Book contents

Contents

• 1 Nonlinear Signal Processing
  • 1.1 Signal Processing Model
  • 1.2 Signal and Noise Models
  • 1.3 Fundamental Problems in Noise Removal
  • 1.4 Algorithms
• 2 Statistical Preliminaries
  • 2.1 Random Variables and Distributions
  • 2.2 Signal and Noise Models
  • 2.3 Estimation
  • 2.4 Some Useful Distributions
• 3 1001 Solutions
  • 3.1 Trimmed Mean Filters
  • 3.2 Other Trimmed Mean Filters
  • 3.3 L-Filters
  • 3.4 C-Filters
  • 3.5 Weighted Median Filters
  • 3.6 Ranked-Order and Weighted Order Statistic Filters
  • 3.7 Multistage Median Filters
  • 3.8 Median Hybrid Filters
  • 3.9 Edge-Enhancing Selective Filters
  • 3.10 Rank Selection Filters
  • 3.11 M-Filters
  • 3.12 R-Filters
  • 3.13 Weighted Majority with Minimum Range Filters
  • 3.14 Nonlinear Mean Filters
  • 3.15 Stack Filters
  • 3.16 Generalizations of Stack Filters
  • 3.17 Morphological Filters
  • 3.18 Soft Morphological Filters
  • 3.19 Polynomial Filters
  • 3.20 Data-Dependent Filters
  • 3.21 Decision-Based Filters
  • 3.22 Iterative, Cascaded, and Recursive Filters
  • 3.23 Some Numerical Measures of Nonlinear Filters
  • 3.24 Discussion
• 4 Statistical Analysis and Optimization of Nonlinear Filters
  • 4.1 Methods Based on Order Statistics
  • 4.2 Stack Filters
    • 4.2.1 Output Distribution of a Stack Filter
    • 4.2.2 Joint Distribution of Two Stack Filters
    • 4.2.3 Output Moments of a Stack Filter
    • 4.2.4 Rank Selection Probabilities of Stack Filters
    • 4.2.5 Optimization of Stack Filters
    • 4.2.6 Stack Filter Optimization in the Boolean Lattice
  • 4.3 Multistage and Hybrid Filters
  • 4.4 Discussion
• 5 Exercises
• Bibliography
• Index