## Statistical-information-based performance criteria for Richardson-Lucy image deblurring

JOSA A, Vol. 19, Issue 7, pp. 1286-1296 (2002)

http://dx.doi.org/10.1364/JOSAA.19.001286

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### Abstract

Iterative image deconvolution algorithms generally lack objective criteria for deciding when to terminate iterations, often relying on *ad hoc* metrics for determining optimal performance. A statistical-information-based analysis of the popular Richardson–Lucy iterative deblurring algorithm is presented after clarification of the detailed nature of noise amplification and resolution recovery as the algorithm iterates. Monitoring the information content of the reconstructed image furnishes an alternative criterion for assessing and stopping such an iterative algorithm. It is straightforward to implement prior knowledge and other conditioning tools in this statistical approach.

© 2002 Optical Society of America

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.2000) Image processing : Digital image processing

(100.3020) Image processing : Image reconstruction-restoration

**Citation**

Sudhakar Prasad, "Statistical-information-based performance criteria for Richardson-Lucy image deblurring," J. Opt. Soc. Am. A **19**, 1286-1296 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-7-1286

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### References

- H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
- W. K. Pratt, Digital Image Processing, 2nd ed. (Wiley, New York, 1991).
- R. L. Lagendijk and J. Biemond, Iterative Identification and Restoration of Images (Kluwer, Norwell, Mass., 1991).
- M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).
- E. S. Meinel, “Origins of linear and nonlinear recursive restoration algorithms,” J. Opt. Soc. Am. A 3, 787–799 (1986).
- A. S. Carasso, “Linear and nonlinear image deblurring: a documented study,” SIAM J. Numer. Anal. 36, 1659–1689 (1999).
- B. R. Hunt, “Prospects for image restoration,” Int. J. Mod. Phys. C 5, 151–178 (1994).
- B. R. Hunt, “Superresolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1995).
- D. G. Sheppard, B. R. Hunt, and M. W. Marcellin, “Iterative multiframe superresolution algorithms for atmospheric-turbulence-degraded imagery,” J. Opt. Soc. Am. A 15, 978–992 (1998).
- W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
- L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
- D. L. Snyder, M. I. Miller, L. J. Thomas, Jr., and D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imaging 6, 228–238 (1987).
- D. L. Snyder and M. I. Miller, “The use of sieves to stabilize images produced with the EM algorithm for emission tomography,” IEEE Trans. Nucl. Sci. NS-32, 3864–3872 (1985).
- D. L. Snyder and M. I. Miller, Random Point Processes in Time and Space, 2nd ed. (Springer-Verlag, New York, 1991).
- H. J. Trussell, “Convergence criteria of iterative restoration methods,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 129–136 (1983).
- J. Llacer and E. Veklerov, “Feasible images and practical stopping rules for iterative algorithms in emission tomography,” IEEE Trans. Med. Imaging 8, 186–193 (1989).
- J. Llacer, “On the validity of hypothesis testing for feasibility of image reconstruction,” IEEE Trans. Med. Imaging 9, 226–230 (1990).
- S. J. Reeves, “Generalized cross-validation as a stopping rule for the Richardson–Lucy algorithm,” Int. J. Imaging Syst. Technol. 6, 387–391 (1995).
- P. B. Fellgett and E. H. Linfoot, “On the assessment of optical images,” Philos. Trans. R. Soc. (London) A 247, 369–407 (1955).
- C. L. Fales and F. O. Huck, “An information theory of image gathering,” Inf. Sci. (New York) 57, 245–285 (1991).
- F. O. Huck, C. L. Fales, and Z. Rahman, “An information theory of visual communication,” Philos. Trans. R. Soc. London Ser. A 354, 2193–2248 (1996).
- S. Prasad, “Information capacity of a seeing-limited imaging system,” Opt. Commun. 177, 119–134 (2000).
- S. Prasad, “Information theoretic perspective on the formation, detection and processing of images from a seeing limited telescope,” in Proceedings of the AMOS Technical Conference (Maui Economic Development Board, Maui, HI, 1999), pp. 339–349.
- J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, “Information-theoretic image formation,” IEEE Trans. Inf. Theory 44, 2094–2123 (1998).
- C. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423, 623–656 (1948).
- B. R. Frieden, “Restoring with maximum likelihood and maximum entropy,” J. Opt. Soc. Am. 62, 511–518 (1972).
- S. P. Luttrell, “The use of transinformation in the design of data sampling schemes for inverse problems,” Inverse Probl. 1, 199–218 (1985).
- Y. Vardi and D. Lee, “From image deblurring to optimal investments: maximum likelihood solutions for positive linear inverse problems,” J. R. Statist. Soc. B 55, 569–612 (1993).
- D. L. Snyder, T. J. Schulz, and J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992).
- See, e.g., T. J. Holmes, “Maximum likelihood image restoration adapted for incoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988).

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