On the inversion of multicomponent NMR relaxation and diffusion decays in heterogeneous systems

The analysis of the decay of NMR signals in heterogeneous samples requires the solution of an ill-posed inverse problem to evaluate the distributions of relaxation and diffusion parameters. Laplace transform is the most widely accepted algorithm used to describe the NMR decay in heterogeneous systems. In this article we suggest that a superposition of Fredholm integrals, with different kernels, is a more suitable model for samples in which liquid and solid-like phases are both present. In addition, some algorithms for the inversion of Laplace and Fredholm inverse problems are illustrated. The quadrature methods and regularization function in connection with the use of nonlinear discretization grids are also discussed. The described inversion algorithms are tested on simulated and experimental data, and the role of noise is discussed. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 26A: 78–90, 2005