Maximum Entropy Method for Frequency Domain Fluorescence Lifetime Analysis. 1. Effects of Frequency Range and Random Noise

Abstract

The maximum entropy method (MEM) provides a self-modeling fit to data in which minimization of the χ(2) goodness-of-fit parameter is coupled with maximization of a statistical entropy function. We have found that MEM provides an excellent visual description of the uncertainties, errors, and limitations associated with the distributions which it recovers. To more accurately interpret fluorescence lifetime distributions recovered by the MEM from frequency domain lifetime data, a detailed examination of the effects of frequency range, noise, data set size, and sample heterogeneity was carried out for both simulated and real data. Results clearly demonstrate that the frequency range in which data are collected can affect the number and nature of the fluorescence lifetime components that are recovered by MEM, and the quality of the data at the frequencies that are optimal for a given lifetime is also crucial. Expansion of sufficient data sets to include more frequencies, or more replicates at the same frequencies, provides little improvement over the original data set when the lifetimes are well-windowed by the frequency range. Synergism among multiple components in a sample can affect the recovered distribution, by shifting and splitting poorly windowed components and broadening the recovered peaks for all components. These effects are related to the number of components for which evidence must be found.

Bayesian Maximum Entropy (Two-Dimensional) Lifetime Distribution Reconstruction from Time-Resolved Spectroscopic Data

“…This method states that the optimum regularization value, k opt , should be chosen such that at the MaxEnt solution, v 2 (ĥ kopt )/n t ' 1 6 (2/n t ) holds. In spite of its popularity, 26,31,[74][75][76][77][78] it is well known that the discrepancy criterion provides overestimated k opt values, and so over-smoothed solutions. 21,79 Moreover, the MaxEnt solution provided by this criterion will strongly depend on the assumed noise standard deviation.…”

Analysis of Simulated Fluorescence Intensities Decays by a New Maximum Entropy Method Algorithm

“…Due to the once limited computer memory and low performing computational time, the conjugate gradient method (CG) [22] has been the iterative method widely spread for the solution of equation systems [23]. The necessary compromise between the accuracy of the solution and the convergence speed of the algorithm [24] limited both the number of data points and the number of lifetimes used for reconstructing the desired distribution to a maximum values of about 1,000 and 200 respectively, with the obvious limitation of the information content in the MEM distribution [25, 26]. …”

Maximum Entropy Deconvolution of Infrared Spectra: Use of a Novel Entropy Expression without Sign Restriction

“…5,26,29,31,[74][75][76] Additionally, they have been used with success in the inversion of the Laplace transform in kinetic data obtained by fluorescence, infrared, or UV-vis spectroscopy. 73,[77][78][79][80][81][82] In their form for solutions without a sign restriction, described more than a decade ago, 83,84 they have been used frequently in nuclear magnetic resonance (NMR) spectroscopy, although rarely for deconvolution purposes. 28,[83][84][85][86] In this paper, we first tested the suitability of Shannon-related entropies for the infrared deconvolution problem.…”