Fundamentals of Nonlinear Digital Filtering

by Astola; Jaakko

• ISBN13: 9780849325700
• ISBN10: 0849325706
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-05-21
• Publisher: CRC Press

Summary

This book presents and evaluates current methods and applications in nonlinear digital filtering. Solid introductory material, balanced coverage of theoretical and practical aspects, and dozens of examples provide you with a self-contained, comprehensive information source on nonlinear filtering and its applications. Coverage of all major classes of filters from fundamentals to performance comparison the book covers dozens of classes of filters and, for each class, includes basic ideas, definitions, algorithms, and impulse and step responses that allow direct comparisons of filtering operations. This book is a major contribution of tremendous value to experimentalists, professional signal processing engineers, professors, and students.

Table of Contents

PREFACE	v	(6)
List of Symbols and Abbreviations	xi
1 Nonlinear Signal Processing	1	(20)
1.1 Signal Processing Model	1	(2)
1.2 Signal and Noise Models	3	(1)
1.3 Fundamental Problems in Noise Removal	3	(15)
1.3.1 One-Dimensional Signals Corrupted by Additive White Gaussian Noise	4	(3)
1.3.2 One-Dimensional Signals Corrupted by Impulsive Noise	7	(3)
1.3.3 Mean and Median in Image Filtering	10	(8)
1.3.4 Linear Versus Nonlinear Filtering	18	(1)
1.4 Algorithms	18	(3)
2 Statistical Preliminaries	21	(28)
2.1 Random Variables and Distributions	21	(12)
2.1.1 One-Dimensional Random Variables	21	(7)
2.1.2 Random Vectors and Random Processes	28	(3)
2.1.3 Probability Elements	31	(1)
2.1.4 Transformations of Random Vectors	32	(1)
2.2 Signal and Noise Models	33	(3)
2.3 Estimation	36	(9)
2.3.1 Point Estimation	36	(3)
2.3.2 Maximum Likelihood Estimators	39	(2)
2.3.3 M-Estimators	41	(1)
2.3.4 L-Estimators	42	(1)
2.3.5 R-Estimators	43	(1)
2.3.6 Scale Estimation	44	(1)
2.4 Some Useful Distributions	45	(4)
3 1001 Solutions	49	(164)
3.1 Trimmed Mean Filters	52	(4)
3.1.1 Principles and Properties	52	(2)
3.1.2 Impulse and Step Response	54	(1)
3.1.3 Filtering Examples	54	(2)
3.2 Other Trimmed Mean Filters	56	(10)
3.2.1 Principles and Properties	56	(3)
3.2.2 Impulse and Step Response	59	(1)
3.2.3 Filtering Examples	60	(6)
3.3 L-Filters	66	(4)
3.3.1 Principles and Properties	66	(1)
3.3.2 Impulse and Step Response	67	(1)
3.3.3 Filtering Examples	68	(2)
3.4 C-Filters (Ll-Filters)	70	(3)
3.4.1 Principles and Properties	70	(2)
3.4.2 Impulse and Step Response	72	(1)
3.4.3 Filtering Examples	72	(1)
3.5 Weighted Median Filters	73	(5)
3.5.1 Principles and Properties	73	(3)
3.5.2 Impulse and Step Response	76	(1)
3.5.3 Filtering Examples	76	(2)
3.6 Ranked-Order and Weighted Order Statistic Filters	78	(10)
3.6.1 Principles and Properties	78	(3)
3.6.2 Impulse and Step Response	81	(1)
3.6.3 Filtering Examples	82	(6)
3.7 Multistage Median Filters	88	(9)
3.7.1 Principles and Properties	88	(3)
3.7.2 Impulse and Step Response	91	(1)
3.7.3 Filtering Examples	91	(6)
3.8 Median Hybrid Filters	97	(8)
3.8.1 Principles and Properties	97	(3)
3.8.2 Impulse and Step Response	100	(1)
3.8.3 Filtering Examples	100	(5)
3.9 Edge-Enhancing Selective Filters	105	(4)
3.9.1 Principles and Properties	105	(4)
3.9.2 Impulse and Step Response	109	(1)
3.9.3 Filtering Examples	109	(1)
3.10 Rank Selection Filters	109	(13)
3.10.1 Principles and Properties	109	(10)
3.10.2 Impulse and Step Response	119	(1)
3.10.3 Filtering Examples	119	(3)
3.11 M-Filters	122	(18)
3.11.1 Principles and Properties	122	(10)
3.11.2 Impulse and Step Response	132	(1)
3.11.3 Filtering Examples	133	(7)
3.12 R-Filters	140	(7)
3.12.1 Principles and Properties	140	(2)
3.12.2 Impulse and Step Response	142	(1)
3.12.3 Filtering Examples	143	(4)
3.13 Weighted Majority with Minimum Range Filters	147	(2)
3.13.1 Principles and Properties	147	(1)
3.13.2 Impulse and Step Response	147	(1)
3.13.3 Filtering Examples	148	(1)
3.14 Nonlinear Mean Filters	149	(14)
3.14.1 Principles and Properties	149	(3)
3.14.2 Impulse and Step Response	152	(1)
3.14.3 Filtering Examples	153	(10)
3.15 Stack Filters	163	(4)
3.15.1 Principles and Properties	163	(3)
3.15.2 Impulse and Step Response	166	(1)
3.15.3 Filtering Examples	167	(1)
3.16 Generalizations of Stack Filters	167	(5)
3.16.1 Principles and Properties	167	(5)
3.16.2 Impulse and Step Response	172	(1)
3.16.3 Filtering Examples	172	(1)
3.17 Morphological Filters	172	(7)
3.17.1 Principles and Properties	172	(5)
3.17.2 Impulse and Step Response	177	(1)
3.17.3 Filtering Examples	177	(2)
3.18 Soft Morphological Filters	179	(7)
3.18.1 Principles and Properties	179	(5)
3.18.2 Impulse and Step Response	184	(1)
3.18.3 Filtering Examples	184	(2)
3.19 Polynomial Filters	186	(3)
3.19.1 Principles and Properties	186	(3)
3.19.2 Impulse and Step Response	189	(1)
3.19.3 Filtering Examples	189	(1)
3.20 Data-Dependent Filters	189	(5)
3.20.1 Principles and Properties	189	(4)
3.20.2 Impulse and Step Response	193	(1)
3.20.3 Filtering Examples	193	(1)
3.21 Decision-Based Filters	194	(7)
3.21.1 Principles and Properties	194	(6)
3.21.2 Impulse and Step Response	200	(1)
3.21.3 Filtering Examples	200	(1)
3.22 Iterative, Cascaded, and Recursive Filters	201	(3)
3.22.1 Principles and Properties	201	(2)
3.22.2 Impulse and Step Response	203	(1)
3.22.3 Filtering Examples	203	(1)
3.23 Some Numerical Measures of Nonlinear Filters	204	(8)
3.24 Discussion	212	(1)
4 STATISTICAL ANALYSIS AND OPTIMIZATION OF NONLINEAR FILTERS	213	(34)
4.1 Methods Based on Order Statistics	213	(9)
4.1.1 Joint Distributions of Order Statistics	215	(1)
4.1.2 Analysis of L-Filters	216	(3)
4.1.3 Optimization of L-Filters	219	(3)
4.2 Stack Filters	222	(20)
4.2.1 Output Distribution of a Stack Filter	222	(5)
4.2.2 Joint Distribution of Two Stack Filters	227	(4)
4.2.3 Output Moments of Stack Filters	231	(2)
4.2.4 Rank Selection Probabilities of Stack Filters	233	(4)
4.2.5 Optimization of Stack Filters	237	(2)
4.2.6 Stack Filter Optimization in the Boolean Lattice	239	(3)
4.3 Multistage and Hybrid Filters	242	(3)
4.4 Discussion	245	(2)
5 Exercises	247	(16)
BIBLIOGRAPHY	263	(10)
INDEX	273