Abstract

We examine methods for preprocessing a collection of atmospheric turbulence-degraded short-exposure imagery to improve the resolving power of estimation algorithms. We redefine the method known as frame selection in the context of optimizing estimation results. We compare several measures of image quality with idealized standards, demonstrating their relative ability to rank highly the least-degraded image frames. In particular, we find the Fisher information measure to be the most noise tolerant and robust frame-selection measure. We then examine the resolving implication of removing additive background noise resulting from the sky and telescope. Specifically, we show that background compensation acts as a de facto restoration of the compact object support and leads to furthering the resolving power of estimation methods. Results from simulated imaging scenarios demonstrate the improved ability of a multiframe maximum a posteriori estimator to restore the passband object distribution as well as to further recover the lost spectral content residing beyond the diffraction limit.

© 1999 Optical Society of America

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References

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  1. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  2. D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe superresolution algorithms for atmospheric turbulence-degraded imagery,” J. Opt. Soc. Am. A 15, 978–992 (1998).
    [CrossRef]
  3. B. R. Hunt, P. J. Sementilli, “Description of a Poisson imagery super-resolution algorithm,” in Astronomical Data Analysis Software and Systems I, D. Worral, C. Biemesderfer, J. Barnes, eds. (Astronomy Society of the Pacific, San Francisco, Calif., 1992), pp. 196–199.
  4. B. R. Hunt, “Super-resolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1991).
    [CrossRef]
  5. D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” J. Opt. Soc. Am. 68, 1651–1658 (1978).
    [CrossRef]
  6. J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
    [CrossRef]
  7. R. A. Muller, A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [CrossRef]
  8. M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
    [CrossRef]
  9. S. D. Ford, M. C. Roggemann, B. M. Welsh, “Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images,” Opt. Eng. 35, 1025–1034 (1996).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  11. D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe super-resolution algorithms for atmospheric turbulence-degraded imagery,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 2857–2860.
  12. J. J. Green, B. R. Hunt, “Super-resolution in a synthetic aperture imaging system,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 865–868.
  13. B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, Berlin, 1991).
  14. B. R. Frieden, Physics from Fisher Information (Cambridge U. Press, Cambridge, UK, 1998).
  15. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).
  16. D. Kincaid, W. Cheney, Numerical Analysis (Brooks/Cole, Pacific Grove, Calif., 1991).
  17. M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Lett. 14, 24–41 (1997).
    [CrossRef]
  18. P. J. Sementilli, M. S. Nadar, B. R. Hunt, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
    [CrossRef]
  19. M. S. Nadar, “Minimum cross-entropy formulations in image super-resolution,” Ph.D. dissertation (University of Arizona, Tucson, Az., 1996).
  20. A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

1998 (1)

1997 (1)

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Lett. 14, 24–41 (1997).
[CrossRef]

1996 (1)

S. D. Ford, M. C. Roggemann, B. M. Welsh, “Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images,” Opt. Eng. 35, 1025–1034 (1996).
[CrossRef]

1994 (1)

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

1993 (1)

1991 (1)

B. R. Hunt, “Super-resolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1991).
[CrossRef]

1987 (1)

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

1978 (1)

1974 (1)

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Banham, M. R.

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Lett. 14, 24–41 (1997).
[CrossRef]

Buffington, A.

Cheney, W.

D. Kincaid, W. Cheney, Numerical Analysis (Brooks/Cole, Pacific Grove, Calif., 1991).

Christou, J. C.

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

Cobb, M. L.

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

Ford, S. D.

S. D. Ford, M. C. Roggemann, B. M. Welsh, “Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images,” Opt. Eng. 35, 1025–1034 (1996).
[CrossRef]

Fried, D. L.

Frieden, B. R.

B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, Berlin, 1991).

B. R. Frieden, Physics from Fisher Information (Cambridge U. Press, Cambridge, UK, 1998).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Green, J. J.

J. J. Green, B. R. Hunt, “Super-resolution in a synthetic aperture imaging system,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 865–868.

Hunt, B. R.

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe superresolution algorithms for atmospheric turbulence-degraded imagery,” J. Opt. Soc. Am. A 15, 978–992 (1998).
[CrossRef]

P. J. Sementilli, M. S. Nadar, B. R. Hunt, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
[CrossRef]

B. R. Hunt, “Super-resolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1991).
[CrossRef]

B. R. Hunt, P. J. Sementilli, “Description of a Poisson imagery super-resolution algorithm,” in Astronomical Data Analysis Software and Systems I, D. Worral, C. Biemesderfer, J. Barnes, eds. (Astronomy Society of the Pacific, San Francisco, Calif., 1992), pp. 196–199.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

J. J. Green, B. R. Hunt, “Super-resolution in a synthetic aperture imaging system,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 865–868.

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe super-resolution algorithms for atmospheric turbulence-degraded imagery,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 2857–2860.

Katsaggelos, A. K.

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Lett. 14, 24–41 (1997).
[CrossRef]

Kincaid, D.

D. Kincaid, W. Cheney, Numerical Analysis (Brooks/Cole, Pacific Grove, Calif., 1991).

Marcellin, M. W.

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe superresolution algorithms for atmospheric turbulence-degraded imagery,” J. Opt. Soc. Am. A 15, 978–992 (1998).
[CrossRef]

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe super-resolution algorithms for atmospheric turbulence-degraded imagery,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 2857–2860.

McCarthy, D. W.

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

Muller, R. A.

Nadar, M. S.

P. J. Sementilli, M. S. Nadar, B. R. Hunt, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
[CrossRef]

M. S. Nadar, “Minimum cross-entropy formulations in image super-resolution,” Ph.D. dissertation (University of Arizona, Tucson, Az., 1996).

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Roggemann, M. C.

S. D. Ford, M. C. Roggemann, B. M. Welsh, “Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images,” Opt. Eng. 35, 1025–1034 (1996).
[CrossRef]

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Sementilli, P. J.

P. J. Sementilli, M. S. Nadar, B. R. Hunt, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
[CrossRef]

B. R. Hunt, P. J. Sementilli, “Description of a Poisson imagery super-resolution algorithm,” in Astronomical Data Analysis Software and Systems I, D. Worral, C. Biemesderfer, J. Barnes, eds. (Astronomy Society of the Pacific, San Francisco, Calif., 1992), pp. 196–199.

Sheppard, D. G.

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe superresolution algorithms for atmospheric turbulence-degraded imagery,” J. Opt. Soc. Am. A 15, 978–992 (1998).
[CrossRef]

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe super-resolution algorithms for atmospheric turbulence-degraded imagery,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 2857–2860.

Stoudt, C. A.

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

Welsh, B. M.

S. D. Ford, M. C. Roggemann, B. M. Welsh, “Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images,” Opt. Eng. 35, 1025–1034 (1996).
[CrossRef]

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

Astron. J. (1)

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

IEEE Signal Process. Lett. (1)

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Lett. 14, 24–41 (1997).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

B. R. Hunt, “Super-resolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1991).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Eng. (2)

M. C. Roggemann, C. A. Stoudt, B. M. Welsh, “Image-spectrum signal-to-noise ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence,” Opt. Eng. 33, 3254–3264 (1994).
[CrossRef]

S. D. Ford, M. C. Roggemann, B. M. Welsh, “Frame selection performance limits for statistical image reconstruction of adaptive optics compensated images,” Opt. Eng. 35, 1025–1034 (1996).
[CrossRef]

Other (11)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

D. G. Sheppard, B. R. Hunt, M. W. Marcellin, “Iterative multiframe super-resolution algorithms for atmospheric turbulence-degraded imagery,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 2857–2860.

J. J. Green, B. R. Hunt, “Super-resolution in a synthetic aperture imaging system,” in Proceedings of the International Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 865–868.

B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, Berlin, 1991).

B. R. Frieden, Physics from Fisher Information (Cambridge U. Press, Cambridge, UK, 1998).

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

D. Kincaid, W. Cheney, Numerical Analysis (Brooks/Cole, Pacific Grove, Calif., 1991).

M. S. Nadar, “Minimum cross-entropy formulations in image super-resolution,” Ph.D. dissertation (University of Arizona, Tucson, Az., 1996).

A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

B. R. Hunt, P. J. Sementilli, “Description of a Poisson imagery super-resolution algorithm,” in Astronomical Data Analysis Software and Systems I, D. Worral, C. Biemesderfer, J. Barnes, eds. (Astronomy Society of the Pacific, San Francisco, Calif., 1992), pp. 196–199.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

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Figures (6)

Fig. 1
Fig. 1

Image of the Hubble Space Telescope, taken from the shuttle during the 1994 servicing mission, for use as the object in our preprocessing study.

Fig. 2
Fig. 2

Effectiveness of various image-quality standards (top) and measures (bottom) in the selection of high-quality frames from 20-dB SNR imagery for multiframe processing.

Fig. 3
Fig. 3

Decreasing imaging SNR as background strength increases from 0 to 100 times the object brightness.

Fig. 4
Fig. 4

Improved restoration by use of background-compensated imagery (solid curve) compared with restoration by use of raw imagery (dashed curves) across a range of SNR’s in 7-cm. seeing.

Fig. 5
Fig. 5

MFPMAP estimations from visible wavelength imagery with no preprocessing (top) and with background-compensation preprocessing (bottom).

Fig. 6
Fig. 6

MFPMAP estimations from long-wave infrared wavelength imagery with no preprocessing (top) and with background-compensation preprocessing (bottom).

Tables (3)

Tables Icon

Table 1 Summary of Image-Quality Standards

Tables Icon

Table 2 Summary of Image-Quality Measures

Tables Icon

Table 3 Summary of Correlations between Quality Standards and Measures across Noise Levels

Equations (13)

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Pr5.6 exp-0.1557Dro2,
gi(x, y)=(f*hi)(x, y)i=1N.
fˆ=arg maxf i=1Np(gi|f )p(f ).
fˆ n+1(x, y)=f^n(x, y)expg((n))N(x, y)[(fˆ n*h((n))N)(x, y)]-1×*h((n))N+(x, y),x, y,
M2=-x,yψi(x, y)log ψi(x, y),
ψi(x, y)=gi(x, y)x,yg(x, y).
M3=4×x,y[ψi(x, y)]*[ψi(x, y)].
ISNR=10×log10 1N i=1Nf-gi2f-fˆ2.
gi(x, y)=(f*hi)(x, y)+bi(x, y)i.
SNR(f¯, bo)=10×log10 f¯(f¯+bo)1/2.
b^o=1χ¯ i=1Nx,yχ¯gi(x,y),
gic(x, y)=gi(x, y)-b^o,gi(x, y)>b^o0,otherwise,i, x, y.
fˆ n+1(x, y)=fˆ n(x, y)expg((n))N(x, y)[(fˆ n*h((n))N)(x, y)]-1 *h+((n))N(x, y)x, y,

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