Maximum likelihood estimation for superimposed exponentially decaying fluorescence processes

We address the problem of estimating the components of superimposed exponentially decaying signals. Usual estimation techniques, e.g. least squares or eigenvalue and eigenvector based methods, are not adequate for exponentionally decaying fluorescence processes due to their rather simple signal modelling. Therefore, we introduce a better suited parametric model by exploiting the statistical properties of the exponentially decaying emission of fluorescence photons (time dependent Poisson statistics). Using this model maximum likelihood estimates for the fluorescence intensity spectrum and the decay parameters are derived. The performance of the maximum likelihood estimates is compared with the least squares estimates by means of simulations and real data experiments. The results indicate the superiority of the maximum likelihood estimates