Abstract
Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013.
Highlights
Low-resolution nuclear magnetic resonance (LRNMR) relaxometry has emerged as a powerful new tool for identifying molecular species and to study their dynamics even in complex materials
Note that the term Low-resolution nuclear magnetic resonance (LR-NMR) is used in other contexts such as time-domain NMR, ex situ NMR, and portable NMR
PDCO (13,20) is a convex optimization solver implemented in Matlab
Summary
Low-resolution nuclear magnetic resonance (LRNMR) relaxometry has emerged as a powerful new tool for identifying molecular species and to study their dynamics even in complex materials. This technology is widely used in industrial quality control for the determination of solid-to-liquid and oil-to-water ratios in materials as diverse as oil-bearing rock, food emulsions, and plant seeds (1). It offers great potential for characterization and quantification of components in different materials in their whole conformation. Spin–spin interactions are the main relaxation mechanism in a CPMG (Carr, Purcell, Meiboom and Gill) pulse sequence (4,5)
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