Transformada Inversa De Laplace Para Análise De Sinais De Ressonância Magnética Nuclear De Baixo Campo

Abstract

INVERSE LAPLACE TRANSFORM FOR SIGNAL ANALYSIS OF LOW FIELD NUCLEAR MAGNETIC RESONANCE. 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.

Non-Invasive Method to Predict the Composition of Requeijão Cremoso Directly in Commercial Packages Using Time Domain NMR Relaxometry and Chemometrics

“…Similar behavior was observed for T 1 values; The sample with the highest moisture (red line) had a significantly higher T 1 value than the sample with the lowest moisture (black line). T 2 and T 1 relaxation spectra of the three RC samples estimated by the Inverse Laplace transform (ILT) are shown respectively in Figure 1 c,d [ 35 ]. The mean T 2 and T 1 relaxation curves show the presence of two populations, agreeing with previous studies in the literature, which reported that the T 2 relaxation in RC is mainly bi-exponential [ 16 , 17 ].…”

“… ( a ) CPMG and ( b ) CWFP-T 1 relaxation curves of three RC samples with different chemical compositions and the respective relaxation spectra ( c , d ) obtained with the ILT algorithm [ 35 ]. RC samples with the lowest, medium, and the highest moisture contents are the black, blue, and red lines, respectively.…”