Maximum likelihood restoration and choice of smoothing parameter in deconvolution of image data subject to Poisson noise

Computational Statistics and Data Analysis

Volumn 26, Issue 4, 1998, Pages 393-410

  Hudson, H Malcolm ^a   Lee, Thomas C M ^a  

^a NONE

Author keywords

Cross validation; Deconvolution; Fast computation; Regularization; Statistical algorithms

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; STATISTICAL METHODS;

CROSS VALIDATION; DECONVOLUTION; MAXIMUM LIKELIHOOD RESTORATION; MAXIMUM PENALIZED LIKELIHOOD (MPL); POISSON NOISE;

IMAGE RECONSTRUCTION;

EID: 0032488773     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(97)00041-8     Document Type: Article

References (44)

1. Besag, J., 1986. On the statistical analysis of dirty pictures. J. Roy. Statist. Soc. Ser. B 48, 259-302.
2. Besag, J., Green, P., 1993. Spatial statistics and Bayesian computation. J. Roy. Statist. Soc. Ser. B 55 25-38.
3. Brillinger, D., 1981. Time Series: Data Analysis and Theory. Holden-Day, San Francisco.
4. Chan, K.P.-S., Kay, J.W., 1991. Smoothing parameter selection in image restoration. In: Roussas, G. (Ed.), Nonparametric Functional Estimation and Related Topics, NATO Advanced Study Institute, Kluwer, Dortrecht, pp. 201-211.
5. Chornboy, E., Chen, C., Miller, M., Miller, T., Snyder, D., 1990. An evaluation of maximum likelihood reconstruction for SPECT. IEEE Trans. Med. Imaging MI-9, 99-110.
6. Coakley, K.J., 1991. A cross-validation procedure for stopping the EM algorithm and deconvolution of neutron depth profiling spectra. IEEE Trans. Nucl. Sci. 38, 9-15.
7. Coakley, K., Llacer, J., 1991. The use of Cross-Validation procedure as a stopping rule in Emission Computed Tomography image reconstruction. In: SPIE Proc. Image Phys: Med. Imaging V, vol. 1443, pp. 226-233.
8. Galatsanos, N.P., Katsaggelos, A.K., 1992. Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation. IEEE Trans. Image Proc. 1, 322-336.
9. Geman, S., Geman, D., 1984. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell. 6, 721-735.
10. Geman, S., McClure, D., 1987. Statistical methods for tomographic image reconstruction. In: Proceedings of the 46th Session ISI, Bulletin ISI, vol. 52.
11. Gidas, B., Hudson, H.M., 1991. A two stage EM algorithm with applications in emission tomography, Technical Report 39, Brown University, Complex System Report.
12. Girard, D.A., 1987. Optimal regularized reconstruction in computerized tomography. SIAM J. Sci. Statist. Comput. 8(6), 934-950.
13. L procedures: Comments, new results and applications to image recovery problems. Comput. Statist. 10, 205-231.
14. Green, P., 1984. Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives (with discussion). J. Roy. Statist. Soc. Ser. B 46, 149-192.
15. Green, P., 1990a. Bayesian reconstruction from emission tomography data using a modified EM algorithm. IEEE Trans. Med. Imaging MI-9, 84-93.
16. Green, P., 1990b. On use of the EM algorithm for penalized likelihood estimation. J. Roy. Statist. Soc. Ser. B 52, 443-452.
17. Green, P., Silverman, B., 1994. Nonparametric Regression and Generalized Linear Models, Chapman & Hall, London.
18. Grenander, U., 1981. Abstract Inference, Wiley, New York.
19. Hall, P., 1987. On the processing of a motion-blurred image. SIAM J. Appl. Math. 47, 441-453.
20. Hall, P., Koch, I., 1992. On the feasibility of cross-validation in image analysis. SIAM J. Appl. Math. 52, 259-313.
21. Hall, P., Titterington, D., 1987. Common structure of techniques for choosing smoothing parameters in regression problems. J. Roy. Statist. Soc. Ser. B 49, 184-198.
22. Hanson, K.M., 1990. Method of evaluating image-recovery algorithms based on task performance. J. Opt. Soc. Amer. 7, 1124-1302.
23. Hebert, T., Leahy, R., 1989. A generalized EM algorithm for 3-D Bayesian reconstruction from poisson data using Gibbs priors. IEEE Trans. Med. Imaging MI-8, 194-202.
24. Hudson, H.M., 1974. Empirical Bayes estimation, Ph.D. thesis, Stanford University, Technical Report No. 58, Dept. Statistics.
25. Hudson, H.M., 1978. A natural identity for exponential families with applications in multiparameter estimation. Ann. Statist. 6, 473-484.
26. Hudson, H.M., Ma, J., Green, P., 1994. Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes. Statist. Methods Med. Res. 3, 41-61.
27. Jain, A., 1989. Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ.
28. Johnson, V., 1994. A note on stopping Rules for EM-ML algorithm reconstructions of ECT images. IEEE Trans. Med. Imaging 13, 569-571.
29. Kozek, A.S., 1994. On a partial cross validation in nonparametric regression. In: Proceedings of the Interface, 26, pp. 187-191.
30. McCullagh, P., Neider, J.A., 1989. Generalized Linear Models, 2nd ed., Chapman & Hall, London.
31. O'Sullivan, F., Pawitan, Y., 1996. Bandwidth selection for indirect density estimation based on corrupted histogram data. J. Amer. Statist. Assoc. 91 (434), 610-626.
32. Pawitan, Y., O'Sullivan, F., 1993. Data dependent bandwidth selection for emission computed tomography reconstruction. IEEE Trans. Med. Imaging 12, 167-172.
33. Poggio, T., Torre, V., Koch, C., 1985. Computational vision and regularization theory. Nature 317, 314-319.
34. Reeves, S.J., Mersereau, R.M., 1992. Blur identification by the method of Generalized Cross Validation. IEEE Trans. Image Proc. 1, 301-311.
35. Rice, J., 1986. Choice of smoothing parameter in deconvolution problems. Contemp. Math. 59, 137-151.
36. Shepp, L., Vardi, Y., 1982. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging MI-2, 113-122.
37. Shumway, R.H., 1988. Applied Statistical Time Series Analysis, Prentice Hall, Englewood Cliffs, NJ.
38. Silverman, B.W., Jones, M.C., Wilson, J.D., Nychka, D.W., 1990. A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography (with discussion). J. Roy. Statist. Soc. Ser. B 52, 271-324.
39. Solo, V., 1988. Linear image restoration: An analytical study, Technical Report 88-VS-May-1988, Dept. of ECE, The Johns Hopkins Univ., Baltimore, MD.
40. Stefanski, L., Carroll, R.J., 1990. Deconvoluting kernel density estimators. Statistics 21, 169-184.
41. Thompson, A.M., Brown, J.C., Kay, J.W., Titterington, D.M., 1991. A study of methods of choosing the smoothing parameter in image restoration by regularization. IEEE Trans. Pattern Anal. Machine Intell. 13, 326-339.
42. Titterington, D.M., 1985. Common structure of smoothing techniques in statistics. Internat. Statist. Rev. 53, 141-170.
43. Vardi, Y., Shepp, L., Kaufman, A., 1985. A statistical model for positron emission tomography (with discussion). J. Amer. Statist. Assoc. 80, 8-20.
44. Wilson, D., Baddeley, A., Owens, R., 1997. A new metric for grey-scale image comparison. Internat. J. Comput. Vision, 24, 5-17.