Quantifying uncertainty in NMR T 2 spectra using Monte Carlo inversion
Relaxation and diffusion data are often analyzed using a Laplace inversion algorithm that incorporates regularization. Regularization is used because Laplace inversion with finite and noisy data is an ill-conditioned problem for which many solutions exist for a given data set. This paper reports a d...
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| Veröffentlicht in: | Journal of magnetic resonance (1997) Jg. 196; H. 1; S. 54 - 60 |
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| Sprache: | Englisch |
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2009
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| Abstract | Relaxation and diffusion data are often analyzed using a Laplace inversion algorithm that incorporates regularization. Regularization is used because Laplace inversion with finite and noisy data is an ill-conditioned problem for which many solutions exist for a given data set. This paper reports a different approach. Instead of finding a “best” solution by some
ad hoc criterion, we developed an efficient Monte Carlo algorithm that generates thousands of probable solutions from which the statistical properties of the solution can be analyzed. We find that although all of the individual solutions are spiky, the mean solution spectrum is smooth and similar to the regularized solution. From the Monte Carlo solutions we obtain probability distributions for quantities derived from the spectrum, such as porosity and bound fluid. This ability to characterize the uncertainty of such quantities is novel. |
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| AbstractList | Relaxation and diffusion data are often analyzed using a Laplace inversion algorithm that incorporates regularization. Regularization is used because Laplace inversion with finite and noisy data is an ill-conditioned problem for which many solutions exist for a given data set. This paper reports a different approach. Instead of finding a “best” solution by some
ad hoc criterion, we developed an efficient Monte Carlo algorithm that generates thousands of probable solutions from which the statistical properties of the solution can be analyzed. We find that although all of the individual solutions are spiky, the mean solution spectrum is smooth and similar to the regularized solution. From the Monte Carlo solutions we obtain probability distributions for quantities derived from the spectrum, such as porosity and bound fluid. This ability to characterize the uncertainty of such quantities is novel. |
| Author | Prange, Michael Song, Yi-Qiao |
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| References | G. Rodriguez-Yam, R. Davis, L. Scharf, Efficient Gibbs sampling of truncated multivariate normal with application to constrained linear regression, Tech. Rep., Colorado State University, 2004. Lawson, Hanson (bib5) 1974 Sivia, Skilling (bib7) 2006 Kleinberg (bib1) 1996; vol. 8 Tikhonov, Arsenin (bib2) 1977 Gull (bib4) 1989 Philippe, Robert (bib12) 2003; 13 Robert, Casella (bib11) 2004 Devroye (bib8) 1986 E. Kermidas, S. Kaufman (Eds.), Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints, Computing Science and Statistics. in: Proceedings of the 23rd Symposium in the Interface, Interface Foundation of North America, Fairfax, VA, 1991. Skilling (bib3) 1989 Parker, Song (bib6) 2005; 174 |
| References_xml | – reference: E. Kermidas, S. Kaufman (Eds.), Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints, Computing Science and Statistics. in: Proceedings of the 23rd Symposium in the Interface, Interface Foundation of North America, Fairfax, VA, 1991. – volume: 174 start-page: 314 year: 2005 end-page: 324 ident: bib6 article-title: Assigning uncertainties in the inversion of NMR relaxation data publication-title: Journal of Magnetic Resonance – volume: vol. 8 start-page: 4960 year: 1996 end-page: 4969 ident: bib1 article-title: Well logging publication-title: Encyclopedia of Nuclear Magnetic Resonance – start-page: 53 year: 1989 end-page: 71 ident: bib4 article-title: Developments in maximum entropy data analysis publication-title: Maximum Entropy and Bayesian Methods – year: 1977 ident: bib2 article-title: Solution of Ill-posed Problems – reference: G. Rodriguez-Yam, R. Davis, L. Scharf, Efficient Gibbs sampling of truncated multivariate normal with application to constrained linear regression, Tech. Rep., Colorado State University, 2004. – volume: 13 start-page: 179 year: 2003 end-page: 186 ident: bib12 article-title: Perfect simulation of positive gaussian distributions publication-title: Statistics and Computing – year: 1986 ident: bib8 article-title: Non-Uniform Random Variate Generation – year: 2006 ident: bib7 article-title: Data Analysis: A Bayesian Tutorial – year: 2004 ident: bib11 article-title: Monte Carlo Statistical Methods – year: 1974 ident: bib5 article-title: Solving Least Squares Problems – start-page: 45 year: 1989 end-page: 52 ident: bib3 article-title: Classic maximum entropy publication-title: Maximum Entropy and Bayesian Methods |
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| SubjectTerms | Diffusion Laplace inversion Monte Carlo Relaxation Uncertainty |
| Title | Quantifying uncertainty in NMR T 2 spectra using Monte Carlo inversion |
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