Simple MATLAB and Python scripts for multi-exponential analysis

Abstract

Multi-exponential decay is prevalent in magnetic resonance spectroscopy, relaxation, and imaging. This paper describes simple MATLAB and Python functions and scripts for regularized multi-exponential analysis methods for 1D and 2D data and example test problems and experiments. Regularized least-squares solutions provide production-quality outputs with robust stopping rules in ~5 and ~20 lines of code for 1D and 2D inversions, respectively. The software provides an open-architecture simple solution for transforming exponential decay data to the distribution of their decay lifetimes. Examples from magnetic resonance relaxation of a complex fluid, a Danish North Sea crude oil, and fluid mixtures in porous materials—brine/crude oil mixture in North Sea reservoir chalk—are presented. Developed codes may be incorporated in other software or directly used by other researchers, in magnetic resonance relaxation, diffusion, and imaging or other physical phenomena that require multi-exponential analysis.