Bruno Torrésani

Marie-Christine Roubaud, Jean-Marc Lina, Julie Carrier et al.

The wavelet Maximum Entropy on the Mean (wMEM) approach to the MEG inverse problem is revisited and extended to infer brain activity from full space-time data. The resulting dimensionality increase is tackled using a collection of techniques , that includes time and space dimension reduction (using respectively wavelet and spatial filter based reductions), Kronecker product modeling for covariance matrices, and numerical manipulation of the free energy directly in matrix form. This leads to a smooth numerical optimization problem of reasonable dimension, solved using standard approaches. The method is applied to the MEG inverse problem. Results of a simulation study in the context of slow wave localization from sleep MEG data are presented and discussed. Index Terms: MEG inverse problem, maximum entropy on the mean, wavelet decomposition, spatial filters, Kronecker covariance factorization, sleep slow waves.

Adrien Meynard, Bruno Torrésani

A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random signals. The focus is on time warping and amplitude modulation, and an approximate maximum-likelihood approach based on suitable approximations in the wavelet transform domain is developed. This paper provides theoretical analysis of the approximations, and introduces JEFAS, a corresponding estimation algorithm. The latter is tested and validated on synthetic as well as real audio signal.

Helene Lachambre, Benjamin Ricaud, Guillaume Stempfel et al.

This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation technique for non-stationary signals. We illustrate our approach and the earlier one by addressing three time-frequency analysis problems to show the improvements achieved by the use of optimal lattice and window: close frequencies distinction, frequency estimation and SNR estimation. The results are presented, when possible, with real world audio signals.