PREFACE |
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v | (6) |
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List of Symbols and Abbreviations |
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xi | |
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1 Nonlinear Signal Processing |
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1 | (20) |
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1.1 Signal Processing Model |
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1 | (2) |
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1.2 Signal and Noise Models |
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3 | (1) |
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1.3 Fundamental Problems in Noise Removal |
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3 | (15) |
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1.3.1 One-Dimensional Signals Corrupted by Additive White Gaussian Noise |
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4 | (3) |
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1.3.2 One-Dimensional Signals Corrupted by Impulsive Noise |
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7 | (3) |
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1.3.3 Mean and Median in Image Filtering |
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10 | (8) |
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1.3.4 Linear Versus Nonlinear Filtering |
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18 | (1) |
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18 | (3) |
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2 Statistical Preliminaries |
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21 | (28) |
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2.1 Random Variables and Distributions |
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21 | (12) |
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2.1.1 One-Dimensional Random Variables |
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21 | (7) |
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2.1.2 Random Vectors and Random Processes |
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28 | (3) |
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2.1.3 Probability Elements |
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31 | (1) |
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2.1.4 Transformations of Random Vectors |
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32 | (1) |
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2.2 Signal and Noise Models |
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33 | (3) |
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36 | (9) |
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36 | (3) |
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2.3.2 Maximum Likelihood Estimators |
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39 | (2) |
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41 | (1) |
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42 | (1) |
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43 | (1) |
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44 | (1) |
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2.4 Some Useful Distributions |
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45 | (4) |
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49 | (164) |
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52 | (4) |
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3.1.1 Principles and Properties |
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52 | (2) |
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3.1.2 Impulse and Step Response |
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54 | (1) |
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54 | (2) |
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3.2 Other Trimmed Mean Filters |
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56 | (10) |
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3.2.1 Principles and Properties |
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56 | (3) |
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3.2.2 Impulse and Step Response |
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59 | (1) |
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60 | (6) |
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66 | (4) |
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3.3.1 Principles and Properties |
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66 | (1) |
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3.3.2 Impulse and Step Response |
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67 | (1) |
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68 | (2) |
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3.4 C-Filters (Ll-Filters) |
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70 | (3) |
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3.4.1 Principles and Properties |
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70 | (2) |
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3.4.2 Impulse and Step Response |
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72 | (1) |
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72 | (1) |
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3.5 Weighted Median Filters |
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73 | (5) |
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3.5.1 Principles and Properties |
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73 | (3) |
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3.5.2 Impulse and Step Response |
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76 | (1) |
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76 | (2) |
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3.6 Ranked-Order and Weighted Order Statistic Filters |
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78 | (10) |
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3.6.1 Principles and Properties |
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78 | (3) |
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3.6.2 Impulse and Step Response |
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81 | (1) |
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82 | (6) |
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3.7 Multistage Median Filters |
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88 | (9) |
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3.7.1 Principles and Properties |
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88 | (3) |
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3.7.2 Impulse and Step Response |
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91 | (1) |
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91 | (6) |
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3.8 Median Hybrid Filters |
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97 | (8) |
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3.8.1 Principles and Properties |
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97 | (3) |
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3.8.2 Impulse and Step Response |
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100 | (1) |
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100 | (5) |
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3.9 Edge-Enhancing Selective Filters |
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105 | (4) |
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3.9.1 Principles and Properties |
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105 | (4) |
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3.9.2 Impulse and Step Response |
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109 | (1) |
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109 | (1) |
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3.10 Rank Selection Filters |
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109 | (13) |
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3.10.1 Principles and Properties |
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109 | (10) |
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3.10.2 Impulse and Step Response |
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119 | (1) |
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3.10.3 Filtering Examples |
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119 | (3) |
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122 | (18) |
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3.11.1 Principles and Properties |
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122 | (10) |
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3.11.2 Impulse and Step Response |
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132 | (1) |
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3.11.3 Filtering Examples |
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133 | (7) |
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140 | (7) |
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3.12.1 Principles and Properties |
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140 | (2) |
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3.12.2 Impulse and Step Response |
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142 | (1) |
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3.12.3 Filtering Examples |
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143 | (4) |
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3.13 Weighted Majority with Minimum Range Filters |
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147 | (2) |
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3.13.1 Principles and Properties |
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147 | (1) |
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3.13.2 Impulse and Step Response |
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147 | (1) |
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3.13.3 Filtering Examples |
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148 | (1) |
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3.14 Nonlinear Mean Filters |
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149 | (14) |
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3.14.1 Principles and Properties |
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149 | (3) |
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3.14.2 Impulse and Step Response |
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152 | (1) |
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3.14.3 Filtering Examples |
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153 | (10) |
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163 | (4) |
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3.15.1 Principles and Properties |
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163 | (3) |
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3.15.2 Impulse and Step Response |
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166 | (1) |
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3.15.3 Filtering Examples |
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167 | (1) |
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3.16 Generalizations of Stack Filters |
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167 | (5) |
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3.16.1 Principles and Properties |
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167 | (5) |
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3.16.2 Impulse and Step Response |
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172 | (1) |
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3.16.3 Filtering Examples |
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172 | (1) |
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3.17 Morphological Filters |
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172 | (7) |
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3.17.1 Principles and Properties |
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172 | (5) |
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3.17.2 Impulse and Step Response |
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177 | (1) |
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3.17.3 Filtering Examples |
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177 | (2) |
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3.18 Soft Morphological Filters |
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179 | (7) |
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3.18.1 Principles and Properties |
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179 | (5) |
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3.18.2 Impulse and Step Response |
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184 | (1) |
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3.18.3 Filtering Examples |
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184 | (2) |
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186 | (3) |
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3.19.1 Principles and Properties |
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186 | (3) |
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3.19.2 Impulse and Step Response |
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189 | (1) |
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3.19.3 Filtering Examples |
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189 | (1) |
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3.20 Data-Dependent Filters |
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189 | (5) |
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3.20.1 Principles and Properties |
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189 | (4) |
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3.20.2 Impulse and Step Response |
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193 | (1) |
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3.20.3 Filtering Examples |
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193 | (1) |
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3.21 Decision-Based Filters |
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194 | (7) |
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3.21.1 Principles and Properties |
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194 | (6) |
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3.21.2 Impulse and Step Response |
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200 | (1) |
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3.21.3 Filtering Examples |
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200 | (1) |
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3.22 Iterative, Cascaded, and Recursive Filters |
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201 | (3) |
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3.22.1 Principles and Properties |
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201 | (2) |
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3.22.2 Impulse and Step Response |
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203 | (1) |
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3.22.3 Filtering Examples |
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203 | (1) |
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3.23 Some Numerical Measures of Nonlinear Filters |
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204 | (8) |
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212 | (1) |
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4 STATISTICAL ANALYSIS AND OPTIMIZATION OF NONLINEAR FILTERS |
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213 | (34) |
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4.1 Methods Based on Order Statistics |
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213 | (9) |
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4.1.1 Joint Distributions of Order Statistics |
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215 | (1) |
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4.1.2 Analysis of L-Filters |
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216 | (3) |
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4.1.3 Optimization of L-Filters |
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219 | (3) |
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222 | (20) |
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4.2.1 Output Distribution of a Stack Filter |
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222 | (5) |
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4.2.2 Joint Distribution of Two Stack Filters |
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227 | (4) |
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4.2.3 Output Moments of Stack Filters |
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231 | (2) |
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4.2.4 Rank Selection Probabilities of Stack Filters |
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233 | (4) |
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4.2.5 Optimization of Stack Filters |
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237 | (2) |
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4.2.6 Stack Filter Optimization in the Boolean Lattice |
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239 | (3) |
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4.3 Multistage and Hybrid Filters |
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242 | (3) |
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245 | (2) |
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247 | (16) |
BIBLIOGRAPHY |
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263 | (10) |
INDEX |
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273 | |