Multiscale analysis of multi-channel signals

Abstract: I: Amplitude and phase relationship between alpha and beta oscillations in the human EEG We have studied the relation between two oscillatory patterns within EEG signals (oscillations with main frequency 10 Hz and 20 Hz), with wavelet-based methods. For better comparison, a variant of the continuous wavelet transform, was derived. As a conclusion, the two patterns were closely related and 70-90 % of the activity in the 20 Hz pattern could be seen as a resonance phenomenon of the 10 Hz activity.II: A local discriminant basis algorithm using wavelet packets for discrimination between classes of multidimensional signals We have improved and extended the local discriminant basis algorithm for application on multidimensional signals appearing from multichannels. The improvements includes principal-component analysis and crossvalidation- leave-one out. The method is furthermore applied on two classes of EEG signals, one group of control subjects and one group of subjects with type I diabetes. There was a clear discrimination between the two groups. The discrimination follows known differences in the EEG between the two groups of subjects.III: Improved classification of multidimensional signals using orthogonality properties of a time-frequency library We further improve and refine the method in paper2 and apply it on 4 classes of EEG signals from subjects differing in age and/or sex, which are known factors of EEG alterations. As a method for deciding the best basis we derive an orthogonalbasis- pursuit-like algorithm which works statistically better (Tukey's test for simultaneous confidence intervals) than the basis selection method in the original local discriminant basis algorithm. Other methods included were Fisher's class separability, partial-least-squares and cross-validation-leave-one-subject out. The two groups of younger subjects were almost fully discriminated between each other and to the other groups, while the older subjects were harder to discriminate.