Adaptive Order-Statistic LMS Filters

The LMS-based adaptive order-statistic filters are presented in this paper. The adaptive Ll-filters as extension of the adaptive L-filter for two-dimensional filtering of noisy greyscale images is studied too. Their adaptation properties are studied by three types of noise, the additive white Gaussian noise, the impulsive noise or both, respectively. Moreover, the impulsive noise has the fixed noise value (Salt & Pepper noise). The problem of pixel value multiplicity and determination its position in the ordered input vector for adaptive Ll-filter is shown in this article. The two types of images with different of image complexity are used to demonstration of the power of time-spatial ordering

Robust detail-preserving signal extraction

We discuss robust filtering procedures for signal extraction from noisy time series. Particular attention is paid to the preservation of relevant signal details like abrupt shifts. moving averages and running medians are widely used but have shortcomings when large spikes (outliers) or trends occur. Modifications like modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Better solutions can be based on robust regression techniques, which even work in real time because of increased computational power and faster algorithms. Reviewing previous work we present filters for robust signal extraction and discuss their merits for preserving trends, abrupt shifts and local extremes as well as for the removal of outliers

Characteristics of a detail preserving nonlinear filter.

by Lai Wai Kuen.Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.Includes bibliographical references (leaves [119-125]).Abstract --- p.iAcknowledgement --- p.iiTable of Contents --- p.iiiChapter Chapter 1 --- IntroductionChapter 1.1 --- Background - The Need for Nonlinear Filtering --- p.1.1Chapter 1.2 --- Nonlinear Filtering --- p.1.2Chapter 1.3 --- Goal of the Work --- p.1.4Chapter 1.4 --- Organization of the Thesis --- p.1.5Chapter Chapter 2 --- An Overview of Robust Estimator Based Filters Morphological FiltersChapter 2.1 --- Introduction --- p.2.1Chapter 2.2 --- Signal Representation by Sets --- p.2.2Chapter 2.3 --- Robust Estimator Based Filters --- p.2.4Chapter 2.3.1 --- Filters based on the L-estimators --- p.2.4Chapter 2.3.1.1 --- The Median Filter and its Derivations --- p.2.5Chapter 2.3.1.2 --- Rank Order Filters and Derivations --- p.2.9Chapter 2.3.2 --- Filters based on the M-estimators (M-Filters) --- p.2.11Chapter 2.3.3 --- Filter based on the R-estimators --- p.2.13Chapter 2.4 --- Filters based on Mathematical Morphology --- p.2.14Chapter 2.4.1 --- Basic Morphological Operators --- p.2.14Chapter 2.4.2 --- Morphological Filters --- p.2.18Chapter 2.5 --- Chapter Summary --- p.2.20Chapter Chapter 3 --- Multi-Structuring Element Erosion FilterChapter 3.1 --- Introduction --- p.3.1Chapter 3.2 --- Problem Formulation --- p.3.1Chapter 3.3 --- Description of Multi-Structuring Element Erosion Filter --- p.3.3Chapter 3.3.1 --- Definition of Structuring Element for Multi-Structuring Element Erosion Filter --- p.3.4Chapter 3.3.2 --- Binary multi-Structuring Element Erosion Filter --- p.3.9Chapter 3.3.3 --- Selective Threshold Decomposition --- p.3.10Chapter 3.3.4 --- Multilevel Multi-Structuring Element Erosion Filter --- p.3.15Chapter 3.3.5 --- A Combination of Multilevel Multi-Structuring Element Erosion Filter and its Dual --- p.3.21Chapter 3.4 --- Chapter Summary --- p.3.21Chapter Chapter 4 --- Properties of Multi-Structuring Element Erosion FilterChapter 4.1 --- Introduction --- p.4.1Chapter 4.2 --- Deterministic Properties --- p.4.2Chapter 4.2.1 --- Shape of Invariant Signal --- p.4.3Chapter 4.2.1.1 --- Binary Multi-Structuring Element Erosion Filter --- p.4.5Chapter 4.2.1.2 --- Multilevel Multi-Structuring Element Erosion Filter --- p.4.16Chapter 4.2.2 --- Rate of Convergence of Multi-Structuring Element Erosion Filter --- p.4.25Chapter 4.2.2.1 --- Convergent Rate of Binary Multi-Structuring Element Erosion Filter --- p.4.25Chapter 4.2.2.2 --- Convergent Rate of Multilevel Multi-Structuring Element Erosion Filter --- p.4.28Chapter 4.3 --- Statistical Properties --- p.4.30Chapter 4.3.1 --- Output Distribution of Multi-Structuring Element Erosion Filter --- p.4.30Chapter 4.3.1.1 --- One-Dimensional Statistical Analysis of Multilevel Multi-Structuring Element Erosion Filter --- p.4.31Chapter 4.3.1.2 --- Two-Dimensional Statistical Analysis of Multilevel Multi-Structuring Element Erosion Filter --- p.4.32Chapter 4.3.2 --- Discussions on Statistical Properties --- p.4.36Chapter 4.4 --- Chapter Summary --- p.4.40Chapter Chapter 5 --- Performance EvaluationChapter 5.1 --- Introduction --- p.5.1Chapter 5.2 --- Performance Criteria --- p.5.2Chapter 5.2.1 --- Noise Suppression --- p.5.5Chapter 5.2.2 --- Subjective Criterion --- p.5.16Chapter 5.2.3 --- Computational Requirement --- p.5.20Chapter 5.3 --- Chapter Summary --- p.5.23Chapter Chapter 6 --- Recapitulation and Suggestions for Further WorkChapter 6.1 --- Recapitulation --- p.6.1Chapter 6.2 --- Suggestions for Further Work --- p.6.4Chapter 6.2.1 --- Probability Measure Function for the Two-Dimensional Filter --- p.6.4Chapter 6.2.2 --- Hardware Implementation --- p.6.5ReferencesAppendice

Frequency shift filtering for cyclostationary signals.

The frequency-shift (FRESH) filter is a structure which exploits the spectral correlation of cyclostationary signals for removing interference and noise from a wanted signal. As most digital communication signals are cyclostationary, FRESH filtering offers certain advantages for interference rejection in a communications receiver. This thesis explores the operation and application of FRESH filters in practical interference scenarios. The theoretical background to cyclostationarity is clarified with graphical interpretations of what cyclostationarity is, and how a FRESH filter exploits it to remove interference. The effects of implementation in a sampled system are investigated, in filters which use baud rate related cyclostationarity, leading to efficiency improvements. The effects of varying the wanted signal pulse shape to enhance the cyclostationarity available to the FRESH filter are also investigated. A consistent approach to the interpretation of the FRESH filter's operation is used throughout, while evaluating the performance in a wide range of realistic channel conditions. VLF radio communication is proposed as one area where interference conditions are particularly suitable for the use of FRESH filtering. In cases of severe adjacent channel interference it is found that a FRESH filter can almost completely remove the interferer. The effects of its use with an impulse rejection technique are also investigated. Finally, blind adaptation of FRESH filters through exploitation of carrier related cyclostationarity is investigated. It is found that one existing method loses the advantage of FRESH filtering over time invariant linear filtering. An improvement is proposed to the latter which restores its performance to that of a trained FRESH filter, and also reveals that carrier related cyclostationarity can be exploited, in some cases, by a simpler method. J