Laplace inversion of low‐resolution NMR relaxometry data using sparse representation methods

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is base...

Numerical Methods for Laplace Transform Inversion

Sparse representation of data

The amount of electronic data available today as well as its dimensionality and complexity increases rapidly in many scientific areas including biology, (bio-)chemistry, medicine, physics and its application fields like robotics, bioinformatics or multimedia technologies. Many of these data sets are very complex but have also a simple inherent structure which allows an appropriate sparse repres...

Broadband Geo Acoustic Inversion from Sparse Data Using Genetic Algorithms

Matched eld acoustic inversion techniques were investigated using data from sparsely populated vertical receiving arrays and a single receiver element The purpose of considering sparse data sets is to investigate under simulation the feasibility of reducing the number and complexity of acoustic measurements needed for geo acoustic inversion The entire bandwidth of the Geo Acoustic Inversion Wor...

Inversion of the Laplace transform

Let J% exp(-PQf(t) dt = F(P) P > 0 where b > 0 is a given number. We give a formula for f (t) in terms of F (p) , p > 0. The object of this Letter is to give a formula for the inverse Laplace transform in which the data used are given on the semi-axis p > 0 only. Let P>O where b > 0 is a fixed number. We have (1, formula 4.14.1) where Jo is a Bessel function. It follows from (1) and (2) that s,...