Handling non-negativity in deconvolution of physiological signals: a nonlinear stochastic approach

A stochastic interpretation of Tikhonov regularization has been recently proposed to attack some open problems of deconvolution when dealing with physiological systems, i.e., in addition to ill-conditioning, infrequent and nonuniform sampling and necessity of having credible confidence intervals. However, the possible violation of the non-negativity constraint cannot be dealt with on firm statistical grounds, since the model of the unknown signal is compatible with negative realizations. In this paper, we propose a new model of the unknown input which excludes negative values. The model is embedded within a Bayesian estimation framework to calculate, by resorting to a Markov chain Monte Carlo algorithm, a nonlinear estimate of the unknown input given by its a posteriori expected value. Applications to simulated and real hormone secretion/pharmacokinetic problems are presented which show that this nonlinear approach is more accurate than the linear one. In addition, more realistic confidence intervals are obtained.