Image denoising in mixed poissongaussian noise

IEEE Transactions on Image Processing

Volumn 20, Issue 3, 2011, Pages 696-708

  Luisier, Florian ^a   Blu, Thierry ^b   Unser, Michael ^a  

^a EPFL   (Switzerland)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Filterbank; Gaussian noise; image denoising; MSE estimation; Poisson noise; thresholding; unbiased risk estimate

Indexed keywords

GAUSSIAN NOISE; IMAGE DENOISING; MSE ESTIMATION; POISSON NOISE; THRESHOLDING; UNBIASED RISK ESTIMATES;

ESTIMATION; FLUORESCENCE MICROSCOPY; GAUSSIAN NOISE (ELECTRONIC); IMAGE SEGMENTATION; NOISE POLLUTION CONTROL; OPTIMIZATION;

RISK PERCEPTION;

ALGORITHM; ARTICLE; CYTOLOGY; FLUORESCENCE MICROSCOPY; IMAGE PROCESSING; METHODOLOGY; MOON; NORMAL DISTRIBUTION; POISSON DISTRIBUTION; STATISTICAL MODEL; TOBACCO;

ALGORITHMS; IMAGE PROCESSING, COMPUTER-ASSISTED; MICROSCOPY, FLUORESCENCE; MODELS, STATISTICAL; MOON; NORMAL DISTRIBUTION; POISSON DISTRIBUTION; TOBACCO;

EID: 79951834945     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2073477     Document Type: Article

References (44)

1. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, "Image denoising using scale mixtures of Gaussians in the wavelet domain," IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338-1351, Nov. 2003.
2. F. Luisier, T. Blu, and M. Unser, "A new sure approach to image denoising: Interscale orthonormal wavelet thresholding," IEEE Trans. Image Process., vol. 16, no. 3, pp. 593-606, Mar. 2007. (Pubitemid 46431959)
3. T. Blu and F. Luisier, "The SURE-LET approach to image denoising," IEEE Trans. Image Process., vol. 16, no. 11, pp. 2778-2786, Nov. 2007. (Pubitemid 350141850)
4. T. Le, R. Chartrand, and T. J. Asaki, "A variational approach to reconstructing images corrupted by Poisson noise," J. Math. Imaging Vis., vol. 27, no. 3, pp. 257-263, Apr. 2007. (Pubitemid 46664094)
5. R. H. Chan and K. Chen, "Multilevel algorithm for a Poisson noise removal model with total-variation regularization," Int. J. Comput. Math., no. 5, pp. 1-18, May 2007.
6. A. Sawatzky, C. Brune, J. Müller, and M. Burger, "Computer analysis of images and patterns," in Total Variation Processing ofImages with Poisson Statistics. New York: Springer, 2009, pp. 533-540.
7. F. J. Anscombe, "The transformation of Poisson, binomial and negative-binomial data," Biometrika, vol. 35, no. 3/4, pp. 246-254, Dec. 1948.
8. D. L. Donoho, "Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data," in Proc. Symp. Appl. Math., 1993, pp. 173-205.
9. F. Murtagh, J.-L. Starck, and A. Bijaoui, "Image restoration with noise suppression using a multiresolution support," Astron. Astrophys. SupplementSeries, vol. 112,pp. 179-189, 1995.
10. P. Fryzlewicz and G. P. Nason, "A Haar-Fisz algorithm for Poisson intensity estimation," J. Comput. Graph. Stat., vol. 13, no. 3, pp. 621-638, Sep. 2004. (Pubitemid 39159775)
11. K. E. Timmermann and R. D. Nowak, "Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 846-862, Apr. 1999.
12. E. D. Kolaczyk, "Bayesian multi-scale models for Poisson processes," J. Amer. Stat. Assoc., vol. 94, no. 447, pp. 920-933, Sep. 1999.
13. H. Lu, Y. Kim, and J. M. M. Anderson, "Improved Poisson intensity estimation: Denoising application using Poisson data," IEEE Trans. Image Process., vol. 13, no. 8, pp. 1128-1135, Aug. 2004.
14. S. Lefkimmiatis, P. Maragos, and G. Papandreou, "Bayesian inference on multiscale models for Poisson intensity estimation: Applications to photon-limited image denoising," IEEE Trans. Image Process., vol. 18, no. 8, pp. 1724-1741, Aug. 2009.
15. E. D. Kolaczyk, "Nonparametric estimation of intensity maps using Haar wavelets and Poisson noise characteristics," Astrophys. J., vol. 534, pp. 490-505, 2000.
16. K. Hirakawa and P. Wolfe, "SkellamShrink: Poisson intensity estimation for vector-valued data," in Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'09), Apr. 2009, pp. 3441-3444.
17. K. Hirakawa and P. J. Wolfe, "Efficient multivariate Skellam Shrinkage for denoising photon-limited image data: An empirical bayes approach," in Proc. IEEE Int. Conf. Image Processing (ICIP'09), Cairo, Egypt, Nov. 7-11, 2009, pp. 2961-2964.
18. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," Journal of the American Statistical Association, vol. 90, no. 432, pp. 1200-1224, Dec. 1995. (Pubitemid 126093135)
19. F. Luisier, C. Vonesch, T. Blu, and M. Unser, "Fast interscale wavelet denoising of Poisson-corrupted images," Signal Processing, vol. 90, no. 2, pp. 415-427, Feb. 2010.
20. C. Stein, "Estimationofthemeanofamultivariatenormaldistribution, " The Annals of Statistics, vol. 9, pp. 1135-1151, 1981.
21. E. D. Kolaczyk, "Wavelet shrinkage estimation of certain Poisson intensity signals using corrected thresholds," Statistica Sinica, vol. 9, no. 1, pp. 119-135, Jan. 1999.
22. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
23. C. Charles and J. Rasson, "Wavelet denoising of Poisson-distributed data and applications," Comput. Stat. Data Anal., vol. 43, no. 2, pp. 139-148, 2003. (Pubitemid 36708986)
24. R. D. Nowak and R. G. Baraniuk, "Wavelet-domain filtering for photon imaging systems," IEEE Trans. Image Process., vol. 8, no. 5, pp. 666-678, May 1999.
25. A. Antoniadis and T. Sapatinas, "Wavelet shrinkage for natural exponential families with quadratic variance functions," Biometrika, vol. 88, no. 3, pp. 805-820, 2001. (Pubitemid 33771025)
26. S. Sardy, A. Antoniadis, and P. Tseng, "Automatic smoothing with wavelets for a wide class of distributions," J. Comput. Graph. Stat., vol. 13, no. 2, pp. 399-423, Jun. 2004.
27. E. D. Kolaczyk and R. D. Nowak, "Multiscale likelihood analysis and complexity penalized estimation," Ann. Stat., vol. 32, no. 2, pp. 500-527, 2004. (Pubitemid 41250303)
28. R. M. Willett and R. D. Nowak, "Multiscale Poisson intensity and density estimation," IEEE Trans. Inf. Theory, vol. 53, no. 9, pp. 3171-3187, Sep. 2007.
29. M. Jansen, "Multiscale Poisson data smoothing," J. Royal Stat. Soc. B, vol. 68, no. 1, pp. 27-48, 2006. (Pubitemid 43415334)
30. B. Zhang, J. M. Fadili, and J.-L. Starck, "Wavelets, ridgelets, and curvelets for Poisson noise removal," IEEE Trans. Image Process., vol. 17, no. 7, pp. 1093-1108, Jul. 2008.
31. B. Zhang, J. Fadili, J.-L. Starck, and J.-C. Olivo-Marin, "Multiscale variance-stabilizing transform for mixed-Poisson-Gaussian processes and its applications in bioimaging," in Proc. IEEE Int. Conf. Image Process. (ICIP'07), Oct. 16-19, 2007, vol. 6, pp. VI-233-VI-236.
32. P. Besbeas, I. D. Feis, and T. Sapatinas, "A comparative simulation study of wavelet shrinkage estimators for Poisson counts," Int. Stat. Rev., vol. 72, no. 2, pp. 209-237, Aug. 2004. (Pubitemid 38939454)
33. M. Raphan and E. P. Simoncelli, "Optimal denoising in redundant representations," IEEE Trans. Image Process., vol. 17, no. 8, pp. 1342-1352, Aug. 2008.
34. Hudson, "A natural identity for exponential families with applications in multiparameter estimation," Ann. Stat., vol. 6, no. 3, pp. 473-484, May 1978.
35. K.-W. Tsui and S. J. Press, "Simultaneous estimation ofseveral Poisson parameters under K-normalized squared error loss," Ann. Stat., vol. 10, no. 1, pp. 93-100, Mar. 1982.
36. S. Ramani, C. Vonesch, and M. Unser, "Deconvolution of 3-D fluorescence micrographs with automatic risk minimization," in Proc. 5th IEEE Int. Symp. Biomed. Imaging: From Nano to Macro (ISBI'08), Paris, France, May 14-17, 2008, pp. 732-735.
37. 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. Cambridge, MA: MIT Press, 2007, pp. 1145-1152.
38. J.-L. Starck, D. L. Donoho, and E. J. Candes, "Very high quality image restoration by combining wavelets and curvelets," in Wavelets: Applications in Signal and Image Processing IX, A. F. Laine, M. A. Unser, and A. Aldroubi, Eds. Bellingham, WA: SPIE, 2001, vol. 4478, pp. 9-19. (Pubitemid 35152957)
39. M. Fadili, J.-L. Starck, and L. Boubchir, "Morphological diversity and sparse image denoising," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., Apr. 2007, vol. 1, pp. I-589-I-592.
40. M. Elad and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., vol. 15, no. 12, pp. 3736-3745, Dec. 2006. (Pubitemid 44811686)
41. C. Vonesch, F. Aguet, J.-L. Vonesch, and M. Unser, "The colored revolution of bioimaging," IEEE Signal Process. Mag., vol. 23, no. 3, pp. 20-31, May 2006.
42. J. Pawley, "Sources of noise in three-dimensional microscopical data sets," in Three-Dimensional Confocal Microscopy: Volume InvestigationofBiologicalSpecimens. New York: Academic, 1994,pp.47-94.
43. S. Delpretti, F. Luisier, S. Ramani, T. Blu, and M. Unser, "Multiframe SURE-LET denoising of timelapse fluorescence microscopy images," in Proc. 5th IEEE Int. Symp. Biomed. Imaging: From Nano to Macro, Paris, France, May 14-17, 2008, pp. 149-152.
44. J. Boulanger, C. Kervrann, J. Salamero, J.-B. Sibarita, P. Elbau, and P. Bouthemy, "Patch-based non-local functional for denoising fluorescence microscopy image sequences," IEEE Trans. Med. Imaging, vol. 29, pp. 442-454, 2010.