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Introduction

The electroencephalogram (EEG), which is recorded from electrodes placed on the scalp, reflects the electrical activity of the brain. The signal is extremely complex and reveals both rhythmical and transient features, hence time-frequency methods are often considered an optimal choice for its analysis. Matching pursuit (MP, [1]) offers some extra advantages: high resolution, local adaptivity to transient structures, and compatibility of its time-frequency parameterization with definitions of EEG structures used in the traditional, visual analysis [2] [3] [4]. In spite of that, its widespread application is limited by the algorithm's complexity. This paper describes one of the basic problems encountered in practical applications of MP to large amounts of data: statistical bias of the parametrization. As a solution, we propose a modified version of the algorithm--MP with stochastic dictionaries, where the parameters of the dictionary's waveforms are randomized before each decomposition by drawing their values from continuous ranges.

Sections I-A and I-B review some basic ideas behind matching pursuit and the Gabor dictionary, as proposed in [1]. Section II introduces stochastic dictionaries and describes implementation of the corresponding MP algorithm. Section III illustrates the bias-free parametrization of EEG structures (III-A) and gives an example of another possible application of the proposed idea: time-frequency representation of structures of changing frequency (III-B).



Subsections
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Next: Matching pursuit Up: Stochastic Time-Frequency Dictionaries for Previous: Stochastic Time-Frequency Dictionaries for
Piotr J. Durka 2001-03-23