Abstract

We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high- performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramér–Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramér–Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

© 2008 Optical Society of America

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2006 (4)

I. Kopriva, D. J. Garrood, and V. Borjanovic, “Single-frame blind image deconvolution by non-negative sparse matrix factorization,” Opt. Commun. 266, 456-464 (2006).
[CrossRef]

C. L. Matson and A. Haji, “Biased Cramér-Rao lower bound calculations for inequality-constrained estimators,” J. Opt. Soc. Am. A 23, 2702-2713 (2006).
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C. L. Matson and D. W. Tyler, “Primary and secondary superresolution by data inversion,” Opt. Express 14, 456-473(2006).
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D. Robinson and P. Milanfar, “Statistical performance analysis of super-resolution,” IEEE Trans. Image Process. 15, 1413-1428 (2006).
[CrossRef]

2005 (1)

2004 (1)

H. R. Ingleby and D. R. McGaughey, “Parallel multiframe blind deconvolution using wavelength diversity,” Proc. SPIE 5562, 58-64 (2004).
[CrossRef]

2003 (1)

2002 (1)

L. C. Roberts, Jr., and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114, 1260-1266 (2002).
[CrossRef]

2001 (1)

P. Stoica and T. L. Marzetta, “Parameter estimation problems with singular information matrices,” IEEE Trans. Signal Process. 49, 87-90 (2001).
[CrossRef]

1999 (3)

1998 (2)

1997 (1)

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 23, 550-560 (1997).
[CrossRef]

1996 (2)

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13, 43-64 (1996).
[CrossRef]

D. Kundur and D. Hatzinakos, “Blind image deconvolution revisited,” IEEE Signal Process. Mag. 13, 61-63 (1996).
[CrossRef]

1994 (2)

O. Shavli and E. Weinstein, “Maximum likelihood and lower bounds in system identification with non-Gaussian inputs,” IEEE Trans. Inf. Theory 40, 328-339 (1994).
[CrossRef]

Y. Yang, N. P. Galatsanos, and H. Stark, “Projection-based blind deconvolution,” J. Opt. Soc. Am. A 11, 2401-2409 (1994).
[CrossRef]

1993 (3)

1992 (3)

T. J. Holmes, “Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach,” J. Opt. Soc. Am. A 9, 1052-1061 (1992).
[CrossRef] [PubMed]

H. Miura and N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375-379 (1992).
[CrossRef]

H. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322-336 (1992).
[CrossRef]

1990 (1)

A. M. Darling, “Blind deconvolution for referenceless speckle imaging,” Proc. SPIE 1351, 590-599 (1990).
[CrossRef]

1989 (1)

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353-356 (1989).
[CrossRef]

1988 (2)

B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 547-549 (1988).

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

1987 (1)

1984 (1)

1983 (1)

1975 (1)

T. G. Stockham, Jr., T. M. Cannon, and R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678-692 (1975).
[CrossRef]

1973 (1)

K. T. Knox and B. J. Thompson, “New methods for processing speckle pattern star images,” Astrophys. J. 182, L133-L136 (1973).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

1970 (1)

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

1966 (1)

Antonius, P.

J. L. Jensen, J. A. Jensen, P. F. Stetson, and P. Antonius, “Multi-processor system for real-time deconvolution and flow estimation in medical ultrasound,” in Proceedings 1996 IEEE Ultrasonics Symposium (IEEE, 1996), pp. 1197-1200.
[CrossRef]

Ayers, G. R.

Baba, N.

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

H. Miura and N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375-379 (1992).
[CrossRef]

Bates, R. H. T.

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353-356 (1989).
[CrossRef]

R. G. Lane and R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180-188 (1987).
[CrossRef]

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
[CrossRef]

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998).
[CrossRef]

Borjanovic, V.

I. Kopriva, D. J. Garrood, and V. Borjanovic, “Single-frame blind image deconvolution by non-negative sparse matrix factorization,” Opt. Commun. 266, 456-464 (2006).
[CrossRef]

Bresler, Y.

G. Harikumar and Y. Bresler, “Analysis and comparative evaluation of techniques for multichannel blind deconvolution,” in Proceedings of the 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing (IEEE, 1996), pp. 332-335 .
[CrossRef]

Byrd, R. H.

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 23, 550-560 (1997).
[CrossRef]

Cannon, T. M.

T. G. Stockham, Jr., T. M. Cannon, and R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678-692 (1975).
[CrossRef]

Chen, Y.

Chi, C. Y.

C. Y. Chi and C. H. Hsi, “2-D blind deconvolution using Fourier series-based model and higher-order statistics with application to texture synthesis,” in Proceedings of the Ninth IEEE Signal Processing Workshop on Statistical and Array Processing (IEEE, 1988), pp. 216-219.

Dainty, J. C.

G. R. Ayers and 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 Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, 1984), Chap. 7.

Darling, A. M.

A. M. Darling, “Blind deconvolution for referenceless speckle imaging,” Proc. SPIE 1351, 590-599 (1990).
[CrossRef]

Davey, B. L. K.

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353-356 (1989).
[CrossRef]

Dolne, J. J.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, 1992).

Fried, D. L.

Friedlander, B.

D. Yellin and B. Friedlander, “Multichannel system identification and deconvolution: performance bounds,” IEEE Trans. Signal Process. 47, 1410-1414 (1999).
[CrossRef]

Galatsanos, H. P.

H. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322-336 (1992).
[CrossRef]

Galatsanos, N. P.

Garrood, D. J.

I. Kopriva, D. J. Garrood, and V. Borjanovic, “Single-frame blind image deconvolution by non-negative sparse matrix factorization,” Opt. Commun. 266, 456-464 (2006).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Gerwe, D. R.

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Addison-Wesley, 1992), Chap. 5.

Goodman, J. W.

J. W. Goodman, Introduction To Fourier Optics, 3rd ed.(Roberts & Company, 2005).

Haji, A.

Harikumar, G.

G. Harikumar and Y. Bresler, “Analysis and comparative evaluation of techniques for multichannel blind deconvolution,” in Proceedings of the 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing (IEEE, 1996), pp. 332-335 .
[CrossRef]

Hatzinakos, D.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13, 43-64 (1996).
[CrossRef]

D. Kundur and D. Hatzinakos, “Blind image deconvolution revisited,” IEEE Signal Process. Mag. 13, 61-63 (1996).
[CrossRef]

Holmes, T. J.

Hsi, C. H.

C. Y. Chi and C. H. Hsi, “2-D blind deconvolution using Fourier series-based model and higher-order statistics with application to texture synthesis,” in Proceedings of the Ninth IEEE Signal Processing Workshop on Statistical and Array Processing (IEEE, 1988), pp. 216-219.

Huang, T. S.

R. Y. Tsai and T. S. Huang, “Multiframe image restoration and registration,” in Advances in Computer Vision and Image Processing, R. Y. Tsai and T. S. Huang, eds (JAI, 1984), Vol. 1, pp. 317-339.

Hunt, B. R.

Idell, P. S.

Ingebretsen, R. B.

T. G. Stockham, Jr., T. M. Cannon, and R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678-692 (1975).
[CrossRef]

Ingleby, H. R.

H. R. Ingleby and D. R. McGaughey, “Parallel multiframe blind deconvolution using wavelength diversity,” Proc. SPIE 5562, 58-64 (2004).
[CrossRef]

Isobe, S.

Jensen, J. A.

J. L. Jensen, J. A. Jensen, P. F. Stetson, and P. Antonius, “Multi-processor system for real-time deconvolution and flow estimation in medical ultrasound,” in Proceedings 1996 IEEE Ultrasonics Symposium (IEEE, 1996), pp. 1197-1200.
[CrossRef]

Jensen, J. L.

J. L. Jensen, J. A. Jensen, P. F. Stetson, and P. Antonius, “Multi-processor system for real-time deconvolution and flow estimation in medical ultrasound,” in Proceedings 1996 IEEE Ultrasonics Symposium (IEEE, 1996), pp. 1197-1200.
[CrossRef]

Katsaggelos, A. K.

H. P. Galatsanos and A. K. Katsaggelos, “Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation,” IEEE Trans. Image Process. 1, 322-336 (1992).
[CrossRef]

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

Knox, K. T.

K. T. Knox and B. J. Thompson, “New methods for processing speckle pattern star images,” Astrophys. J. 182, L133-L136 (1973).
[CrossRef]

Kopriva, I.

I. Kopriva, D. J. Garrood, and V. Borjanovic, “Single-frame blind image deconvolution by non-negative sparse matrix factorization,” Opt. Commun. 266, 456-464 (2006).
[CrossRef]

Kundur, D.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13, 43-64 (1996).
[CrossRef]

D. Kundur and D. Hatzinakos, “Blind image deconvolution revisited,” IEEE Signal Process. Mag. 13, 61-63 (1996).
[CrossRef]

Kuwamura, S.

Labeyrie, A.

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

Lane, R. G.

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353-356 (1989).
[CrossRef]

R. G. Lane and R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180-188 (1987).
[CrossRef]

Lee, D. J.

Lohmann, A. W.

Marcellin, M. W.

Marzetta, T. L.

P. Stoica and T. L. Marzetta, “Parameter estimation problems with singular information matrices,” IEEE Trans. Signal Process. 49, 87-90 (2001).
[CrossRef]

Matson, C. L.

McCallum, B. C.

B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 547-549 (1988).

McGaughey, D. R.

H. R. Ingleby and D. R. McGaughey, “Parallel multiframe blind deconvolution using wavelength diversity,” Proc. SPIE 5562, 58-64 (2004).
[CrossRef]

Milanfar, P.

D. Robinson and P. Milanfar, “Statistical performance analysis of super-resolution,” IEEE Trans. Image Process. 15, 1413-1428 (2006).
[CrossRef]

Miura, H.

H. Miura and N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375-379 (1992).
[CrossRef]

Miura, N.

Nakao, Z.

Neyman, C. R.

L. C. Roberts, Jr., and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114, 1260-1266 (2002).
[CrossRef]

Nocedal, J.

C. Zhu, R. H. Byrd, and J. Nocedal, “L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 23, 550-560 (1997).
[CrossRef]

Noguchi, M.

Paxman, R. G.

R. G. Paxman and J. H. Seldin, “Fine-resolution astronomical imaging with phase-diverse speckle,” Proc. SPIE 2029, 287-298 (1993).
[CrossRef]

Porat, B.

B. Porat, Digital Processing of Random Signals -Theory and Methods (Prentice-Hall, 1994), Chap. 3.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, 1992).

Roberts, L. C.

L. C. Roberts, Jr., and C. R. Neyman, “Characterization of the AEOS adaptive optics system,” Publ. Astron. Soc. Pac. 114, 1260-1266 (2002).
[CrossRef]

Robinson, D.

D. Robinson and P. Milanfar, “Statistical performance analysis of super-resolution,” IEEE Trans. Image Process. 15, 1413-1428 (2006).
[CrossRef]

Roggemann, M. C.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “Practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Schall, H. B.

Schulz, T. J.

Seldin, J. H.

R. G. Paxman and J. H. Seldin, “Fine-resolution astronomical imaging with phase-diverse speckle,” Proc. SPIE 2029, 287-298 (1993).
[CrossRef]

Shavli, O.

O. Shavli and E. Weinstein, “Maximum likelihood and lower bounds in system identification with non-Gaussian inputs,” IEEE Trans. Inf. Theory 40, 328-339 (1994).
[CrossRef]

Sheppard, D. G.

Stark, H.

Stetson, P. F.

J. L. Jensen, J. A. Jensen, P. F. Stetson, and P. Antonius, “Multi-processor system for real-time deconvolution and flow estimation in medical ultrasound,” in Proceedings 1996 IEEE Ultrasonics Symposium (IEEE, 1996), pp. 1197-1200.
[CrossRef]

Stockham, T. G.

T. G. Stockham, Jr., T. M. Cannon, and R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678-692 (1975).
[CrossRef]

Stoica, P.

P. Stoica and T. L. Marzetta, “Parameter estimation problems with singular information matrices,” IEEE Trans. Signal Process. 49, 87-90 (2001).
[CrossRef]

Tamura, S.

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Figures (10)

Fig. 1
Fig. 1

PCID parallel architecture.

Fig. 2
Fig. 2

PCID parallel 2D FFT flow chart.

Fig. 3
Fig. 3

(a) Execution times and (b) scalability factors for the PCID algorithm for 128 × 128 measurement frames.

Fig. 4
Fig. 4

(a) Execution times and (b) scalability factors for the PCID algorithm for 512 × 512 measurement frames.

Fig. 5
Fig. 5

Two objects used in the PCID sample variance and CRB comparison study: (a) OCNR and (b) two-circ.

Fig. 6
Fig. 6

Two PSFs used in the PCID sample variance and CRB comparison study: (a) tripsf and (b) one realization of atmpsf.

Fig. 7
Fig. 7

Representative measurement frames of the Space Shuttle.

Fig. 8
Fig. 8

Two image restorations of the Space Shuttle produced by the PCID algorithm.

Fig. 9
Fig. 9

Two representative measurement frames of the HST.

Fig. 10
Fig. 10

Two PCID restorations of the HST.

Tables (2)

Tables Icon

Table 1 Mean, Minimum, and Maximum Values of the PCID/CRB Ratios for the Described Scenarios

Tables Icon

Table 2 Ten-Frame Blind PCID/CRB Ratios for Scenario (3)

Equations (17)

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i m ( x ) = o ( x ) * h m ( x ) + n m ( x ) ,
J [ o ^ ( x ) , h ^ 1 ( x ) , , h ^ M ( x ) ] = m = 1 M n = 1 N 2 1 σ m 2 ( x n ) + i m ( x n ) [ i m ( x n ) i ^ m ( x n ) ] 2 + γ g [ o ^ ( x n ) , h ^ 1 ( x n ) , , h ^ M ( x n ) ] ,
i ^ m ( x ) = h ^ m ( x ) * h r ( x ) * o ^ ( x ) ,
g [ o ^ ( x ) , h ^ 1 ( x ) , , h ^ M ( x ) ] = n = 1 N 2 o ^ 2 ( x n ) .
i ^ m ( x ) = h ^ m ( x ) * o ^ ( x ) .
var ( Φ ^ u ) diag ( F 1 ) ,
F p q = E { ln [ f ( y ; Φ ) ] Φ p ln [ f ( y ; Φ ) ] Φ q } ,
var ( Φ ^ b ) diag [ ( I + Φ b Φ ) F 1 ( I + Φ b Φ ) T ] ,
y m = H m θ + η m .
y = H θ + η ,
F = [ F 11 . . . F ( M + 1 ) 1 . . 0 . . . 0 . F ( M + 1 ) 1 F ( M + 1 ) ( M + 1 ) ] ,
[ F 11 ] p q = m = 1 M n = 1 N 2 h m ( x n x p ) h m ( x n x q ) i m ( x n ) + σ m 2 ( x n ) ,
[ F m 1 ] p q = n = 1 N 2 h m ( x n x p ) [ o ( x n x q ) o ( x n x N 2 ) ] i m ( x n ) + σ m 2 ( x n ) .
[ F m m ] p q = n = 1 N 2 [ o ( x n x p ) o ( x n x N 2 ) ] [ o ( x n x q ) o ( x n x N 2 ) ] i m ( x n ) + σ m 2 ( x n ) .
I + Φ b Φ = [ G 11 . 0 . 0 . G ( M + 1 ) ( M + 1 ) ] ,
[ G 11 ] p q = h reg ( x p x q ) .
H ( f ) = ( 1 0.97 f 1 / f c ) ( 1 0.97 f 2 / f c ) ,

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