中科院数学与系统科学研究院

数学研究所

数学物理研讨班

报告人：   Prof. Di Ge（ITSI, Universite de Rennes 1, France）

题  目：Multi-source impulse deconvolution, an application to electromyographic signals

时  间：2018.04.20（星期五），09:00-10:00

地  点：数学院南楼N913室

摘  要：

This work is part of a collaboration between the IRCCyN (UMR 6597) and the SMI centre (Sensory-Motor Interaction, Aalborg University, Denmark) aiming at developing decomposition methods for electromyographic signals (EMG). The applications are manifold, e.g., aid to diagnostics.

Such signals can be modeled as a noisy sum of I components, each as the response of a linear system excited by a pulse train. The model parameters are estimated using a Bayesian technique. Prior laws on the continuous parameters are chosen so that the marginal a posteriori distributions are analytic. Firstly, we proposed a deterministic method by maximization of the posterior distribution. The major difficulty is in estimating the pulse trains. These discrete parameters constitute a combinatorial space, of which the search for the maximum is treated by the Tabu algorithm. Secondly, to avoid setting parameters associated with the Tabu algorithm, we adopted the efficient framework of a Bayesian approach coupled with MCMC techniques. A hybrid Gibbs algorithm is proposed in which a Metropolis-Hastings step samples the impulse trains, thus avoiding a computation load of exponential complexity, while ensuring the irreducibility of the Markov chain. Techniques from the MCMC algorithm for the deconvolution of Bernoulli-Gaussian processes are applied. In particular, the re-sampling of scale and the marginalization of the amplitudes are adapted to the physical model that takes into account the variability of the pulses’ amplitudes.

The algorithms are validated on simulated EMG signals and the experimental signals.