Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach

Tatiana V. Yakovleva; Nicolas S. Kulberg

doi:doi:10.11648/j.ajtas.20130203.15

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Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach

Tatiana V. Yakovleva, Nicolas S. Kulberg

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 3)

Received: 30 April 2013 Published: 10 June 2013

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 3)
DOI	10.11648/j.ajtas.20130203.15
Page(s)	67-80
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Rice Distribution, Maximum Likelihood Method, MR Imaging, Two-Parametric Analysis

References

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[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.
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APA Style

Tatiana V. Yakovleva, Nicolas S. Kulberg. (2013). 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, 2(3), 67-80. https://doi.org/10.11648/j.ajtas.20130203.15

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ACS Style

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. Am. J. Theor. Appl. Stat. 2013, 2(3), 67-80. doi: 10.11648/j.ajtas.20130203.15

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AMA Style

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. Am J Theor Appl Stat. 2013;2(3):67-80. doi: 10.11648/j.ajtas.20130203.15

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@article{10.11648/j.ajtas.20130203.15,
  author = {Tatiana V. Yakovleva and Nicolas S. Kulberg},
  title = {Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {3},
  pages = {67-80},
  doi = {10.11648/j.ajtas.20130203.15},
  url = {https://doi.org/10.11648/j.ajtas.20130203.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130203.15},
  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.},
 year = {2013}
}

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TY  - JOUR
T1  - Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach
AU  - Tatiana V. Yakovleva
AU  - Nicolas S. Kulberg
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DO  - 10.11648/j.ajtas.20130203.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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PB  - Science Publishing Group
SN  - 2326-9006
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AB  - 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.
VL  - 2
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ER  -

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Author Information

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

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APA Style

Tatiana V. Yakovleva, Nicolas S. Kulberg. (2013). 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, 2(3), 67-80. https://doi.org/10.11648/j.ajtas.20130203.15

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ACS Style

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. Am. J. Theor. Appl. Stat. 2013, 2(3), 67-80. doi: 10.11648/j.ajtas.20130203.15

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AMA Style

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. Am J Theor Appl Stat. 2013;2(3):67-80. doi: 10.11648/j.ajtas.20130203.15

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@article{10.11648/j.ajtas.20130203.15,
  author = {Tatiana V. Yakovleva and Nicolas S. Kulberg},
  title = {Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {3},
  pages = {67-80},
  doi = {10.11648/j.ajtas.20130203.15},
  url = {https://doi.org/10.11648/j.ajtas.20130203.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130203.15},
  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.},
 year = {2013}
}

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TY  - JOUR
T1  - Noise and Signal Estimation in MRI: Two-Parametric Analysis of Rice-Distributed Data by Means of the Maximum Likelihood Approach
AU  - Tatiana V. Yakovleva
AU  - Nicolas S. Kulberg
Y1  - 2013/06/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajtas.20130203.15
DO  - 10.11648/j.ajtas.20130203.15
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 67
EP  - 80
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130203.15
AB  - 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.
VL  - 2
IS  - 3
ER  -

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