Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 3, May 2013, Pages: 67-80
Received: Apr. 30, 2013; Published: Jun. 10, 2013
Views 3365      Downloads 151
Authors
Tatiana V. Yakovleva, Department of Algorithm Theory and Coding Mathematical Principles, Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS, Moscow, Russia
Nicolas S. Kulberg, Department of Algorithm Theory and Coding Mathematical Principles, Institution of Russian Academy of Sciences Dorodnicyn Computing Centre of RAS, Moscow, Russia
Article Tools
PDF
Follow on us
Abstract
The paper’s subject is the elaboration of a new approach to image analysis on the basis of the maximum likelihood method. This approach allows to get simultaneous estimation of both the image noise and the signal within the Rician statistical model. An essential novelty and advantage of the proposed approach consists in reducing the task of solving the system of two nonlinear equations for two unknown variables to the task of calculating one variable on the basis of one equation. Solving this task is important in particular for the purposes of the magnetic-resonance images processing as well as for mining the data from any kind of images on the basis of the signal’s envelope analysis. The peculiarity of the consideration presented in this paper consists in the possibility to apply the developed theoretical technique for noise suppression algorithms’ elaboration by means of calculating not only the signal mean value but the value of the Rice distributed signal’s dispersion, as well. From the view point of the computational cost the procedure of the both parameters’ estimation by proposed technique has appeared to be not more complicated than one-parametric optimization. The present paper is accented upon the deep theoretical analysis of the maximum likelihood method for the two-parametric task in the Rician distributed image processing. As the maximum likelihood method is known to be the most precise, its developed two-parametric version can be considered both as a new effective tool to process the Rician images and as a good facility to evaluate the precision of other two-parametric techniques by means of their comparing with the technique proposed in the present paper.
Keywords
Rice Distribution, Maximum Likelihood Method, MR Imaging, Two-Parametric Analysis
To cite this article
Tatiana V. Yakovleva, Nicolas S. Kulberg, Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 3, 2013, pp. 67-80. doi: 10.11648/j.ajtas.20130203.15
References
[1]
T. Wang and T. Lei, "Statistical analysis of MR imaging and its application in image modeling," in Proc. IEEE Int. Conf. Image Processing and Neural Networks, vol. I, 1994, pp. 866–870.
[2]
S. O. Rice, "Mathematical analysis of random noise," Bell Syst. Technological J., vol. 23, p. 282, 1944.
[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.
[4]
A. Papoulis, Probability, Random Variables and Stochastic Processes, 2nd ed. Tokyo, Japan: McGraw-Hill, 1984.
[5]
H. Gudbjartsson and S. Patz, "The Rician distribution of noisy MRI data", Magn. Reson. Med., vol.34, pp.910—914, 1995.
[6]
A. Macovski, "Noise in MRI", Magn. Reson. Med., vol. 36, No.3, pp.494—497, 1996.
[7]
G. Gerig, O. Kubler, R. Kikinis, and F. A. Jolesz, "Nonlinear anisotropic filtering of MRI data," IEEE Trans. Med. Imag., vol. 11, pp. 221–232, June 1992.
[8]
G. Z. Yang, P. Burger, D. N. Firmin, and S. R. Underwood, "Structure adaptive anisotropic filtering for magnetic resonance image enhancement," in Proc. CAIP, pp. 384–391, 1995.
[9]
S. J. Garnier and G. L. Bilbro, "Magnetic resonance image restoration," J. Math. Imag., Vision, vol. 5, pp. 7—19, 1995.
[10]
G. McGibney and M. R. Smith, "An unbiased signal-to-noise ratio measure for magnetic resonance images," Med. Phys., vol. 20, no. 4,pp. 1077—1078, 1993.
[11]
Jan Sijbers, Arnold J. den Dekker, Paul Scheunders, and Dirk Van Dyck, "Maximum-Likelihood Estimation of Rician Distribution Parameters", IEEE Transactions on Medical Imaging, vol.17, No 3, p.p. 357—361, June 1998.
[12]
Jeny Rajan, Ben Jeurissen, Marleen Verhoye, Johan Van Audekerke and Jan Sijbers, "Maximum likelihood estimation based denoising of magnetic resonance images using restricted local neighborhoods". Physics in Medicine and Biology, vol. 56, issue 16, pp. 2011. DOI: 10.1088/0031-9155/56/16/009
[13]
Jeny Rajan, Dirk Poot, Jaber Juntu and Jan Sijbers, "Noise measurement from magnitude MRI using local estimates of variance and skewness", Phys. Med. Biol. 55, p.p.441–449, 2010.
[14]
J. Sijbers & A. J. den Dekker, "Maximum Likelihood estimation of signal amplitude and noise variance from MR data". Magn Reson Med 51(3):586—594, 2004.
[15]
L. He & I. R. Greenshields , "A Nonlocal Maximum Likelihood Estimation Method for Rician Noise Reduction in MR images". IEEE Trans Med Imaging 28:165—172, 2009.
[16]
Aja-Fernandez, S.; Alberola-Lopez, C.; Westin, C.-F. Noise and Signal Estimation in Magnitude MRI and Rician Distributed Images: A LMMSE Approach // IEEE Transactions on Image Processing, vol. 17, issue 8, pp. 1383—1398, 2008.
[17]
C. F.M. Carobbi, M. Cati, "The absolute maximum of the likelihood function of the Rice distribution:existence and uniqueness, IEEE Trans. on Instrumentation and Measurement, vol 57, No 4, April 2008, pp. 682-689.
[18]
Rytov, S.М. Introduction into Statistical Radio-physics. P.1. Random processes. — Мoscow: Nauka, 1976 (in Russian).
[19]
P.J.Bickel, K.A.Doksum, Mathematical Statistics, Holden-Day, Inc., 1983.
[20]
М. Abramowitz and I. Stegun (eds.) Handbook of Mathematical Functions with formulas, graphics and mathematical tables. National Bureau of Standards, applied mathematics series-55; Issued June 1964.
[21]
T. Yakovleva. "Two-parametric method of noise and signal determination in magnetic resonance imaging: mathematical substantiation", unpublished.
[22]
Young, Phillip M., et al. "MR imaging findings in 76 consecutive surgically proven cases of pericardial disease with CT and pathologic correlation." The international journal of cardiovascular imaging 28.5 (2012): 1099-1109.
[23]
Samarin, Andrei, et al. "PET/MR imaging of bone lesions–implications for PET quantification from imperfect attenuation correction." European journal of nuclear medicine and molecular imaging 39.7 (2012): 1154-1160.
[24]
Hualong Zu, Qixin Wang, Mingzhi Dong,Liwei Ma, Liang Yin, Yanhui Yang. "Compressed Sensing Based Fixed-Point DCT Image Encoding", Advances in Computational Mathematics and its Applications, 2.2 (2012): 259-262
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186