Chapter 5 Wavelet Transform ............................................................................. 79
5.1
Introduction and Overview...................................................... 79
5.2 From FT to STFT .................................................................... 79
5.3 One-Dimensional Continuous Wavelet Transform .................. 86
5.4 One-Dimensional Discrete Wavelet Transform ....................... 88
5.4.1 Discrete Wavelet Transform on Discrete Signals .......90
5.5 Two-Dimensional Wavelet Transform ..................................... 94
5.5.1 Two-Dimensional Discrete Wavelet Transform ......... 94
5.6 Main Applications of DWT ..................................................... 96
5.6.1 Filtering and Denoising ..............................................96
5.6.2 Compression ............................................................... 98
5.7 Discrete Wavelet Transform in MATLAB ® ............................99
5.8 Summary .................................................................................99
Problems.............................................................................................99
Chapter 6 Other Signal and Image Processing Methods .................................. 101
6.1 Introduction and Overview.................................................... 101
6.2 Complexity Analysis ............................................................. 101
6.2.1 Signal Complexity and Signal Mobility ................... 101
6.2.2 Fractal Dimension .................................................... 102
6.2.3 Wavelet Measures ..................................................... 103
6.2.4 Entropy ..................................................................... 104
6.3 Cosine Transform .................................................................. 104
6.4 Introduction to Stochastic Processes ..................................... 107
6.4.1 Statistical Measures for Stochastic Processes .......... 107
6.4.2 Stationary and Ergodic Stochastic Processes ........... 109
6.4.3 Correlation Functions and Power Spectra ................ 111
6.5 Introduction to Information Theory ...................................... 114
6.5.1 Entropy ..................................................................... 114
6.5.2 Data Representation and Coding.............................. 116
6.5.3 Hoffman Coding ...................................................... 117
6.6 Registration of Images ........................................................... 118
6.7 Summary ............................................................................... 121
Problems........................................................................................... 122
Chapter 7 Clustering and Classification ............................................................ 125
7.1 Introduction and Overview.................................................... 125
7.2
Clustering versus Classification............................................. 125
7.3
Feature Extraction ................................................................. 127
7.3.1 Biomedical and Biological Features ......................... 128
7.3.2 Signal and Image Processing Features ..................... 128
7.3.2.1 Signal Power in Frequency Bands ............ 128
7.3.2.2 Wavelet Measures ..................................... 129
7.3.2.3 Complexity Measures ............................... 129
7.3.2.4 Geometric Measures ................................. 129
ix
Contents
5.1
Introduction and Overview...................................................... 79
5.2 From FT to STFT .................................................................... 79
5.3 One-Dimensional Continuous Wavelet Transform .................. 86
5.4 One-Dimensional Discrete Wavelet Transform ....................... 88
5.4.1 Discrete Wavelet Transform on Discrete Signals .......90
5.5 Two-Dimensional Wavelet Transform ..................................... 94
5.5.1 Two-Dimensional Discrete Wavelet Transform ......... 94
5.6 Main Applications of DWT ..................................................... 96
5.6.1 Filtering and Denoising ..............................................96
5.6.2 Compression ............................................................... 98
5.7 Discrete Wavelet Transform in MATLAB ® ............................99
5.8 Summary .................................................................................99
Problems.............................................................................................99
Chapter 6 Other Signal and Image Processing Methods .................................. 101
6.1 Introduction and Overview.................................................... 101
6.2 Complexity Analysis ............................................................. 101
6.2.1 Signal Complexity and Signal Mobility ................... 101
6.2.2 Fractal Dimension .................................................... 102
6.2.3 Wavelet Measures ..................................................... 103
6.2.4 Entropy ..................................................................... 104
6.3 Cosine Transform .................................................................. 104
6.4 Introduction to Stochastic Processes ..................................... 107
6.4.1 Statistical Measures for Stochastic Processes .......... 107
6.4.2 Stationary and Ergodic Stochastic Processes ........... 109
6.4.3 Correlation Functions and Power Spectra ................ 111
6.5 Introduction to Information Theory ...................................... 114
6.5.1 Entropy ..................................................................... 114
6.5.2 Data Representation and Coding.............................. 116
6.5.3 Hoffman Coding ...................................................... 117
6.6 Registration of Images ........................................................... 118
6.7 Summary ............................................................................... 121
Problems........................................................................................... 122
Chapter 7 Clustering and Classification ............................................................ 125
7.1 Introduction and Overview.................................................... 125
7.2
Clustering versus Classification............................................. 125
7.3
Feature Extraction ................................................................. 127
7.3.1 Biomedical and Biological Features ......................... 128
7.3.2 Signal and Image Processing Features ..................... 128
7.3.2.1 Signal Power in Frequency Bands ............ 128
7.3.2.2 Wavelet Measures ..................................... 129
7.3.2.3 Complexity Measures ............................... 129
7.3.2.4 Geometric Measures ................................. 129
ix
Contents