Inverse Laplace transformation of noisy data using Fisher information

Abstract

Inverse problems arise in many areas of research and applications The Fredholm integral equation of the first kind with an exponential decay kernel is an ill-posed inverse problem In this thesis the equation is studied using the Tikhonov regularization method with Fisher information as a regularization function A numerical algorithm for solving the Fredholm integral equation is outlined to obtain well-defined solutions and an optimal unique solution is determined by the L-curve criterion In our study several sets of simulated data are created from the log-normal distribution function to evaluate the performance of our algorithm We show that the algorithm can efficiently recover broad single-peak distributions and double-peak distributions with higher accuracy than the well-known algorithms of the maximum-entropy method and CONTIN

Date of Award	2014 Jul 14
Original language	English
Supervisor	Su-Long Nyeo (Supervisor)