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• W2898237183 abstract "Two-dimensional nuclear magnetic resonance measurements are ubiquitous in the literature, with correlations of longitudinal ${T}_{1}$ and transverse ${T}_{2}$ relaxation times used extensively to characterize porous media. Decomposition of the signal acquired in the time domain to a pseudocontinuous distribution of relaxation times is achieved using numerical inversion. A popular technique to generate a stable solution to this ill-posed problem in the presence of noise is Tikhonov regularization with a non-negativity constraint imposed on the output. However, coupling of the longitudinal and transverse eigenfunctions can generate eigenvalue pairs with apparent ${T}_{2}>{T}_{1}$ and negative amplitude. Such apparent signal components are encountered in the classic example of Brownstein-Tarr ``slow'' diffusion in an isolated pore, and in weakly coupled pores governed by different relaxation rates. We show that when negative-amplitude components comprise $ensuremath{ge}1%$ of the total signal, the solution achieved by non-negative Tikhonov regularization is sufficiently distorted to prevent robust interpretation. We demonstrate two alternative inversion methods that recover the negative-amplitude components: (1) half-bound Tikhonov regularization assigns a negative amplitude to any peak with apparent ${T}_{2}>{T}_{1}$, and (2) the optimization problem is expressed as a ${ensuremath{ell}}_{2}$ regression with ${ensuremath{ell}}_{1}$ penalization and a solution estimated using a primal-dual algorithm without constraint on the output sign. These methods are applicable to ${T}_{1}ensuremath{-}{T}_{2}$ experiments on porous materials characterized by a hierarchy of length scales, such as biological cells, cement, and limestone." @default.
• W2898237183 created "2018-11-02" @default.
• W2898237183 creator A5000038988 @default.
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• W2898237183 date "2018-10-25" @default.
• W2898237183 modified "2023-10-18" @default.
• W2898237183 title "Numerical inversion methods for recovering negative amplitudes in two-dimensional nuclear magnetic resonance relaxation-time correlations" @default.
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• W2898237183 doi "https://doi.org/10.1103/physreve.98.043308" @default.
• W2898237183 hasPublicationYear "2018" @default.
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