Efficient multivariate skellam shrinkage for denoising photon-limited image data: An empirical Bayes approach

Proceedings - International Conference on Image Processing, ICIP

Volumn , Issue , 2009, Pages 2961-2964

  Hirakawa, Keigo ^a   Wolfe, Patrick J ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Image denoising; Poisson distribution; Wavelets

Indexed keywords

BAYESIAN NETWORKS; COMPUTERIZED TOMOGRAPHY; DIFFERENTIAL EQUATIONS; IMAGE PROCESSING; IMAGING SYSTEMS; PHOTONS; SHRINKAGE;

BAYESIAN ESTIMATORS; BAYESIAN MODEL; COMPUTATIONALLY EFFICIENT; COMPUTED TOMOGRAPHY SCAN; CONDITIONAL EXPECTATION; DE-NOISING; EMPIRICAL BAYES APPROACH; HAAR WAVELETS; IMAGE DATA; IMAGE DENOISING; LINEAR DIFFERENTIAL EQUATION; MARGINAL LIKELIHOOD; MEAN ESTIMATORS; MEAN-SQUARE; POISSON DATA; RECURSIVE PROPERTY; STATE-OF-THE-ART APPROACH; TEST IMAGES; TRANSFORM COEFFICIENTS;

POISSON DISTRIBUTION;

EID: 77951969025     PISSN: 15224880     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICIP.2009.5413334     Document Type: Conference Paper

References (16)

1. P. Besbeas, I. De Feis, and T. Sapatinas, "A comparative simulation study of wavelet shrinkage estimators for Poisson counts," Int. Statist. Rev., vol. 72, pp. 209-237, 2004.
2. E. D. Kolaczyk, "Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds," Statist. Sinica, vol. 9, pp. 119-135, 1999.
3. R. D. Nowak and R. G. Baraniuk, "Wavelet-domain filtering for photon imaging systems," IEEE Trans. Image Process., vol. 8, pp. 666-678, 1999.
4. A. Antoniadis and T. Sapatinas, "Wavelet shrinkage for natural exponential families with quadratic variance functions," Biometrika, vol. 88, pp. 805-820, 2001.
5. M. L. Clevenson and J. V. Zidek, "Simultaneous estimation of the means of independent Poisson laws," J. Am. Statist. Ass., vol. 70, pp. 698-705, 1975.
6. J. T. Hwang, "Improving upon standard estimators in discrete exponential families with applications to Poisson and Negative Binomial cases," Ann. Statist., vol. 10, pp. 857-867, 1982.
7. M. Raphan and E. P. Simoncelli, "Learning to be Bayesian without supervision," in Advances in Neural Information Processing Systems 19, B. Schölkopf, J. Platt, and T. Hoffman, Eds., pp. 1145-1152. MIT Press, Cambridge, 2007.
8. E. D. Kolaczyk, "Bayesian multiscale models for Poisson processes," J. Am. Statist. Ass., vol. 94, pp. 920-921, 1999.
9. K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Info. Theory, vol. 45, pp. 846-862, 1999.
10. J. G. Skellam, "The frequency distribution of the difference between two Poisson variates belonging to different populations," J. R. Statist. Soc., vol. 109, pp. 296, 1946.
11. K. Hirakawa and P. J. Wolfe, "Skellamshrink: Poisson intensity estimation for vector-valued data," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., 2009.
12. K. Hirakawa and P. J. Wolfe, "Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data," submitted manuscript, available at http://arxiv.org/abs/0905.3217, 2009.
13. F. Luisier, C. Vonesch, T. Blu, and M. Unser, "Fast Haar-wavelet denoising of multidimensional flourescence microscopy data," in Proc. IEEE Int. Sympos. Biomed. Imaging, June 2009.
14. P. Fryzlewicz and G. P. Nason, "A Haar-Fisz algorithm for Poisson intensity estimation," J. Computat. Graph. Statist., vol. 13, pp. 621-638, 2004.
15. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Am. Statist. Ass., vol. 90, pp. 1200-1224, 1995.
16. NIH National Library of Medicine, "Visual human project," available at http://www.nlm.nih.gov.