CONTENTS

Preface

Acknowledgments

1   Introduction: Why Wavelets?

2   Vectors and Matrices

2.1   Vectors, Inner Products, and Norms

Problems

Computer Lab

2.2   Basic Matrix Theory

Problems

Computer Lab

2.3   Block Matrix Arithmetic

Problems

Computer Lab

3   An Introduction to Digital Images

3.1   The Basics of Grayscale Digital Images

Problems

Computer Labs

3.2   Color Images and Color Spaces

Problems

Computer Labs

3.3   Qualitative and Quantitative Measures

Problems

Computer Labs

3.4   Huffman Encoding

Problems

Computer Labs

4   Complex Numbers and Fourier Series

4.1   The Complex Plane and Arithmetic

Problems

Computer Lab

4.2   Complex Exponential Functions

Problems

4.3   Fourier Series

Problems

Computer Lab

5   Convolution and Filters

5.1   Convolution

Problems

Computer Lab

5.2   Filters

Problems

Computer Lab

5.3   Convolution as a Matrix Product

Problems

6   The Haar Wavelet Transformation

6.1   Constructing the Haar Wavelet Transformation

Problems

Computer Labs

6.2   Iterating the Process

Problems

Computer Labs

6.3   The Two-Dimensional Haar Wavelet Transformation

Problems

Computer Labs

6.4   Applications: Image Compression and Edge Detection

Problems

Computer Labs

7   Daubechies Wavelet Transformations

7.1   Daubechies Filters of Length 4 and 6

Problems

Computer Labs

7.2   Daubechies Filters of Even Length

Problems

Computer Labs

7.3   Algorithms for Daubechies Wavelet Transformations

Problems

Computer Labs

8   Orthogonality and Fourier Series

8.1 Fourier Series and Lowpass ...

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