Multivariate temporal dictionary learning for EEG.

This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate spatial and temporal modeling is required. Inter-channels links are taken into account in the spatial multivariate model, and shift-invariance is used for the temporal model. Multivariate learned kernels are informative (a few atoms code plentiful energy) and interpretable (the atoms can have a physiological meaning). Using real EEG data, the proposed method is shown to outperform the classical multichannel matching pursuit used with a Gabor dictionary, as measured by the representative power of the learned dictionary and its spatial flexibility. Moreover, dictionary learning can capture interpretable patterns: this ability is illustrated on real data, learning a P300 evoked potential.

Single-receiver geoacoustic inversion using modal reversal.

This paper introduces a single-receiver geoacoustic-inversion method based on dispersion analysis and adapted to low-frequency impulsive sources in shallow-water environments. In this context, most existing methods take advantage of the modal dispersion curves in the time-frequency domain. Inversion is usually performed by matching estimated dispersion curves with simulated replicas. The method proposed here is different. It considers the received modes in the frequency domain. The modes are transformed using an operator called modal reversal, which is parameterized using environmental parameters. When modal reversal is applied using parameters that match the real environment, dispersion is compensated for in all of the modes. In this case, the reversed modes are in phase and add up constructively, which is not the case when modal reversal is ill-parameterized. To use this phenomenon, a criterion that adds up the reversed modes has been defined. The geoacoustic inversion is finally performed by maximizing this criterion. The proposed method is benchmarked against simulated data, and it is applied to experimental data recorded during the Shallow Water 2006 experiment.

Modal depth function estimation using time-frequency analysis.

Acoustic propagation in shallow water is characterized by a set of depth-dependent modes, the modal depth functions, which propagate in range according to their horizontal wavenumbers. For inversion purposes, modal depth function estimation in shallow water is an issue when the environment is not known. Classical methods that provide blind mode estimation rely on the singular value decomposition of the received field at different frequencies over a vertical array of transducers. These methods require that the vertical array spans the full water column. This is obviously a strong limitation for the application of such methods in an operational context. To overcome these shortcomings, this study proposes to replace the spatial diversity constraint by a frequency diversity condition, and thus considers the case of a field emanating from an impulsive source. Indeed, because of the discrete nature of the wavenumber spectrum and due to their dispersive behavior, the modes are separated in the time-frequency domain. This phenomenon enables the design of a modal filtering scheme for signals received on a single receiver. In the case of a vertical receiver array, the modal contributions can be isolated for each receiver even when using a partial water column spanning array. This method thus eliminates the receiving constraints of classical methods of modal depth function estimation, although it imposes the use of an impulsive source. The developed algorithm is benchmarked on numerical simulations and validated on laboratory experimental data recorded in an ultrasonic waveguide. Practical applications are also discussed.