E-Book Overview
Although visual analysis of EEGs has been the state of the art in electroencephalography for 70 years, advanced signal processing methods offer a superior alternative in numerous biomedical clinical and research applications. This first-of-its-kind guide bridges the gap from visual analysis to signal processing techniques, providing engineers, researchers, and clinicians with an innovative, clear methodology for biomedical signal analysis. The book covers various applications in sleep, ERD/ERS, pharmaco-EEG, and epilepsy research, featuring full mathematical details to help engineers and researchers modify procedures or design all-new frameworks for biomedical signal analysis. Including a web link where readers can freely download the software used in the applications, this unique resource will prove indispensable to all biomedical engineers and researchers looking to broaden the applicability of EEGs and blaze new trails in biomedical signal analysis and research.
E-Book Content
Matching Pursuit and Unification in EEG Analysis
This book is part of the Artech House Engineering in Medicine and Biology Series, Martin L. Yarmush and Christopher J. James, Series Editors. For a list of recent related Artech House titles, please turn to the back of this book.
Matching Pursuit and Unification in EEG Analysis Piotr Durka
artechhouse.com
Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress.
British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library.
ISBN 13: 978-1-58053-304-1
Cover design by Igor Valdman
© 2007 ARTECH HOUSE, INC. 685 Canton Street Norwood, MA 02062
All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark.
10 9 8 7 6 5 4 3 2 1
Contents Foreword Preface
ix xi
I Some Basic Notions
1
Chapter 1 Signal: Going Digital 1.1 Sampling 1.2 Drawback: Aliasing 1.3 Advantage: Checksums
3 4 5 8
Chapter 2 Analysis 2.1 Inner Product—A Measure of Fit 2.2 Orthogonality 2.3 Frequency and Phase
11 11 15 16
Chapter 3 Spectrum 3.1 Example Calculations 3.2 Uncertainty Principle and Resolution 3.3 Real-World Spectra
19 21 25 26
Chapter 4 Between Time and Frequency 4.1 Spectrogram 4.2 Interpretation of the Spectrogram 4.3 Wavelets 4.4 Wigner Transform and Cross-Terms
29 29 32 33 35
v
vi
Matching Pursuit and Unification in EEG Analysis
References
38
Chapter 5 Choosing the Representation 5.1 Gabor Dictionary 5.2 Adaptive Approximation 5.3 Matching Pursuit 5.4 Time-Frequency Energy Density References
39 39 41 43 44 46
Chapter 6 Advantages of Adaptive Approximations 6.1 Explicit Parameterization of Transients 6.2 Automatic Negotiation of Time-Frequency Tradeoff 6.3 Freedom from Arbitrary Settings 6.4 A Unified Framework
47 47 50 52 53
Chapter 7 Caveats and Practical Issues 7.1 Dictionary Density 7.2 Number of Waveforms in the Expansion 7.3 Statistical Bias 7.4 Limitations of Gabor Dictionaries References
55 55 57 58 59 60
II EEG Analysis
61
Chapter 8 Parameteriz