Abstract

In this paper, we present an algorithm for the restoration of images with an unknown, spatially-varying blur. Existing computational methods for image restoration require the assumption that the blur is known and/or spatially-invariant. Our algorithm uses a combination of techniques. First, we section the image, and then treat the sections as a sequence of frames whose unknown PSFs are correlated and approximately spatially-invariant. To estimate the PSFs in each section, phase diversity is used. With the PSF estimates in hand, we then use a technique by Nagy and O’Leary for the restoration of images with a known, spatially-varying blur to restore the image globally. Test results on star cluster data are presented.

© 2006 Optical Society of America

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  1. J. Biretta, "WFPC and WFPC 2 instrumental characteristics," in The Restoration of HST Images and Spectra II, R. J. Hanisch and R. L. White, eds., pp. 224-235 (Space Telescope Science Institute, Baltimore, MD, 1994).
  2. H. J. Trussell and S. Fogel, "Identification and restoration of spatially variant motion blurs in sequential images," IEEE Trans. Image Proc. 1, 123-126 (1992).
  3. R. G. Paxman, B. J. Thelen, and J. H. Seldin, "Phase-diversity correction of turbulence-induced space-variant blur," Opt. Lett. 19, 1231-1233 (1994).
  4. M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, FL, 1996).
  5. M. Faisal, A. D. Lanterman, D. L. Snyder, and R. L. White, "Implementation of a Modified Richardson-Lucy Method for Image Restoration on a Massively Parallel Computer to Compensate for Space-Variant Point Spread Function of a Charge-Coupled Device Camera," J. Opt. Soc. Am. A 12, 2593-2603 (1995).
  6. A. F. Boden, D. C. Redding, R. J. Hanisch, and J. Mo, "Massively Parallel Spatially-Variant Maximum Likelihood Restoration of Hubble Space Telescope Imagery," J. Opt. Soc. Am. A 13, 1537-1545 (1996).
  7. J. G. Nagy and D. P. O’Leary, "Restoring images degraded by spatially-variant blur," SIAM J. Sci. Comput. 19, 1063-1082 (1998).
    [CrossRef]
  8. R. A. Gonsalves, "Phase diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).
  9. C. R. Vogel, T. Chan, and R. J. Plemmons, "Fast algorithms for phase diversity-based blind deconvolution," in Adaptive Optical System Technologies, vol. 3353 (SPIE, 1998).
  10. R. G. Paxman, T. Schulz, and J. Fienup, "Joint estimation of object and aberrations by using phase diversity," J. Opt. Soc. Am. A 9, 1072-1085 (1992).
  11. L. Gilles, C. R. Vogel, and J. M. Bardsley, "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," Inverse Probl. 18, 237-252 (2002).
    [CrossRef]
  12. J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999).
  13. H.-M. Adorf, "Towards HST restoration with space-variant PSF, cosmic rays and other missing data," in The Restoration of HST Images and Spectra II, R. J. Hanisch and R. L. White, eds., pp. 72-78 (1994).
  14. H. J. Trussell and B. R. Hunt, "Image Restoration of Space-Variant Blurs by Sectional Methods," IEEE Trans. Acoust.Speech, Signal Processing 26, 608-609 (1978).
  15. J. G. Nagy and D. P. O’Leary, "Fast iterative image restoration with a spatially varying PSF," in Advanced Signal Processing Algorithms, Architectures, and Implementations VII, F. T. Luk, ed., vol. 3162, pp. 388-399 (SPIE, 1997).
  16. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic Publishers, Dordrecht, 2000).
  17. P. C. Hansen, Rank-deficient and discrete ill-posed problems (SIAM, Philadelphia, PA, 1997).
  18. C. R. Vogel, Computational Methods for Inverse Problems (SIAM, Philadelphia, PA, 2002).

2002 (1)

L. Gilles, C. R. Vogel, and J. M. Bardsley, "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," Inverse Probl. 18, 237-252 (2002).
[CrossRef]

1998 (1)

J. G. Nagy and D. P. O’Leary, "Restoring images degraded by spatially-variant blur," SIAM J. Sci. Comput. 19, 1063-1082 (1998).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

1992 (2)

H. J. Trussell and S. Fogel, "Identification and restoration of spatially variant motion blurs in sequential images," IEEE Trans. Image Proc. 1, 123-126 (1992).

R. G. Paxman, T. Schulz, and J. Fienup, "Joint estimation of object and aberrations by using phase diversity," J. Opt. Soc. Am. A 9, 1072-1085 (1992).

1982 (1)

R. A. Gonsalves, "Phase diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

1978 (1)

H. J. Trussell and B. R. Hunt, "Image Restoration of Space-Variant Blurs by Sectional Methods," IEEE Trans. Acoust.Speech, Signal Processing 26, 608-609 (1978).

Bardsley, J. M.

L. Gilles, C. R. Vogel, and J. M. Bardsley, "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," Inverse Probl. 18, 237-252 (2002).
[CrossRef]

Boden, A. F.

Faisal, M.

Fienup, J.

Fogel, S.

H. J. Trussell and S. Fogel, "Identification and restoration of spatially variant motion blurs in sequential images," IEEE Trans. Image Proc. 1, 123-126 (1992).

Gilles, L.

L. Gilles, C. R. Vogel, and J. M. Bardsley, "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," Inverse Probl. 18, 237-252 (2002).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, "Phase diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Hanisch, R. J.

Hunt, B. R.

H. J. Trussell and B. R. Hunt, "Image Restoration of Space-Variant Blurs by Sectional Methods," IEEE Trans. Acoust.Speech, Signal Processing 26, 608-609 (1978).

Lanterman, A. D.

Mo, J.

Nagy, J. G.

J. G. Nagy and D. P. O’Leary, "Restoring images degraded by spatially-variant blur," SIAM J. Sci. Comput. 19, 1063-1082 (1998).
[CrossRef]

O’Leary, D. P.

J. G. Nagy and D. P. O’Leary, "Restoring images degraded by spatially-variant blur," SIAM J. Sci. Comput. 19, 1063-1082 (1998).
[CrossRef]

Paxman, R. G.

Redding, D. C.

Schulz, T.

Seldin, J. H.

Snyder, D. L.

Thelen, B. J.

Trussell, H. J.

H. J. Trussell and S. Fogel, "Identification and restoration of spatially variant motion blurs in sequential images," IEEE Trans. Image Proc. 1, 123-126 (1992).

H. J. Trussell and B. R. Hunt, "Image Restoration of Space-Variant Blurs by Sectional Methods," IEEE Trans. Acoust.Speech, Signal Processing 26, 608-609 (1978).

Vogel, C. R.

L. Gilles, C. R. Vogel, and J. M. Bardsley, "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," Inverse Probl. 18, 237-252 (2002).
[CrossRef]

White, R. L.

IEEE Trans. Image Proc. (1)

H. J. Trussell and S. Fogel, "Identification and restoration of spatially variant motion blurs in sequential images," IEEE Trans. Image Proc. 1, 123-126 (1992).

Inverse Probl. (1)

L. Gilles, C. R. Vogel, and J. M. Bardsley, "Computational Methods for a Large-Scale Inverse Problem Arising in Atmospheric Optics," Inverse Probl. 18, 237-252 (2002).
[CrossRef]

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

Opt. Eng. (1)

R. A. Gonsalves, "Phase diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).

Opt. Lett. (1)

SIAM J. Sci. Comput. (1)

J. G. Nagy and D. P. O’Leary, "Restoring images degraded by spatially-variant blur," SIAM J. Sci. Comput. 19, 1063-1082 (1998).
[CrossRef]

Speech, Signal Processing (1)

H. J. Trussell and B. R. Hunt, "Image Restoration of Space-Variant Blurs by Sectional Methods," IEEE Trans. Acoust.Speech, Signal Processing 26, 608-609 (1978).

Other (9)

J. G. Nagy and D. P. O’Leary, "Fast iterative image restoration with a spatially varying PSF," in Advanced Signal Processing Algorithms, Architectures, and Implementations VII, F. T. Luk, ed., vol. 3162, pp. 388-399 (SPIE, 1997).

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic Publishers, Dordrecht, 2000).

P. C. Hansen, Rank-deficient and discrete ill-posed problems (SIAM, Philadelphia, PA, 1997).

C. R. Vogel, Computational Methods for Inverse Problems (SIAM, Philadelphia, PA, 2002).

J. Biretta, "WFPC and WFPC 2 instrumental characteristics," in The Restoration of HST Images and Spectra II, R. J. Hanisch and R. L. White, eds., pp. 224-235 (Space Telescope Science Institute, Baltimore, MD, 1994).

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, FL, 1996).

C. R. Vogel, T. Chan, and R. J. Plemmons, "Fast algorithms for phase diversity-based blind deconvolution," in Adaptive Optical System Technologies, vol. 3353 (SPIE, 1998).

J. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999).

H.-M. Adorf, "Towards HST restoration with space-variant PSF, cosmic rays and other missing data," in The Restoration of HST Images and Spectra II, R. J. Hanisch and R. L. White, eds., pp. 72-78 (1994).

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