Preface p. xi
Chapter 1 Introduction p. 1
Chapter 2 Wavelet Fundamentals p. 7
2.1 From Fourier Analysis to Wavelet Analysis p. 7
2.1.1 Fourier Series p. 8
2.1.2 Fourier Transform p. 9
2.1.3 Window Fourier Transform (WFT) p. 10
2.1.4 Window Measures p. 11
2.1.5 Wavelet Basis p. 12
2.2 Continuous Wavelet Transform (CWT) and DWT p. 14
2.2.1 Multiresolution Analysis p. 15
2.2.2 DWT p. 18
2.2.3 Types of Wavelets p. 19
2.3 Multiwavelets p. 22
2.4 Wavelet Design p. 29
2.4.1 Orthogonal Wavelet Construction from Orthonormal Quadratic Mirror Filter p. 29
2.4.2 Construction of an OPTFR Multiwavelet p. 31
References p. 34
Selected Bibliography p. 35
Appendix 2A p. 35
2A.1 Decomposition and Reconstruction Sequences for Orthogonal Basis p. 35
2A.2 Decomposition and Reconstruction Sequences for Semi-Orthogonal Basis p. 36
2A.3 Decomposition and Reconstruction Sequences for Biorthogonal Basis p. 36
2A.4 Graphing the Approximation Functions p. 37
Chapter 3 Wavelet Algorithms and Associated Techniques p. 41
3.1 DWT and Filter-Bank Algorithm Based on MRA p. 41
3.1.1 Decimation and Interpolation p. 41
3.1.2 2D Wavelet Algorithm p. 47
3.2 Lifting Scheme for the DWT p. 49
3.2.1 Laurent Polynomial (LP) p. 50
3.2.2 Modulation Matrix and Polyphase Matrix p. 51
3.2.3 The Euclidean Algorithm p. 52
3.2.4 Lifting Algorithm p. 53
3.3 Wavelet Packet-Symmetrical Tree Algorithm p. 55
3.3.1 Wavelet Packet Algorithms p. 57
3.4 Markov Random Field (MRF) p. 58
3.4.1 SA Algorithm p. 63
3.4.2 ICM Algorithm p. 64
3.5 Artificial Neural Networks (ANNs) p. 64
3.6 Anisotropic Diffusion p. 76
References p. 77
Chapter 4 Wavelet Applications to the Processing of SAR Images p. 79
4.1 Speckle Noise Properties in Wavelet Domains p. 79
4.1.1 SAR Fundamentals p. 79
4.1.2 Analysis of Speckle Noise and Wavelet Processing of SAR Images p. 81
4.1.3 Smoothing Effect of Wavelet-Based Speckle Filtering p. 88
4.2 Noise Removal in SAR Images p. 96
4.2.1 Combination of Wavelet and Anisotropic Diffusion p. 96
4.2.2 Wavelet Thresholding for SAR Image Denoising p. 112
4.2.3 Directional Clutter Removal of Aerial Images Using the X-Ray Wavelet Transform and the MRF p. 129
References p. 138
Chapter 5 SAR Image Compression p. 141
5.1 Choosing a Wavelet for SAR Image Compression p. 143
5.1.1 Bit Allocation and Quantization p. 144
5.1.2 Compression Results p. 145
5.2 Wavelet-Based Tree-Structured Image Compression Methods p. 147
5.2.1 EZW Algorithm p. 148
5.2.2 SPIHT Algorithm p. 151
5.3 Compression of 3D Remote Sensing Image by SPIHT p. 156
5.3.1 Compression of Multispectral SAR Image by SPIHT-Like Algorithm p. 156
5.3.2 Embedded Wavelet-Based Coding of 3D Oceanographic Data with Land Masses p. 160
5.4 Simultaneous Speckle Removal and Image Compression for SAR Images p. 163
References p. 168
Chapter 6 Detection and Classification Using Wavelets in Remote Sensing p. 171
6.1 Wayside Bearing Fault Detection p. 171
6.1.1 Feature Selection p. 172
6.1.2 Texture Classification p. 187
6.1.3 Wavelet-Based Technique for Coastline Detection p. 194
6.1.4 Oceanic Internal Wave Detection p. 196
References p. 199
Chapter 7 Wavelet Application to Screening Mammography p. 203
7.1 Detection of Malignant Masses p. 203
7.1.1 Fractal Analysis p. 204
7.1.2 DWT-Based MMRF Segmentation p. 206
7.1.3 Classification of Tumorous Regions p. 208
7.1.4 Feature Generation and Region Merging p. 210
7.2 Detection of Microcalcification Clusters p. 214
7.2.1 Microcalcification p. 214
7.2.2 MIAS Database Description and Detection Criteria p. 215
7.2.3 Algorithm Development p. 215
7.2.4 DWT-Based Algorithm and Results p. 216
References p. 223
About the Authors p. 225
Index p. 227