Analyzing large amounts of sleep electroencephalogram (EEG) data by means of the matching pursuit (MP) algorithm, we encountered a statistical bias of the decomposition, resulting from the structure of the applied dictionary. As a solution, we propose stochastic dictionaries, where the parameters of the dictionary's waveforms are randomized before each decomposition. The MP algorithm was modified for this purpose and tuned for maximum time-frequency resolution. Examples of applications of the new method include parameterization of EEG structures and time-frequency representation of signals with changing frequency.

This paper presents a summary of time-frequency analysis of the electrical activity of the brain (EEG). It covers in details two major steps: introduction of wavelets and adaptive approximations. Presented studies include time-frequency solutions to several standard research and clinical problems, encountered in analysis of evoked potentials, sleep EEG, epileptic activities, ERD/ERS and pharmaco-EEG. Based upon these results we conclude that the matching pursuit algorithm provides a unified parametrization of EEG, applicable in a variety of experimental and clinical setups. This conclusion is followed by a brief discussion of the current state of the mathematical and algorithmical aspects of adaptive time-frequency approximations of signals.

We present the four key areas of research—preprocessing, the volume conductor, the forward problem, and the inverse problem—that affect the performance of EEG and MEG source imaging. In each key area we identify prominent approaches and methodologies that have open issues warranting further investigation within the community, challenges associated with certain techniques, and algorithms necessitating clarification of their implications. More than providing definitive answers we aim to identify important open issues in the quest of source localization.