Adaptive Time-Frequency Models for Single-Trial M/EEG Analysis

Learning from M/EEG data with variable brain activation delays

Magneto- and electroencephalography (M/EEG) measure the electromagnetic signals produced by brain activity. In order to address the issue of limited signal-to-noise ratio (SNR) with raw data, acquisitions consist of multiple repetitions of the same experiment. An important challenge arising from such data is the variability of brain activations over the repetitions. It hinders statistical analysis such as prediction performance in a supervised learning setup. One such confounding variability is the time offset of the peak of the activation, which varies across repetitions. We propose to address this misalignment issue by explicitly modeling time shifts of different brain responses in a classification setup. To this end, we use the latent support vector machine (LSVM) formulation, where the latent shifts are inferred while learning the classifier parameters. The inferred shifts are further used to improve the SNR of the M/EEG data, and to infer the chronometry and the sequence of activations across the brain regions that are involved in the experimental task. Results are validated on a long-term memory retrieval task, showing significant improvement using the proposed latent discriminative method.

Graph-based variability estimation in single-trial event-related neural responses

Extracting information from multitrial magnetoencephalography or electroencephalography (EEG) recordings is challenging because of the very low SNR, and because of the inherent variability of brain responses. The problem of low SNR is commonly tackled by averaging multiple repetitions of the recordings, also called trials, but the variability of response across trials leads to biased results and limits interpretability. This paper proposes to decode the variability of neural responses by making use of graph representations. Our approach has several advantages compared to other existing methods that process single-trial data: first, it avoids the a priori definition of a model for the waveform of the neural response; second, it does not make use of the average data for parameter estimation; third, it does not suffer from initialization problems by providing solutions that are global optimum of cost functions; and last, it is fast. We proceed in two steps. First, a manifold learning algorithm, based on a graph Laplacian, offers an efficient way of ordering trials with respect to the response variability, under the condition that this variability itself depends on a single parameter. Second, the estimation of the variability is formulated as a combinatorial optimization that can be solved very efficiently using graph cuts. Details and validation of this second step are provided for latency estimation. Performance and robustness experiments are conducted on synthetic data, and results are presented on EEG data from a P300 oddball experiment.

A space-frequency analysis of MEG background processes

In MEG source localization the estimated source parameters will be more reliable when the spatiotemporal covariance of the noise and background activity is taken into account. Since this covariance is in general too large to estimate based on the data and to invert efficiently, different parametrizations have been proposed in the literature. These models can be seen as special cases of the general decomposition of the covariance into a sum of Kronecker products of spatial matrices X(n) and temporal matrices T(n) (Van Loan, 2000). In this study we investigate the assumption of the matrices T(n) being Toeplitz. If so, the covariance matrix in the space-frequency domain will have an approximate block-diagonal structure, facilitating inversion, which is a prerequisite for source localization. In this study we address the question whether the Toeplitz approximation is valid for data sets obtained in visual evoked field, auditory evoked field, somatosensory evoked field experiments and data sets containing spontaneous activity. It turns out that on average 87% is in the block-diagonal of the sample covariance, which is close to the values obtained for real Toeplitz matrices T(n). This implies that the space-frequency domain is very interesting for source localization since the major part of the entire covariance can be incorporated in that domain straightforwardly. Finally, the two major processes in the background activity are characterized in terms of their spatial and frequency patterns, yielding a focal and a non-focal pattern in 8 of 10 data sets analyzed in this study. The focal pattern represents the alpha frequency at parieto-occipital areas, whereas the non-focal pattern is more widespread both in space and in frequency.

Topography-time-frequency atomic decomposition for event-related M/EEG signals

We present a method for decomposing MEG or EEG data (channel x time x trials) into a set of atoms with fixed spatial and time-frequency signatures. The spatial part (i.e., topography) is obtained by independent component analysis (ICA). We propose a frequency prewhitening procedure as a pre-processing step before ICA, which gives access to high frequency activity. The time-frequency part is obtained with a novel iterative procedure, which is an extension of the matching pursuit procedure. The method is evaluated on a simulated dataset presenting both low-frequency evoked potentials and high-frequency oscillatory activity. We show that the method is able to recover well both low-frequency and high-frequency simulated activities. There was however cross-talk across some recovered components due to the correlation introduced in the simulation.