A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation

IEEE Transactions on Image Processing

Volumn 21, Issue 8, 2012, Pages 3454-3466

  Luisier, Florian ^a   Blu, Thierry ^b   Wolfe, Patrick J ^c  

^a HARVARD UNIVERSITY   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^c UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Chi square distribution; filterbank transform; image denoising; magnetic resonance (MR) imaging; Rician noise; unbiased risk estimation

Indexed keywords

CHI-SQUARE DISTRIBUTION; CHI-SQUARE RANDOM VARIABLES; DE-NOISING; HAAR WAVELET TRANSFORM; IMAGE DATA; MAGNETIC RESONANCE IMAGES; MEAN SQUARED ERROR; MR IMAGES; PARAMETERIZED; RICIAN NOISE; RISK ESTIMATION; SHRINKAGE ESTIMATOR; STATE-OF-THE-ART METHODS; TWO DEGREES OF FREEDOM;

ESTIMATION; FILTER BANKS; IMAGE DENOISING; MAGNETIC RESONANCE; MAGNETIC RESONANCE IMAGING; PROBABILITY DISTRIBUTIONS;

RISK PERCEPTION;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; CHI SQUARE DISTRIBUTION; COMPUTER ASSISTED DIAGNOSIS; HUMAN; IMAGE ENHANCEMENT; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL NOISE RATIO; STATISTICAL ANALYSIS; WAVELET ANALYSIS; PROCEDURES;

ALGORITHMS; CHI-SQUARE DISTRIBUTION; DATA INTERPRETATION, STATISTICAL; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL-TO-NOISE RATIO; WAVELET ANALYSIS;

EID: 84864151725     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2012.2191565     Document Type: Article

References (48)

1. G. Wright, "Magnetic resonance imaging," IEEE Signal Process. Mag., vol. 14, no. 1, pp. 56-66, Jan. 1997.
2. C. L. Epstein, Introduction to the Mathematics of Medical Imaging, 2nd ed. Philadelphia, PA: SIAM, 2008.
3. R. M. Henkelman, "Measurement of signal intensities in the presence of noise in MR images," Med. Phys., vol. 12, no. 2, pp. 232-233, 1985. (Pubitemid 15089010)
4. M. Lustig, D. Donoho, J. Santos, and J. Pauly, "Compressed sensing MRI," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 72-82, Mar. 2008.
5. H. Gudbjartsson and S. Patz, "The Rician distribution of noisy MRI data," Mag. Reson. Med., vol. 34, no. 6, pp. 910-914, 1995.
6. R. D. Nowak, "Wavelet-based Rician noise removal for magnetic resonance imaging," IEEE Trans. Image Process., vol. 8, no. 10, pp. 1408- 1419, Oct. 1999. (Pubitemid 30524087)
7. A. Pižurica, 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.
8. J. V. Manjón, J. Carbonell-Caballero, J. J. Lull, G. García-Martí, L. Martí-Bonmatí, and M. Robles, "MRI denoising using non local means," Med. Image Anal., vol. 12, no. 2, pp. 514-523, 2008.
9. S. Aja-Fernández, M. Niethammer, M. Kubicki, M. E. Shenton, and C.- F. Westin, "Restoration of DWI data using a Rician LMMSE estimator," IEEE Trans. Med. Imag., vol. 27, no. 10, pp. 1389-1403, Oct. 2008.
10. S. Aja-Fernndez, C. Alberola-Lopez, and C.-F.Westin, "Noise and signal estimation in magnitude MRI and Rician distributed images: A LMMSE approach," IEEE Trans. Image Process., vol. 17, no. 8, pp. 1383-1398, Aug. 2008.
11. H. Liu, C. Yang, N. Pan, E. Song, and R. Greens, "Denoising 3D MR images by the enhanced non-local means filter for Rician noise," Mag. Reson. Imag., vol. 28, no. 10, pp. 1485-1496, 2010.
12. T. Thaipanich and C.-C. J. Kuo, "An adaptive nonlocal means scheme for medical image denoising," Proc. SPIE, vol. 7623, pp. 76230-1-76230- 12, Feb. 2010.
13. J. Sijbers, A. J. den Dekker, P. Scheunders, and D. V. Dyck, "Maximumlikelihood estimation of Rician distribution parameters," IEEE Trans. Med. Imag., vol. 17, no. 3, pp. 357-361, Jun. 1998. (Pubitemid 128747690)
14. J. Sijbers and A. J. den Dekker, "Maximum-likelihood estimation of signal amplitude and noise variance from MR data," Mag. Reson. Med., vol. 51, no. 3, pp. 586-594, 2004. (Pubitemid 38298673)
15. L. He and I. Greenshields, "A nonlocal maximum likelihood estimation method for Rician noise reduction in MR images," IEEE Trans. Med. Imag., vol. 28, no. 2, pp. 165-172, Feb. 2009.
16. S. P. Awate and R. T. Whitaker, "Feature-preserving MRI denoising: A nonparametric empirical Bayes approach," IEEE Trans. Med. Imag., vol. 26, no. 9, pp. 1242-1255, Sep. 2007. (Pubitemid 47383445)
17. A. Foi, "Noise estimation and removal in MR imaging: The variancestabilization approach," in Proc. IEEE Int. Symp. Biomed. Imag., Mar.- Apr. 2011, pp. 1809-1814.
18. A. Buades, B. Coll, and J. M. Morel, "A review of image denoising algorithms, with a new one," Multiscale Model. Simul., vol. 4, no. 2, pp. 490-530, Jul. 2005. (Pubitemid 43890582)
19. P. Coupé, P. Yger, S. Prima, P. Hellier, C. Kervrann, and C. Barillot, "An optimized blockwise non local means denoising filter for 3D magnetic resonance images," IEEE Trans. Med. Imag., vol. 27, no. 4, pp. 425-441, Apr. 2008. (Pubitemid 351479137)
20. Y. Gal, A. J. H. Mehnert, A. P. Bradley, K. McMahon, D. Kennedy, and S. Crozier, "Denoising of dynamic contrast-enhanced MR images using dynamic nonlocal means," IEEE Trans. Med. Imag., vol. 29, no. 2, pp. 302-310, Feb. 2010.
21. J. B. Weaver, Y. Xu, D. M. Healy, and L. D. Cromwell, "Filtering noise from images with wavelet transforms," Magn. Reson. Med., vol. 21, no. 2, pp. 288-295, 1991.
22. Y. Xu, J. Weaver, D. Healy, and J. Lu, "Wavelet transform domain filters: A spatially selective noise filtration technique," IEEE Trans. Image Process., vol. 3, no. 6, pp. 747-758, Nov. 1994.
23. J. C. Wood and K. M. Johnson, "Wavelet packet denoising of magnetic resonance images: Importance of Rician noise at low SNR," Magn. Reson. Med., vol. 41, no. 3, pp. 631-635, 1999. (Pubitemid 29152910)
24. S. Zaroubi and G. Goelman, "Complex denoising of MR data via wavelet analysis: Application for functional MRI," Magn. Reson. Imag., vol. 18, no. 1, pp. 59-68, 2000. (Pubitemid 30036142)
25. P. Bao and L. Zhang, "Noise reduction for magnetic resonance images via adaptive multiscale products thresholding," IEEE Trans. Med. Imag., vol. 22, no. 9, pp. 1089-1099, Sep. 2003.
26. 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)
27. 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)
28. F. Luisier and P. J. Wolfe, "Chi-square unbiased risk estimate for denoising magnitude MR images," in Proc. IEEE Int. Conf. Image Process., Brussels, Belgium, Sep. 2011, pp. 1593-1596.
29. L. D. Brown, Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory. Hayward, CA: Institute of Mathematical Statistics, 1986.
30. R. R. Coifman and D. L. Donoho, "Translation invariant de-noising," in Lecture Notes in Statistics: Wavelets and Statistics. New York: Springer- Verlag, 1995, pp. 125-150.
31. G. Nason and B. W. Silverman, The Stationary Wavelet Transform and Some Statistical Applications. New York: Springer-Verlag, 1995.
32. A. Gyaourova, C. Kamath, and I. K. Fodor, "Undecimated wavelet transforms for image de-noising," Lawrence Livermore National Laboratory, Livermore, CA, Tech. Rep., 2002.
33. J.-L. Starck, J. Fadili, and F. Murtagh, "The undecimated wavelet decomposition and its reconstruction," IEEE Trans. Image Process., vol. 16, no. 2, pp. 297-309, Feb. 2007. (Pubitemid 46421673)
34. F. Luisier, T. Blu, and M. Unser, "Image denoising in mixed Poisson- Gaussian noise," IEEE Trans. Image Process., vol. 20, no. 3, pp. 696- 708, Mar. 2011.
35. P. B. Patnaik, "The non-central ?2- and f -distribution and their applications," Biometrika, vol. 36, nos. 1-2, pp. 202-232, 1949.
36. D. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
37. K. Hirakawa, F. Baqai, and P. J. Wolfe, "Wavelet-based Poisson rate estimation using the Skellam distributions," Proc. SPIE, vol. 7246, pp. 1-12, Feb. 2009.
38. F. Luisier, C. Vonesch, T. Blu, and M. Unser, "Fast interscale wavelet denoising of Poisson-corrupted images," Signal Process., vol. 90, no. 2, pp. 415-427, 2010.
39. D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, Dec. 1995. (Pubitemid 126093135)
40. S. G. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Trans. Image Process., vol. 9, no. 9, pp. 1522-1531, Sep. 2000.
41. L. Sendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency," IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2744-2756, Nov. 2002. (Pubitemid 35312118)
42. 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. 1138-1351, Nov. 2003.
43. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612, Apr. 2004.
44. J. Sijbers, D. Poot, A. J. Dekker, and W. Pintjens, "Automatic estimation of the noise variance from the histogram of a magnetic resonance images," Phys. Med. Biol., vol. 52, no. 5, pp. 1335-1348, 2007. (Pubitemid 46646391)
45. J. Rajan, D. Poot, J. Juntu, and J. Sijbers, "Noise measurement from magnitude MRI using local estimates of variance and skewness," Phys. Med. Biol., vol. 55, no. 16, pp. 441-449, 2010.
46. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image denoising by sparse 3D transform-domain collaborative filtering," IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080-2095, Aug. 2007. (Pubitemid 47225460)
47. M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representations," IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4311-4322, Nov. 2006. (Pubitemid 44637761)
48. D. Ville and M. Kocher, "Non-local means with dimensionality reduction and SURE-based parameter selection," IEEE Trans. Image Process., vol. 20, no. 9, pp. 2683-2690, Sep. 2011.