Wavelet based multiresolution zero-crossing representations

122 Pages·2017·2.47 MB·English

Iowa State University Capstones, Theses and
Retrospective Theses and Dissertations
Dissertations
2000
Wavelet based multiresolution zero-crossing
representations
Muhammad Akbar Khan Afzal
Iowa State University
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Afzal, Muhammad Akbar Khan, "Wavelet based multiresolution zero-crossing representations " (2000).Retrospective Theses and
Dissertations. 12670.
https://lib.dr.iastate.edu/rtd/12670
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Wavelet based multiresolution zero-crossing representations
by
Muhammad Akbar Khan Afzal
A dissertation submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Major: Electrical Engineering (Communications and Signal Processing)
Major Professor: Satish S. Udpa
Iowa State University
Ames, Iowa
2000
Copyright © Muhammad Akbar Khan Afzal , 2000. All rights reserved.
UMI Number 9977309
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Graduate College
Iowa State University
This is to certify- that the Doctoral dissertation of
Muhanunad Akbar Khan Afzal
has met the dissertation requirements of Iowa State University
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iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS xi
ABSTRACT xiii
CHAPTER 1 INTRODUCTION 1
Signal Representation 1
Properties of a Signal Representation 1
Multiresolution Representation of a Signal 2
Zero-Crossing Representation of a Signal and its Applications 3
Structure of the Dissertation 4
CHAPTER 2 BACKGROUND AND LITERATURE SURVEY . . . 5
Zero-Crossing Processing for Time-Series Analysis 5
Zero-Crossings in Modulation Theor>- 6
Scale-Space and Wavelet Transform Zero-Crossings 7
Reconstruction from Signal Zero-Crossings 8
Polynomial Assumption 9
Curtis and Oppenheim 10
Rotem and Zeevi 11
Sanz and Huang 13
Hummel and Moniot 14
Mallat 15
IV
CHAPTER 3 THEORY OF MULTISCALE ZERO-CROSSING REP­
RESENTATION 17
Assumptions and Notation 17
Zero-Crossing Representation 17
Convexity of the Zero-Crossing Representation 18
Octave Filterbank for Signal Decomposition 20
Completeness of Filterbank Output 21
Zero-Crossings of the Filterbank Output 23
Uniqueness of Zero-Crossings of Filterbank Output 23
CHAPTER 4 SIGNAL RECOVERY FROM ZERO-CROSSING REP­
RESENTATION 26
Introduction 26
Projection on Convex Sets 28
Projection on the Set of ZCR 29
Projection on Dyadic Wavelet Space 30
Projection on Sum Signal ZCR 30
The POCS Algorithm 31
Reconstruction Results 32
CHAPTER 5 TIME INVARIANT MULTISCALE ZERO-CROSSING
REPRESENTATION 35
Translation Dependence of Discrete Wavelet Transform 35
Averaged Basis Projection Approach 36
All Basis Averaged Projection 42
Relation Between Stationary Wavelet Transform (SWT) and Discrete
Wavelet Transform (DWT) for Orthogonal W'avelets 43
Time-Invariant ZCR 45
V
Reconstruction Results 46
Error Due to Quantization of Zero-Crossing Point 46
Convergence of Reconstruction Algorithm 50
CHAPTER 6 APPLICATIONS 53
Classification of Ultrasonic XDE Signals 53
Introduction 53
Approach 56
ZCR of Images 65
Signal Denoising 68
Introduction 68
Methodology- 69
Application of ZCR Based Denoising to Magnetic Flux Leakage Data
Obtained from Seamless Gas Pipelines 73
CHAPTER 7 SUMMARY AND DISCUSSION 84
Summary of Results 84
Contribution of Work 86
APPENDIX A PROOF OF PROPOSITION 1 87
Discrete Wavelet Transform (DWT) 87
Stationary- Wavelet Transform (SWT) 87
Proposition I 89
An example for the proof of proposition 1 (L = 2) 92
APPENDIX B PROJECTOR ON THE SET OF ZERO-CROSSING
REPRESENTATION 94
BIBLIOGRAPHY 97
vi
LIST OF TABLES
Table 6.1 \[LP neural network parameters used in this study 62
Table 6.2 MLP classification results 64