Noise and signal estimation in magnitude MRI and Rician distributed images: A LMMSE approach

IEEE Transactions on Image Processing

Volumn 17, Issue 8, 2008, Pages 1383-1398

  Aja Fernández, Santiago ^a,b   Alberola López, Carlos ^a   Westin, Carl Fredrik ^b  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b BRIGHAM AND WOMEN S HOSPITAL   (United States)

Author keywords

Linear minimum mean square error (LMMSE) estimator; MRI filtering; Noise estimation; Rician noise

Indexed keywords

BEAMFORMING; BLOCK CODES; IMAGE ENHANCEMENT; MAGNETIC RESONANCE IMAGING; MEAN SQUARE ERROR; PROBABILITY DISTRIBUTIONS; SIGNAL RECEIVERS;

CLOSED-FORM SOLUTIONS; DYNAMIC ESTIMATIONS; FEATURE PRESERVATIONS; LINEAR MINIMUM MEAN SQUARE ERROR (LMMSE) ESTIMATOR; LOCAL MEANS; LOCAL STATISTICS; LOCAL VARIANCES; MRI FILTERING; NOISE ESTIMATION; NOISE POWERS; PROBABILITY DENSITIES; RAYLEIGH AND RICIAN MODELS; RICIAN NOISE; SAMPLE DISTRIBUTIONS; SAMPLE STATISTICS; SIGNAL ESTIMATIONS;

PROBABILITY DENSITY FUNCTION;

ALGORITHM; ARTICLE; ARTIFACT; BRAIN; COMPUTER ASSISTED DIAGNOSIS; HISTOLOGY; IMAGE ENHANCEMENT; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; REGRESSION ANALYSIS; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; STATISTICAL ANALYSIS; STATISTICAL MODEL;

ALGORITHMS; ARTIFACTS; BRAIN; DATA INTERPRETATION, STATISTICAL; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; LEAST-SQUARES ANALYSIS; MAGNETIC RESONANCE IMAGING; MODELS, STATISTICAL; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 48349108270     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2008.925382     Document Type: Article

References (35)

1. D. Drumheller, "General expressions for Rician density and distribution functions," IEEE Trans. Aerosp. Electron. Syst., vol. 29, no. 2, pp. 580-588, Apr. 1993.
2. H. Gudbjartsson and S. Patz, "The Rician distribution of noisy MRI data," Magn. Reson. Med., vol. 34, pp. 910-914, Aug. 1995.
3. S. Basu, T. Fletcher, and R. Whitaker, "Rician noise removal in diffusion tensor MRI," in Proc. MICCAI, 2006, vol. 1, pp. 117-125.
4. R. Henkelrnan, "Measurement of signal intensities in the presence of noise in MR images," Med. Phys., vol. 12, no. 2, Mar. 1985.
5. G. McGibney and M. Smith, "Un unbiased signal-to-noise ratio measure for magnetic resonance images," Med. Phys., vol. 20, no. 4, pp. 1077-1078, Jul. 1993.
6. J. Sijbers, A. J. den Dekker, P. Scheunders, and D. Van Dyck, "Maximum-likelihood estimation of Rician distribution parameters," IEEE Trans. Med. Imag., vol. 17, no. 3, pp. 357-361, Jun. 1998.
7. J. Sijbers, A. J. den Dekker,D.Van Dyck, and E. Raman, "Estimation of signal and noise from Rician distributed dala," in Proc. Int. Conf. Signal Processing Communications, Las Palmas de Gran Canaria, Spain, Feb. 1998, pp. 140-142.
8. J. Sijbers and A. J. den Dekker, "Maximum likelihood estimation of signal amplitude and noise variance form MR data," Magn. Reson. Imag., vol. 51, pp. 586-594, Feb. 2004.
9. L. Jiang and W. Yang, "Adaptive magnetic resonance image denoting using mixture model and wavelet shrinkage," presented at the 7th Digital Image Computing: Techniques and Applications, Sydney, Australia, Dec. 2003.
10. M. D. DeVore, A. D. Lanterman, and J. A. O'Sullivan, "ATR performance of a Rician model for SAR images," in Proc. SPIE, ISSV 4050, Orlando, FL, Apr. 2000, pp. 34-37.
11. T. Marzetta, "EM algorithm for estimating the parameters of multivariate complex Rician density for polarimetric SAR," in Proc. ICASSP, May 1995, vol. 5, pp. 3651-3654.
12. P. Fillard, V. Arsigny, X. Pennec, and N. Ayache, "Clinical DT-MRI estimation, smoothing and fiber tracking with log-euclidean metrics," in Proc. IEEE Int. Symp. Biomedical Imaging, Apr. 2006, pp. 786-789.
13. R. Nowak, "Wavelet-based Rician noise removal for magnetic resonance imaging," IEEE Trans. Image Process., vol. 8, no. 10, pp. 1408-1419, Oct. 1999.
14. 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.
15. M. Lysaker, A. Lundervold, and X. Tai, "Noise removal using fourth order partial differential equations with applications to medical magnetic resonance imaging in space and time," IEEE Trans. Image Process., vol. 12, no. 12, pp. 1579-1590, Dec. 2003.
16. T. McGraw, B. C. Vemuri, Y. Chen, M. Rao, and T. Mareci, "DT-MRI denoising and neuronal fiber tracking," Med. Imag. Anal., vol. 8, pp. 95-111, Jun. 2004.
17. C. B. Ann, Y. C. Song, and D. J. Park, "Adaptive template filtering for signal-to-noise ratio enhancement in magnetic resonance imaging," IEEE Trans. Med. Imag., vol. 18, no. 6, pp. 549-556, Jun. 1999.
18. S. Awate and R. W. RT, "Nonparametric neighborhood statistics for MRI denoising," in Proc. Int. Conf. Inf. Process. Med. Imaging, 2005, vol. 3565, pp. 677-688.
19. C. G. Koay and P. J. Basser, "Analytically exact correction scheme for signal extraction from noisy magnitude MR signals," J. Magn. Reson. vol. 179, pp. 317-322, Apr. 2006.
20. M. Martin-Fernández, C. Alberola-López, J. Ruiz-Alzola, and C.-F. Westin, "Sequential anisotropic Wiener filtering applied to 3-D MRI data," Magn. Reson. Imag., vol. 25, pp. 278-292, Feb. 2007.
21. J. Hu and N. C. Beaulieu, "Accurate closed-form approximations to Ricean sum distributions and densities," IEEE Commun. Lett., vol. 9, no. 2, pp. 133-135, Feb. 2005.
22. M. K. Simon, Probability Distributions Involving Gaussian Random Variables. Norwell, MA: Kluwer, 2002.
23. J. Sijbers, A. J. den Dekker, J. Van Audekerke, M. Verhoye, and D. Van Dyck, "Estimation of the noise in magnitude MR images," Magn. Reson. Imag., vol. 16, no. 1, pp. 87-90, Jan. 1998.
24. J. Sijbers, A. J. den Dekker, D. Poot, M. Verhoye, N. Van Camp, and A. Van der Linden, "Robust estimation of the noise variance from background MR data," presented at the SPIE Medical Imaging: Image Processing, Mar. 2006.
25. J. Sijbers, D. Poot, A. J. den Dekker, and W. Pintjenst, "Automatic estimation of the noise variance from the histogram of a magnetic resonance image," Phys. Med. Biol., vol. 52, pp. 1335-1348, Feb. 2007.
26. R. Salvador, A. Peña, D. K. Menon, T. Carpenter, J. Pickard, and E. T. Bullmore, "Formal characterization and extension of the linearized diffusion tensor model," Human Brain Map., vol. 24, pp. 144-155, Feb. 2005.
27. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.
28. D. Collins, A. Zijdenbos, V. Killokian, J. Sled, N. Kabani, C. Holmes, and A. Evans, "Design and construction of a realistic digital brain phantom," IEEE Trans. Med. Imag., vol. 17, no. 3, pp. 463-468, Mar. 1998.
29. A. Papoulis, Probability, Random Variables, and Stochastic Processes 3rd ed. Boston, MA: McGraw-Hill, 1991.
30. N. C. Beaulieu, "An infinite series for the computation of the complementary probability distribution function of a sum of independent ramdom variables and its application to the sum of Rayleigh random variables," IEEE Trans. Commun., vol. 38, no. 9, pp. 1463-1474, Sep. 1990.
31. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1964.
32. J. S. Lim, Two Dimensional Signal and Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1990.
33. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612, Apr. 2004.
34. S. Aja-Fernández, R. San-José-Estépar, C. Alberola-López, and C. Westin, "Image quality assesment based on local variance," in Proc. 28th IEEE EMBS, New York, Sep. 2006, pp. 4815-4818.
35. Live Database. Laboratory for Image and Video Engineering (LIVE) [Online]. Available: Http://live.ece.utexas.edu/research/quality/ subjective.htm The Univ. Texas, Austin