Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing

CONTENTS

PREFACE

ACKNOWLEDGMENTS

1 VECTOR SPACES, SIGNALS, AND IMAGES

1.1 Overview

1.2 Some Common Image Processing Problems

1.3 Signals and Images

1.4 Vector Space Models for Signals and Images

1.5 Basic Waveforms—The Analog Case

1.6 Sampling and Aliasing

1.7 Basic Waveforms—The Discrete Case

1.8 Inner Product Spaces and Orthogonality

1.9 Signal and Image Digitization

1.10 Infinite-dimensional Inner Product Spaces

1.11 Matlab Project

2 THE DISCRETE FOURIER TRANSFORM

2.1 Overview

2.2 The Time Domain and Frequency Domain

2.3 A Motivational Example

2.4 The One-dimensional DFT

2.5 Properties of the DFT

2.6 The Fast Fourier Transform

2.7 The Two-dimensional DFT

2.8 Matlab Project

3 THE DISCRETE COSINE TRANSFORM

3.1 Motivation for the DCT—Compression

3.2 Other Compression Issues

3.3 Initial Examples—Thresholding

3.4 The Discrete Cosine Transform

3.5 Properties of the DCT

3.6 The Two-dimensional DCT

3.7 Block Transforms

3.8 JPEG Compression

3.9 Matlab Project

4 CONVOLUTION AND FILTERING

4.1 Overview

4.2 One-dimensional Convolution

4.3 Convolution Theorem and Filtering

4.4 2D Convolution—Filtering Images

4.5 Infinite and Bi-infinite Signal Models

4.6 Matlab Project

5 WINDOWING AND LOCALIZATION

5.1 Overview: Nonlocality of the DFT

5.2 Localization via Windowing

5.3 Matlab Project

6 FILTER BANKS

6.1 Overview

6.2 The Haar Filter Bank

6.3 The General One-stage Two-channel Filter Bank

6.4 Multistage Filter Banks

6.5 Filter Banks for Finite Length Signals

6.6 The 2D Discrete Wavelet Transform ...