Feature-preserving MRI denoising: A nonparametric empirical bayes approach

IEEE Transactions on Medical Imaging

Volumn 26, Issue 9, 2007, Pages 1242-1255

  Awate, Suyash P ^a,b   Whitaker, Ross T ^a  

^a University of Utah   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Denoising; Empirical Bayes (EB); Information theory; Markov random fields (MRF); Nonparametric statistics

Indexed keywords

INFORMATION THEORY; ITERATIVE METHODS; MAGNETIC RESONANCE IMAGING; MARKOV PROCESSES; OPTIMIZATION; STATISTICAL METHODS;

EMPIRICAL BAYES (EB) ESTIMATION; ITERATED CONDITIONAL ENTROPY REDUCTION (ICER); MARKOV RANDOM FIELDS (MRF); NONPARAMETRIC STATISTICS;

MEDICAL IMAGING;

ALGORITHM; ARTICLE; ARTIFACT; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BAYES THEOREM; BIOLOGICAL MODEL; BRAIN; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; HISTOLOGY; HUMAN; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ALGORITHMS; ARTIFACTS; ARTIFICIAL INTELLIGENCE; BAYES THEOREM; BRAIN; COMPUTER SIMULATION; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; MODELS, NEUROLOGICAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SUBTRACTION TECHNIQUE;

EID: 34548537289     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2007.900319     Document Type: Article

References (44)

1. D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans, "Design and construction of a realistic digital brain phantom," IEEE Trans. Med. Imag., vol. 17, no. 3, pp. 463-468, Jun. 1998.
2. X. Tai, K. Lie, T. Chan, and S. Osher, Eds., Image Processing based on Partial Differential Equations. New York: Springer, 2005.
3. G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of MRI data," IEEE Trans. Med. Imag., vol. 11, no. 2, pp. 221-232, Jun. 1992.
4. M. Lysaker, A. Lundervold, and X. Tai, "Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time," IEEE Trans. Image Process., vol. 12, no. 12, pp. 1579-1590, Dec. 2003.
5. A. Fan, W. Wells, J. Fisher, M. Çetin, S. Haker, R. Mulkern, C. Tempany, and A. Willsky, "A unified variational approach to denoising and bias correction in MR," Inf. Proc. Med Imag., pp. 148-159, 2003.
6. S. Basu, P. T. Fletcher, and R. T. Whitaker, "Rician noise removal in diffusion tensor MRI," Med Imag. Comput. Comput. Assist. Intervention, pp. 117-125, 2006.
7. D. Healy and J. Weaver, "Two applications of wavelet transforms in magnetic resonance imaging," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 840-860, Mar. 1992.
8. M. Hilton, T. Ogden, D. Hattery, G. Jawerth, and B. Eden, Wavelet Denoising of Functional MRI Data, pp. 93-114, 1996.
9. R. Nowak, "Wavelet-based Rician noise removal for magnetic resonance imaging," IEEE Trans. Image Process., vol. 8, no. 10, pp. 1408-1419, Oct. 1999.
10. A. Pizurica, W. Philips, I. Lemahieu, and M. Acheroy, "A versatile wavelet domain noise filtration technique for medical imaging," IEEE Trans. Med Imag., vol. 22, no. 3, pp. 323-331, Mar. 2003.
11. S. P. Awate and R. T. Whitaker, "Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering," in Proc. IEEE Int. Conf Comput. Vision Pattern Recognition, Jun. 2005, vol. 2, pp. 44-51.
12. S. P. Awate and R. T. Whitaker, "Unsupervised, information- theoretic, adaptive image filtering for image restoration," IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 3, pp. 364-376, Mar. 2006.
13. K. Fukunaga and L. Hostetler, "The estimation of the gradient of a density function, with applications in pattern recognition," IEEE Trans. Inf. Theory, vol. 21, no. 1, pp. 32-40, Jan. 1975.
14. D. Comaniciu and P. Meer, "Mean shift: A robust approach toward feature space analysis," IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 5, pp. 603-619, May 2002.
15. A. Buades, B. Coll, and J. M. Morel, "A non-local algorithm for image denoising," in IEEE Int. Conf. Comp. Vis. Pattern Recog., 2005, vol. 2, pp. 60-65.
16. A. Buades, B. Coll, and J. M. Morel, "A review of image denoising algorithms, with a new one," Multiscale Modeling Simulation, vol. 4, no. 2, pp. 490-530, 2005.
17. G. Casella, "An introduction to empirical Bayes analysis," Amer. Statistician, vol. 39, no. 2, pp. 83-87, 1985.
18. H. Robbins, "The empirical Bayes approach to statistical decision problems," Ann. Math. Stat., vol. 35, no. 1, pp. 1-20, 1964.
19. T. Weissman, E. Ordentlich, G. Seroussi, S. Verdu, and M. Weinberger, "Universal discrete denoising: Known channel," IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 5-28, Jan. 2005.
20. G. Motta, E. Ordentlich, I. Ramirez, G. Seroussi, and M. J. Weinberger, "The DUDE framework for continuous tone image denoising," in Int. Conf. Imag. Proc., 2005, pp. 345-348.
21. C. B. Cordy and D. R. Thomas, "Deconvolution of a distribution function," J. Amer. Statistical Assoc., vol. 92, no. 440, pp. 1459-1465, 1997.
22. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. R. Stat. Soc., vol. B, no. 39, pp. 1-38, 1977.
23. G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions. New York: Wiley, 1997.
24. J. Besag, "On the statistical analysis of dirty pictures," J. R. Stat. Soc., vol. 48, pp. 259-302, 1986.
25. S. Z. Li, Markov Random Field Modeling in Computer Vision. New York: Springer, 1995.
26. S. C. Zhu and D. Mumford, "Prior learning and gibbs reaction-diffusion," IEEE Trans. Pattern Anal. Mach. Intell., vol. 19, no. 11, pp. 1236-1250, Nov. 1997.
27. J. Huang and D. Mumford, "Statistics of natural images and models," in Proc IEEE Comp. Vis. Pattern Recognit., 1999, pp. 1541-1547.
28. A. Lee, K. Pedersen, and D. Mumford, "The nonlinear statistics of high-contrast patches in natural images," Int. J. Comput. Vision, vol. 54, no. 1-3, pp. 83-103, 2003.
29. E. Parzen, "On the estimation of a probability density function and the mode," Ann. Math. Stat., vol. 33, pp. 1065-1076, 1962.
30. S. P. Awate, "Adaptive Markov Models with Information-Theoretic Methods for Unsupervised Image Restoration and Segmentation," Ph.D., School Comput., Univ. Utah, Salt Lake City, 2006.
31. S. P. Awate and R. T. Whitaker, "Nonparametric neighborhood statistics for MRI denoising," in Proc Int. Conf. Inf. Process. Med. Imag., 2005, vol. 3565, Lect. Notes Comp. Sci., pp. 677-688.
32. E. Levina, "Statistical issues in texture analysis," Ph.D., Dept. Stat., Univ. California, Berkeley, 1997.
33. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed. New York: McGraw-Hill, 2001.
34. W. Hoeffding and H. Robbins, "The central limit theorem for dependent random variables," Duke Math. J., vol. 15, pp. 773-780, 1948.
35. K. N. Berk, "A central limit theorem for m-dependent random, variables with unbounded m," Ann. Prob., vol. 1, no. 2, pp. 352-354, 1973.
36. U. Grenander, Abstract Inference. New York: Wiley, 1975.
37. S. Geman and C. R. Hwang, "Nonparametric maximum, likelihood estimation by method of sieves," Ann. Stat., vol. 10, no. 2, pp. 401-414, 1982.
38. J. Bilmes, "A gentle tutorial on the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models", Univ. Berkeley, Berkeley, CA, Tech. Rep., 1997.
39. M. Fashing and C. Tomasi, "Mean shift is a bound optimization," IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 3, pp. 471-474, Mar. 2005.
40. J. Sijbers, A. den Dekker, P. Scheunders, and D. V. Dyck, "Maximum likelihood estimation of Rician distribution parameters," IEEE Trans. Med. Imag., vol. 17, no. 3, pp. 357-361, Jun. 1998.
41. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 7, pp. 629-639, Jul. 1990.
42. R. Malladi and J. Sethian, "Image processing via level set curvature flow," Proc. Natl. Acad. Sci. USA, vol. 92, pp. 7046-7050, 1995.
43. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal Mach. Intell., vol. 14, no. 3, pp. 367-383, Mar. 1992.
44. S. Z. Li, "On discontinuity-adaptive smoothness priors in computer vision," IEEE Trans. Pattern Anal Mach. Intell., vol. 17, no. 6, pp. 576-586, Jun. 1995.