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Resolution and uncertainty of Laplace inversion spectrum
1Schlumberger-Doll Research, Ridgefield, CT 06877, USA. ysong@slb.com
Magnetic Resonance Imaging
|May 1, 2007
Summary
Analyzing nuclear magnetic resonance (NMR) data with Laplace inversion is challenging due to reliability issues. This study presents methods to assess spectral resolution and establish bounds for integral quantities, improving NMR data analysis.
Area of Science:
- Nuclear Magnetic Resonance Spectroscopy
- Applied Mathematics
- Data Analysis
Background:
- Laplace inversion is a standard technique for analyzing nuclear magnetic resonance (NMR) data.
- It is used to derive the spectrum of decay time constants, such as the T(2) spectrum.
- The ill-conditioned nature of Laplace inversion complicates the assessment of spectral reliability and error.
Purpose of the Study:
- To address the challenges in determining the reliability and error of spectra obtained via Laplace inversion.
- To introduce methods for analyzing the resolution of the resulting decay time constant spectra.
- To provide a framework for obtaining bounds of integral quantities from these spectra.
Main Methods:
- Development and application of novel methods for resolution analysis in Laplace inversion.
- Implementation of techniques to calculate bounds for integral quantities of the derived spectra.
- Validation of methods using simulated and experimental nuclear magnetic resonance data.
Main Results:
- Quantifiable measures for assessing the resolution of T(2) spectra obtained through Laplace inversion.
- Reliable bounds for integral quantities, enhancing the interpretability of NMR relaxation data.
- Demonstrated improvement in the error estimation and reliability assessment of Laplace inversion results.
Conclusions:
- The presented methods offer a robust approach to evaluating the quality of NMR spectra derived from Laplace inversion.
- These techniques enhance the confidence in interpreting decay time constant distributions and associated integral parameters.
- This work contributes to more accurate and reliable analysis of nuclear magnetic resonance data.
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