Linear and nonlinear techniques for the deconvolution of hormone time-series

Pulsatile hormone secretion is usually investigated by measuring hormone concentration in samples of peripheral plasma. Here, the deconvolution of hormone time series to reconstruct the instantaneous secretion rate of glands is considered. Various techniques are discussed and compared in order to overcome the ill-conditioning of the problem and reduce the computational burden. In particular, linear techniques based on least squares, maximum a posteriori (MAP) estimation, and Wiener filtering are compared. A new nonlinear MAP estimator that keeps into account the non-Gaussian distribution of the unknown signal is worked out and shown to yield the best results. The performances of the algorithms are tested on simulated time series as well as on series of luteinizing hormone.