Piotr J. Durka

Bio: Piotr J. Durka is an academic researcher from University of Warsaw. The author has contributed to research in topics: Sleep spindle & Matching pursuit. The author has an hindex of 28, co-authored 70 publications receiving 2551 citations. Previous affiliations of Piotr J. Durka include University of Warmia and Mazury in Olsztyn.

Introduction to Wavelet Analysis

Abstract: Wavelet transform and multiresolution decomposition are described. Examples of the application of orthogonal wavelet transform to acoustic evoked potentials and otoacoustic emissions (OEA) are given and basic features of wavelet packets and wavelet network methods are characterized. An approach that enables the identification of local signal structures - a generalization of wavelet transform called Matching Pursuit - is presented. In the framework of this method the signal is decomposed into time-frequency ‘atoms', which offers a possibility of determination of an ‘instantaneous frequency’ with the accuracy close to the theoretical limit. The method is illustrated by application to OAE signals. The advantages and limitations of the methods presented are discussed.

Single evoked potential reconstruction by means of wavelet transform

Abstract: We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach -- the wavelet representation of the signal Wavelets were introduced by Grossman and Morlet in 1984 The method is based on the multiresolution signal decomposition Wavelets are already used for speech recognition, geophysics investigations and fractal analysis This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal We would like to introduce wavelet formalism for the first time to brain signal analysis One of the most important problems in this field is the analysis of evoked potentials This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used This method is based on several assumptions Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent These assumptions have been challenged eg the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis In view of the works of Sayers et al (1974) and Basar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases Several attempts to overcome the limitation of the averaging method have been made Heintze and Kunkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments This was possible under two condiitons: high signal to noise ratio and clear separation of the EEG and EP spectra These assumptions are not easy to fulfill, though Cerutti et al (1987) modeled background EEG activity by means of an AR process and event related brain activity by ARMA In this way they were able to find a filter extracting single EP Nevertheless, their method was not quite free of assumptions, since they since they used averaged EP to define their ARMA filter In the following we shall briefly describe the method of the multiresolution decomposition and we will apply it to the analysis and reconstruction of single evoked potentials

From wavelets to adaptive approximations: time-frequency parametrization of EEG

Abstract: 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.

Stochastic time-frequency dictionaries for matching pursuit

Abstract: 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.

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.