A computational method for the restoration of images with an unknown, spatially-varying blur
Optics Express, Vol. 14, Issue 5, pp. 1767-1782 (2006)
http://dx.doi.org/10.1364/OE.14.001767
Enhanced HTML
Acrobat PDF (275 KB)
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
OCIS Codes
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
ToC Category:
Image Processing
History
Original Manuscript: December 5, 2005
Revised Manuscript: February 24, 2006
Manuscript Accepted: February 25, 2006
Published: March 6, 2006
Virtual Issues
Vol. 1, Iss. 4 Virtual Journal for Biomedical Optics
Citation
Johnathan Bardsley, Stuart Jefferies, James Nagy, and Robert Plemmons, "A computational method for the restoration of images with an unknown, spatially-varying blur," Opt. Express 14, 1767-1782 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-5-1767
Sort: Year | Journal | Reset
References
- 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).
- 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). [CrossRef]
- 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). [CrossRef] [PubMed]
- M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, FL, 1996).
- 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). [CrossRef]
- 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). [CrossRef]
- J. G. Nagy and D. P. O’Leary, "Restoring images degraded by spatially-variant blur," SIAM J. Sci. Comput. 19, 1063-1082 (1998). [CrossRef]
- R. A. Gonsalves, "Phase diversity in adaptive optics," Opt. Eng. 21, 829-832 (1982).
- 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).
- 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). [CrossRef]
- 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. Nocedal and S. J. Wright, Numerical Optimization (Springer-Verlag, New York, 1999). [CrossRef]
- 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).
- D. A. Fish, J. Grochmalicki, and E. R. Pike, "Scanning singular-value-decomposition method for restoration of images with space-variant blur," J. Opt. Soc. Am. A 13, 1-6 (1996). [CrossRef]
- 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). [CrossRef]
- 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). [CrossRef]
Cited By |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
Figures
|
|
|
|
| Fig. 1. | Fig. 2. | Fig. 3. |
|
|
|
|
| Fig. 4. | Fig. 5. | Fig. 6. |
|
|
|
|
| Fig. 7. | Fig. 8. | Fig. 9. |
|
|
|
|
| Fig. 10. | Fig. 11. | Fig. 12. |





OSA is a member of 