin, R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” in Image Reconstruction and Restoration, Timothy J. Schulz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2302, 2302–2319 (1994).
[CrossRef]

Schulz, T. J.

Seldin, J. H.

J. H. Seldin, R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” in Image Reconstruction and Restoration, Timothy J. Schulz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2302, 2302–2319 (1994).
[CrossRef]

Smithson, R. C.

Tomita, H.

von der Luhe, O.

O. von der Luhe, “Speckle imaging of solar small scale structure I. Methods,” Astron. Astrophys. 268, 374–390 (1993); O. von der Luhe, “Speckle imaging of solar small scale structure II: Study of small scale structure in active regions,” Astron. Astrophys. 281, 889–910 (1994).

Appl. Opt.

Astron. Astrophys.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).

O. von der Luhe, “Speckle imaging of solar small scale structure I. Methods,” Astron. Astrophys. 268, 374–390 (1993); O. von der Luhe, “Speckle imaging of solar small scale structure II: Study of small scale structure in active regions,” Astron. Astrophys. 281, 889–910 (1994).

Astrophys. J.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Opt. Rev.

N. Miura, K. Ohsawa, N. Baba, “Parallel blind deconvolution applied to solar images,” Opt. Rev. 1, 208–210 (1994).
[CrossRef]

Other

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. Soc. Photo-Opt. Instrum. Eng.74, 225–233 (1976).
[CrossRef]

P. Nisenson, “Single speckle frame imaging using Ayers–Dainty blind deconvolution,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 299–308.

J. H. Seldin, R. G. Paxman, “Phase-diverse speckle reconstruction of solar data,” in Image Reconstruction and Restoration, Timothy J. Schulz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2302, 2302–2319 (1994).
[CrossRef]

J. C. Dainty, “Stellar speckle interferometry,” in Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 255–280.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Segmentation from multiple frames. ⊗ denotes convolution.

Fig. 2
Fig. 2

a, Diffraction-limited object for simulation and b, the generated PSF; c, d, degraded images for bias ratios of 0.0 and 0.8, respectively; e, windows for M = 3 (solid line only) and for M = 5 (both solid and dashed lines). The PSF is displayed with ten contour lines and is magnified twice.

Fig. 3
Fig. 3

Radial-mean plots of the average power spectrum (in log scale) for the bias ratios of 0.8 (solid curve) and 0.0 (dashed curve).

Fig. 4
Fig. 4

Reconstructed objects and PSF’s for various values of N and M when the bias ratio is 0.0: a, 3 and 3; b, 3 and 5; c, 10 and 5; d, 20 and 5.

Fig. 5
Fig. 5

Reconstructed objects and PSF’s when the bias ratio is 0.8: a, c, and d, N = M = 3; b, N = 20 and M = 5. a and b should be compared with Figs. 4a and 4d, respectively; c and d are reconstructed with higher limit frequency and larger size of support region, respectively, than in a.

Fig. 6
Fig. 6

Error metric (solid curves) and MSE (dashed curves) versus iteration number. Figures 6a and 6b and Figs. 6c and 6d correspond to Figs. 4a and 4d and Figs. 5a and 5b, respectively.

Fig. 7
Fig. 7

Solar image reconstruction: a, b, observed images with different fields of view; c, d, objects reconstructed from a and b, respectively; e, f, PSF’s estimated from a and b, respectively; g, observed image with the best seeing at observation, where the field of view is same as for b.

Tables (1)

Tables Icon

Table 1 Computer Simulation Results

Equations (45)

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i n ( x , y ) = o ( x , y ) * p n ( x , y ) ,
g n ( x , y ) = h 1 ( x , y ) { o ( x , y ) * p n ( x , y ) } ,
g n ( x , y ) = { h 2 ( x , y ) o ( x , y ) } * p n ( x , y ) + d n ( x , y ) ,
f m n ( x , y ) = w m ( x , y ) g n ( x , y ) = { w m ( x , y ) o ( x , y ) } * p n ( x , y ) + c m n ( x , y ) ,
c m n ( x , y ) = w m ( x , y ) [ { w m ( x , y ) o ( x , y ) } * p n ( x , y ) ] - w m ( x , y ) [ { w m ( x , y ) o ( x , y ) } * p n ( x , y ) ] ,
w m ( x , y ) = 1 - w m ( x , y ) , ( n = 1 , , N ) ,
f m n ( x , y ) = o m ( x , y ) * p n ( x , y ) ,
o m ( x , y ) = w m ( x , y ) o ( x , y ) ,
F m n ( u , v ) = O m ( u , v ) P n ( u , v ) ,
{ O m ( u , v ) A ( u , v ) ( m = 1 , , M ) , P n ( u , v ) / A ( u , v ) ( n = 1 , , N ) } .
E = 1 B n = 1 N m = 1 M f ˜ m n ( x , y ) - o ˜ m ( x , y ) * p ˜ n ( x , y ) 2 d x d y ,
B = n = 1 N m = 1 M w m ( x , y ) i n ( x , y ) 2 d x d y ,
E = 1 B n = 1 N e n ,
e n = m = 1 M f ˜ n m ( x , y ) - o ˜ m ( x , y ) * p ˜ n ( x , y ) 2 d x d y .
P ˜ n ( u , v ) = F ˜ m n ( u , v ) O ˜ m * ( u , v ) O ˜ m ( u , v ) 2 ,
O ˜ m ( u , v ) = F ˜ m n ( u , v ) P ˜ n * ( u , v ) P ˜ n ( u , v ) 2
O ˜ m ( u , v ) = F ˜ m n ( u , v ) P ˜ n * ( u , v ) P ˜ n ( u , v ) 2 W 2 ( u , v ) T ( u , v ) .
P ˜ n ( u , v ) = F ˜ m n ( u , v ) O ˜ m * ( u , v ) O ˜ m ( u , v ) 2 W 2 ( u , v ) T ( u , v ) .
O ˜ ( u , v ) = G n ( u , v ) P ˜ n * ( u , v ) P ˜ n ( u , v ) 2 W 2 ( u , v ) T ( u , v ) .
P n ( u , v ) = F m n ( u , v ) / O m ( u , v ) + C m n ( u , v ) / O m ( u , v ) ,
p n ( x , y ) = P n ( x , y ) + FT - 1 [ C m n ( u , v ) / O m ( u , v ) ,
W ( u , v ) = T ( u c f / c l , v c f / c l ) ,
O ( u , v ) W ( u , v ) , P n ( u , v ) W ( u , v ) / T ( u , v ) .
R ( r ) - n l n l / N m ,
E 0 l = 1 B n = 1 N m = 1 M S m n l 2 d x d y ,
E k l = 1 B n = 1 N m = 1 M S m n l + o m * δ p n l + δ o m l * p n 2 d x d y ,
S m n l = w m ( o * Δ p n l + Δ o l * p n ) , p n l = p n + Δ p n l , p n l + 1 - p n l = δ p n l , o m l = o m + Δ o m l , o m l + 1 - o m l = δ o m l , o l = o + Δ o l , o l + 1 - o l = δ o l ,
E 0 l + 1 = 1 B n = 1 N m = 1 M S m n l + o m * δ p n l + δ o m l * p n + m n l 2 d x d y ,
m n l = w m [ ( w m o ) * δ p n l ] - w m ( o m * δ p n l ) + w m [ ( w m δ o l ) * p n ] - w m ( δ o m l * p n ) ,
Q o = h 2 ( x , y ) o ˜ ( x , y ) - o ( x , y ) 2 d x d y / h 2 ( x , y ) o ( x , y ) 2 d x d y ,
Q p = 1 N n p ˜ n ( x , y ) - p n ( x , y ) 2 d x d y / p n ( x , y ) 2 d x d y ,
E = 1 B n = 1 N m = 1 M f ˜ m n - o ˜ * p ˜ n 2 d x d y .
E 0 l = 1 B n = 1 N m = 1 M f m n - c m , n l - o m l * p n l 2 d x d y ,
E k l = 1 B n = 1 N m = 1 M f m n - c m , n l - o ¯ m l * p ¯ n l 2 d x d y ,
c m n l = w m [ ( w m o l ) * p n l ] - w m [ ( w m o l ) * p n l ] ,
p n l = p n + Δ p n l = p ¯ n l - 1 , p n l + 1 - p n l = δ p n l , o m l = o m + Δ o m l = o ¯ m l - 1 , o m l + 1 - o m l = δ o m l , o l = o + Δ o l , o l + 1 - o l = δ o l .
o m l * p n l o m * p n + o m * Δ p n l + Δ o m l * p n ,
c m n l = w m { [ w m ( o + Δ o l ) ] * ( p n + Δ p n l ) } - w m { [ w m ( o + Δ o l ) ] * ( p n + Δ p n l ) } .
c m n l c m n - o m * Δ p n l - Δ o m l * p n + S m n l ,
S m n l = w m [ o * Δ p n l + Δ o l * p n ] ,
E 0 l 1 B n = 1 N m = 1 M S m n l 2 d x d y ,
E k l 1 B n = 1 N m = 1 M S m n l + o m * δ p n l + δ o m l * p n 2 d x d y ,
E 0 l + 1 1 B n = 1 N m = 1 M S m n l + 1 2 d x d y .
S m n l + 1 = w m [ o * Δ p n l + 1 + Δ o l + 1 * p n ] = w m [ o * ( Δ p n l + δ p n l ) + ( Δ o l + δ o l ) * p n ] = S m n l + w m [ o * δ p n l + δ o l * p n ] = S m n l + o m * δ p n l + δ o m l * p n + m n l ,
m n l = w m [ ( w m o ) * δ p n l ] - w m ( o m * δ p n l ) + w m [ ( w m δ o l ) * p n ] - w m ( δ o m l * p n ) .

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