Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression

Abstract

A spatial-temporal model for the description of electroencephalographic (EEG) data is introduced that combines smooth reconstruction in the spatial domain and autoregressive representation in the time domain. Its spatial aspect is formulated in a general framework that covers interpolation, smoothing, and regression. Contrary to the multivariate time series models used for EEG analysis up to date, the introduced model provides a smooth spatial reconstruction of the EEG cross-spectrum, keeping the condition of nonnegative definiteness. As an instance of practical importance, the case in which the spatial reconstruction is based on spherical splines is developed in detail. Illustrative examples are presented that show the flexibility of the model to describe both normal and abnormal EEG data.

Topographic Time-Frequency Decomposition of the EEG

“…The second objective will be that the reconstructed topographies will be spatially as smooth as possible. This objective can be justified by the basic properties of the electric leadfield, which acts as smoothing operator and implies that measurements at neighboring electrodes should have similar values (Pascual et al, 1988;Jimenez et al, 1995). Furthermore, the smoothness argument fits well into the framework of functional data analysis (Ramsay and Silverman, 1997).…”

Protocol Design Challenges in the Detection of Awareness in Aware Subjects Using EEG Signals

“…• • Extraction using parametric time series models: This technique is customary in the construction of some brain computer interfaces. [16][17][18][19][20][21] In our study, the EEG signals were extracted by fitting to them order-3 autoregressive models (AR(3)). 22 The resulting set of model coefficients (without the variance of the model driving noise) was subsequently used in the classification task.…”

Nonlinearity in normal human EEG: cycles, temporal asymmetry, nonstationarity and randomness, not chaos

“…Except that of the short-lag nonlinearity, detected in a part of the datasets(Table 1).8 The process described is not considered as a model generating EEG, like, for example, that proposed byJansen and Rit (1995), nor as a time-series model estimated from EEG data (e.g.,Jimenez et al 1995).…”