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| Preface | |
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| Acknowledgments | |
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| Introduction: Why Wavelets? | |
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| Vectors and Matrices | |
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| Vectors, Inner Products, and Norms | |
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| Problems | |
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| Computer Lab | |
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| Basic Matrix Theory | |
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| Problems | |
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| Computer Lab | |
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| Block Matrix Arithmetic | |
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| Problems | |
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| Computer Lab | |
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| An Introduction to Digital Images | |
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| The Basics of Grayscale Digital Images | |
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| Problems | |
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| Computer Labs | |
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| Color Images and Color Spaces | |
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| Problems | |
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| Computer Labs | |
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| Qualitative and Quantitative Measures | |
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| Problems | |
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| Computer Labs | |
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| Huffman Encoding | |
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| Problems | |
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| Computer Labs | |
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| Complex Numbers and Fourier Series | |
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| The Complex Plane and Arithmetic | |
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| Problems | |
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| Computer Lab | |
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| Complex Exponential Functions | |
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| Problems | |
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| Fourier Series | |
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| Problems | |
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| Computer Lab | |
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| Convolution and Filters | |
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| Convolution | |
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| Problems | |
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| Computer Lab | |
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| Filters | |
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| Problems | |
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| Computer Lab | |
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| Convolution as a Matrix Product | |
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| Problems | |
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| The Haar Wavelet Transformation | |
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| Constructing the Haar Wavelet Transformation | |
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| Problems | |
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| Computer Labs | |
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| Iterating the Process | |
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| Problems | |
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| Computer Labs | |
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| The Two-Dimensional Haar Wavelet Transformation | |
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| Problems | |
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| Computer Labs | |
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| Applications: Image Compression and Edge Detection | |
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| Problems | |
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| Computer Labs | |
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| Daubechies Wavelet Transformations | |
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| Daubechies Filters of Length 4 and 6 | |
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| Problems | |
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| Computer Labs | |
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| Daubechies Filters of Even Length | |
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| Problems | |
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| Computer Labs | |
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| Algorithms for Daubechies Wavelet Transformations | |
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| Problems | |
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| Computer Labs | |
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| Orthogonality and Fourier Series | |
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| Fourier Series and Lowpass Filters | |
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| Problems | |
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| Building G([omega]) from H([omega]) | |
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| Problems | |
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| Coiflet Filters | |
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| Problems | |
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| Computer Labs | |
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| Wavelet Shrinkage: An Application to Denoising | |
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| An Overview of Wavelet Shrinkage | |
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| Problems | |
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| Computer Labs | |
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| VisuShrink | |
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| Problems | |
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| Computer Labs | |
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| SureShrink | |
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| Problems | |
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| Computer Labs | |
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| Biorthogonal Filters | |
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| Constructing Biorthogonal Filters | |
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| Problems | |
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| Biorthogonal Spline Filters | |
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| Problems | |
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| Computer Lab | |
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| The Cohen-Daubechies-Feauveau 9/7 Filter | |
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| Problems | |
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| Computer Lab | |
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| Computing Biorthogonal Wavelet Transformations | |
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| Computing the Biorthogonal Wavelet Transformation | |
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| Problems | |
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| Computer Labs | |
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| Computing the Inverse Biorthogonal Wavelet Transformation | |
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| Problems | |
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| Computer Labs | |
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| Symmetry and Boundary Effects | |
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| Problems | |
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| Computer Labs | |
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| The JPEG2000 Image Compression Standard | |
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| An Overview of JPEG | |
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| Problems | |
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| Computer Lab | |
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| The Basic JPEG2000 Algorithm | |
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| Problems | |
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| Lifting and Lossless Compression | |
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| Problems | |
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| Computer Lab | |
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| Examples | |
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| Computer Lab | |
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| Basic Statistics | |
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| Descriptive Statistics | |
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| Problems | |
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| Sample Spaces, Probability, and Random Variables | |
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| Problems | |
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| Continuous Distributions | |
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| Problems | |
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| Expectation | |
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| Problems | |
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| Two Special Distributions | |
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| Problems | |
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| References | |
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| Index | |