Inverse Laplace Transform for signal analysis of low field nuclear magnetic resonance

Abstract

The objective of this work is to describe the mathematical procedure denominated 'Inverse Laplace Transform' used to process Low Field Nuclear Magnetic Resonance signals of experiments as CPMG, Inversion Recovery and Saturation Recovery. Also, we present a developed script, “ILT Origin script” v.1, in the environment of the software Origin Lab 9 to execute it. The presented ILT is executed with an algorithm of non-negative last square, with Tikhonov regularization and singular values decomposition. The main features of the code were tested using simulated and experimental signals, and in order to validate the results the same sets of data were analyzed using similar ILT softwares. The developed scripts for Origin Lab, Matlab and other languages are available for free for scientific and teaching uses.