Open AccessLaplace inversion of low‐resolution NMR relaxometry data using sparse representation methods
Author(s) -
Berman Paula,
Levi Ofer,
Parmet Yisrael,
Saunders Michael,
Wiesman Zeev
Publication year - 2013
Publication title -
concepts in magnetic resonance part a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.229
H-Index - 49
eISSN - 1552-5023
pISSN - 1546-6086
DOI - 10.1002/cmr.a.21263
Subject(s) - relaxometry , regularization (linguistics) , convex optimization , sparse approximation , inverse problem , laplace transform , algorithm , computer science , mathematical optimization , compressed sensing , relaxation (psychology) , solver , mathematics , regular polygon , artificial intelligence , magnetic resonance imaging , mathematical analysis , spin echo , social psychology , geometry , radiology , medicine , psychology
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 L 2 ‐norm regularization. However, sparse representation methods via L 1 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 L 1 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.