title: Stabilization of the inverse Laplace transform of multiexponential decay through introduction of a second dimension.
abstract: We propose a new approach to stabilizing the inverse Laplace transform of a multiexponential decay signal, a classically ill-posed problem, in the context of nuclear magnetic resonance relaxometry. The method is based on extension to a second, indirectly detected, dimension, that is, use of the established framework of two-dimensional relaxometry, followed by projection onto the desired axis. Numerical results for signals comprised of discrete T1 and T2 relaxation components and experiments performed on agarose gel phantoms are presented. We find markedly improved accuracy, and stability with respect to noise, as well as insensitivity to regularization in quantifying underlying relaxation components through use of the two-dimensional as compared to the one-dimensional inverse Laplace transform. This improvement is demonstrated separately for two different inversion algorithms, non-negative least squares and non-linear least squares, to indicate the generalizability of this approach. These results may have wide applicability in approaches to the Fredholm integral equation of the first kind.
authors.affiliation: Laboratory of Clinical Investigation, National Institute on Aging, National Institutes of Health, Baltimore, MD 21224, USA.
authors.forename: Hasan
authors.initials: H
authors.lastname: Celik
authors.forename: Mustapha
authors.initials: M
authors.lastname: Bouhrara
authors.forename: David A
authors.initials: DA
authors.lastname: Reiter
authors.forename: Kenneth W
authors.initials: KW
authors.lastname: Fishbein
authors.forename: Richard G
authors.initials: RG
authors.lastname: Spencer
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D019327:Copper Sulfate / Q000737:chemistry; D003627:Data Interpretation, Statistical; D005782:Gels; D008279:Magnetic Resonance Imaging; D009682:Magnetic Resonance Spectroscopy / Q000706:statistics & numerical data*; D015233:Models, Statistical; D019047:Phantoms, Imaging; D059629:Signal-To-Noise Ratio
chemical_list: D005782:Gels; D019327:Copper Sulfate
keywords: Fredholm integral; Inverse problems; NMR relaxometry
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